Dealing with Creationism in Astronomy

Geocentrism vs. the Barycenter

2012-01-22T19:30:00.000-05:00

I have often noted how, due to the interconnected nature of scientific disciplines, pseudo-sciences often have negative impacts far beyond their claimed 'goal'. To make their pseudo-science correct, pseudo-scientists must often violate or even break principles so fundamental that it makes some modern technologies impossible (see Technomystics)

So it is with biblical geocentrism claims.

This is an additional follow-on to Mr. Martin's In Response to Dr Bridgmans “Stupid Geocentrist Tricks“. I've already made some reply in the comments to the original article. Most of Mr. Martin's statements were rants where the same errors were being repeated and expanded upon, but one very fundamental error caught my attention.

Martin: “One of the problems found in the link above is that of the ad hoc nature of the barycenter, which produces conflicts within the Newtonian model and Kepler’s orbital laws.“

Any 'conflicts' between the Newtonian and Keplerian model stem from Mr. Martin's own misunderstanding.

The barycenter (AKA center of mass) is a consequence of Newton's laws and is perfectly consistent with them (wikipedia). All objects with mass have a center of mass, and the barycenter can be defined for any combination of masses. A ball has a barycenter, the center of mass of a uniform sphere is at the geometric center of the sphere. A chair has a barycenter. An automobile has a barycenter, as do all the parts within it. A ship at sea has a barycenter. A rock sitting on a hillside has a barycenter.

The barycenter still exists even if the body (or bodies) under consideration is in motion. Imagine the differences in the motions of the moving parts, such as valves, camshafts, pistons, and belts, and their barycenters, in the interior of an automobile engine:

While the car is at rest
While the car is moving on the road under its own power
While the car is idling on a flatbed train car while the train is moving.

All these motions are well defined mathematically and are far from ad hoc. Automobile engineers understand them.

The barycenter allows us to analyze a system with many parts by providing a method of analyzing the system a few components at a time.

When combined with a central force law (a force that acts along a line between the two particles under consideration), the barycenter has the additional utility that the motion of a system of particles can be analyzed in two parts - the motion AROUND the center of mass, and the motion OF the center of mass. The center of mass then provides a convienent frame of reference for analyzing the system. Engineers and astronomers use this fact routinely.

Here are derivations, starting from Newtonian classical mechanics, deriving Kepler's laws and the center of mass from Newtonian force and gravitational laws. These derivations illustrate how the motion of the two objects under gravity can be separated into these two separate motions. These are presented for undergraduate physics classes.

Kepler's laws, refined by Newton, describe the motion of two bodies RELATIVE TO EACH OTHER, not relative to the barycenter, as seen in the derivations linked above.

Using my N-body code, I've actually run several simulations of how the same Keplerian 2-body system appears in different reference frames, specifically an arbitrary frame, a center-of-mass (barycenter) frame, and a reference frame centered on the more massive object where Kepler's Laws apply (see Doin' Real Science: Simulating Particles). I have a few demonstrations of Mr. Martin's claimed problem configurations (described below) in preparation for future posts.

Mr. Martin elaborates on his nonsense, repeating many of the claims from other posts...

Invalidations of Newton's and Kepler's orbital mechanics

Here’s some simple invalidations of Newton’s and Kepler’s orbital mechanics –

1. The orbital mechanics of Newton dictates the earth orbits the sun’s center of mass in an ellipse, yet Newtonian mechanics states the earth also orbits the solar system barycenter. As the solar system barycenter is almost never at the center of mass of the sun, then the earth simply cannot be orbiting the sun in an ellipse. Therefore Newton’s principle of barycentric motion invalidates Kepler’s laws of elliptical motion.

2. Newton’s orbital mechanics dictates the earth orbits the sun’s center of mass in an ellipse. Newton’s orbital mechanics dictates the earth orbits the earth-moon barycenter ever month. Now if the earth is fixed in its elliptical orbit around the sun, then both the earth-moon barycenter and the moon orbit the earth every month, to maintain the earths elliptical orbit shape around the earth every year. Yet if this occurs, Newton’s notion of the barycenter as the center of mass about which the masses orbit as affirmed in the sun-earth motion and then denied in the earth-moon motion. As Newton’s center of mass concludes to a contradiction with more than two bodies in motion, the theory of the center of mass and with it, mass as a cause of gravity, is invalidated.

3. Newton’s orbital mechanics dictates the earth orbits the solar system’s center of mass in an ellipse. Yet, Newton’s orbital mechanics dictates the earth orbits the earth-moon barycenter every month. To properly account for the Earth’s monthly motion around the earth-moon barycenter and the motion of the earth around the solar system barycenter, the earth cannot be orbiting the solar system barycenter in an ellipse as demonstrated above, so the other options available to explain the sun-earth-moon orbits are –

A- The earth-moon barycenter orbits the solar system barycenter in an ellipse. But this option is not in accord with Newton’s notion of a barycenter, where it is a stationary point, relative to the motion of bodies. Furthermore, if the earth-moon barycenter orbits the solar system barycenter, then the earth’s yearly orbit does not conform to Kepler’s orbital laws.

B- The Earth-moon barycentric motion is independent of the earth-solar system barycentric motion. But such movements are never independent in the real, indicating Newton’s notion of the barycenter is not a reflection of the real.

C- The earth does not orbit in the Earth-moon barycentric motion, nor does it move around the solar system barycenter, but is stationary at the barycenter of the universe. This solution gives some respectability to Newton’s notion of the barycenter, but is normally denied by modern science out of blind prejudice.

All of these statements demonstrate the same conceptual failure, that Mr. Martin regards the barycenter (center of gravity, center of mass) and/or the focus of planetary orbits, as if they must be a FIXED point in space.

But that is wrong. I can define a reference frame attached to any object, or point in space, that I choose. All the frames are equivalent. It is a fact that some reference frames are more convenient for calculation than others (which makes the Earth a preferred frame ONLY when we are near the Earth).

The barycenter of the Earth moves around the Earth-Moon barycenter. The barycenter of Earth-Moon system moves around the barycenter of the Solar System (and the Sun). The barycenter of the solar system moves around the barycenter of the Galaxy. There is no conflict in these nested motions, just as there are no conflicts for the moving parts of the engine inside a moving car.

Thanks to Newton's laws, and this can be proven with mathematical rigor, the barycenter provides a point where, in the case of NO EXTERNAL forces, a body can be treated as point moving along the trajectory of the barycenter. It is a useful principle to understand for anyone designing or building mechanical systems as noted in Q4 of Geocentrism: Failing More Basic Physics...

To believe the Geocentrist claim of a problem with barycentric and Keplerian motion is to believe that the past 300 years of the development of mechanics (and all the inventions developed from that knowledge) is incorrect. Perhaps Mr. Martin thinks these developments were some kind of fluke, unrelated to the mathematics that guided the way?

Mr. Martin repeatedly implies that mathematical models have no actual connection to reality, arguing that a condition that exists mathematically does not exist 'in the real'. If the fact that engineers and scientists use these concepts to build real things doesn't make it 'real', then what does make these concepts, and the larger concepts we derive from them, real? Once in this Geocentrist fantasy-land, one's only choice is to believe that all space flight is a hoax. To maintain such a delusion, you have to avoid watching satellites go overhead (Wikipedia, Hobby Space: Satellite Watching).

That the math works might be mysterious to some, but the simple fact is the math does provide accurate predictions of reality (see Mathematics, the Language of Science). The power of that description has made modern technology possible. Mr. Martin and his co-horts have provided no such capability.

The math Works. Geocentrist pseudo-science does not.

Some other interesting resources on the topic:

Another Big Bang Prediction Confirmed. More Headaches for the Infinite Age Cosmologies

2012-01-15T19:09:00.000-05:00

One of the major predictions of the Big Bang cosmology is the abundance of the chemical elements immediately after the expansion cooled to the point that nuclear reactions could no longer take place. This would create a time between the Big Bang itself (Wikipedia), and star formation, where the universe would be filled with nothing but H, D, He, and trace amounts of lithium.

Eventually stars will form and nucleosynthesis will begin again, 'cooking' these initial elements into heavier elements such as carbon, oxygen and others (Wikipedia). We've detected a great deal of evidence for this process. Older, lower mass (and therefore longer lived) stars tend to have lower amounts of the elements heavier than helium (low metallicity).

But this element formation process will not be uniformly distributed. Regions with stars will form these heavier elements at higher rates, and supernovae and other explosive events will expel them back into the interstellar medium. We expect regions such as galaxies and clusters of galaxies to have a higher fraction of these heavier elements leaving the regions between galaxies with a lower fraction of heavy elements. This non-uniformity in mixing means that there might still be some regions of the cosmos where unprocessed 'pristine' material from the original nucleosynthesis might be found.

We now have news that some of this left-over material may have indeed been found.
Here's a press report:
Discovery.com: Pristine Big Bang Gas Found

And here is a link to the paper published in Science magazine:
Science: Detection of Pristine Gas Two Billion Years After the Big Bang

Most cosmological alternatives to the Big Bang are either much younger (such as those advocated by young-Earth creationists) or of infinite age (advocated by Plasma Cosmology and Electric Universe, among others).

But infinite age cosmologies have a host of problems, rarely acknowledged by their advocates.

In a universe of infinite age, everything has had enough time to reach its equilibrium configuration, which means there is no free energy left which can be liberated. Basically, an infinite age universe is a dead universe and there is no energy available for even life to function.
Most infinite age cosmologies try to avoid the problem described above by advocating some mechanism for matter to be spontaneously created. While such a process would violate conservation of energy (COE), there are known quantum processes which can violate COE for very short intervals, therefore, we can't rule this possibility out at 100% confidence (but the difference with 100% would very, very, VERY tiny). Conservation of energy could be violated on a level below our current ability to detect it.

However, if material were created spontaneously, it would most likely be distributed roughly uniformly throughout the cosmos and pristine material would constantly be mixed with highly-processed material. Anyone advocating an infinite-age cosmos would have a difficult time extracting a region of hydrogen and helium, at high purity, out of a mixture that includes heavy elements.

Here's some references that address some of the questions that get raised by energy issues in Big Bang cosmology: Machines Like Us: Does the Big Bang violate Conservation of Energy?

These discussions always generate confusion because General Relativity does define conserved quantities that we equate to energy defined on a cosmological time scale, but the definition does not map cleanly to small times scales, such as looking at the entire cosmos vs. energy conservation on the Earth. Sean Carroll gives a variation of the explanation here: Cosmic Variance: Energy is not Conserved.

This confusion has allowed various cranks to exploit the terminology to promote bad science.
Machines Like Us: Does the Big Bang violate the 2nd Law of Thermodynamics?

For a description of how we learned that symmetry principles are behind the conservation laws, see this chapter from the online text "Conceptual Physics".

"Are You Smarter Than a 17th-Century Geocentrist"

2012-01-07T08:42:00.002-05:00

This little goodie came through recently on one of the many mailing lists I'm on, from the Louisville (Kentucky) Area Skeptics:

January 11, 2012

Jan Science Cafe- Chris Graney "Are You Smarter Than a 17th-Century Geocentrist?"

Unfortunately, it's a little farther away than I'm able to travel on short notice, but it looks like fun. Hopefully I'll hear some reports about it.

Electric Universe Fantasies & Heliopause Electrons

2012-01-02T19:24:00.000-05:00

Dr. Donald Scott, whose Electric Universe promotional activites have been discussed on this site before has published an (alledged) update to his Electric Sun model:

Thunderbolts: Voyager 1 Updates Solar Electron Flux

Dr. Scott claims to use Voyager data to update his incoming electron flux to 10^7 electrons per cubic meter, a 100 times increase over his previous estimate. He subsequently uses this to downgrade the estimate of the Sun-heliopause voltage drop to 6.25 million volts.

“NASA’s observation (#3 above) that the direction of the solar wind actually reverses (begins to flow sunward) out near the heliopause is further confirmation that the analogy between the behavior of the Sun’s surrounding plasma and what is observed in laboratory “gas” (plasma) discharge tubes is a valid one.”

Note that we still get NO information on the voltage system actually driving this claimed discharge tube. Since we detect no synchrotron emission from the current stream (detectable at radio wavelengths), it's existence is as mystical as the diety that makes the Sun rise each day.

This continued failure on the part of EU 'theorists' places their 'model' in a far weaker position than the standard heliospheric bow-shock model, where particles moving out from the Sun eventually reach a distance where the outflow balances with the interstellar medium flowing around the Sun. We've observed this around other stars (see Hubble Finds Stars That 'Go Ballistic', Wikipedia: Bow Shock). We observe these bow-shock structures under many conditions where there clearly are no large-scale electric fields controlling their structure.

For a closer look, here's the original Voyager press release:

NASA/JPL: NASA's Voyager Hits New Region at Solar System Edge

Note that the JPL article says that Voyager reports a 100-fold increase in the electron intensity (flux) from elsewhere in the galaxy, but does not actually report a value. Also note that this is the flux of energetic electrons from the rest of the galaxy, NOT the relatively low-energy free electrons in the interstellar medium. But these inconvenient distinctions do not deter Dr. Scott. He just multiplies his original numbers (apparently from some estimate made around 1979) by 100. These values Dr. Scott is using are not necessarily the ones Voyager was actually reporting (I actually have a query pending to get the actual numbers. I had hoped I would have heard back on this by now).

But beyond that, nothing's really changed. EU still requires mystical properties for charged particles, much of which I covered in my earlier posts on this particular EU solar model (which is very different from Wal Thornhill's model):

The Solar Capacitor Model. I.
The Solar Capacitor Model. II.
The Solar Capacitor Model. III.

I can re-run the simulations from these past articles with Dr. Scott's revised numbers, but it doesn't improve the comparison to actual data much. The general effects are:

Increasing the electron density to lower the voltage drop increases all the particle densities. This still creates a problem for the radiation environment to which satellites and astronauts are exposed.
Reducing the voltage drop lowers the particles speeds. This is still HARD radiation, dangerous to satellites and astronauts.

Here's some more issues raised by Dr. Scott's 'interpretation' of the JPL release:

If inbound electrons are now being measured by Voyager in the heliopause region, why weren't they detected closer to the Sun? How do the electrons deliver their energy to the Sun if they don't travel the remaining 100 AUs to the Sun? Again, EU must invoke some magical property for electrons. According to the standard heliosphere model, the number of inbound electrons are increasing because the flux of outbound electrons has decreased sufficiently that the inbound electrons are not being scattered off their trajectory.
What happens to electrons moving through a 10 billion volt drop, or even a 6.25 million volt drop? How is their energy transferred when they impact the Sun? We've been able to generate electron beams of this energy, and higher, for DECADES. See SLAC’s Electron Beam Gets Astrophysical. We know exactly how these electron beams behave. We know what happens when they hit matter, like the surface of the Sun, or the dark side of a planet, or a satellite, or an astronaut in a space suit. This detail is also something that designers of everything from discharge tubes to CRTs MUST know, but EU 'theorists' apparently do not.

Most electrical engineers I've worked with understand the concept of an energy budget - you don't attach appliances to your generator if the generator can't support your load. You must understand the energy budget of your equipment, whether it be your home, or a satellite or a spacecraft, or your physical system.

This very basic fact is apparently not understood by Electric Universe 'theorists'.

"The End of the World as we Know It" with Stuart Robbins

2011-12-30T19:47:00.000-05:00

Stuart Robbins, who operates the PseudoAstronomy blog and podcast was recently interviewed on the Point of Inquiry Podcast.

Stuart covers a broader range of topics than I, including things such as the Moon Landing Hoax, astrology and more recently the 2012 silliness. I've followed a lot of Stuart's work, especially where it overlaps with my focus.

I've used one of the nuclear physics web tools developed by Stuart in examining some nucleosynthesis claims made by Barry Setterfield.

Stuart and I have possibly crossed paths a number of times, perhaps at the Washington AAS meetings, but I don't think we've actually met as yet.

Doin' Real Science: Simulating Particles

2011-11-12T19:53:00.000-05:00

Many times on this blog, I challenge the purveyors of various pseudo-sciences to demonstrate their claims to the same standards that mainstream scientists must meet. One of these criteria is that real science must make testable predictions. In the physical sciences, this usually means numerical predictions which can be compared to actual measurements, whether in situ or observations. When they're not evading the question completely, pseudo-scientists and their supporters construct all manner of excuses why they should be exempt from these standards.

To make the numerical predictions, modern scientists usually rely on computers to do the repeated mathematical calculations (sometimes called 'number crunching') that these types of predictions require. Once the programs are written, the computer can perform them tirelessly.

One tool in many researchers toolbox is some type of particle simulation, used to study interactions and motions of many particles. Codes written for an arbitrary number of particles, N, are usually called N-body codes.

I first wrote my own N-body code in 1979 in AppleSoft BASIC on an Apple II computer (wikipedia), in my early college years (the FIRST time I tried to complete my degree). Back then, computational libraries for solving differential equations existed only for large scientific systems. On smaller computers, you had to write your own, but plenty of documentation of the techniques was available. One of the most popular techniques for solving these types of differential equations are the Runge-Kutta integrators (wikipedia).

Today, computer hardware is readily available, as are numerical processing libraries. Numerical N-body solvers are simple enough that a competent programmer in high school could write their own.

So for this project, I've updated my N-body code. I've written the new version in Python (v2.7) and using the Python numerical libraries: numpy, scipy, matplotlib, and others (for more info on the installation). I've also written an interface to generate rendered output using the POVray rendering package.

N-body Test Runs

In testing these types of codes, we usually perform runs on simple configurations where the solution is available in a known form. Here's the results from a 2-body gravitational run, the Kepler Problem (wikipedia). The program allows me to generate tables of particle positions once, after which I can read these tables and construct different types of plots. Here I plot the results of the run in reference frame in which the velocities and positions are originally defined.

For a full-quality version of the movie, download here (8MB).

Note that for the two objects, there is a point that lies on a line between the two particles that represents the center-of-mass (wikipedia), or barycenter, of the two particles. In this configuration, the center-of-mass moves in a straight line and at a uniform speed. This is a property of the center-of-mass that can be mathematically proven for a system of particles interacting by a central force (where the force acts along the line between the particles).

Now let's define some of our mathematical terms:

x(A),y(A), z(A) = x, y, z coordinates of object A in the original coordinate system

x(CM), y(CM), z(CM) = x, y, z coordinates of center-of-mass in original coordinate system

Next we can plot the exact same data points, but this time we re-compute their positions in a reference frame where the center-of-mass is not moving. We do this by computing the center-of-mass of the two particles at each time step (x(CM), y(CM), z(CM)) of the simulation, and then compute the position of the particles relative to that center-of-mass:

x(A,CM), y(A,CM), z(A,CM) = coordinates of object A in the CM coordinate system, where the center-of-mass is translated to the origin, (0,0,0)

x(A,CM) = x(A) - x(CM)
y(A,CM) = y(A) - x(CM)

For simplicity in plotting, I've restricted the simulation run to motion in 2-dimensions, x and y, with z=0. For this type of problem, it can also be mathematically proven that if the particles start with all positions and velocities in the z-direction equal to zero, they will remain zero at future times.

Now we can plot the particle trajectories in the CM reference frame, which generates the following plot.

For a full-quality version of the movie, download here (9MB).

Now the two particles revolve around their mutual center-of-mass (position 0,0 in the plot), always keeping the center-of-mass on the line between them. It can similarly be mathematically proven that in a system of particles interacting by central forces, the motion can always be separated into the motion of the particles moving around the center-of-mass, and the motion of the entire system along the center of mass.

Finally, we complete the Kepler 2-body problem by plotting the two particles in a coordinate system where the larger body represents the origin of the coordinate system. This is the coordinate system of the original Kepler problem, and the coordinate system where Kepler's Laws (wikipedia) are defined. To do this, we again use the exact same set of points generated in the simulation, and subtract the position of the larger body at each time step. So

x(A,ref), y(A,ref), z(A,ref) = position of object A, in the coordinate system where the origin is object ref.

x(A,ref) = x(A) - x(A) = 0.0
y(A,ref) = y(A) - y(A) = 0.0
Object A resides at the origin in this coordinate system.

x(B,ref) = x(B) - x(A)
y(B,ref) = y(B) - y(A)

Plotting these results for each point in the simulation generates the movie

For a full-quality version of the movie, download here (9MB).

We also plot the position of the center-of-mass in this new coordinate system, which appears to orbit the main body.

For this simulation, I've chosen 1 AU as the unit of distance, and 1 year as the unit of time. The large body is 10 solar masses and the smaller is 1 solar mass. I've chosen the starting positions and velocities so that the orbits are sufficiently elliptical that you can see motions relative to the center-of-mass. Competent scientists could use the information in these plots to estimate such additional parameters as speeds at apoapsis and periapsis. Do EU 'theorists' know how to determine this information from the simulation?

To illustrate the flexibility of these types of programs, I can also generate simulations of electromagnetic systems. Here I have a plot of some electrons and nuclei (hydrogen, deuterium, tritium, helium-3, helium-4) in a configuration where an external electric (yellow arrow) and magnetic field (blue arrow) are at right angles to each other.

For a full-quality version of the movie, download here (27MB).

This visualization was generated using the POVray renderer. Currently, electromagnetic interactions between particles are not included in the simulation run, but will be added in the future.

Note that I have placed Creative Commons notices (BY-NC) on these movies for a reason (see Setterfield Again...). Any website which hosts these movies must include a proper credit to me and a link back to this page.

Coming on Deck...

These are some opening samples of what can be done. But this is just the tip of the iceberg of what can be done with this tool.

Future topics for this thread:

An introduction to N-Body simulations
The physics and mathematics of N-Body simulations
Some features of my particular implementation
How do we test/validate the simulations?

Some additional problems where I already have tests running:

Lagrange Points
Lagrange Points with an extra planet
Three-body systems such as Sun-Earth-Moon
Three-body systems such as Sun-Earth-Jupiter
Solar system model (Sun + eight planets)
Various particle and electromagnetic field configurations

Future models on my “to explore“ list

The “Tatooine system“, Kepler 16AB (NASA, Exoplanet Catalog)
Lorentz Slingshot (see 365 days of astronomy podcast)
Velikovsky's Venus (what would happen to a planet launched out of Jupiter?)
The Newton-Coulomb problem, or what if the Sun and planets had significant electric charge?

Future enhancements

Particle-in-Cell (PIC) support to accommodate more realistic plasma models (wikipedia). This moves the code in a direction suitable to run a version of Peratt's galaxy simulations. Will I be generating testable models while Siggy_G is still generating excuses?

Suggestions for other configurations to study are welcome, PROVIDED they include a description of the principle the configuration can be used to test or illustrate.

And Still the Pseudo-Scientists Can't Meet the Standards

One of the popular whines from pseudo-scientists is that they could produce worthy results if they had the same funding as the mainstream scientists.

Gee, I'm sure a lot of practicing scientists would like to have that kind of funding as well, in the rare cases where it exists.

Most scientists are not paid to do research full time. I certainly am not. Often research is a part-time project, done between teaching classes or doing support work (writing analysis software, archiving datasets, visualization production) for other science projects.

Note that I did not have any grant to work on this project. I didn't have to hire an army, or even one programmer, beyond myself. Beyond the computer and operating system, I used open-source software available to anyone. This was done on commercial grade computer systems (laptop & desktop), with the laptop used primarily for code development and testing, and the desktop system used for running the more heavy-duty processing of full simulations.

The code was developed in my spare time (though some components of the development have already found application in my day job).

I'm Still Here...

2011-11-06T19:51:00.000-05:00

But just as last year around this time, other responsibilities eat away at the time I can devote to this project.

There has been a family genealogy trip to Gettysburg, PA. It seems that while I had ancestors on both the Union and Confederate side at Gettysburg, their regiments were placed and timed such that they never actually shot at each other. Lucky for me...

Then there was Halloween, and a weekend craft project making R2P2 (below), inspired by the Dalek O'Lantern.

And there are the regular fall holiday activities, gatherings, yard cleanup, etc.

In addition to all this, I am forced to move my main site due to Apple's changes to the MobileMe (iCloud) web hosting policies. I expect my original "Dealing with Creationism in Astronomy" website will move (and might undergo a name change) sometime in Spring, 2012. Stay tuned.

So my posting frequency for the next few months will probably be very irregular. However, I am using the time to organize a large series of posts on a theme relevant to posts over the past year, a preview to be posted soon.

Pseudoscience and the Technomystic II

2011-10-15T19:54:00.000-04:00

This is a continuation of the previous post (Pseudoscience and the Technomystic) with a more specific example from earlier comments.

Consider this comment in a previous thread by EU supporter, Siggy_G, complaining about how I repeatedly emphasize the coupling of science with modern technology:

Siggy_G: The “bundling“ I referred to, as often seen around here: taking all achievements related to technology, the mechanical launch itself, GPS-systems and what not, mentioning that in relation to the standard sun model or big bang cosmology, and labelling it as a confirmation of the model or theory itself. It would be as if Electric Universe proponents should mention all the electric/digital engineering behind practically ALL technology today, including everything used in astrophysics, and bundle it up as a confirmation of the Electric Universe notions... Would that be acceptable?

Is Siggy_G claiming that the Newton's laws of motion and gravitation used in predicting the motions of the planets are NOT the same laws of motion used to launch satellites into Earth orbit to distant parts of the solar system?

If that is the case, how does Siggy_G think it is actually done?

If physicists don't use the same knowledge base obtained in the classes we take on theoretical mechanics when they go to work for the flight dynamics division of the various space agencies around the world, WHERE do they get the knowledge to do the trajectory planing for these missions, often years in advance?

As for Siggy_G's 'challenge' to bundle modern technology with EU notions, I invite him to do so, but consider just some of the questions I had to address, and he must face:

1) Where did the “electric/digital” engineering come from? Were iPads, digital cameras, modern home computers, etc., invented with no prior knowledge? Did the inventor have a block of raw materials (silicon, copper, etc) in their garage and one day built a modern cell phone?

2) Where did the semiconductor electronics that are the active components of those devices come from? What knowledge base was needed to make them? Did someone just throw together some raw chemicals in a vat and one day a microprocessor chip came out?

3) What about the materials used to make semiconductors themselves? Were they just some random combination of materials someone thought up in their garage? Are they naturally-occurring? Some are, but most of the semiconductors we use today were designed in the lab. How did we design those semiconductors? Were they just a random combination of chemicals, or was there physics and mathematics that guided the development? If you claim this, cite relevant references.

4) Does Siggy_G know that for years, the first discovered semiconductors were used as crystal diodes (wikipedia: Crystal-diode) in early radio receivers, but no one understood why this material had the non-linear rectification behavior it had? Their electronic characteristics defied explanation by classical (Maxwell) electromagnetism. It would take the development of quantum mechanics to turn the curious properties of semiconductors into a useful tool, and astrophysics provided critical information along the way:

• Scott Rebuttal. III. The Importance of Quantum Mechanics
• More Astrophysics & Quantum Mechanics Connections

Now let's look at Siggy_G's challenge from another direction...

5) How is the use of a CCD camera to take astronomical images proof, or even evidence, of Electric Universe claims?

6) If you want to claim that the use or form of a particular tool is evidence of EU, then what about all the things we learned from astronomical images on photographic film *before* the invention of CCDs?

7) Is film chemistry as proof that the universe is actually chemical? What does that imply for EU?

8) What about all the knowledge we obtained through naked-eye observations for centuries before that, with measurements performed via spider-web reticles?

Without addressing these types of questions, any such construction that Siggy_G proposes is the equivalent of "Joe is really smart and invented 'X', and he believes 'Y'. Therefore 'Y' must be true." Let's make a concrete example by filling in X & Y:

Johannes Kepler discovered the first laws of planetary motion, and also practiced astrology. Therefore astrology must be true.

And it is easy to generate even more bizarre examples from the history of science.

I've documented how equations used for computing nuclear reactions in stars are the same equations used in nuclear medicine, the development of nuclear chemistry, nuclear reactors and even nuclear weapons. Why did so many of the researchers involved in the early development of nuclear reactors and nuclear weapons also have prior contributions in stellar nuclear astrophysics (individuals such as Enrico Fermi (wikipedia), Edward Teller (wikipedia) and Hans Bethe (wikipedia))?

That's the standard I've used in "Cosmos In Your Pocket". I have been considering a more tutorial-style technical appendix that shows these connections in more detail.

What about the quantum tunneling relationship which Bethe used in 1939 to compute the rate of the p+p->d nuclear reaction, the first step of the proton-proton chain (wikipedia)? Can Siggy_G demonstrate that it is NOT the same quantum relationship which Esaki used in 1950s to develop the tunnel diode (wikipedia)?

Have we seen a similar tracing of the knowledge base of basic electro-magnetism to a concise mathematical model of an electrically powered star? To make an equivalent analysis for the Electric Universe, then Siggy_G would have to demonstrate something like the amount of energy carried by a cosmic scale electric current, sufficient to power the Sun, generates a magnetic field consistent with what we measure for the Sun.

OPPS!

I've already done that (see Electric Cosmos: The Solar Resistor Model), and the results weren't encouraging. For Siggy_G to make a truly equivalent EU 'rebuttal', he would essentially have to solve this problem as well as answer the questions I've posed under “Challenges”.

So I invite Siggy_G to write his response, but I'm not holding my breath.

Pseudoscience and the Technomystic

2011-10-10T19:43:00.000-04:00

One of the key themes that I try to emphasize in this blog is the unity of science and modern technology.

The science of cosmology is really just the extension of the same physical principles we have discovered on the Earth and have incorporated into our technology. See some of my previous posts on this topic:

In some cases, the physical principles were understood from cosmological evidence before they were testable in the laboratory.

The Cosmos In Your Pocket: Expanded & Revised

The technological leadership the United States enjoyed in the post WWII era was due in no small part to the emphasis of science in the U.S. educational system in that time frame. The decline of U.S. leadership in these fields can easily be tied to the decline of science understanding among the general population and pseudo-science has certainly been a component of that decline.

One of the problems run into by pseudo-scientists is that when they deny some well-established aspect of modern astronomy or cosmology, such as the energy source of stars, etc., they are denying a knowledge base is tightly connected to the same understandings of nuclear physics, atomic physics, electromagnetism, etc. used in technologies we use every day.

To defend their ignorance, the pseudoscientists eventually reach the point that they must deny how a number of well-established technologies work. In the process, they sometimes manufacture alternative explanations which they try to make consistent with whatever alternative 'framework' they are trying to maintain. For all intents an purposes, their alternative explanations evokes a quote from Arthur C. Clarke:

“Any sufficiently advanced technology is indistinguishable from magic.” - Arthur C. Clarke (wikipedia)

For lack of a better term, I'll call such an individual a technomystic.

Here's a few examples:

* Geocentrism: Our ability to travel in space depends on Newton's laws of motion and gravity, theories which do not define an absolute origin in space. These equations are invariant under translation and rotation - the interactions between planetary bodies and spacecraft depend only on their RELATIVE positions, and not on any absolute spatial reference frame. This is why we can use the exact same mathematics to get a spacecraft in orbit around other planets in the solar system as we use to orbit the Earth. Some Geocentrists go so far as to deny space flight even takes place (such as claimed at Moving World - Deception). The equivalence of all reference frames is built into modern star trackers used in the navigation of satellites (see Ubiquitous Aberrations) so this theory is actually tested 24/7 on satellites around the solar system.

* Relativity Denial: This is often a component of Geocentrism but it is also often invoked by Electric Universe supporters and some Young-Earth Creationists. A number of modern technologies require high-precision measurement, with accuracy on the nano-second time scales, where relativity has already been demonstrated to become important in technologies such as the GPS system. Most of the deniers invoke claims by researchers who are, at best, peripherally involved with GPS technologies, and I have yet to find one that has actually done the critical clock synchronization and/or signal time-of-flight analyses. (see Scott Rebuttal. I. GPS & Relativity, GPS, Relativity & Geocentrism)

* Space Weather: The Electric Sun model advocated by the Electric Universe supporters, claims the region of space from the Sun to the heliopause is radically different from the conditions discovered by mainstream astronomy. Conditions in this region can be hazardous to the operation of satellites and even the lives of astronauts. Yet while mainstream astronomy and heliophysics understands the environment sufficiently to setup forecasting systems to protect assets in space (Space Weather Prediction Center), EU supporters evade demonstrating an equivalent capability, even when the data to do it are all publicly available.

* Young-Earth/Young-Universe Creationism: Young-Earth creationists try to get around technology implications of their 'science' by moving their changes back in time or far in space, such as the work by Barry Setterfield (see A Changing Speed of Light?). However, this still creates problems for atomic/nuclear physics & applications as we detect a number of nuclear and atomic spectral lines in distant space with the same characteristics in Earth laboratories. In this case, the safest theology are various flavors of Old-Earth Creationism (such as advocated by Reasons to Believe, etc.).

In most cases, it is difficult to get these technomystics to explain HOW many of the affected technologies actually work in their 'worldview'. Short of claiming the technology itself is an outright fraud, the only clear answer we can get from them is that the technology does NOT work the way the physicists and engineers who designed and built the critical components say that it work and documented in many textbooks and design specifications. I have found no examples of these technologies being developed and built by those who deny the fundamental physics, though we have many 'reinterpretations' of how these technologies work from those who, at best, were peripherally involved in the development.

Next: More exploration of the science & technology connection...

Electric Sun, Electric Comets & 'Conspiracies'

2011-10-05T21:23:00.000-04:00

I got a good chuckle this week when I stumbled across this on the Thunderbolts Forum:
NASA Wiped Imagery of Comet Hitting Sun

Here's a few more rational evaluations:

Bad Astronomy: The comet and the Coronal Mass Ejection
Astronomy Picture of the Day: Comet and CME on the Sun
Sungrazing Comets from the Solar Physics group @ U.S. Naval Research Lab

The Electric Universe claims fail because EU supporters fail to compare this event to all the times that CMEs occur without a comet approaching the Sun. Consider all these events from about a week in October-November 2003:

‪Solar storm Halloween 2003 SOHO EIT and SOHO LASCO‬

The 'snow' that strikes the camera after CMEs directed Earthward are the protons and other ions in the CME. Some of particles scatter in the instrument at angles that let them cut across multiple pixels in the imager and create the occasional 'dash' structures that last for one image (as opposed to a comet that you would be able to track across multiple frames).

Reading: "Cosmical Electrodynamics" by Alfven & Falthammer

2011-10-02T19:48:00.000-04:00

Some time ago Dave Smith listed a few texts which were regarded by EU supporters as primary references. There were three entries: Tony Peratt's Physics of the Plasma Universe), Cosmic Plasma by Hannes Alfven, and the Alfven & Falthammer text, Cosmical Electrodynamics, 2nd edition as EU references (see comment).

I had read Physics of the Plasma Universe some years ago. Just recently, I finished reading the 1963 edition of Cosmical Electrodynamics (hereafter designated as CosEl for brevity).

In this text, did I find a testable model of the Electric Sun or Electric Comets?

No.

What did I discover?

On pp 14-15, Alfven presents an example of charge separation in the solar corona and how it generates a very large voltage which will act to remove the charge separation. This is why large charge separations cannot endure in cosmic environments, contrary to many of the claims of EU supporters (see Charge Separation in Space). In the text, there was no mention of even the possibility that the Sun could be predominantly powered by external electric currents. As I have documented elsewhere in this blog, Alfven was NOT a supporter of the electrically-powered solar/stellar model.

I've had some EU supporters complain about the use of the term 'ionized gas' in scientific press releases or other writing for the general public instead of 'plasma'. I've spoken to some science writers who note that the term 'plasma' is more often associated with blood and health issues in the mind of the general public. 'Ionized gas' removes that ambiguity. On page 134 of CosEl, even Alfven notes that 'ionized gas' and 'plasma' are often used synonymously.

In one of Alfven's papers from the 1980s (Recollection of Early Cosmic Ray Research), Alfven seems to suggest that Enrico Fermi took his idea of particle acceleration, a process that is today called Fermi Acceleration (wikipedia). Yet on pages 38-39 of CosEl, published in 1963, Alfven describes the Fermi process with no mention of possible contributions by himself. Why is this? Was Alfven mis-remembering the origins of this process in the 1980s?

On pg 68-70, CosEl describes the process of radiation loss by charged particles moving in magnetic field, the origin of cyclotron (wikipedia) and synchrotron radiation (wikipedia). This process has been identified in cosmic systems by mainstream astronomy and is credited to Alfven. This radiation has been used as signature to identify current and electric fields in galactic jets (see Electric Universe: Measurement of the Electric Current in a Kpc-Scale Jet). The radiation from this process was also the spike through the heart of Tony Peratt's galaxy model (Scott Rebuttal. II. The Peratt Galaxy Model vs. the Cosmic Microwave Background). Even Peratt's own analysis revealed that current streams needed for the Peratt model should have been readily visible in the cosmic microwave background maps (Electric Universe: More data refuting the EU galaxy model), a fact repeatedly denied by EU supporters.

Chapter three goes into a derivation of the magnetohydrodynamical equations (MHD, wikipedia) and some basic applications. Many of the examples explore the infinite conductivity/frozen-in conditions which magnetic fields can exhibit when imbedded in a highly-conductive plasma. In spite of many of Alfven's comments to the contrary (On Frozen-In Field Lines and Field-Line Reconnection) picked up by the EU supporters (The Electric Sky, pp 120-127), this approximation is perfectly legitimate in medium and high density plasmas (CosEl, pg 191), but in low-density plasmas, such as planetary magnetospheres (wikipedia), it is probably not valid. Many of the complaints are equivalent to claiming that we shouldn't teach projectile motion with Newtonian physics because air resistance is not included, in spite of the numerous applications where it gives results of acceptable accuracy.

On pp 121-124, Alfven discusses the Cowling theorem and the mechanisms of self-exciting dynamos. Yet the dynamo model is strongly criticized by Donald Scott (The Electric Sky, pg 115, 127). Despite Scott's criticisms, these dynamo models have already generated far more testable predictions (YouTube.com) than we've ever found from any EU 'theorist'. Why should we believe Don Scott over Alfven on this topic?

For its day, Cosmical Electrodynamics was a perfectly good introduction to plasma physics, covering many of the aspects of charged particles in fields covered in many other plasma physics texts (such as those below from my collection). We also see mention of early theoretical ideas and experimental work in applying kinetic theory to solving problems in plasma physics (pp 135) (see Vlasov Equation, wikipedia). These and other techniques have improved considerably since CosEl was written in 1963, as noted by Peratt (Advances in Numerical Modeling of Astrophysical and Space Plasmas, 1997). Today, mathematical modeling is a powerful tool for plasma physics, suitable for many engineering and commercial applications (see Electric Universe: Plasma Modeling vs. 'Mystic Plasma' and related posts). Yet EU supporters repeatedly deny these advancements when it generates results in conflict with their cosmological claims.

I found NOTHING in CosEl that invalidates the basic tests I have done on Electric Sun models. The fact is that CosEl repeatedly uses conservation principles in many of the analyses, just as I have done in analyzing Electric Sun models (Electric Cosmos: The Solar Resistor Model, Electric Cosmos: The Solar Capacitor Model. III), If EU supporters want to say that my analyses are not applicable, then they are really saying that CosEl is full of nonsense. CosEl did serve to remind me of additional plasma tests which can be applied against EU silliness such as the Electric Sun model.

Cosmical Electrodynamics provides yet another example of the disconnect of EU 'theories' with reality. EU supporters want to present Alfven, Peratt, etc. as primary leaders in their 'science', but then want to discount the fact that much of the work by these same researchers actually DISPROVES most EU claims.

To paraphrase a recent statement by Jon Stewart on The Daily Show, I'd say that EU's biggest problem is they are at war with their own talking points!

Perhaps Mr. Smith should have read Cosmical Electrodynamics more carefully before he recommended it...

References from Cosmical Electrodynamics

Hydrodynamic and hydromagnetic stability, S. Chandrasekhar, 1961 (Dover Publications)
Gaseous Conductors, J.D. Cobine, 1941

Modern References

“Computer Simulation Using Particles” R.W. Hockney & J.W. Eastwood
“Plasma Physics: An Introduction to the Theory of Astrophysical, Geophysical & Laboratory Plasmas” Peter A. Sturrock
“Principles of Plasma Physics” Nicholas A. Krall & Alvin W. Trivelpiece
“Classical Electrodynamics, 2nd Edition” J.D. Jackson

Note that I have all of these references on my shelves, contrary to EU claims that astronomers don't study electrodynamics.

Tidbits on Extrasolar Planets and Polonium Halos

2011-09-18T20:19:00.000-04:00

I've been busy with a number of other projects of late, both work-related, and/or relevant to this blog, which has encroached on my writing time. I may actually miss a few posts in the coming weeks as I work through these other projects.

One project near completion is my own N-body simulation (scholarpedia) code written in Python and running on modern hardware. It can generate several types of plots and I can even generate output through the POVray ray-tracing software to make movies. I've been testing the code with gravitational and electromagnetic problems. This program will be used to provide a couple of visual examples for subjects discussed on this blog and I hope to start write-ups for it soon.

A side-benefit of developing the N-body code was that I also solved an algorithm issue that aided in the development of different work-related project - a small plasma simulation using PIC (Particle-in-Cell, wikipedia) methods.

Since I don't have a full regular post, I'll update on some recent news and other activities relevant to this blog.

More Exoplanets Imaged Directly
One of the YEC claims I've covered before (Another failed creationist prediction?)
suggested we would never have direct evidence of extra-solar planets. Flying in the face of that claim are even more images of these extra-solar planets:
Wired: Exoplanet Portraits: Direct Images of Other Worlds

The discovery methods behind these extra-solar planets are also additional examples of of how astronomy knowledge grows by expanding on our existing knowledge base. Many of these extra-solar planets were too faint to be imaged directly by technology of the day and many were first detected by their gravitational effects. This approach has enjoyed much success throughout the history of astronomy and is currently part of the strategy in searching for Dark Matter (On Dark Matter. I: What & Why?, On Dark Matter. II: An Exotic Hack?)

Mystical Migrating Polonium...
I've already written a fair amount on Robert Gentry's claims about polonium halos (Polonium Halos as Evidence of a Young Earth? Polonium Halos). Here's an update with some new data I've uncovered.

I recently completed reading Richard Rhodes' book, "The Making of the Atomic Bomb" (Barnes & Noble). In the chapter discussing the development of the neutron initiator for the atomic bomb (pp 579-580 in the Easton Press Collector's Edition), the author mentions an interesting problem with the polonium used in the initiator:

Thomas shipped the Po on platinum foil in sealed containers, but another nasty characteristic of polonium caused shipping troubles: for reasons never satisfactorily explained by experiment, the metal migrates from place to place and can quickly contaminate large areas. "This isotope has been observed to migrate upstream against a current of air." notes a postwar British report on polonium, "and to translocate under conditions where it would appear to be doing so of its own accord." Chemists at Los Alamos learned to look for it embedded in the walls of shipping containers when Thomas' foils came up short.

So even outside granites and micas, polonium has a track record of moving around on its own.

The problem is mentioned again in "Contribution of Chemistry in Early Day Los Alamos" by Penneman and Meade. However, the authors of this report attribute the polonium migration to the recoil of the atom due to the alpha-particle decay. I'm a little dubious of that claimed cause as one would probably expect to see similar behavior in other alpha-decay radioisotopes near the mass of polonium. To my knowledge, polonium is unique in this migration characteristic in this part of the isotope table. However, the decay channel through radon is part of the polonium decay chain. Note in my chart below:

If your polonium sample has some trace of Po-218 (half-life approximately 3 minutes) from this decay series, some fraction of the nuclei will beta-decay (two green arrows) up to Rn-218 where transition to a gas phase can allow the isotope to move. Later, the nuclei can alpha decay (red arrows) back to Po-214 (half-life approximately 160 microseconds) and some may decay to Po-210 (half-life approximately 138 days). I suspect this migrated polonium is actually from traces of Po-218 in the original sample. If you only perform chemical tests to identify polonium, researchers might not notice that the isotopic composition of the sample. The alternate branches in this decay series suggest one could test this hypothesis looking for migration of other isotopes in the Rn-218 decay.

So we see that polonium can move around in modern times WITHOUT divine assistance!

9/20/2011 update: fixed some typos.

Electric Universe Apologetics, or, With Friends Like These...

2011-09-10T19:45:00.010-04:00

(I had really hoped to get this out sooner, but other things kept intervening. Sorry Jon.)

Back in May, 2011, Jon Voisey of “The Angry Astronomer”, wrote a story for Universe Today which was also picked up at PhysOrg.com:

• Universe Today: Energizing the Filaments of NGC 1275,
• PhysOrg: Energizing the Filaments of NGC 1275,

As part of the article, Jon pointed out that this release would probably be exploited by the Electric Universe (EU) crowd as 'evidence' for their claims. He was very quickly proven correct as the comment stream at phys.org became filled with comments from EU supporters.

There was one entry by a particularly long-winded commenter hiding behind the pseudonym “HannesAlfven” in the phys.org posts:

“To be clear, there will come a day when EU proponents create their own curriculum, based upon their own interpretations of observations and experimentation. Once this occurs -- and it is absolutely inevitable -- these quantitative models will be refined.”

I summarized a number of issues EU 'theorists' like to ignore in a recent post (Challenges for Electric Universe 'Theorists'). The problems of standard cosmology pale in comparison to the problems of EU claims which supporters repeatedly ignore.

So let's break up “HannesAlfven's” statement into smaller pieces to better explore its high density of nonsense...

“there will come a day when EU proponents create their own curriculum, based upon their own interpretations of observations and experimentation”

Science in the classroom is supposed to be well established - Newton's Laws, gravitation, thermodynamics, electromagnetism, quantum mechanics, nuclear physics. Maybe a little speculative stuff is sprinkled in areas on the scientific frontier, to demonstrate that not all problems have been solved. I suspect neutrinos were mentioned in 1940s physics classes even though not a single one had yet been detected directly.

But since EU theories, such as the Electric Sun and galaxy-generating currents, have numerous problems, it cannot be considered as well-established so it does not belong in the classroom.

“HannesAlfven” proceeds to arrogantly claim that EU adoption “ is absolutely inevitable”.

While the standard model of the Sun has great (but not perfect) success, EU supporters have yet to demonstrate that their model can do things as simple as predict solar wind particle densities and speeds, issues vital for the safety of satellites and astronauts. This is something the standard model does quite well. Without this basic capability, EU will have a hard time designing radiation shielding for space flight. How will anyone adopting EU 'theories' maintain a presence in space if they don't know how to shield their satellites? EU's 'inevitable' adoption spells death for the space-faring capability of the adopter.

And finally, there's the really ROTFL close “...these quantitative models will be refined.”

Huh? Which quantitative models are those? WHERE are they?

Of course, the really funny part of this statement is the claim that the EU models just need to be 'refined'.

Astronomical models off by a factor of 2, or even a factor of 10, need 'refinement'. When a model's predictions are off by factors of thousands or more, as EU models are (see Electric Cosmos: The Solar Resistor Model, Electric Cosmos: The Solar Capacitor Model. III., etc.), saying the models will be 'refined' is a joke more akin to a self-delusion.

But even more interesting about “HannesAlfven's” statement and attitude is how similar it is to the stated tactics and goals of Creationism and Intelligent Design movement - they want to push their material into the classroom first - and THEN they'll refine their 'scientific support'.

This same tactic was used in Dover PA by ID supporters. This was the reason for the Dover 'Intelligent Design' Trial (wikipedia).

EU supporters constantly try to promote their cause, not with actual scientific facts and testable hypotheses (like real scientists) but as a conflict of worldviews or a 'culture war', a tactic used in religion or politics.

The fact is that science works regardless of your worldview or culture. A cell phone or satellite works based on the quality of the science, and quality of the construction and maintenance, independent of whether you 'believe' it will work.

However, one's worldview or culture can strongly impact whether one can actually build the technologies that science enables - those who don't understand the science behind a cell phone or satellite will never be able to design it or build one from the fundamentals.

Geocentrism's "Quantized Planetary Orbits"

2011-09-03T19:37:00.003-04:00

Mr. Martin responds to "Stupid Geocentrist Tricks" with In Response to Dr Bridgmans "Stupid Geocentrist Tricks". I've already made some reply in the comments to the previous article.

One of the statements in Martin's response that really caught my attention was

Martin: "6. Quantized planetary orbits – a law of planetary distances matches the preferred redshift of quasars with a ratio of 1:1.23."

I conducted several searches to find more details about this claim, but only found it quoted in a number of online locations with no details of its justification. I could find nothing describing details of the ill-defined 'law of planetary distances'.

But that wasn't too severe a problem. After all, information on planetary distances in the solar system are readily available. I collected some values from NinePlanets.org, Appendix 1a: Solar System Data.
I included the values for the asteroid Ceres and even Pluto to increase the number of possible data points.

In the table below, I present the data and the analysis. For each planet, I have the distance (actually the length of the orbit's semi-major axis) from the Sun (heliocentric distance) in kilometers, which is often designated with the letter a (column 2). I then compute the ratio of the distance of the planet (n) and the distance of the planet immediately before it (n-1) (column 3). Since there is no prior planet, we can't set the value of this ratio for Mercury. We then compare this result to the claimed value (column 4) and report the percent error, 100.0*(actual-predicted)/predicted (column 5).

Planet	semi-major axis (km)	a(n)/a(n-1)	claimed ratio	% error
Mercury	57,910,000	N/A	N/A	N/A
Venus	108,200,000	1.87	1.23	52%
Earth	149,600,000	1.38	1.23	12%
Mars	227,940,000	1.52	1.23	24%
Ceres	446,000,000	1.96	1.23	59%
Jupiter	778,330,000	1.75	1.23	42%
Saturn	1,429,400,000	1.84	1.23	49%
Uranus	2,870,990,000	2.01	1.23	63%
Neptune	4,504,300,000	1.57	1.23	28%
Pluto	5,913,520,000	1.31	1.23	7%

Note that not only is there significant deviation from the claimed value, but the claimed value of 1.23 isn't even a mean or median value of the actual data. In fact, the claimed value is smaller than all the actual values.

As an additional check, I also constructed some plots using a planetary ephemeris file available at the JPL Solar System Dynamics web site. The distance ratios are again computed based on the orbital semi-major axes. The error bars are computed using the range of heliocentric distances driven by the orbital eccentricities.

Click to enlarge

We can also plot the ratio connecting the inner planet on the horizontal axis and the outer planet on the vertical axis and compare to the claimed ratio.

Click to enlarge

Again, the agreement with the claimed 'quantization' ratio is very poor. But for Pluto (and it is no longer considered a planet so can that apply?), the error bars do not even overlap with the line marking the 1.23 ratio.

So what gives? This poor fit agreement between actual data and the predicted line do not coincide with any generally agreed definition of quantization (wikipedia). The scatter in the actual data points suggests that even some modification of the claimed 'quantization rule' would not improve the situation. Again, it appears the Geocentrists are incapable of doing even basic math. Or could it be that the Geocentrists know their statement is false and think their supporters are too ignorant to do basic math to check them?

If Mr. Martin or other Geocentrist supporter wishes to clarify this claim with a link to a specific analysis, I will allow them to post a link with more details OF JUST THIS PARTICULAR CLAIM OF QUANTIZED PLANETARY ORBITS. Anything else will be rejected.

Miscellaeous News: Adam & Eve, Creationism in the classroom

2011-08-27T18:30:00.006-04:00

I've been a little distracted of late, with either prep and/or cleanup from earthquakes (Wow! My first earthquake where it was clearly an earthquake!) and hurricanes along the U.S. east coast, so here's a post of some creation/evolution news items of relevance.

I like posting the slashdot link to many of these despite the rather low signal-to-noise ratio of the comment. The slashdot audience is sufficiently technically and scientifically savvy that the comments often include interesting and relevant side-links not included in the main story.

Slashdot: Evangelical Scientists Debate Creation Story
Evangelicals Question The Existence Of Adam And Eve
by Barbara Bradley Hagerty

Some interesting quotes from the article:

Venema is part of a growing cadre of Christian scholars who say they want their faith to come into the 21st century.

This must happen, or Christians risk scientific and technological illiteracy vital to maintaining a growing a modern society. Many of the creationists who comment in this blog have no idea of how many of the technologies they use depend on science which they wish to deny.

“From my viewpoint, a historical Adam and Eve is absolutely central to the truth claims of the Christian faith,“ says Fazale Rana, vice president of Reasons To Believe

I'm a bit disappointed in this as I do follow some of RTBs content. Their astronomy is pretty good but I often disagree with some of their theological content. I find it interesting that as more extrasolar planets are discovered, their position seems to be slowly migrating away from a doctrine that humans must be the only intelligent life in the cosmos.

BioLogos and the June 2011 “Christianity Today” Cover Story

Slashdot: Teacher Cannot be Sued for Denying Creationism

NCSE: A final victory in Texas
Creationists loose big in a case over science textbooks.

Setterfield, SED (Stochastic Electrodynamics), and NASA

2011-08-20T18:19:00.048-04:00

I recently received an e-mail query in regards to Barry Setterfield's activities. I've been a little slack keeping up on that front as Mr. Setterfield began attaching many of his claims to the Electric Universe and I've had a lot of activity there.

The query reported that a Dutch site was suggesting that NASA was using a theory called SED for futuristic propulsion and that SED was related to Barry Setterfield's zero-point energy (ZPE) driver for his theory of c-decay (for more details on the problems with Setterfield's work, see additional links).

After a few searches, I found an English translation that was probably the original source of the information, which turned out to be the Zero Point Energy page on Setterfield's site.

Setterfield's page is largely a combination of quotations from more legitimate work spun together with Setterfield's own claims to make them appear consistent. Setterfield often tries to connect his work to other, more legitimate work, probably in an attempt to raise his own credibility. Most of it is pure nonsense that fails numerous other tests as documented in many other analyses.

Setterfield spends a lot of time trying to connect his use of the Zero-Point Energy (ZPE) to Stochastic Electrodynamics (SED), and then makes the NASA connection:

Setterfield: “On the positive side, NASA and other organizations have hired SED physicists in order to discover a power source for spacecraft and earth-bound applications utilizing the ZPE.”

Just What Is SED?

SED is Stochastic Electrodynamics (wikipedia), basically an idea to explain quantum mechanical principles by incorporating some randomness in electrodynamics through an interaction with the zero-point energy (wikipedia).

SED is NOT Setterfield's idea.

SED's origin can be traced back to the 1960s. While SED has enjoyed some successes in matching predictions of some quantum phenomena, it has not been uniformly successful. Even one of its original proponents regards it as something of a failure. From Trevor Marshall, one of the developers of SED:

“While achieving some notable successes, for example with the Casimir effect, SED must overall be judged a failure.“

Not everyone has given up on SED and are exploring other variants:
Contribution from stochastic electrodynamics to the understanding of quantum mechanics

Zero-point energy has often been invoked to support a number of pseudo-scientific claims, such as various types of 'free-energy' devices. I've yet to find any demonstration of one of these devices that can conclusively produce more energy than goes into it from other sources. Bob Park has written about some of these devices in his book, "Voodoo Science" (wikipedia).

Setterfield's statement that NASA is hiring SED physicists is a bit dated. The group was chartered to explore possible advanced propulsion techniques and there was some examination of possible applications of ZPE. However, the group was shut down some years ago due to budget cuts (NASA: Breakthrough Propulsion Physics). I've not seen any evidence that the ZPE explorations by this group used any of Setterfield's 'ideas'.

The bottom line is that NASA is NOT using any of Setterfield's ideas related to the ZPE or even the SED methodology.

The Electric Universe Connection

Towards the end of Setterfield's ZPE page, Setterfield appears to be actively courting the Electric Universe advocates.

Setterfield: “It is interesting that some of the Thunderbolts group of correspondents do not accept the ZPE. In this context I might point out that there are a diverse group of correspondents there and not everyone has the same views. Furthermore, I presented a major paper about the ZPE and the redshift at a science conference in June, and Dave Talbott of Thunderbolts was there to hear it!”

The presentation in question is apparently based on Setterfield's ZPE paper: “Zero Point Energy and the Redshift“, PROCEEDINGS of the NPA 6(2):1-10, 2010. This is apparently a follow-on to material I've written about before:

Geocentrism: Laser Ranging Experiments

2011-08-13T19:20:00.024-04:00

Mr. Martin responds to "Stupid Geocentrist Tricks" with In Response to Dr Bridgmans "Stupid Geocentrist Tricks". I've already made some reply in the comments to the previous article.

Mr. Martin's response is a collection of nonsense that can only be maintained if one is never required to test their claims against real physical measurements.

Martin: "2. Science has demonstrated physical phenomena occur relative to earth as though the earth was stationary relative to the rest of the universe. As such, the geocentric model alone is the correct model."

All of Mr. Martins 'proofs' of Geocentrism rely exclusively on experiments done on the Earth, while ignoring similar experiments elsewhere in space.

Martin: "If Dr Bridgman denies this problem exists then let him have a look at a similar situation with the lunar laser ranging experiment. According to Dr Tom Murphy the experiment works by the mirror deforming according to relativity theory, causing the laser to bounce back in the mirror frame along a different line from which it entered, thereby the laser returns safely back to the moving earth. A clear indication of the mirror deformation is shown here figure 2, page 2 - http://www.physics.ucsd.edu/~tmurphy/apollo/doc/velocity.pdf"

Here's an upper-level link to a larger collection of Dr. Murphy's documentation of Lunar Retro-Reflector (LRR) experiments.

The Murphy paper discusses the aberration effect that must be considered in lunar ranging. I have already demonstrated that aberration effects have been measured and utilized for navigation purposes by satellites around the solar system (see Geocentrism: Ubiquitous aberrations) so Mr. Martin's claim that this is evidence for a motionless Earth are moot.

The LRR is not the only laser ranging experiment. I can think of three that have operated, or are operating, around the solar system:

MOLA was in orbit around Mars,
LOLA is currently in lunar orbit,
Messenger is at Mercury

(see Planetary Laser Altimetry). All these instruments operate by bouncing laser signals off the surface of the planet. All operate around the particular planet they orbit as if that planet were the center of the universe, or even as if the instrument itself were the center of the universe. The lasers use the exact same value of 'c' in computing their range from timing even though they are in motion relative to the Earth. This is as expected from relativity.

If the Earth were truly a distinguished coordinate system as Mr. Martin claims, then you would expect these laser altimeters to operate differently when orbiting another planet. Mr. Martin evades specifying what would be different in their operation. The simple fact is the laser altimeters operate exactly like they do when based the Earth, or Earth orbit, as predicted/expected by relativity.

This is not an idle question. If there were a way to distinguish a frame of absolute motion, it would be possible to build an actual 'speedometer' to ride aboard a spacecraft, instead of using the complex combination of spacecraft orientation and remote Doppler measurements currently required. If Geocentrists are correct, they should be able to prove their case by the invention of such a device.

Mr. Martin whines that Dr. Murphy won't respond to him. That is no mystery. People doing real work don't enjoy wasting their work time with Mr. Martin's type of silliness, whereas I do this as a hobby outside my day job.

Mr. Martin cannot produce an experiment operating around the other planets, or in the space between them, that suggests Geocentrism is true. There are many experiments operating in these regions providing evidence that Geocentrism is false.

Goodies from my Recent Excursions

2011-08-06T19:04:00.001-04:00

Misconceptions in Sun-Earth Science
TEN THINGS YOU THOUGHT YOU KNEW ABOUT SUN-EARTH SCIENCE

From the education group for the IBEX mission, there's some plasma-science based Games & Activities. Of particular interest is Magnetic Pinball.

Other plasma simulation explorations:

Simulations and Games by Kipton Barros
Interactive 3D visualization of particle trajectories in a plasma

I've written about the IBEX results and implications for claims of an electrically-powered Sun (and stars)

Miscellaneous Links on Geocentrism & Relativity Denial

2011-07-30T18:53:00.039-04:00

If this post was released through the scheduled posting mechanism, it means I've been too busy to complete a post this week.

So I use this opportunity to post a few links of interest I've accumulated.

Geocentrism Disproved: How Newton's Laws Prove the Earth Orbits the Sun , A Ken Cole and Robert Sungenis Dialogue
Special and General Relativity Cosmology Calculator. This includes a detailed description of the Michelson-Morley Experiment (MMX)
Reflections on Relativity
Einstein's Theory of Relativity - How You as Engineer should View it Not all engineers deny the reality of relativity. This is an interesting introduction to the theory.
Baez Usenet Physics FAQ

Things are a bit hectic right now with some short travel for a talk and local conference. I may extend the hiatus to make more progress on posts that have been on my 'To Do' list for too long.

Stupid Geocentrist Tricks

2011-07-23T20:12:00.255-04:00

James Philips responded to “Heliocentrism's 'Vested Interests'...” with a number of comments which I will address in this post.

Most of Mr. Phillips' claims suggest he is either ignoring or (deliberately?) misrepresenting much of the material I have already described in earlier posts of how coordinate systems are defined and used in astronomy. These coordinate systems, verified by many experiments, make it impossible to define an absolute frame of rest.

Here's some excerpts from previous posts defining these issues:

Geocentrism: Galileo was wrong?

Excerpt: Phil notes the distinction of geocentrism as a reference frame, a convenient way to relate measurements, and Geocentrism as a physically distinct frame that defines an absolute rest, so that the Earth is unmoving, unmovable, and not even rotating. Astronomers use alternative references frames all the time - choosing the frames convenient for the analysis of the problem at hand - there are a number of them for the Earth and the Sun, which I utilize in my day job.

Geocentrism: Does NASA use Geocentrism?

Excerpt: Why would they not? Why would you reference everything with heliocentric coordinates if you are in orbit around the Earth? Or in orbit around Mars? The heliocentric coordinates are just a coordinate transformation away from any other coordinate system you choose to use.

You use the model appropriate to the scale of the problem you are solving. A geocentric model can be sufficiently accurate near the Earth, but deviates as one moves further away from the Earth. When traveling between planets, NASA routinely transitions between the frame of the Earth, to the heliocentric frame, and to the frame of the target planet when the spacecraft gets near.

The bottom line is that any coordinate can be used interchangeably, provided you do the correct transformation between them.

The use of any coordinate system, even geocentric systems, is generally a matter of convenience, and does not (and by relativity cannot), define any kind of frame of absolute rest, which is the general interpretation of Modern Geocentrism (wikipedia). In the blue sections below, 'B' is Mr. Phillips' marking of quotations from the original post, “Heliocentrism's 'Vested Interests'..., while 'JP' indicates Mr. Phillips' response in the comment section.

B: As for my viciousness (maliciousness), why would anyone in their right mind listen to 'knowledge' which does not come from some actual accomplishment in the field they are claiming?

JP: But Dr. Bridgman, the knowledge posted on your blog by geocentrists (and others!) challenging you has come from peer reviewed and published scientific papers. What are you so afraid of?

Geocentrists are not promoting peer-reviewed science. They are twisting the interpretation of peer-reviewed science. Every time I check the details of papers referenced by Mr. Phillips and others, I find very inaccurate reporting of the results. Mr. Bennett (mentioned later) directed me to some papers by R.V. Jones and others claiming the papers validated aether theory. I finally retrieved the full papers and supporting citations and will have a future post with another example of gross misrepresentation of scientific results.

B: Would you accept medical advice from an actor or other non-medical professional?

JP: I think the best medical professionals agree that it is always wise to seek a second or even a third opinion, and that is what we shall do here, in a moment, and we shall request our second opinion from Dr. Einstein if you don't mind (or, frankly, even if you do).

But it does seem as if you are suggesting here that truth is determined by academic credential. Surely you must admit that the whole history of scientific advancement shows us the fallacy of your implication above. In fact, if we think about it, every single scientific discovery begins life as the act of one single mind, advancing an hypothesis in direct contradiction to the established wisdom of the rest of the scientific establishment, doesn't it?

By your 'lone mind going against the establishment' criteria and rhetorical games, we can cherry-pick our evidence and prove that the world is flat. I have actually played this exercise with a creationist, where I used many of the creationist rhetorical games to 'prove' the Earth was indeed flat. The creationist gave up after just a few rounds.

Using rhetorical logic, Zeno 'proved' it was impossible for Achilles to overtake the tortoise (wikipedia). Such games in rhetoric, or 'logic' don't make it true, much less useful. Also see Item 6 of: Seven Warning Signs of Bogus Science, by Robert L. Park, Ph.D, (Quackwatch)

Truth determined by academic credentials? You have the cart before the horse. Success at determining and expanding scientific understanding determined the academic credentials. Many of those 'academic credentials' were earned developing an accurate understanding of how atoms work that make small computers possible today, and understanding how gravity works which eventually made spaceflight possible. I'm still waiting for a successful 'geocentrist' algorithm for interplanetary navigation. Or are Geocentrists (again) going to opt for trying to steal, er, 'relabel' the standard coordinate transformation techniques and claim it is the same as the geocentrists theory?

It is apparent that you want us to shut up and accept your word.

I submit this is hardly an authentic expression of the honest scientific mindset.

I don't want to you accept my word.

I insist that Geocentrists adhere to the same standards that real scientists must accept. Hence it is the Geocentrists who must demonstrate the validity of their science through such tests as finding Lagrange points, etc. (see Geocentrism: Does NASA use Geocentrism?). I want the Geocentrists to put their money where their mouth is. Let's see the Geocentrists actually DO something with their 'science'. If they can't do that, then it is they who is asking others to accept their word.

Are your readers not ashamed of you, since you are a teacher? And how unfortunate are your students if they are indoctrinated in this way, instead of being invited to work through these questions carefully and honestly.

Students ARE required to work through the theories carefully in physics and astronomy classes as anyone who's taken a real physics class knows. Most physics students know that many of those equations in the engineering texts come from Newton's laws and other more fundamental principles. A disturbing number of engineers seem to just blindly accept these equations and then deny much of the science behind them. The better engineers understand the science behind the equations and can develop technology beyond rote applications of engineering formulae.

B: There are plenty of people that do that and worse (see What's the Harm?), and they can pay a high price for ignorance.

JP: But Dr. Bridgman, there is nothing in your link which addresses the question of whether heliocentrism has been scientifically proven. In fact, in a moment, we are going to allow Dr. Einstein to teach you that it has not been.

It is well known that you censor the comments of geocentrists such as Dr. Robert Bennett and Rick DeLano, who have already pointed out the key fallacy embedded in your article here; that is, you assert that only the heliocentric reference frame is scientifically valid, when even Dr. Einstein and his scientific heirs insist it is not.

There is NO preferred frame (beyond convenience for a given application). Such a fact cannot 'prove' heliocentrism, but it is sufficient to disprove Geocentrism.

But the real hoot is Mr. Phillips resorts to spinning quotes of Einstein and other developers of relativity to support his position, even though those quotations favor the equality of ALL reference frames, with favor to none. Of course, the Einstein arguments are only valid if RELATIVITY is valid.

So after spending a large part of his comments DENYING relativity, Mr. Phillips now invokes relativity when it is convenient?

Unfortunately, physical laws are not a cafeteria plan, where you can pick-and-choose which physical laws you wish to believe.

Bob Sungenis is your astronaut

B: If you convince someone that a toxin is not poisonous, and they take a dose of the toxin and die, who is morally responsible for the death? You? Or do you just claim that it was their choice and go on your merry way?
JP: Why, that would be *you*, Dr. Bridgeman. But please allow a geocentrist to apply the remedy.

This is exactly the type of answer I expected. So let's put it in a clearer perspective.

You have a rocket (multi-stage) with a life support capsule capable of sustaining a human occupant for, say 10 hours or so.

Bob Sungenis is your astronaut.

Mr. Martin & Mr. Phillips are in charge of designing the flight trajectory. The goal is to successfully launch Dr. Sungenis into orbit, have him circle the Earth three times (to guarantee the flight has indeed achieved a sustainable orbit) and then return to Earth at a pre-defined destination.

The spacecraft will be built making sure the star trackers don't correct for aberration (or perhaps only an earth-based aberration), since the spacecraft will be in a different reference frame. This error would be small, but perhaps not entirely negligible. Mr. Martin & Mr. Phillips must calculate the amount of fuel needed to perform the trajectory (with some reasonable margin of safety). They must also compute the times and angles needed to apply the thrust to direct the rocket into orbit and for the re-entry maneuver.

So will Dr. Sungenis make it back safely to Earth, or is he a potential Darwin Award candidate?

If Mr. Martin & Mr. Phillips' calculation result in the spacecraft being placed on a bad trajectory, and consequently Dr. Sungenis' death, are they guilty of murder?

Remember that NASA and other space agencies do these types of calculations routinely, launching humans into space (okay perhaps not so much for a while as the last space shuttle has just landed :^(. Is Geocentrism's 'science' up to the task?

Note that this is strong test of the geocentrist claim that the Earth is not rotating.

Considering the extensive efforts being make to facilitate commercial access to space, this exercise may actually be testable in the not-to-distant future. In fact, I'd be interested in working with other organizations to design an actual protocol for such tests, similar to the JREF paranormal challenge.

B: Real lives depend on the proper computation of spacecraft trajectories, and not just the lives of astronauts (more below). The Geocentrists have offered nothing but rhetorical games to back their claims - nothing of the rigor required by science and engineering beyond a word game to relabel the mathematics.

JP: Balderdash. The mathematics have been rigorously worked out and published nearly a century ago, in order to make mathematically precise the expression of Relativity's *foundational* postulate, that there exists no “best“ referencer frame.

[ stuff deleted ]

Again, Mr. Phillips is apparently supporting relativity? Relativity demonstrates the equivalence of ALL coordinate systems as a frame of reference.

Then Mr. Phillips flip-flops yet again, trying to deny the validity of relativity with the claim below:

JP: But wait a minute, Dr. Bridgman. Isn't it true that GPS uses a geocentric reference frame?

Why, it certainly is: ttp://www.satsleuth.com/GPS_ECEF_Datum_transformation.htm

So?

I dealt with this issue in Geocentrism: Does NASA use Geocentrism? Since the great majority of GPS customers are on the Earth, why wouldn't we use the Earth as a key coordinate system? If we built a GPS system in orbit around Mars, we would use a Mars-centered coordinate system, and but for the parameter values that describe the planet and its atmosphere, the equations would be identical (A GPS System for Mars).

So how does this prove Geocentrism, that the Earth defines a frame of absolute rest?

That GPS uses a geocentric system is irrelevant to geocentrism being a 'favored' coordinate system beyond matters of convenience. They are already in planning for a positioning system to work ANYWHERE in the solar system. Which coordinate systems do you think it will use?

In fact, it has been shown by Wang and Hatch that all of the JPL software used for GPS and deerp space satellite navigation does “the entire calculation“ in the Earth-centered inertial (ECI) frame:

Really? Mr. Phillips didn't check his 'facts' very carefully.

While the JPL GPS software uses geocentric coordinate systems, it also uses ICRF for celestial reference, as noted in Geocentrism: Ubiquitous Aberrations. But that is not the software used for 'deerp (sic) space satellite navigation', where ephemerides are based on ICRF, a system based on the solar-system barycenter (as described in Geocentrism: Does NASA use Geocentrism?).

“…NavCom Technology, Inc. has licensed software developed by the Jet Propulsion Lab (JPL) which, because of historical reasons, does the entire computation in the ECI frame. Because of some discrepancies between our standard earth-centered earth-fixed solution results and the JPL results, we investigated the input parameters to the solution very carefully. The measured and theoretical ranges computed in the two different frames agreed precisely, indicating that the Sagnac correction had been applied in each frame.“--Ruyong Wang and Ronald R. Hatch, Conducting a Crucial Experiment of the Constancy of the Speed of Light Using GPS, ION GPS 58th Annual Meeting / CIGTF 21st Guidance Test Symposium, 2002, p. 500.

So, Dr. Bridgman, it seems that *real engineers* writing *real software* for *real spacecraft* in fact use the very earth-centered frames you insist cannot be correct.

I've been accumulating some info on Mr. Hatch's claims for some months now. Notice that Mr. Hatch's work has only been published in the ION CONFERENCE PROCEEDINGS (conference proceedings generally published papers from anyone who pays the conference fee), while none of his material has appeared in ION's peer-reviewed publication. Mr. Hatch's errors are far too extensive to add to this already too-long post, so they're being collected for a future post.

Mr. Phillips apparently doesn't know what it means to 'license' software. He also claims I say one cannot use geocentric frames, contrary to my statements in Geocentrism: Does NASA use Geocentrism?

Mr Phillips is becoming a bore.

See how important it can be to get a second opinion, Doctor Bridgeman?

Well, I could continue on mano a mano with all the rest of your comments, but if anyone reading all that I've responded to still wants to keep a closed mind on the question of geocentrism there's perhaps not too much else to say at this point.

The greatest scientists have approached the great scientific paradigms of their day with an open mind, not a closed one. Truth be known, even the greatest ones today have not closed their mind to geocentrism even if many of them may be pre-disposed due to atheistic inclinations to reject it out of hand!

If we have a better world today as Dr. Bridgman talks about it is due at least in part to the fact that the great scientists retain an open mind not a closed one. This is a simple fact which should not even be necessary to point out.

And again Mr. Phillips' arguments degenerate into the standard drivel.

So let's summarize...

In his same set of comments, Mr. Phillips both advocates and denies relativity.

Mr. Phillips has incorrectly claimed that I have stated heliocentrism is an absolute favored frame and that it is invalid to use geocentric reference frames. In both cases I have referenced recent posts illustrating I have not made such claims. This is the kind of 'bearing of false witness' so common in creationist circles, which give Christianity a bad name and which I have complained about before (Creationist Junk Debunked).

This suggests Mr Phillips is making stuff up to stay in the game (see Reason Seen More as Weapon Than Path to Truth). Mr. Phillips has reached the point that he is arguing in circles and is wasting my time. Similar nonsensical responses from him or others will be rejected in the comments.

Challenges for Geocentrists

Since Mr. Phillips has accused me of asking readers to 'take my word for it', let me clarify the questions that Geocentrists must answer, lest they be guilty of insisting readers take THEIR word for it.

First, when Geocentrists wish to respond to any comments on this blog, the must first clearly specify which flavor of Geocentrism are they supporting: A totally non-rotating Earth? Perhaps a rotating Earth but fixed in the solar system? Some other 'flavor'? Failure to do so will result in comment rejection.

1) If Geocentrists want to claim that the GEI/ECI/ECRF or GEO frames is favored, how would you tell? What differences would one expect in the equations? What make GEI/GEO a favored coordinate system, beyond personal preference?

2) Let's consider for a moment the possibility that Wang & Hatch are correct and that the speed of light is 'c' only in the ECI reference frame. But Sungenis uses the null MMX result as evidence that the Earth is not rotating, i.e. that 'c' is fixed in the GEO frame. But the GEO frame rotates relative to the ECI frame! Relativity explains this in full mathematical detail today. How do Geocentrist's explain this inconsistency?

3) There are already proposals to install atomic clocks on Mars-orbiting satellites to make a GPS system to support rover and human operations on that planet (The global positioning system, relativity, and extraterrestrial navigation). According to relativity, the equations for such a system in a Mars-centered coordinate system would look precisely like the Earth-centered system but for parameter values describing the planet's mass, size and atmosphere. If relativity is incorrect, can the Geocentrists provide the equation systems needed to successfully support Mars exploration, or will Geocentrists be, like their 'science', limited to the Earth?

4) Some months ago, Rick DeLano claimed that Geocentrism could explain the Lagrange points, five points of stability in the restricted 3-body problem (Wikipedia), and one of the predictions of Newtonian gravity and laws of motion. I challenged him to demonstrate it, considering that we make use of these locations in a number of operating space missions.

The Geocentrists have been strangely silent on this so I add this to the official list.

Electric Universe: Measurement of the Electric Current in a Kpc-Scale Jet

2011-07-16T18:45:00.011-04:00

A couple of weeks ago, I came across a paper on the Cornell preprint server that I suspected the Electric Universe (EU) crowd would pick up before long...

“Measurement of the Electric Current in a Kpc-Scale Jet”
Kronberg, Philipp P.; Lovelace, Richard V. E.; Lapenta, Giovanni; Colgate, Stirling A.

I'm sure the EUers will be all over this, claiming that it means mainstream science is finally coming around to their ideas. But if they actually read the original paper, and not just the press-releases, they would discover that they were wrong (again)...

The introduction of the paper reveals that this work is actually based on a model for galactic jets that dates back to 1976 with work by Roger Blandford (Accretion disc electrodynamics - A model for double radio sources) and independently by Lovelace (Dynamo model of double radio sources), one of the co-authors of the current paper.

The model relies on the jets of plasma being collimated by a magnetic field and particle flows driven by an electric field created by an accreting black hole. The model has been studied heavily since first proposed by Lovelace and Blandford. The electromagnetic properties of the jet are determined through the rotation measure (RM) of the Faraday Effect (wikipedia). Through this method, they obtained an electron density of 1.4e-5 electrons/cc and a current of 3.8e17 amps directed away from the galactic nucleus.

I suspect EUers will want to compare this result with the Alfven galaxy model, but there may be a problem with that. The earliest reference I can find where Alfven suggested something similar is in a few paragraphs in a paper from 1977:

Electric currents in cosmic plasmas by Hannes Alfven.
Alfven describes a galaxy central radio source as a unipolar inductor, but the description is very qualitative. There is not even a single numerical estimate of currents expected or the visible flux.

Alfven went into a little more detail in 1978 with
Double Radio Sources and the New Approach to Cosmical Plasma Physics by Hannes Alfven

providing at least a graphic, but still no way to estimate the luminosity and other characteristics one could expect to measure from Alfven's proposed galaxy configuration. An examination of the citation lists for both of Alfven's papers reveals no citations for either Blandford or Lovelace. Two years after the fact, Alfven was not acknowledging others who not only preceded his effort, but developed the model in far more detail.

When you look at the contributions made by others prior to Alfven, one begins to realize that Alfven's work described little that wasn't already known. The only aspect of the model that could be considered as a contribution by Alfven could be recognizing the need for a return circuit in the 1977 paper. However, I regard the rigor of the 'return circuit' questionable. MHD simulation volumes are generally modeled as closed systems so the same flows have to return full circle, but the intergalactic medium (IGM) is not a closed system. Charge imbalances can be remedied by charges flowing back towards the galactic center from the IGM, but nothing requires them to be the same particles emitted in original the jets of the galaxy, just that the quantities are sufficient to balance the charge.

Probably the greatest deficiency of Alfven's papers is that while Alfven describes the central engine as a unipolar inductor, there is NO information on how such a structure could be built in Nature. Alfven's central source is a black box with no way to even estimate its power capabilities. For all intents and purposes, Alfven's unipolar inductor could've been a machine built by alien civilizations in all these radio galaxies.

Meanwhile, mainstream astronomy had an object that fit the bill for creating a unipolar inductor (AKA a homopolar generator, Wikipedia): an accreting black hole. The theory had sufficient mathematical development that one could develop testable predictions with it. Accreting plasma around a black hole forms a highly conducting layer just outside the event horizon, making a near perfect conductor that couples to magnetic field generated by the differentially rotating accretion disk. This idea is also related to work by Blandford and Znajek (Electromagnetic extraction of energy from Kerr black holes). Black holes have also been treated as resistors and rotors in circuit elements in a number of configurations (see Black Holes: The Membrane Paradigm, 1986, and related papers by Kip Thorne).

It is ironic that objects EU supporters most deny exist (black holes & neutron stars) are the best known producers of large electric fields in the cosmos.

Problems for Electric Universe

Alfven was NOT the first to propose this configuration for radio galaxies. He made, at best, only very minor contributions to the model, and nothing that contributed to testing the model against actual observations.
The Blandford & Lovelace model, like Alfven's model, is inconsistent with Peratt model because the current seen is strictly a product of the galaxy's central engine, and not due an external source. See (Scott Rebuttal. II. The Peratt Galaxy Model vs. the Cosmic Microwave Background, Still no electric currents powering the galaxies...).
Perhaps the greatest problem it makes for EU is that it demonstrates that we can measure extragalactic currents. This means the EU whines about undetectable 'dark currents' are moot.
In Blandford (1976), the author even notes that his proposed configuration “therefore acts as a unipolar inductor, generating an electric field, E, in the inertial frame.” It demonstrates that astronomers have long considered the effects of electric fields and currents in the cosmos, in spite of EU denials.

While I was researching & assembling this post, Nereid pointed me to this on the Thunderbolts site:
Universe's Highest Electric Current Found
Funny, it appears some thunderbolt forum members actually read the paper, but I have yet to see any acknowledgement of how long ago this model was actually proposed.

Heliocentrism's 'Vested Interests'...

2011-07-09T19:09:00.020-04:00

I guess since the facts are against the Geocentrists, they have nothing better to argue.

James Philips (link): Please allow me to make the following observation. I note that generally those who seek to counter (not necessarily including yourself) John Martin and others who hold to the geocentric model of the universe on various blogsites (and sometimes websites) do so with a certain and peculiar viciousness. Such viciousness (maliciousness?) includes sarcasm to the nth degree and various gratuitous ad hominem attacks such as questioning the sanity or asserting the insanity of those who would even question the heliocentric model. This common type of rottweiler/pit bull seemingly fanatical kind of response to those who simply disagree with or question the heliocentric model certainly leaves one to wonder why the degree of viciousness.

To James Philips:

As for my viciousness (maliciousness), why would anyone in their right mind listen to 'knowledge' which does not come from some actual accomplishment in the field they are claiming? Would you accept medical advice from an actor or other non-medical professional? There are plenty of people that do that and worse (see What's the Harm?), and they can pay a high price for ignorance.

If you convince someone that a toxin is not poisonous, and they take a dose of the toxin and die, who is morally responsible for the death? You? Or do you just claim that it was their choice and go on your merry way?

Real lives depend on the proper computation of spacecraft trajectories, and not just the lives of astronauts (more below). The Geocentrists have offered nothing but rhetorical games to back their claims - nothing of the rigor required by science and engineering beyond a word game to relabel the mathematics.

If Geocentrists want to essentially claim 1+1=3 with no evidence other than their say-so, and they are doing it in such a way that OTHERS will pay the price of Geocentrist ignorance, then Geocentrists are in no position to complain about the level of disrespect they are given.

My goal is that no one pays for Geocentrists' ignorance except the Geocentrists who are propagating (and a number of them are profiting) from spreading the ignorance.

James Phillips (link): “One thing is certain: the lives and careers of a good number of individuals in the scientific community are strongly tied to an ironclad maintenance of the heliocentric model.“

Indeed. And not just in the scientific community...

There are the lives of astronauts who must be able to trust their navigation. Where's those geocentric navigation algorithms for them to compute their trajectories? Haven't seen one yet, and suspect I never will. So no Geocentists will be traveling beyond the Earth.

There are also the lives of people on Earth depending on earth and space weather forecasting that requires satellites in space. Global communications depends on satellite technology. If you don't know where your satellite is, you'll have a heck of a time getting the data back from it.

YOUR life is better because of the heliocentric model, whether you choose to acknowledge it or not.

If someone wants to pontificate Geocentrist nonsense, then I suggest they move to a undeveloped country which does not have these advantages, where their ignorance will be welcomed and they can do less harm. Otherwise they just look like hypocrites, reaping advantages of a technology that they clearly have no clue how it actually works. Others who do know how it works will reap the benefits of better-paying jobs and other economic advantages.

Choose that route, and you'll have to give up your computer, your GPS-enabled cell-phone, any satellite-TV or similar service. Since modern weather forecast simulations are initialized and checked using data from orbiting satellites, you'll have to give up using long-range weather forecasts. If you get energy from any main power grids, the safety of those grids from eruptive solar phenomena is monitored by a fleet of solar-observing satellites, such as ACE, GeoTail, SOHO, STEREO (YouTube: Sentinels of the Heliosphere). And these are just the first order benefits. I could go on about the spin-off benefits of the supporting technologies that were developed to achieve these capabilities.

Give up heliocentrism, and everyone in a modern society loses. You lose as well, regardless of whether you are willing to believe it, or admit it.

But then, history is full examples of societies that fell from their pinnacle due to their collective dogmatic acceptance of some ignorance.

Challenges for Electric Universe 'Theorists'

2011-07-02T17:50:00.003-04:00

I've been mining the rather substantial amount of content which I have developed on this site and via email correspondence and attempting to consolidate it into a form suitable for summary and reference.

See "Challenges for Electric Universe 'Theorists'" in the sidebar.

I expect to expand this as new content is developed here.

Polonium Halos

2011-06-25T19:57:00.000-04:00

I haven't written anything on Robert Gentry's claims about polonium haloes in a while. My major piece on this topic was Polonium Halos as Evidence of a Young Earth? on my main site which covered aspects of the radioactive decay series ignored by Mr. Gentry.

However the NCSE has recently published a few articles related to the geology of these halos.

Origin of Polonium Halos by Lorence G Collins & Barbara J Collins
“Polonium Haloes“ Refuted: A Review of “Radioactive Halos in a Radio-Chronological and Cosmological Perspective“ by Robert V. Gentry by Thomas A. Baillieul

Geocentrism: Ubiquitous Aberrations

2011-06-18T19:21:00.138-04:00

One of the popular attack points for pseudo-scientists is to go after the earliest measurements which supported a theory such as relativity, under the notion that the entire acceptance of the theory is based only on these measurements.

The major error with this approach is that it ignores the fact that many theories, once well-established in many experiments, are integrated into many precision measurement techniques. This means the original theory gets tested every time the measurement technique or technology is used.

Consider the phenomenon of stellar aberration (wikipedia). Aberration is a consequence of the fact that we see objects by the light they emit (or reflect) and that the speed of light is finite.

Everyone is probably familiar with the effect of aberration. The popular analogy is of walking through rainfall. Even though the rain may be falling vertically, to the walking observer, the rain appears to be falling at an angle.

In the case of light from distant objects, the change in the angle of propagation for the moving observer means that the object under observation will appear at a different position, relative to a given coordinate system, than it appears to an observer at rest in that system. In the case of the Earth moving around the Sun, this effect makes stars appear to trace out ellipses on the sky. The aspect of the ellipse varies depending on the angle of the star relative to the plane of the Earth's orbit, the ecliptic. At the ecliptic pole, the effect makes the star move around in a circle, while in the plane of the Earth's orbit, the star appears to move back and forth. The maximum value of this aberration angle is about 20 seconds of arc, about 1/90th the diameter of the full Moon (about 30 minutes of arc). This aberration angle created some problems for the first attempts to measure the parallax (wikipedia) of stars as it is much larger than parallax angles for the nearest stars.

Aberration in Practice
The effect of aberration is sufficiently small, that it is of no real concern in casual astronomical observation, when precision pointing not required. When more precision is required, the contribution of aberration becomes important.

Catalogs of stars and ephemerides of planets are generally computed with the position of the object in a specific reference frame. However, when it comes to pointing telescopes or similar light-based instruments at these stars and planets, the position and velocity of the observer relative to reference frame of the catalog must be known, as well as the velocity of the target object relative to the reference frame. This result is then used to compute the pointing corrections needed for the telescope to properly position the star or planet in the field-of-view. Note that the catalogs are constructed from telescope measurements and the aberration effects in the telescope reference frame must be REMOVED to make the catalog entry (ADS). This makes it possible to use the catalog in a different reference frame.

Resources for understanding stellar aberration:

Aberration and other types of position corrections are important for astrometric (wikipedia) missions where the goal is to determine positions of objects in space with high precision. The Hipparcos mission (ESA, wikipedia) was the first large-scale astrometric mission, cataloging over 100,000 stars with precision parallaxes. An additional mapper on the satellite obtained position information on over a million stars. Due to a rocket failure, the Hipparcos spacecraft did not achieve the planned geosynchronous orbit, but ended up in a highly-elliptical transfer orbit. This accident would create a radically different aberration measure from that of the originally planned circular orbit.
FAQ entry about stellar (and other) aberration effects on the Hipparcos astrometry mission

The ancients navigated by knowing the positions of the stars. Modern navigation, requires high-precision for astronomical positions. Today, these positions provide the inertial reference frame (wikipedia) used for many precision navigation systems on the Earth, such as GPS. Most people don't even think about the connection of the GPS receiver in their phone with the ICRF (USNO) or its successor, ICRF2 (NASA), but this reference system is used to establish accurate positions of the GPS satellites.

But the positions aren't just important for navigation on the Earth. The orientation of a spacecraft relative to a reference coordinate system determines how applications of thrust by the spacecraft will move it. Even a small error in the spacecraft direction angle, magnified by the spacecraft motion over millions of kilometers at high speeds, can create a huge error in the final position.

To determine the orientation of a spacecraft, devices called star-trackers are mounted to the spacecraft to obtain information on the spacecraft orientation. Modern star trackers are very precise. Ball Aerospace has models (Ball Aerospace) with 3 and 0.2 arcsec positional accuracy - small enough that aberration effects must be included.

Spacecraft Math by Stephen Leake (2009)
High-Fidelity Measurement Models for Optical Spacecraft Navigation, John A. Christian and E. Glenn Lightsey
Gravity Probe B needed high-accuracy pointing (20 milli-arcseconds!) in order to do its experiment: Covariant calculation of general relativistic effects in an orbiting gyroscope experiment, Twenty milliarcsec pointing system for the Rolling GP-B Spacecraft

Aberration on the Leading Edge...
As the need for more accurate positional measurements increases, the inclusion of aberration is even more important.

Gaia (ESA) is the follow-on astrometry mission to Hipparcos, with the goal of collecting accurate stellar parallaxes on a billion stars. For more details, see Reference Systems, Conventions, and Notations for Gaia by U. Bastian (2007).

For astrometry missions requiring micro-arcsecond precision, we'll will actually have to include the effects of the motion of the solar system barycenter moving around the galactic center, a phenomenon called secular aberration: Astrometric Effects of Secular Aberration. Sergei M. Kopeikin and Valeri V. Makarov, ApJ 131, 1471 (2006).

Astrometric Software
The effects of aberration are included in astrometric software libraries such as NOVAS (USNO) and SPICE (NASA/JPL), which is actively used for satellite trajectory planning. Here's a direct link to the documentation of the subroutine for computing the position of the satellite relative to the target, which includes corrections for stellar & planetary aberration (spkezr).

In Summary
Aberration has been measured from reference frames other than the Earth. Spacecraft in Earth orbit and going to other planets must compute a different barycentric velocity correction to accurately account for aberration effects. Positional corrections due to aberration must be included to define inertial reference frames for accurate navigation, including GPS systems on Earth.

With their interest in ignoring relativistic effects such as aberration, Biblical Geocentrists have still failed to demonstrate that they are competent to navigate satellites anywhere in the solar system. Any nation that expects to either travel in space, or reap other benefits of space-faring capability, should view Biblical Geocentrism as a recipe for lost satellites and lost astronauts.

Thanks to Scott Snell, a flight software engineer at NASA/Goddard, for directing me to some of the public data available on star-trackers.

What The Electric Universe 'Theorists' Won't Tell You...

2011-06-11T19:40:00.067-04:00

This is a response to the anonymous commenter in the thread:
Electric Universe: Real Plasma Physicists Use Mathematical Models!
I've also posted a similar, shorter response to the article at dad2059.

In indicated quotes from the commentor in red: Anonymous Poster:

Mathematics aside, most relevant scientific discoveries are initially serendipitous and/or conceptual postulates. This appeal to show current (PC/EU) research which corroborates studies and articles over 20 years old is fallacious.

Fallacious? Not at all. Real science is subjected to constant revisions and updates as new data become available. It is rare enough for a scientific reference to be iconic and ACTIVE references after 20 years, but with NO newer work? If you are using material this old as your PRIMARY references, it limits EU to:

1) It is a historical or religious reference, perhaps where the 'original intent' of the author is under examination. This option supports my view the EU is more of an ideological or religious movement (see The Electric Universe & Creationism);

2) It is a DEAD science. The commenter is basically saying there has been no new discoveries in plasma physics since the work of Alfven or Peratt and that plasma physics has been a stagnant science.

Loads of new missions and data impact PC/EU models, yet all the verbal claims of EU proponents have yet to generate one viable computation model where the theoretical model gives numbers even close to the new data. The Peratt galaxy model has yet to be shown consistent with modern cosmological microwave background measurements (see Scott Rebuttal. II. The Peratt Galaxy Model vs. the Cosmic Microwave Background, Still no electric currents powering the galaxies...) Has anyone in PC/EU even mapped locations of current streams across the sky they need to power stars and galaxies in their model? Not that I've been able to find!

Meanwhile, REAL plasma physicists have been revising and improving their mathematical models, to the point of commercial viability. The commenter conveniently evaded the other posts in this topic.
    •    Electric Universe: Real Plasma Physicists BUILD Mathematical Models
    •    Electric Universe: Plasma Physics for Fun AND Profit!
    •    Electric Universe: Plasma Modeling vs. 'Mystic Plasma'

REAL plasma physicists have had significant success with numerical plasma models, in spite of EU's (theological?) position that it can't be done.

The Steady State Theory (sic) and Relativistic Physics have been accepted models for over two decades themselves. Most of the salient data was collected many years ago. Just because you can quantitatively show relevance on paper or electronically, without any way to reproduce those findings in the lab, does not make the ideas of the Standard Model or “Einsteinian Mechanics“ more concrete.

The commenter obviously does not know how quickly science can be integrated into technology. This is possible because we can define how many physical processes operate through mathematical means.

In addition, processes important in astrophysics get testing all the time, and not just in laboratories. I've documented a number of examples in these articles:

    •    Astronomy as an 'Unprovable' Science
    •    The Cosmos In Your Pocket - Updated
    •    Testing Science at the Leading Edge
    •    'Out There' Astrophysics Impacts Technology (again)
    •    Testing Science at the Leading Edge... II
    •    “Real” Science vs. “Cosmological” and “Origins” Science

In the 1930s, Hans Bethe (wikipedia) and Edward Teller (wikipedia) developed the physical and mathematical techniques for understanding the energy generation in stars by nuclear processes. They subsequently used these same techniques to develop the atomic & hydrogen bombs in the 1940s & 50s. How did they do this? They used the microphysics, the same reaction rate and energy generation equations from small-scale laboratory experiments and computed them for the different environments of energy release in the center of a star (under very high pressure) and in a lower pressure environment (the Earth's atmosphere). Even today, there is much data and theory exchanged between nuclear astrophysicists and nuclear weapon designers.

We have yet to see such a demonstration from those who claim the Sun and stars are powered by external electric currents.

Many of the unusual instruments that were used to collect leading edge data decades ago are part of standard instrumentation today - atomic clocks, Michelson interferometers, lasers, etc. so these theories are subjected to continual testing everywhere the technology is used. Principles such as relativity are tested every time someone uses a GPS receiver, regardless of EU & creationist denials. Relativity becomes even more important when we use GPS to do high-precision positions of other satellites. We are already in the planning stages of a GPS system that could operate throughout the Solar System. Thanks to relativity, we knew what relativistic correction was needed for the GPS clocks before they were launched!

All those electrical engineers supporting EU and denying relativity (and insinuating other scientists are incompetent or worse) have yet to build a guaranteed relativity-free GPS receiver.

There is a lot of merit to Alfven's Plasma Cosmology as well as some EU ideas which make more intuitive sense than any ideas of “Dark This/That.“

'Intuitive' does not make the science correct. Quantum mechanics is incredibly un-intuitive, yet those aspects of it, which could be readily predicted through mathematics, enabled us to replace large vacuum tubes with microscopic transistors which make modern electronics possible. What matters in science is that one can make numerical predictions that can be compared to data and observations.

The physics community is one big circle jerk for the most part. The same can be said for biology and chemistry too. Unless someone is willing to stray from the status quo, a profession will become prone to self aggrandizing and auto-kudos.

'Circle jerk'? This sounds more like a description of EU 'theorists'. They build cosmic-scale circuits with no EMF to drive them - the electrical equivalent of perpetual motion machines, yet conveniently ignore where the energy comes from that drives that EMF. They invoke electrons which can't emit synchrotron radiation in a magnetic field for some mysterious reason, a process well-established experimentally. EU 'theorists' hide behind the archaic term “Dark Current” which is no longer used in modern plasma studies since it is now well understood (Dark current has a radically different interpretation in modern physics - wikipedia).

The neutrino took 25 years from postulate to direct detection, but in between that time there were numerous experiments which were consistent with the neutrino's existence. For 'Dark Matter', a subatomic particle, below the detection threshold of our current technology, is the simplest solution.

• On Dark Matter. I: What & Why?
• On Dark Matter. II: An Exotic Hack?

If M-Theory is all that modern theoretical physics has to offer, and it in itself is built upon the accepted physics modalities, then don't expect that mankind will be able to jump to that epic next step which will allow us to truly understand the intricacies of It All, and allow us to be successful universal wayfarers.

M-theory, whether valid or not, has nothing to do with why PC/EU is a failure. PC/EU fails from very basic considerations from electromagnetism and mechanics.

As for the 'universal wayfarers', considering the EU/PC has yet to produce a usable, reproducible model of the heliospheric and interstellar environment, those 'universal wayfarers' will have some serious problems dealing with the field and radiation environment. I have repeatedly made light of these problems and received nothing but excuses from the EU 'theorists' instead of actual, testable models.

The commentor closes with:

You never stifle a brainstorming session with negativity or filtering. If you folks had an IQ above 125 you'd know this, but sadly even the so-called intellectually adept are just barely above average. Your numbers mean jack if they propose abstract absurdities.

Einstein felt quantum mechanics made absurd predictions, yet QM and its absurd predictions made possible the computer on which you are reading this. Nature is under no obligation to adhere to what anyone believes is 'not absurd'. What matters is what we can test with experiments and observations.

If you were an astronaut traveling to Mars, would you accept a QUALITATIVE value for the level of radiation your ship can take from a CME before the astronaut's health is seriously impacted? The CCMC does that today using the standard solar model.

If you operated the northern electrical grid, would you accept a QUALITATIVE value for the level of voltage induced in your long distance power lines by a CME striking the Earth's magnetic field? The CCMC does that TODAY, using the standard solar model.

After the STEREO spacecraft can no longer view the far side of the Sun, as an astronaut, would you accept a QUALITATIVE value for whether an active region has formed out of view and is about come around the limb, with the potential of blasting you with radiation from a solar flare? Helioseismology gives us this capability, but it works using a very different solar structure than ES supporters claim.

Current standard models for the solar environment (very different from the ES model) can generate QUANTITATIVE values for these parameters!

The people you want to call 'sub-125 IQ circle jerks' have real accomplishments. What can EU demonstrate?

Update 6/22: Fixed some grammatical errors.

Geocentrism: Failing More Basic Physics...

2011-06-04T19:32:00.119-04:00

This is a continuation of my response to the comment stream placed in this blog post by Mr. John Martin.

Mr. Martin's claims quickly become more bizarre due to the fact he has built them on of many of the false premises he made, which I addressed in my first response (Geocentrism: Failing Basic Physics...). Mr. Martin claims he has had some physics and is an engineer, yet it appears he is incapable of doing even the basic math and geometry which he would need to understand, and correct, his misconceptions.

Questions referenced in this comment.

Dr. Bridgman said – “Sungenis' 'evidence' consists of selective interpretation of the geometric fact that you can move your coordinate origin to any convenient location - including the Earth - and ignoring the fact that this trick applies everywhere. He completely ignores the dynamical aspects of the problem that make these coordinate systems different when actually moving from planet to planet. The really funny part is he is basically using a relativistic argument to make his case, then tries to prove relativity wrong.” JM- Sungenis’ evidence for geocentrism is all encompassing and shows the science experiments used to determine the motion of the earth through space are all consistent with a stationary earth surrounded by an aether flow. Furthermore, the large scale structure of the universe also points to the earth being at the center of the universe. Combining these evidences, a powerful case is made for a stationary earth at the center of the universe, just as it was made by the See more... creator. I invite you to review your position on this matter as a matter of scientific truth. Dr. Bridgman said – “I've seen no evidence that his 'theory' can answer any of the questions that must be dealt with by satellite designers and astronauts.” JM- What are these problems and why is it not possible to address them with a stationary earth? Please present evidence for your claims.

It is not impossible. It can always be done by transforming to heliocentric coordinate systems when needed, but that can be done from any point in space or planet - it does not favor the Earth in any way. If you want to do the entire calculation in a geocentric system with some 'aether' to account for the coriolis and other forces, then supporters of geocentrism must demonstrate that this works from first principles.

Basically, Geocentrists need to produce the algorithm that enables us to compute the forces this 'aether' creates at any given position and time. Then they need to demonstrate that this can produce the same paths we observe for planets, and design for spacecraft.

Everything I've seen from Geocentrists is a cheat, trying to take someone else's heliocentric solution and then moving the origin to the Earth. They don't appear to have the competence, or courage, it takes to actually transform the known equations of motion, Newtonian gravity and acceleration, well-tested in everything from laboratories to mechanics to spacecraft, to a reference frame where the body of the Earth is not rotating (Wikipedia: Frame of Reference, Non-inertial frames). Once you can compute the forces at any point, particle positions and velocities at any time can be computed.

Evidence for my claims - yeah - no one is using Geocentrists methods (whatever they actually are) to successfully navigate to other planets.

Q1 - Why is it that Newtonian mechanics requires instantaneous action at a distance to account for gravity and this is taken seriously by science?

Q1: Newton was uncomfortable with “action at a distance“. He eventually adopted the solution of noting that his gravitational force law gave predictions to planetary motions that matched observation and left it to others to figure out further details of how it worked. This is common in empirical science. The gas laws (wikipedia) were used for years before we knew about molecules and statistical mechanics.

Q2- What is the mechanism proposed by science what is consistent with Newtonian physics to permit the force of gravity to be effective instantaneously over large distances?

Q2: I don't know. Magic Pixies? Angels? Not really relevant to the fact that the force equation works. Others have proposed theories for a finite speed of gravity. Einstein's theory subsequently provided a model for the 'speed of gravity' (wikipedia).

Q3 - Relativity says gravity is caused by a completely different mechanism of a bending of the space time continuum. As this mechanism is very much unlike the Newtonian mechanism for gravity, why are the two mechanisms routinely acknowledged within modern science?

Q3: and yet in the limit of weak fields, the central-force problem derived from Einstein's field equations reduce to Newton's equations for motion by gravity. i.e. it works. If you don't believe it, do the mathematics yourself. The process is also outlined in many introductory textbooks on general relativity.

Q4- Why is it that the notion of the barycenter is fundamentally flawed and yet it is taken seriously by modern science and is routinely used in planetary flight path calculations when using Kepler’s laws? For example a planet is said to obey Kepler’s laws by taking an elliptical flight path around the sun as one of its foci, yet that same planets is also said to travel around the solar system barycenter as one of its foci, which is not at the center of the sun. This singular inconsistency seems to be routinely ignored by modern science, yet Kepler’s laws are routinely stated to be compatible with Newton’s laws and reflective of real planetary flight paths. Please comment.

Q4: The concept of a barycenter (center-of-mass) is a fundamental concept of mechanics and a consequence of Newton's Laws (wikipedia) and applies to far more systems than celestial mechanics. Ever seen a see-saw? Ever used a lever? Do you know why a bridge is stable (or unstable)? What about an automobile or an aircraft or a rocket? You claim to have some physics background, but it is painfully apparent that you don't understand even these basic concepts.

Q5 – Modern sciences understanding of the physical cause of gravity is not well understood. Why then is Newtonian mechanics and relativity theory used against geocentrism when such theories merely make assumptions concerning the mechanism for gravity and then produce equations based upon those assumptions? After all if those assumptions are not well established by science experiment, then objections to geocentrism are at best only objections, based upon models founded upon assumptions about the nature of gravity. Please comment. . . .

Q5: You have yet to demonstrate any operational knowledge of gravity, so it is clear that YOUR understanding of gravity (and mechanics) is deficient, as demonstrated by your claims above. Modern science has sent humans and spacecraft to the Moon and other planets thanks to how well we understand gravity. We launched satellites into orbit in spite of the fact we had no precision tests of Newtonian gravity between the surface of the Earth and the orbit of the Moon. Talk about a GAP in a scientific theory! Do Geocentrist models have any equivalent accomplishment?

We don't “know“ what electrons are. Does that make my 'Magic Pixie' model correct, or even a viable contender? There is no "proof" that the Earth is round (and technically, it isn't)

"not well established by science experiment"??? According to whom? You who has (knowingly?) misrepresented Kepler's Laws, and apparently cannot do basic geometry, trigonometry, or mechanics? You've demonstrated that you can't even do the BASICS required for celestial navigation or travel, so why should I, or anyone else, believe you?

If our understanding of gravity was as poor as you suggest, we would have never made it into space.

Your 'arguments' are, at best, an attempt to 'muddy the facts'. You try to detour the fact that the language of modern science is mathematics (see Mathematics: The Language of Science) and not weak rhetorical games. Science requires you to provide a demonstration that your Geocentrism claims are equivalent, in the language of science, or your claims are useless (see Crank Science: Worse than Wrong).

Questions referenced in this comment.

Q6 – The Foucault pendulum is routinely used as apparent evidence for the moving earth. The pendulum is said to swing in a plane parallel to the fixed stars, whilst the earth rotates underneath the pendulum. How does modern science explain the force produced by the fixed stars that causes the pendulum to swing in a fixed plane relative to the stars?

Q6: It's called inertia, (Wikipedia: Inertia, Foucault Pendulum)

Q7 -Why does the pendulum apparently overcome the gravity fields of the sun and moon and not swing in a plane following those bodies and yet not overcome the gravity fields of the distant stars?

Q7: This reads like some distorted interpretation of Mach's Principle (wikipedia), which is a (hypothetical) explanation of inertia. Compute the torque that would be produced by the Sun & Moon on the pendulum configuration. What kind of precession rate would it produce? What would it take to measure the effect?

Q8 - Why doesn’t a Foucault pendulum that points towards the earth’s center of mass continue to do so throughout the day when the pendulum is traveling along with the rotating earth?

Q8: Huh? The local vertical of the pendulum will always point along the direction vector of the local acceleration of gravity.

Q9 - Why doesn’t a Foucault pendulum merely follow the rotating earth and continue to swing in a plane with the moving earth and thereby have no variation of the plane direction with the earth’s daily rotation?

Q9: Inertia. Some of the mathematics for understanding it in a rotating frame is described on the Wikipedia page.

Closing Comments

I don't mind trying to clarify things that are not on the web or don't necessarily have a good explanation. But as I have referenced above, there is loads of material online which Mr. Martin has apparently never bothered to read, or has read and decided to ignore (most likely the latter). Some web searches indicate that very similar questions have been asked before on various science sites.

Mr. Martin's remaining queries (here and here) have deteriorated into a series of questions that read more like homework problems for an undergraduate physics class. When questions like this would appear in the USENET physics forums, the popular response was “we don't do your homework problems for you. Learn the physics.”

Mr. Martin relativity 'problems' are set up trying to measure all the velocities relative to some cosmological reference frame, even though such a construction violates the principle of relativity. This is an apparent attempt to claim these effects have only been measured relative to the Earth, but the fact is we have measured aberration effects from high-precision astrometric spacecraft such as Hipparcos (wikipedia) in a highly-elliptical orbit where the velocity is significantly different from the Earth.   Star-trackers flown on many spacecraft must include the effect of stellar aberration for precision navigation. We HAVE measured stellar aberrations from locations other than the Earth (more goodies on this for a future post!).

Apparently Mr. Martin couldn't type “Planetary aberration” into Google (wikipedia).

Like most advocates of pseudoscience, they often come up with ideas where they think that THEY are the first to think of it and then never do any actual research as to what others have done. That is usually a bad bet for any science that has been developed for over 50 years (see Doin' Astronomy (and Science in General)...).

Some of the queries above, and most of the remaining queries, will be added to my collection of similar items for sorting into topics where I can deal with them in a more consolidated manner.

Some Relevant Resources

    •    "Spherical Astronomy" by Robin Green. Particularly check out pg 193, “Planetary aberration”.
    •    The best source I've used on introductory relativity that has problems like Mr. Martin describes is “Spacetime Physics” by Edwin F Taylor, John Archibald Wheeler. This book is an excellent resource for understanding the nuances of special relativity.
    •    Good Math, Bad Math: Relativistic Crap from an IDist
    •    "Achieving better than 1 minute accuracy in the Heliocentric and Barycentric Julian Dates"

Geocentrism: Failing Basic Physics...

2011-05-28T18:55:00.002-04:00

John Martin attempts a 'Gish Gallop' (RationalWiki) of comments in response to this post (Geocentrism: Does NASA use Geocentrism?). These questions, and some additional, also appear to be available on John Martin's blog. Most of the comments demonstrate a very poor level of understanding of topics ranging from basic geometry to physics. This commonly occurs if someone bases their scientific understanding on interpretations of press releases with an incorrect or incomplete understanding of the more fundamental physical concepts.

It's not clear how many of these were Mr. Martin's own thoughts or some regurgitation of material from another source. However, considering how many of the answers I readily found online, it is clear that Mr. Martin was incapable of doing even the most basic of research.

Q's referenced in this comment

Dr. Bridgman You asked questions concerning lagrange points and space flight paths using geocentrism. It seems to me that if relativity is correct and the earth can be considered as moving, the calculations are then performed in the usual way and then a transform is completed to a stationary earth inertial reference frame. This would enable the flight path and lagrange points to be calculated. Alternatively a mathematical model of a geocentric universe would have to be constructed and the forces caused by the rotating universe included within the calculations to directly calculate the lagrange points and flight paths. According to GWW such mathematical models have been constructed by physicists.

Let me get this straight, you want to do all the calculations in the appropriate (heliocentric) frames, then use a coordinate transformation (a technique valid between ANY locations) to transform to a geocentric frame. So far that is okay.

But if you want use this technique to claim that it supports the Earth as a favored position in space, that would be a lie. This technique will work for any object, whether it be a planet or spacecraft.

Some other implications of Mr. Martin's suggestion:

This type of ploy also brings to light the fact that the heliocentrists can work in ANY convenient coordinate system, but the Geocentrists cannot do squat without the heliocentric techniques. Mr. Martin has basically admitted that Geocentrism claims are useless for any practical problems.
This tactic is also used by Geocentrists and other pseudoscientists to evade doing any actual work themselves that would be required of real science. They want to get by with just saying “We use the heliocentric results done by others and then transform the results to an Earth-centered system and this makes the Earth a favored position“. This is equivalent to stealing the work of others and trying to re-label it as your own.

Geocentrists, like many other pseudo-scientists I've confronted on this blog, seem to be nothing but posers. They want credit and recognition for achievements they have not done.

Many of the questions below erroneously invoke Kepler's Laws. This is disturbing since Mr. Martin claims a degree in engineering yet apparently could not comprehend how many of these issues were covered in the previous post, Geocentrism: Does NASA use Geocentrism? Some of these errors are equivalent to using idealizations of a round earth and invoking the fact that the Earth actually deviates from perfectly round as a basis for claiming that the Earth is flat, or trying to claim the Gas Laws (wikipedia) are incorrect by applying them to the thermal expansion of liquids and solids.

Kepler's Laws (Wikipedia) are actually a special case of Newton's laws and gravitation LIMITED TO THE CASE OF ONLY TWO BODIES (Wikipedia). The instant the question involves more than two bodies, Kepler's Laws become, at best, an approximation. In the case where the system is dominated by a large mass with additional bodies of much smaller masses (such as the Sun being the dominant mass of the solar system), it is still possible to develop perturbation expansions where the orbit is close to Keplerian, but the Keplerian orbital elements (wikipedia) undergo a slow variation with time. This is the method used in algorithms such as VSOP87 (Wikipedia)

If relativity is correct at least according to inertial reference frames, then a rotating and moving shell of stars will produce the same forces on a body as a rotating and moving earth against the fixed stars. Some questions for your consideration –

Q1 - according to Kepler’s first law, See more... “The orbit of every planet is an ellipse with the Sun at one of the two foci.“, yet the center of mass of the sun is always moving around the solar system barycenter. Therefore, as the foci of the planets ellipse moves, does this therefore invalidated the first law, or does the entire ellipse move with the moving foci at the center of the sun?

Q2- If the planet actually orbits the solar system barycenter, why then does Kepler’s first law say otherwise?

Q1, Q2: Failure to understand basic mechanics to the two-body problem (wikipedia).

Q3 - Doesn't the solar system barycenter exclude the center of the sun as being a foci of the planets elliptical orbit?

Q3: Failure to understand basic geometry. It is not a problem when the 'centers' can also move, including the Earth's center. Even Ptolemy's model did this.

Q4- If Kepler’s first law is used in planetary flight paths, this means the solar system barycenter must be ignored, which thereby seems to invalidate Newton’s laws of motion around a common barycenter. Please comment.

Q4: Failure to understand basic mechanics of the Two-body problem (wikipedia).

Q5- Why do Kepler’s laws assume all planets have an elliptical flight path, yet when we take into account the Earth-moon system, the earth moves around the Earth - moon barycenter every month whilst moving along its orbital path around the sun. If the trace out the flight path of the earth relative to the center of mass of the sun as the foci of the ellipse, the earth cannot possibly be traveling in an ellipse, but must move through “absolute space“ in a flower pattern centered on the solar system barycenter. As the earths flight path does not fit into the elliptical orbit pattern required by Kepler’s laws, how are Kepler’s laws used to accurately determine the flights paths of other planets relative to the earth?

Q5: Misapplication of Kepler's Laws to a three-body system (Sun-Earth-Moon). Failure to understand basic mechanics of the 2-body and N-body problem, basic geometry. OrbitSimulator.com,
“Regular Keplerian motions in classical many-body systems“ by Eugene I Butikov

Q6 - If the earth is orbiting around the Earth-moon barycenter every month, why don’t we see the apparent motion of the sun around the earth vary in velocity as the earth gains and loses a velocity component due to its motion relative to the “fixed” sun? In other words – during the monthly cycle there is a time when the earth must orbit in a prograde manner relative to the sun, when orbiting the earth –moon system. Later during the month, the earth continues its earth-moon barycenter motion and must move in a retrograde motion relative to the fixed sun.

Q6: Trajectories look different in different coordinate systems, especially when those coordinate systems vary in time. LRO in Earth Centered and Moon Centered Coordinates

Q's referenced in this comment.

Q7- How are these relative prograde and retrograde motions of the earth on a monthly basis taken into account in the flight path calculations?

Q8- How are the calculations consistent with Kepler’s laws, when the earths flight path through space is not an ellipse, but a complex flower shape?

Q7, Q8: Failure to understand basic geometry. This is a far worse problem if you try to do an interplanetary trajectory calculation in a 'Geocentric' frame. That is the problem Geocentrists must solve. Many references to how this is actually done were linked from the previous post (Geocentrism: Does NASA use Geocentrism?)

Q9 - According to Kepler’s laws, the earth orbits the sun every year in an ellipse. Accordingly the velocity of the earth varies from 30.287 to 29.291 km/s, yet the earths orbital velocity around the earth-moon system is approximately 0.012km/s. This means that if we take into account the monthly orbit velocity of the earth around the E-M barycenter, the earths velocity around the sun will vary from 30.287+-0.012 to 29.291+-0.012, which means the earths orbital velocity around the sun does not comply with Kepler’s laws. How is the flight path of the earth and planets relative to the earth calculated when the earths flight path around the sun does not comply with Kepler’s laws?

Q9: Misapplication of Kepler's Laws to a three-body system (Sun-Earth-Moon).

Q10 – If the earth See more... moves around the E-M barycenter every month, why don’t we observe a monthly parallax of the sun?

Q10: Failure to understand basic geometry and trigonometry. Barycenter offset of Earth-Moon system creates an angle of about 4,640 km / 149,600,000 km = 3.10e-5 radians = 1.78e-3 degrees = 6.40“ of arc. Equivalent Earth rotation = 1.18e-4 hours = 0.426 seconds is the equivalent variation in time. This is if you just consider the Sun, Earth & Moon. While an angle and time of this size could probably be readily measured at a ground-based observatory for a point-like object at night, I invite you to measure this angle to the timing accuracy required, in daytime, with changing atmospheric conditions, for an extended object like the Sun.

Q11 – The sundial is constructed using the equation of time which excludes the motion of the sun around the solar system barycenter. As the sun moves quite a large amount over many years, as shown in this video, - http://www.youtube.com/watch?v=1iSR3Yw6FXo why is the suns motion ignored in the equation of time? Please provide the calculations to demonstrate the suns motion around the solar system barycenter can legitimately be ignored in the equation of time.

Q11: The analemma and equation of time are perturbed due to motions of all the planets around the center of mass and they vary from year to year. This means you cannot define a precise uniform time scale based on the motion of the Sun and why many of these equations refer to the motion of a mean Sun which ignores these variations. Therefore we move over to time systems based on atomic clocks, calibrated for different frames of reference where appropriate. A number of alternative time scales (with conversions and adjustments between them) have been developed to solve these problems:

To be continued...

Balticon 45

2011-05-21T20:59:00.010-04:00

Other activities and priorities have been slowing my post frequency.

On Memorial Day weekend, I expect to be at the Balticon Science Fiction convention in Baltimore, Maryland.

For part of the convention, I will be at the table for the National Capital Area Skeptics.

I'm not on the schedule as a speaker, but I have been asked if I could fill-in should there be a last-minute cancellation. We shall see...

A Science Event in the Maryland/D.C. Area

2011-05-14T10:57:00.000-04:00

(I TRIED to post this earlier this week but Blogger being partially offline did not help.)

ExploreNASA@Goddard

Goddard Space Flight Center will be operating an open house on Saturday, May 14, 2011.

There will be presentations by engineers and scientists, tours of spacecraft facilities and technology demonstrations.

Quantized Redshifts XI. My Designer Universe Meets Some Data and What's Next...

2011-05-07T18:35:00.001-04:00

When we last left our quantized redshift discussion (Quantized Redshifts. X. Testing Our "Designer Universe"), I had just plotted the histogram, sampled radially, of a statistically uniform cosmos sampled to a finite limiting magnitude. This was to simulate how surveys of such a cosmos would appear to astronomers on Earth. I concluded with a plot of survey sampling the universe in redshift (z).

Click to enlarge

Note that I started with a UNIFORM distribution of points/galaxies distributed through the volume and then selected them based on the points brighter than the limiting magnitude of the telescope from a position inside the volume. If the volume were sufficiently large, I would see this same form regardless of where I placed the observer.

The purpose of these exercises was to develop an understanding of how this type of distribution can form. We can now examine the behavior of this histogram with new insights.

For z<0.08, the number of galaxies we see is dominated by the fact that we are counting in a steadily larger and larger sphere. Each point in the histogram is the number of galaxies in a thin spherical shell of thickness delta_z, and radius z, which is increasing as z^2 as we observe deeper into space. However, beyond about z=0.08, we start missing the faintest galaxies because they are fainter than our telescopes can detect, and the counts begin to drop, relative to the number we expect to see. This happens in spite of the fact that we are still seeing a larger and larger volume of space. In a perfectly uniform (and infinite) universe, an observer at any location would see a similar histogram of galaxy counts in distance space (and z-space if they are correlated).

If the graphic looks at little familiar, it might be because it is very similar to the histograms of the galaxy distributions that come from deep sky galaxy surveys and appear in a number of papers.

For comparison, we can plot our model together with a couple of the more well-known deep survey datasets. Because my model universe was assembled using very rough numbers, my histogram curve is a little off, but I can adjust the parameters to generate a better match (or 'fit') with the data. We plot this type of curve along with the profiles of the 2dFGRS (blue) and SDSS DR8 (red) surveys. I've normalized the galaxy count on all the samples to make a more reliable comparison. While not an exact match, the general profile illustrates some of the mechanisms that drive the large-scale shape.

Click to enlarge

We see a similar general distribution, but the real surveys have substantially larger variations than our uniform 'mock catalog'. The two real surveys also have some significant differences with each other. While there is a small overlap in the sky covered by 2dFGRS and SDSS DR8, these two surveys sample different sections of the sky. This is evidence that the universe is NOT spherically symmetric around the Earth since the galaxy distribution has significantly different structures in different directions in the sky. SDSS has an additional 'hump' at z=0.35 (I suspect this is due to a deep volume-limited survey of red luminous elliptical galaxies that was part of SDSS. This also suggests that SDSS is a magnitude-limited survey). 2dFGRS has a significantly larger peak near z=0.12 which is not in SDSS.

We can smooth the fluctuations by choosing larger bins for the data, for example, for bins about 20x larger, or delta_z = 0.02, we get

Click to enlarge

Remember, the red curve corresponds to a perfectly uniform universe with some statistical noise sprinkled in, while blue and green correspond to real galaxy surveys. While not proof, it is certainly evidence that the cosmos is fairly uniform on large scales.

An alternative model might include is that we are seeing the edge of the distribution and that the number of galaxies is actually dropping to zero because we are seeing back to a time when galaxies were just being formed and the density of galaxies was lower.

Note this has spherical (isotropic) coverage from observer position. Most surveys cover only a fraction of the sky at best, and deviations from this mean curve could be due to large structures dominating one direction which are not spherically distributed around the observer.

What Next?
There are a number of ideas I'm exploring for additional posts in this series, but I want to take some time to check them carefully.

- Power Spectra - 1-D vs 3-D data.
Currently, my computations of 3-D power spectra of my mock catalogs are notoriously slow. Catalogs as small as 50,000 galaxies can take several days to process into a power spectrum at reasonable resolution. This has made attempts at code validation difficult. I'm looking at multiprocessing and other techniques to improve this. The big surveys use various complex mathematical techniques to make the computation more manageable - but I will try to avoid this, both for clarity and because the techniques would require substantial coding and debugging and explanation time (note that the FFT is faster than the standard Fourier transform due to a mathematical trick). However, there are numerous concepts that can be addressed using the mathematical theorems of the Fourier transform and power spectra in the meantime.

- Slicing the survey data.
Because all these datasets are publicly available, I have samples of the nearly quarter million galaxies in 2d FGRS and over 800,000 galaxies from SDSS DR8. These two surveys provide some really nice data for visualization. For example, if galaxies were really concentrated in concentric spheres around the Milky Way Galaxy, this should be easy to illustrate by selecting subsets of the surveys in any given direction (choosing sections of the sky of equal angular area).

- Improving the mock catalog.
There are many effects of real physics that are not included in my simulation, which are integrated into professional mock catalogs (see Creating synthetic universes in a computer by Carlton Baugh). Some of the effects I have not included are:

The redshift, z, is not a linear function of distance, r, over the full range
Galaxies interact under gravity, altering their motion with respect to the Hubble flow. This is sometimes called 'clumping'. The gravitational attraction of the galaxies gives them motions not perfectly carried in the Hubble flow, creating a situation where galaxies at a given distance, r, will have a redshift, z, different than indicated by the Hubble relationship. This is also responsible for the "Finger of God" artifact (wikipedia). (see also Redshift-space Distortions, Redshift-distortions)
Galaxy evolution. As the stars in a galaxy evolve, the luminosity and spectra of the galaxy will change.
There is an luminosity correction for the galaxy due to how the redshift alters the amount of light in the visible part of the spectrum - photons from the red end of the spectrum get shifted into the infrared and photons from the ultraviolet end of the spectrum are shifted into the violet. This is also called the k-correction (wikipedia).

While I don't expect to model a catalog to the fantastic level of detail as presented at Mock Galaxy Redshift Catalogs (paper), I will probably use the mock catalogs available here to test and calibrate some of my codes. You should check out the figures on this site. Particularly take a look at the simulations of the SDSS catalog and compare them to some of the actual slices through the real SDSS dataset. Note that this paper was written some years before the actual data was available. These mock catalogs started with uniform distributions of points (galaxies) and then let them move under gravitational attraction.

Links of Interest

2011-05-01T19:29:00.004-04:00

The Science of Why We Don't Believe Science
by Chris Mooney

This article summarizes a number of experiments and studies from psychology on why it is so difficult to change some people's beliefs. While the article goes into how personal beliefs can be strongly influenced by an individual's sense of 'group identity', it doesn't really go into how one defines their 'group identity'. Is it entirely determined by one's social environment, or is it determined more internally.

Some people ask me why I do this blog when it is very clear that I will never change the belief systems of many of the individuals I confront here. The short answer is that I don't expect to change their beliefs - I expect to provide the information that can sway the person who is still 'on the fence'.

One of the more interesting blogs I've started to follow is the dot-physics blog posted by Rhett Allain at Wired magazine. Many of the articles explore applying physics to everyday things.

And now I'll take some time to do a little PSA, since I've spent so much time at a dermatologist's office in recent weeks getting little chunks cut out of me. It's kept me preoccupied and I hope to catch up on the this blog soon.
Skin Cancer Prevention & Early Detection

Upgrading my Scientific Toolbox

2011-04-18T20:54:00.006-04:00

I've been off -the-air a bit more this week as I implement some upgrades to my computing capability.

I now have my desktop & laptop Macs running 10.6 (Snow Leopard) and installing as much software as I can to run 64-bit mode. This will make it easier to handle some of the larger datasets required for this project. I addition, I hope to mirror the working directories between the desktop & laptop systems, adding an extra level to my regular backups.

I'm making the page describing the installation configuration of my scientific tools available here, both for my future reference and in the event others wish to duplicate my setup. Plus, I have repeatedly made use of the descriptions others have placed online and this is just my way to contribute and return the favor.

This project should be complete soon and I can return to more regular posting.

Geocentrism: Does NASA use Geocentrism?

2011-04-09T18:10:00.112-04:00

Here's the rest of my response to James Phillips, from his comment:

“Is it true that N.A.S.A. uses the geocentric model rather than the heliocentric model and if so what is their rationale for doing so.“

This is a very poorly worded question. The short answer is, “Of course they do - where appropriate.”

They use longitude, latitude, and altitude when it is the convenient unit of measure - and they use these quantities on the Earth, Moon, Mars, etc. Why would they not? Why would you reference everything with heliocentric coordinates if you are in orbit around the Earth? Or in orbit around Mars? The heliocentric coordinates are just a coordinate transformation away from any other coordinate system you choose to use.

You use the model appropriate to the scale of the problem you are solving. A geocentric model can be sufficiently accurate near the Earth, but deviates as one moves further away from the Earth. When traveling between planets, NASA routinely transitions between the frame of the Earth, to the heliocentric frame, and to the frame of the target planet when the spacecraft gets near.

NASA also has datasets where the Earth is treated as FLAT. I'm sure the Flat Earthers will regard that as vindication for their interpretation of Scripture (Wikipedia, Flat Earth Society).

Near Earth

For near Earth trajectories, the coordinate system of choice is GEI (Geocentric Earth Inertial) which is fixed with respect to the distant stars. This is the one you use to compute your trajectories as Newton's laws and gravity apply in their simplest form.

If you want to know where your satellite is visible from the surface of the Earth, you use GEO (Geocentric body-fixed) which rotates with respect to GEI. It is simple to convert between these two systems (unless you want to include nutation), just a rotation around the z-axis that completes one rotation in a sidereal day. This coordinate system is often used for transferring data to and from tracking stations. Other coordinate systems I've used in my day job are described here: Coordinate systems and transformations, GEOPHYSICAL COORDINATE TRANSFORMATIONS.

There are similar planetocentric coordinate systems used for close flybys and orbits by spacecraft.

Since there are a number of spacecraft at Mars, which coordinate system do you think they use for tracking spacecraft? See MSL Update to Mars Coordinate Frame Deﬁnitions (2006), pg 6:

“When a spacecraft is in the vicinity of Mars, it is convenient to utilize Mars-centered coordinate systems. These are systems that are centered at the center of the planet itself, as opposed to the system barycenter or on the planet surface. The systems described here are utilized regularly by the ﬂight operations and mission planning teams for JPL Mars missions.”

Beyond the Earth

If you want to compute trajectories farther from the Earth, say to go to Venus, or Mars, or beyond, you compute the trajectories in a heliocentric system (or more accurately a heliocentric barycenter system), again because the laws of motion and gravity apply in their simplest form, which means you can compute future (or past) positions more accurately. There are two methods for doing this.

Compute planetary positions as a full N-body simulation (Scholarpedia).
There are algorithms which start with a reference elliptical orbit (heliocentric barycenter) and then compute how the gravitational forces from the other planets perturb that orbit. These perturbations show up as slow variations in the orbital parameters (called Secular variations of the planetary orbits, or VSOP). From that, you install your spacecraft position and velocity, subject to the same laws of motion and gravity. Once you know the position of your spacecraft in the heliocentric frame, you can compute where the object would appear from any other location by using a coordinate transformation, such as those described above. You would convert to the GEO system if you wanted to know where to point an Earth-based antenna to send commands to your spacecraft or receive data.

Check out JPL: Basics of Space Flight: Interplanetary Trajectories. The web tool JPL: Solar System Dynamics: HORIZONS Web-Interface computes trajectories of many solar system objects and can transform the positions as they would appear at other locations in the solar system. The FAQ on the Horizons system also has info on computing planetary positions which I have utilized.

Orbital dynamics is so precise, we can compute trajectories decades before an actual launch. We can compute if existing boosters have the capability to send a spacecraft onto a given trajectory. If we need a new booster to handle more distance, higher speed, or more payload, we can compute those requirements before we cut a single piece of metal to build it. We don't build the biggest rocket we can, fuel it up, and hope it makes it to the destination. How is that done? (For those who want to bring up the Pioneer Anomaly (Wikipedia), it is looking more and more like this is not new physics, but a very tiny thrust created by emission of heat from the spacecraft).

Strange Way to Run a Cover-up...

This is not just a NASA thing. ESA, Japan, India, China and other countries are sending spacecraft to other planets. Are they part of the coverup as well? All the data and mathematics for computing interplanetary trajectories are a matter of PUBLIC record. Many of these techniques were developed over 100 years before NASA even existed. Amateur astronomers who understand the math can do these computations on their desktop computers to far higher accuracy than those researchers from the 1700s to the 1950s who developed the techniques via hand calculation, slide-rule, and adding machine. Today, this is a project of college undergraduates (see Interplanetary Trajectory Development). I ran simple solar system models on an N-body code I wrote on an Apple II(Wikipedia) back in 1980 while an undergraduate.

With so many people who have the knowledge of how to do this, it's a strange way to run a 'conspiracy' against Geocentrism (Moving-World DECEPTION).

The Real Conspiracy?

Perhaps the more interesting question would be what computations are the supporters of Geocentrism Galileo was Wrong using when they do their graphics? How are they computing the position of, say Jupiter, in the sky on a given date and to what accuracy? Can they compute when the ISS will pass over my location? Are their graphics constructed using software where the computations are in a heliocentric system or are they doing the computations themselves in a geocentric system?

If they're doing the computations themselves, why don't they show their work so that others can use (and test) them as well?

Here's the NASA info on trajectory and navigation for spacecraft:

Planetary Data System Navigation Node. I've actually made use of SPICE kernels on operating missions. Can anyone at Galileo was Wrong make that claim?

Here's some work by people OUTSIDE of NASA

Celestia Uses VSOP87
Stellarium. Uses VSOP87
XEphem
or others

Some months ago, Rick DeLano claimed that Geocentrism could explain the Lagrange points, five points of stability in the restricted 3-body problem (Wikipedia), and one of the predictions of Newtonian gravity and laws of motion. I challenged him to demonstrate it, considering that we make use of these locations in a number of operating space missions.

The Geocentrists have been strangely silent on this.

If you taught Geocentrism in a physics class, how would you use this knowledge to plan spacecraft missions?

Here's a syllabus of an astrodynamics class at Georgia Tech. This is training for people to really do this work. I wonder if any of the Geocentrists could do the homework problems posted here. How would they answer the practical problems of interplanetary navigation in a Geocentric model? As yet, Geocentrists have not demonstrated any competence in this field where they claim so much knowledge. Unless you believe all spaceflight is a hoax (or you chicken out and just claim everything beyond Earth orbit is a hoax), your only other choice with Geocentrism is to terminate all space flight, leaving space travel to other countries less entrenched in dogma.

These are not idle questions of only philosophical interest. Billions of dollars in space assets, the lives of astronauts, even national security, rely on doing this stuff right. Would you trust these things to those who have not demonstrated any competence in the topic?

Quantized Redshifts. X. Testing Our "Designer Universe"

2011-04-03T15:49:00.006-04:00

In the last section, I demonstrated, by a simple exercise, how scientists can make model datasets to test their analysis methods. Of course, once we build these test datasets, we should always conduct some tests on the results to make sure they exhibit the properties we seek for our testing. That is the purpose of this section.

Consider yourself at the center of a uniform distribution of galaxies (homogeneous), all around you, covering the entire sky (isotropic). We'll assume they have a constant mean density (number of galaxies per cubic megaparsec) out to the edge of the distribution (homogeneous). If we have a spherical sampling of galaxies, with a uniform number density, n (galaxies per unit volume), it is easy to compute the number of galaxies per bin, dN, that must be in a thin spherical shell at distance, r, and thickness, dr.

dN = n 4 \pi r^2 dr

This is just the area of the sphere, multiplied by the thickness (to give a volume) all multiplied by the density.

We can compute this function for our array of redshift values using the histogram function. First we create an array of nbins bins in redshift space (zbinning) out to a maximum value of z, maxz.

zbinning=np.arange(0.0,maxz,maxz/nbins)

distribution=np.histogram(redshift,zbinning)[0]

I plot the result for one of the model runs below with maxz=0.512 and nbins=512. 

Figure 1: Click to enlarge

The blue, slightly irregular, line represents the number of galaxies in each bin of redshift values. The irregularities are due to the statistical variation in the model. The black line is an analytic curve of the density distribution. We see that the two curves have excellent agreement, with the blue curve exhibiting slight statistical fluctuations around the expected count given by the black curve.

This is the kind of distribution of galaxies with redshift, z, that we would expect to observe if we were in a VERY large, VERY uniform universe, and our telescopes have infinite sensitivity, i.e. we see all galaxies no matter how faint. This is a very unrealistic assumption, and we we will deal with making it more realistic soon.

As an additional test, we can use our distribution counts to compute the density, n, of each radial shell,

n = dN / ( 4 \pi r^2 dr)

We plot the results below.

Figure 2: click to enlarge

We see that at large distances, the value of n exhibits small fluctuations around the mean density of the input model. That mean density is computed by dividing the total number of galaxies by the total volume of our model cosmos. As we sample distances closer to the observer, the fluctuations get larger and larger. This is not unexpected. At smaller radii, the number of galaxies in the bin gets smaller and this this makes the statistical error in each bin is larger since it can only have an integer number of galaxies in a bin (no fractional galaxies). Our input galaxy density is actually less than 1 galaxy per Mpc^3, so when we sample some bins near the center, the probability of having bins with much less (or more) than the mean number of galaxies can show large fluctuations. After all, at these bin sizes, we can only have integer numbers of galaxies in the bins, either zero or one, but rarely more.

Again, the model behaves as we expect, consistent with our input assumptions.

Making Our Designer Universe More Realistic

But in reality, we do not have telescopes of infinite sensitivity. To simulate the effect of more realistic telescopes, we will assume the telescopes can only see galaxies brighter than a given limiting apparent magnitude, limitingMagnitude. For this experiment, we'll choose a limiting magnitude of 18 and 20. We can plot the distribution of our galaxies in distance vs. apparent magnitude.

First we find the array indices of galaxies in our model catalog that are less than limitingMagnitude:

magLimitIndices=np.nonzero(apparentMagnitude < limitingMagnitude)

With this array of indices, we can then select out the galaxies from our source arrays, distance, apparentMagnitude, making new arrays, of the galaxies that fall in our magnitude limits.

distances = np.take(distance,magLimitIndices[0])
apparentMagnitudes = np.take(apparentMagnitude,magLimitIndices[0])

Figure 3: click to enlarge

In this plot, the red markers represent all galaxies brighter than magnitude 18.0. The green band reveals galaxies fainter than magnitude 18 but brighter than magnitude 20, and blue are the remaining galaxies in our catalog. Note that the distance is a logarithmic scale. Apparent magnitude is a logarithmic rescaling of energy flux.

At small distances, we count very few galaxies. This is why our mean density fluctuated so wildly in the bins for near-Earth distances. Your sampling either caught some galaxies, or it didn't. The further out we go, we see more galaxies along the vertical line of a fixed distance, up until the point our survey starts missing galaxies because they are too faint. At this point, the number of galaxies begins to decline until we reach a distance so great that no galaxy is bright enough to be detected.

How that would look in a histogram?

We can compute the mean density again, as above, but this time plotting the result for each different limiting magnitude. We plot this result below.

distribution=np.histogram(distances,rbinning)[0]

# convert to galaxy density/Mpc^3

density=distribution*1e18/(rbinning[:-1]*rbinning[:-1])/(boundary/nbins)/(4.0*np.pi)

Figure 4: click to enlarge

As before, we have large fluctuations in mean density near the Earth, which decreases as the distance from the Earth increases. But now we have the additional effect of our limiting magnitude of detection. At some distance, the measured density begins to decrease, as our number of galaxies measured at that distance begins to decrease. The red, green, and blue curves in Figure 4 represent the corresponding model color in Figure 3.

Food for Thought: In this exercise, I've examined the case of a survey limited by telescope sensitivity. Suppose we had telescopes that had a much higher magnitude limit, so our survey probed so deep into the cosmos that we saw fewer galaxies because we were sampling a time when galaxies were just forming?

Now we need to sample this dataset constructed in 3-dimensions, into a radially-sampled dataset as done in the first figure of this article. We also compute this histogram for our experimental magnitude-limited surveys.

For each of the subsamples above, we can again compute the histogram in redshift-space.


Figure 5: click to enlarge

The black curve is the radial galaxy count profile one expects for a uniform density. The green curve corresponds to the distribution with a limiting magnitude of 20, and the red curve corresponds to a distribution with a limiting magnitude of 18.

Let's zoom in on the red curve, expanding the vertical scale.

Figure 6: click to enlarge

If you've examined a data from a number of large-scale sky surveys, the profile of the red curve might look a bit familiar.

Next (but probably NOT as soon as next weekend): What Can We Learn from this Model and Questions for Further Exploration

Apology to Dr. Hartnett

2011-03-25T19:24:00.000-04:00

I have discovered the nature of an error in a previous post (Quantized Redshifts. VIII. An Uncommon Power Spectral Density "Blooper") concerning the paper by Hartnett & Hirano, "Galaxy redshift abundance periodicity from Fourier analysis of number counts \$N(z)\$ using SDSS and 2dF GRS galaxy surveys", hereafter labelled HH2007.

My error was that I claimed the x-axes were incorrectly labeled when Hartnett converted them from 'frequency space' to his '\Delta_z space'. These graphics were NOT mislabeled.

I've deleted the content of the original post and set a link to this post, since the great majority of the post was on the erroneous graphic plotting claim. Other issues with HH2007 will be examined in a future post.

How did I make the error?

This error was one of those 'flashes' of 'insight' that occurred only about a week before I wrote the post. That in itself should have made it suspect. It did not receive the: idea - examine - walk away for a few weeks - reexamine - chat about with others - repeat (2 or more times) that other material in HH2007 had received.
I have read HH2007 at least 3 or 4 times. ALL the other critiques of the HH2007 analysis have actually been under development for several years, going through the analysis cycle above several times for verification. If the Delta_z problem had been real, the idea that I would not have noticed it earlier is a bit unlikely. I should been bothered by that.
Customarily, plots are posted with the low value to the left end of the axis, whereas Hartnett (correctly) plotted the large value of Delta_z in Figure 5 of HH2007. The prejudice of the customary axis direction was reinforced in casual examination of the graph on a small laptop screen where font antialiasing made some of the exponents in the axis scale unreadable and I failed to zoom-in on the graphic for a better look. Several other non-standard notations for cosmology and power spectral in HH2007 contributed to confusing the underlying concepts as well.
Having read so many redshift-space analysis papers it is entirely possible that some of the graphics actually became confused with graphics in other papers and a quick examination of HH2007 graphics failed to fully register.
I hurried the analysis, trying to meet a self-imposed schedule of one post per week. I allowed that to rush me into preparing the post without carefully checking the graphics in question beforehand.

What changes do I intend to make to prevent the problem from happening again?

No more one-post-per-week schedule, especially for detailed analysis posts. This blog is a part-time project and some of the ideas explored cannot be examined quickly but require careful examination. Note that it is the pseudo-scientists in the comments of this blog who often try to push me to adhere to their time frame and in this case I foolishly took their bait.
I've wanted to do this for a time and have numerous individuals whom I have consulted on occasion for reviewing material and ideas. I'm going to explore making that a more regular practice.

I doubt these changes will totally eliminate the possibility of an error, but it will reduce it.

I suspect there are some who will attempt to exploit this admission, so why am I doing this? I work in a technical field were there are absolute standards of success and failure. Those who learn from their mistakes and continue on, who don't dogmatically hang on to delusions that they are always right when the evidence is against them, have far more professional success.

Depending on reactions, I may apply some different standards to comment moderation for a time.

Quantized Redshifts. IX. Testing the Null Hypothesis

2011-03-19T19:36:00.031-04:00

We're done with our detour on random number generators and now back on track to testing redshift quantization where I'll apply a PRNG.

A good many amateur cosmologists blindly apply the FFT and PSD to survey data because it is simple and 'obvious'. Yet none seem to ask the question, "If it is so simple, why haven't others done it?" The answer is that others have tried this, and found the 'simple solution' was riddled with false trails. Yet this error is made repeatedly, and in spite of progress in understanding the problems, the method still manages to find its way into peer-reviewed journals.

The implicit assumption in these redshift-space analyses is that a uniform distribution of matter in these surveys would exhibit no peaks at all. If that were true, then all peaks in any PSD would be significant, indicating a real deviation from uniformity. But is it true that a uniform distribution would have no peaks?

Some researchers attempt to test the reality of their peaks in a PSD using what is sometimes called a 'Shuffle Test', moving the data to different bins to see if frequency peaks move. The peaks usually do move, but it should be noted that each frequency bin in the FFT has contributions from EVERY point in the dataset (it is a weighted sum of every data point), so this is no surprise. Sadly, few researchers seem to recognize the implications of this and often proceed to concoct more stranger tests or misapplying tests from different data assumptions. These types of repeated contortions of the same dataset(s) are so unproductive, I have a nickname for this mental trap: "data masturbation".

The only way out of this trap is to test your analysis process with datasets of KNOWN content, subjected to data selection similar to the data in question. In this case, we should first construct a dataset that does NOT have our hypothesized content (the Null Hypothesis), which for a cosmological model, would be a dataset with a uniform distribution of galaxies.

So how would you construct such a test dataset?

Building a Test Universe
What we will do is build a simple 'model universe' with galaxies distributed uniformly, but randomly, in 3-dimensions, x, y, and z. We will create a test sample with numberOfGalaxies, which I've run with numberOfGalaxies = 10,000,000 and larger. in a volume with a defined radius, in parsecs (1 parsec = 3.26 light years). To do this, we will make use of the numpy random number generator (see Mathematical Interlude: Pseudo-Random Number Generators)

import numpy as np
from numpy import random

There are a couple of ways we can do this. One is to assign x,y,z coordinates for numberOfGalaxies using a uniform sampling random number generator over the range -radius to +radius

x=radius*(random.uniform(-1.0,1.0,size = (numberOfGalaxies,)))
y=radius*(random.uniform(-1.0,1.0,size = (numberOfGalaxies,)))
z=radius*(random.uniform(-1.0,1.0,size = (numberOfGalaxies,)))

Once we have this dataset, we can compute the distance to each galaxy from an observer at the center of the dataset at coordinates (0,0,0).

distance = np.sqrt(x*x+y*y+z*z) # convert cartesian coordinates to spherical

This method creates a 'cube' universe to which we can apply observational selections. In the graphics below, the term SimpleCartesianHubbleModel indicates models run using this algorithm.

If we understand probability distributions, it is also possible to generate a table of galaxy distances directly by weighting the uniform probability distribution in a way that makes it match a uniform spherical distribution. In this case, it is done by taking the cube-root of the uniform distribution.

distance = radius*(random.uniform(0.0,1.0,size = (numberOfGalaxies,)))**(1.0/3.0)

Models generated with this algorithm are labeled with SimpleRadialHubbleModel.

In this case, we make the simplifying assumption that all galaxies travel with the Hubble flow, so the redshift value, z, will be computed with a simple, linear Hubble relation, where H0 is the Hubble constant (km/s/Mpc), c is the speed of light in km/s and 1e6 converts parsecs to megaparsecs.

redshift = distance*H0/c/1e6

I've used H0 = 72.0 km/s/Mpc. If we want to include some deviations from the Hubble flow, we can install a simple simulation of this by 'fuzzing' each redshift value with some Gaussian noise of width sigmaSpeed:

redshift = (distance*H0/c/1e6) \
+ random.normal(0.0,sigmaSpeed,size = (numberOfGalaxies,))/c

Some of my simulations are generated with this model for comparison. They will have SimpleHubbleDisperseModel in the graph title.

Next we define an absolute magnitude for all our galaxies. In this case, we will assume a simple Gaussian distribution around a referenceMagitude with a standard deviation of magnitudeWidth for each galaxy. We make no distinction between nearby or more distant galaxies, all galaxies will be part of the same brightness distribution. We do this to simulate the fact that galaxies have a range of luminosities.

absoluteMagnitude = random.normal(referenceMagnitude,magnitudeWidth,size = (numberOfGalaxies,))

Finally, we want to assign an apparentMagnitude to each galaxy, so that we know how bright the galaxies will appear to an observer on the Earth. This way, we can determine which galaxies might be visible to instruments on the Earth. Since we have a distance and absolute magnitude, the apparent magnitude for each galaxy is easy to compute (see Wikipedia: Absolute magnitude):

apparentMagnitude = absoluteMagnitude+5.0*(np.log10(distance)-1.0)

In one of our next steps, we will select only galaxies brighter than a given apparent magnitude (the magnitude visible from Earth) to simulate the fact that our instruments can only see objects brighter than a certain threshold.

This process creates a set of arrays where index i of any one of them corresponds to measurements of a galaxy:

x[i], y[i], z[i], distance[i], redshift[i], apparentMagnitude[i]

These arrays contain the dataset for our simulated universe.

We could look at a small subset, plotting them in 3-D. We don't have the screen resolution to plot the full 10,000,000 galaxies - it would be a completely black ball - so we just plot 2000 galaxies.

So we have our simulation generator. We can run it with different starting seeds in the random number generator to explore different variations of the uniform model.

But first we might want to conduct a few tests on our test dataset, to make sure our simulation has generated a reasonable result for our input assumptions.

Next Weekend: Testing Our Designer Universe

Mathematical Interlude: Pseudo-Random Number Generators

2011-03-12T17:28:00.001-05:00

Many of the projects that I develop for this site require the generation of test datasets. Because real data has some degree of uncertainty in the measurements, good test data should include a sprinkling of randomness to test the robustness of analysis tools developed. Therefore I feel the need to describe a little about the software tools for simulating randomness in data, pseudo-random number generators, or PRNGs.

I have encountered numerous pseudo-scientists who seem to latch onto any terminology scientists actually use with 'pseudo' in the name, such as pseudo-tensor, or pseudo-random number generator and try to leverage the terminology to insinuate the methodology is unreliable.

Since pseudo-random number generators are routinely used by scientists in generating test datasets and testing their algorithms (and I will start using them in the next post), I felt the need to do a pre-emptive strike.

Why Do Scientists Need Random Number Generators?
As mentioned above, often times scientists need to develop software for data analysis to test their algorithms. Sometimes they might add a little random noise to a simulation run to determine how these changes influence their results. Sometimes they just want to create datasets of random noise to determine how such data might be distinguished from a real signal.

Why Are they Called PSEUDO-Random Number Generators (PRNG)?

While the sequences are not truly random, they do pass many of the tests for randomness
Initializing a PRNG with the same 'seed' makes the PRNG generate the same sequences of random numbers. This is valuable for the development of reproducible test processes.
After a certain number of numbers are drawn from the generator with a given seed, the sequence will repeat. The length of this sequence is called its period. Ideally, you want a PRNG with a LONG period.

How Good are Pseudo-Random Number Generators?

Modern PRNGs are very good, suitable for a wide variety of problem-solving and simulation applications.
The primary application for which PRNGs are NOT suitable is cryptography. This is because the underlying engine of PRNGs is deterministic and it is, in principle, possible for a cracker to determine the underlying PRNG sequence with enough samples of cypher-text.

What PRNG is Used by the Python NumPy Module?

The Random module in Numpy uses the Mersenne Twister (Wikipedia) as its underlying engine for generating random numbers (Python Documentation, Statistics in Numpy & Scipy). This is also the generator used in the standard Python library. At one time, these PRNGs were different and this can generate some confusion in online searches.

How many random numbers are in the period used by the Mersenne Twister algorithm?
2**19937-1

>>> 2**19937-1
>>> 4315424797388162648055235516337919839053935043226711505165250541403330680137658
0911304513629318584665545269938257648835317902217334584413909528269154609168019007
8753437413962968019201144864809026614143184432769803000667281049840954515881760771
3296984376213462179039639134128520562761960051310664637664861599423667548653748024
1964350295935168662363909047948347692313978301377820785712419054474332844529183172
9732423108882650813216264694510777078122828294447750226804880578200287646593991647
6626520090056149580034405435369038986289406179287201112083361480844748291354732836
7277879565648307846909116945866230169702401260240187028746650033445774570315431292
9960251877807901193759028631710841496424733789862675033089613749057663409052895722
9001603800057163087519137397955504746815433325347499104624813250451634179655147057
5481459200859472614836213875557116864445789750886277996487304308450484223420629266
5185560243393391908443689210184248446770427276646018529149252772809226975384267702
5733392895440120546589561034765885538663390254628996213264328242574803578623358060
8154696546932563833327670769899439774888526687278527451002963059146963875715425735
5344759797344631006783673933274021499309687782967413915145996023742136298987206114
3141040214723899809096281891589064569393448333099416963229587799584899336674701487
1763494805549996163051541225403465297007721146231355704081493098663065733677191172
8539870957481678162560842128233801686253345864312540346708061352735432707144788768
6186198332077728064480669112571319726258176315131359642954776357636783701934983517
8462144294960757190918054625114143666384189433852576452289347652454631535740468786
2289458856546085620580424689873724369214450923153776984071681983765382377486141962
0704154810637936512319281799900662176646716711347163271548179587700538269439340040
3061700457691135349187874888923429349340145170571716181125795888889277495426977149
9145496239163940148229850253316515114312788020090568084565068188772666098316368838
8490562182226293398654864566908067219170474040889134983568566242806323119852043682
6329415290752972798343429446509992206368781367154091702655772727391329424277529349
0826005858847665231509574170778319100161684756856586731928608820701797603072698499
8735483604237173466025769434723550630174411887414129243895814154910060975221688223
0887611431996472330842380137110927449483557815037586849644585749917772869926744218
3696211376751010832785437940817490940910430840967741447084363242794768920562004272
2796163866914980548983112124467639993195537148401288636074870647956866904857478285
5217054740113945929622177502575565811067452201448981991968635965361551681273982740
7601388996388203187763036687627301575846400427988806918626402686126861808838749395
7381812502227968993026744625577395954246983163786300017127922715140603412990218157
0659650532600775823677398182129087394449859182749999007223592423334567850671186568
8391867477049600162775406253314406190191299837899147125153652003360579935086016788
0768756856237785709525554130490292719222018417250235712444991187021064269456506138
4919373474324503966267799038402386781686809962015879090586549423504699190743519551
0437225445157409678290843360259382257807308802738552615519720440756203267806244488
0349099823216123168779471561340579324954550952805251801012308725877897411581704824
5588971438596754408081313438375502988726739523375296641615501406091607983229239827
2406147832528924797165199369895191878086812211916417477109024806334910917048274412
2828118663244590714578713835123484226138007462191400481815238666604313334487506790
3582838283562688083236575482068479639546383819532174522502682372441363275765875609
1197836532983120667082171493167735643403792897243939867441398918554166122957393566
6861265827123469643837712283899804019973907806144367541567107846340467370240377765
3478173367084844734702056866636158138003692253382209909466469591930161626097920508
7421756703065051395428607508061598353575410321470950842784610567013677397949320242
0299870773101769258204621070221251412042932253043178961626704777611512359793540414
7084870985465426502772057300900333847905334250604119503030001704002887892941404603
3458699263675013550949427505525915816399805231906796107849935808966832992976812624
4231400865703342186809455174050644882903920731671130769513189229659350901862309481
0557519560305240787163809219164433754514863301000915916985856242176563624771328981
6785482462973762495302513603634127683664561750770319774575349128064331765399959943
4330811847014715871281614939442127661422826290995005574698105320661000156029578465
6616193252269412026831159508949671513845195883217147982748879261851417819979034417
2855986077272208666776804260903087546340467370240377765347817336708484473470205686
6636158138003692253382209909466469591930161626097920508742175670306505139542860750
8061598353575410321470950842784610567013677397949320242029987077310176925820462107
0221251412042932253043178961626704777611512359793540414708487098546542650277205730
0900333847905334250604119503030001704002887892941404603345869926367501355094942750
5525915816399805231906796107849935808966832992976812624423140086570334218680945517
4050644882903920731671130769513189229659350901862309481055751956030524078716380921
9164433754514863301000915916985856242176563624771328981678548246297376249530251360
3634127683664561750770319774575349128064331765399959943433081184701471587128161493
9442127661422826290995005574698105320661000156029578465661619325226941202683115950
8949671513845195883217147982748879261851417819979034417285598607727220866677680426
0903087548238033454465663056192413083744527546681430154877108777280110860043258922
6225941396828528349704557106275770142176156526272515340740762540514993198949445910
6414660534305378576709862520049864880961144869258603473714363659194013962706366851
3892996928694918051725568185082988249549548157960631695176587414201597987542734280
2672345248126356915730721315373978104162765371507859850415479728766312294671134815
8529418816432825044466692781137474494898385064375787507376496345148625306383391555
1456900878919553159944629444932352488175999071191357559333821217061914771850549366
3221115722292033114850248756330311801880568507356984158051811871077865395357129601
4372940865270407021924383167290323231567912289419486240594039074452321678019381871
2190921554607684445735785595136133042422061513564575139372709390097072378271012458
5383767833816102339758685489423069609154024998790745346131192396385295075475805820
5625956600817743007191746812655955021747670922460866747744520875607859062334750627
0983285934800677894561696024943928137634956575998474857735539909575573132008090408
3003644649221940993409694873054749430121616568675073574955588234030398987467297545
5060957736921559195480815514035915707129930057027117286252843197413312307617886797
5067842601954367603059903407084814646072789554954877421407535706212171982521929788
69786916734625618430175454903864111585429504569920905636741539030968041471L

(Wow! Isn't Python's long integer type cool?)

That's 6002 digits, in case you were wondering, far more than a googol (Wikipedia), but smaller than a googolplex(Wikipedia).

If you called this generator one billion times per second (10^9 /second), you could run the program for a year and you would have only used about 3.1x10^7 seconds * 10^9 seconds = 3.1 x 10^16 of the numbers in the cycle. There is no concern of repetition of a cycle when using this PRNG.

A Simple Sample
To illustrate the use of the numpy random number generator, here's a simple python program that generates and plots 1500 random x,y pairs with values between zero and one.

import numpy as np
from numpy import random
import matplotlib.pyplot as plt
points=random.uniform(0.0,1.0,size = (1500,2))
ax = plt.subplot(111,aspect='equal')
ax.scatter(points[:,0], points[:,1],color='r',marker='o',s=2,label='random')
plt.show()

How many structures can YOU see in this plot?

For those who will still want to complain...
If you want to complain about PRNGs, then you must demonstrate that a true random number generator (TRNG) will generate significantly different results than a PRNG in the particular application. This is the standard of evidence for anyone wishing to complain about the use of pseudo-random number generators.

Additional References

Pseudorandom number generator
Introduction to Randomness and Random Numbers. Service which generates sequences of true random numbers.
Paul E. Black, "pseudo-random number generator", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 22 June 2010. (accessed 2011-March-03) Available from: http://xlinux.nist.gov/dads/HTML/pseudorandomNumberGen.html

Next Weekend: Quantized Redshifts - Testing the Null Hypothesis

Quantized Redshifts. VIII. An Uncommon Power Spectral Density "Blooper"

2011-03-05T18:23:00.085-05:00

The content of this post has been deleted by the author.

See Apology to Dr. Hartnett for details.

Quantized Redshifts. VII. Common Power Spectral Density "Bloopers"

2011-02-26T18:58:00.053-05:00

A surprising number of researchers seem to regard the PSD (power spectral density) function as some kind of magical tool that 'finds frequencies'.
The PSD is a very powerful tool, but one with which you can 'shoot your own foot off' if you are not careful.

I've laid out the basic mathematics of the PSD, and this will enable us to explore a few basic claims that have been posed in the creationist and other literature.

Can the Power Spectral Density identify a "Center" of a distribution?

First we should make clear that

In Big Bang cosmology (BBC), in the underlying Friedmann-Robertson-Walker metric, every point is a center. No matter where the observer is located, they will interpret the universe around them as being centered on them. See Misconceptions about the Big Bang (Scientific American), "Is it possible to point to a direction in the sky and say "that way is the center of the universe, where the Big Bang started?"
In addition, because of the finite speed of light (which many creationists try to ignore), when we look into the distant cosmos, we are looking into the distant past. Since BBC initiates a starting point from which structures grow and evolve, the further out we observe, the universe will begin to look different as we see younger and younger cosmological structures.

The popular retort that the universe will look different from different locations works only in a case where the universe is static (not evolving) and the speed of light is very large or infinite (which violates loads of atomic spectra we observe in distant galaxies as well as using redshift as a measure of anything). Myself and others have explored the 'decaying speed of light' claims of Barry Setterfield elsewhere (A Changing Speed of Light?).

I have no doubt that many Big Bang opponents will keep repeating this lie.

It has been suggested that the very existence of periodicities in extragalactic Power Spectra is evidence of a geocentric distribution. Russ Humphreys explored this, suggesting that broader peaks in the PSD implied that the Earth was actually slightly offset from the center of the Universe in Humphreys' strangely titled "Our galaxy is the centre of the universe, ‘quantized’ redshifts show".

The major problem with such a claim is that it can be rigorously demonstrated that the PSD is independent of the location of the 'center' of a dataset, and therefore cannot identify the location of the 'center'. I hinted at this by my question in my previous post (Quantized Redshifts. V. Exploring the PSD with Simple Datasets). How do you prove this?

Consider the 1-dimensional case of a some function, f(x) with a 'center' defined as x=0. Now displace that function on the x-axis by the distance, a, so the 'center' is now at x=a. This defines a new function, f':
f'(x') = f(x-a)
because x'=x-a.
To see how this affects the PSD, first, take the Fourier transform of both of these functions:

and

So we see that the Fourier transform of the original function gets multiplied by a complex (real+imaginary) factor

when displaced in position. But the Power Spectral Density is the Fourier transform multiplied by its own complex conjugate

so,

Therefore the PSD of the original function is EXACTLY the same as the PSD of the function with the displaced center. It is impossible for the PSD of a distribution to be used to identify its center. Potentially, one could use the Fourier transform itself to identify a value for the complex offset value found above, but the only way to do this would be to compare the Fourier transforms with a specific model distribution.

This proof is easily extended to three- and four-dimensional transforms.

The bottom line is the PSD cannot identify the center of a distribution.

Adding & Subtracting PSDs

Consider a signal, s(t), that is the sum of two signals, s1(t) and s2(t)

Because the Fourier Transform is linear, it is easy to show

But what about the PSD? From the definition of the PSD:

We see that the PSD of two summed signals are not necessarily equal to the sums of the individual PSDs. There is an additional component which is a type of mixed product of the Fourier transforms of the two input signals. There are useful cases where you CAN demonstrate the mixed term is zero, for example, if you are collecting signal from a source and there is an uncorrelated (random) background signal (see Effects of background counts in RMS normalization).

But in general, this mixed product is not automatically zero.

A similar relationship holds if we wish to subtract one signal from another.

Some researchers attempt to split the PSD into two additive components to justify subtraction of the components they perceive to be part of the distribution of the data. This is an attempt to leave only the oscillating components. The problem is the distribution they wish to subtract often has significant variation as well. It is the responsibility of the researcher to demonstrate that the input components have no correlations, or are correlated in a simple way, but I have not seen this done.

The errors described above are made in a number of papers claiming quantized redshifts and represent a basic misunderstanding of how the Fourier transform and PSD works. These are basic errors that anyone who has who taken a course in mathematical methods for physicists (wikipedia) should not make. One might expect a first-year graduate student or a neophyte to make these types of errors, but not someone with long experience with the PSD.

But what should really be an embarrassment to some journals is that their peer-reviewers did not catch these errors either!

Next Weekend: An Uncommon Power Spectral Density "Blooper"

SpaceMath @ NASA

2011-02-23T19:01:00.010-05:00

In this blog, I have repeatedly brought attention to the fact that the real language of science is mathematics (see Mathematics: The Language of Science), not the rhetorical word games that drive pseudo-science 'arguments'.

Sten Odenwald, who also operates The Astronomy Cafe, also develops math-based lessons with a science & engineering focus for NASA education projects. The lessons are freely available at SpaceMath @ NASA.

SpaceMath hosts, at the time of this writing, about 400 sample problems covering a range of topics from astronomy to space physics to spacecraft engineering, selected for a variety of educational levels. Many use REAL astronomical data. In many cases, the problems are the 'back-of-the-envelope' calculations that lay the ground-work for designing and developing real missions.

Many of these problems are at levels of high school mathematics and science, yet many are more sophisticated than anything I have seen from the pseudo-scientists I have dealt with in this blog. I wonder how many of those pseudo-scientists could even do the problems at SpaceMath@NASA.

Mathematics enables us to plan, build, and launch missions to other planets. It enables us to plot the course to a destination and determine the fuel requirements, years before a launch. The theory of gravity and motion spent over two hundred years applied to the motions of distant planets and stars before the development of rocketry and space flight made them an engineering reality. Mathematical models of space weather enable us to estimate the radiation environments around the solar system so we know how much radiation shielding is needed for instruments or even a crew.

A theory that can't make even close to reasonable numerical predictions in these environments, such as the Electric Sun models or neo-geocentrism, is not only useless (see Crank Science: Worse than Wrong), it is, by definition, a pseudo-science.

But it's worse than that.

If we teach such nonsense as the Electric Universe or neo-gencentrism to our children, who will maintain the national infrastructure of space-based communication and weather satellites? Supporters of these 'alternative sciences' can't provide info on how to do even fundamental computations of things such as the fuel requirements of a rocket to make it to a given orbit, or even estimate how much radiation the crew might receive. If our children can't do that, then how can they maintain these critical national infrastructures, much less be leaders in the exploration of space?

Quantized Redshifts. V. Exploring the PSD with Simple Datasets

2011-02-19T19:16:00.000-05:00

The ready availability of the Fast Fourier Transform (FFT) in numerics libraries on a variety of computing platforms has turned the FFT into a tool available to many researchers. However, the availability of a tool does not mean that its behavior is understood. Too many researchers seem to use the FFT as if it blindly 'finds frequencies' and that these frequencies are physically relevant to their problem of interest.

As I've demonstrated in earlier posts in this series, the fundamental idea behind the Fourier series & transforms is that ALL functions can be decomposed in waves of various frequencies - therefore EVERY SIGNAL will exhibit frequencies in a PSD. The question becomes which frequencies are physically relevant and not an artifact of the data selection and distribution.

An important issue in working with the PSD is to understand just how it behaves with different types of known data as input. Generally, if your data contains a clean, sinusoidal signal, the PSD will generate nice, sharp peaks at the frequency of the signal. But as we will see below, even a little bit of deviation from the perfect, infinite signal changes the PSD.

A note on normalization: For comparisons, I want to maintain a matching scale between analytically computed power spectra using Fourier transforms with the power spectra using the FFT. I have adopted the convention of the previous post (Quantized Redshifts. IV. The Fourier Transform, FFT & PSD) for analytic computations. I have also included a multiplicative factor for normalizing the PSD generated by the FFT. In Python using the numpy library, this can be expressed as

>>> import numpy as np
>>> from numpy import fft

FFT computation. nbins=number of data bins
>>> ff=fft.fft(dataf,nbins)
>>> psd=np.abs(ff)**2/nbins

Analytic computation
>>> psdref=(nbins/(2.0*np.pi))*np.abs(fftref)**2

PSD of Pure Sinusoidal Signal:
First we'll consider the basic case of the sine wave. The ideal sine wave has infinite in duration in time, t, with some well-defined frequency, \omega_0. It is expressed mathematically by

But in the real world, we cannot have a sine wave of infinite duration. All data runs are of finite duration in time and space. Therefore, we will define a sine wave of finite duration, starting at a time \tau and lasting for time, T. Mathematically, this can be expressed as:

We can compute the Fourier transform, and compute the FFT of this system, and we plot them below.

Click to enlarge

In this example, the infinite sine wave produces a PSD that is a delta function (wikipedia) at the frequency of the wave, which I've designated with red in the graphic above. Note that in the above plot, we are plotting the frequency, f, not the angular frequency, \omega. But the PSD generated by the FFT (blue) and the analytic function (green) are slightly different. We see this more clearly in the plot below where we plot the amplitude of the PSD on a logarithmic scale.

Click to enlarge

Here we see that the peak is still at 10Hz, but power leaks into other frequencies, above and below the input frequency. We also see that the two different methods of generating the PSD generate slightly different results. With the normalization chosen, the amplitudes at the higher frequencies differ by a factor of ten.

PSD of A Couple of (Independent) Sine Waves
Next we'll consider the superposition of two overlapping sine waves of finite duration. Because the Fourier Transform is a linear transformation, the Fourier transform of the sum of the Fourier transform of the two input waves. However, when we compute the PSD, we must still compute the product with the total Fourier transform. This means that the PSD of two signals is not necessarily equal to the sum of the PSDs of the individual signals.

Click to Enlarge

Again, we will plot the power on a logarithmic scale so we can see how the two computational techniques vary.

Note that while in this example, the PSD is equal to the sum of the PSDs of the two input signals, this will not always the case for reasons we will see next week.

PSD of a Square Pulse
Finally, we consider a rectangular pulse, which has a constant amplitude, different from zero, for some finite duration, T. To make the inquiry more general, I'll also consider offset from time t=0 by a time \tau.

For the analytic part of the analysis, we compute the Fourier Transform of this function:

And now we compute the power spectrum using the function above, and the FFT. The results are plotted below.

Click to Enlarge

Rather than plotting the full range of the frequency scale for this test, I've zoomed in on the lower frequencies to reveal how the power is distributed in a series of broad peaks. We even see a slight difference in the locations of the peaks when comparing the analytic PSD and the PSD computed from the FFT.

Here again are frequencies in the power spectrum from an input that is clearly perfectly uniform within its boundaries, it has no 'internal structure'.

This is a very counter-intuitive result. What generates all these peaks?

Whatever the origin of the peaks, it means we must be very careful when claiming peaks in a PSD represent actual internal structure in a dataset. To make sure we understand what our analysis techniques are doing, we must test the null hypothesis (Wikipedia) - what kind of PSD is produced if we have a uniform region subjected to the same sampling as our data?

Here's another question. Suppose we change the offset value, \tau. How will the Fourier Transform change? How will the PSD change? Suppose the signal is not a square pulse, will the answers change? How is this question relevant to cosmological power spectral analysis?

Some General Observations

We see that the power spectrum computed by the Fourier Transform and the FFT are indeed different, but still exhibit many of the same qualitative features, such as the locations of local peak values. Some of this difference is due to aliasing, in the Discrete Fourier Transform (DFT).
Narrow features in time or space are broad in frequency and wave number. Well-defined frequencies correspond to infinite waves. Broad structures in spatial dimensions generate low-frequencies in the power spectra.

I've laid the basic mathematical groundwork on what the power spectral density (PSD) is, and how it is computed.

Enough of the introductions. I've now covered enough material to explore some specific errors. Time to get to the meat of our story...

Next Weekend: Common Power Spectral Density "Bloopers"

Quantized Redshifts. IV. The Fourier Transform, FFT & PSD

2011-02-12T18:23:00.001-05:00

Continuing my series on Fourier analysis and its application to power spectra...

Fourier Series begat the Fourier Transform...
The Fourier series is a powerful technique, but had the limitation that it required waves whose wavelengths changed in integral fractions of your scale distance, L or 2L. What happened if you needed wavelengths not subject to that limitation? Some simple manipulations from the calculus enabled the Fourier series to be extended to the realm of continuous functions in the form of the Fourier Transform.

In this section, we'll make some notational changes to bring our conventions more in line with usage in the physics community.

1) We adopt the physics custom of presenting the frequency as angular frequency,

related to the traditional frequency, f,

. Omega is a frequency measured in radians per unit time (there are 2*pi ~6.28 radians in a circle).

2) While studying the Fourier Series, we separated the sine and cosine terms. Now we will combine them into the exponential term which is a complex number (it contains real and imaginary parts) using De Moivre's formula (Wikipedia).

With these revisions, we can then write the Fourier transform as:

The inverse transform, which converts the transform back into the original function, f(t), becomes

3) We can also do the Fourier transform in a spatial (position) coordinate. For this, we will choose x (it could easily be y or z). In this case, the 'conjugate coordinate' is called the wave number, usually designated by the letter k. The wave number is related to the wavelength, lambda, of the wave by the equation

The wave number is the number of waves (or radians of a wave) per unit of distance. Note that in frequency and wavelength, their product is the speed of the wave. Similarly, if we use angular frequency and wave number, it is basic algebra, using the definitions above, to demonstrate the relationship

In the case of spatial dimensions, the Fourier Transforms and its inverse can be written:

As with the Fourier series, these the normalization of these equations can change slightly based on the conventions chosen. This is generally not a problem so long as the conventions are used consistently.

The Discrete Fourier Transform

But the Fourier transform has a problem when applying it to real data because real data generally does not make a truly continuous function. When a measurement is made, it is determined at a specific time, t, and a position, (x,y,z), in a given coordinate system. A full dataset would consist of many of such measurements at discrete times and/or positions.

If we take measurements uniformly sampled in time, at intervals T, then each measurement takes place at a time t_k, where k is an integer.

We would say that T defines our bin size. From this, we can compute the Discrete Fourier Transform (DFT)

where the value of the transform, F, is computed in bins corresponding to discrete frequencies, fn,

We can also define the inverse transformation,

Because of the discrete nature of the time sampling and the finite size of the dataset, this yields a finite frequency resolution. That is, there is a minimum frequency that can be resolved by the DFT. This minimum frequency also defines the minimum frequency that you can resolve for a given dataset. You can make this frequency resolution smaller by increasing the duration of the total amount of data.

The DFT also an upper limit to the frequency which can be identified in a given dataset, called the Nyquist frequency. This frequency can be increased by increasing the the number of samples, N, in a fixed duration of time.

In one-dimensional cases, we can generally freely interchange the pairs of time/frequency and position/wave number.

...begat the Fast-Fourier Transform (FFT)...

With the advent of digital computers, the hunt was on for algorithms that could efficiently use the computational power. While the Fourier transforms were computationally simple, the fact was that researchers wanted to apply these transforms to large amounts of data. Using the standard recipe above, computational time required grew as N^2, where N was the number of samples. If you wanted to compute a transform for four times as many data points, the computation generally took 4^2 = 16 times longer. This would quickly become computationally expensive as dataset became larger.

Enter the Fast-Fourier Transform (FFT), the best known of the algorithms developed by Cooley & Tukey (wikipedia) in the mid-1960s. This technique sped up the computation of the DFT, but with a couple of trade-offs. The speedup was achieved by efficiently allocating the computation in powers of two, and using shift registers inside the processor which could do powers of two operations very quickly. The most notable trade-off was that the algorithm was most optimized with data samples with integral powers of two, such as 2, 4, 8, 16,...1024, 2048, ...16384,... 2^n.

The major implication of this is that the FFT is not identically equal to the Fourier transform of a given function.

...and Power Spectral Density (PSD)

The Fourier transform also has an analog to the Parseval Relation (wikipedia), as noted in Quantized Redshifts. III. How is Fourier Series Related to the PSD? For the Fourier Transform, the relation is

For the Discrete Fourier Transform (DFT) and the Fast-Fourier transform (FFT), this relationship can be written:

By this analogy, we define the Power Spectral Density (PSD), or Power Density Spectra (PDS), or Power Spectra (PS) as

By these definitions, the PSD is always positive (negative power doesn't really make sense). Phase information about the waves in the dataset, which is determined by comparing the real and imaginary components, is partially lost in the PSD.

General Properties and Insights

The DFT and FFT are symmetric functions, so the transform value at frequencies greater than zero is equal to the value at frequencies less than zero. For this reason, we generally only plot the positive frequency side. In the case of the FFT, the array bins corresponding to the negative frequencies are actually stored in the 'upper' half of the array. Often, researchers are only interested in the location of any structures, but in cases where we want to measure the relative power, the researcher may multiply amiplitude of the positive frequencies by two to account for the power in the negative frequencies (and satisfy the Parseval relation).

In the DFT and the FFT, the Fourier transformed term in bin zero (corresponding to zero frequency or a constant), contains information about the symmetry of the function above and below zero. If the term is zero, it means the function contains equal positive and negative amplitudes. For most real datasets where the data are all positive measurements, this quantity is kind of redundant, and often very large compared to the frequency distribution the researcher is interested in. Therefore it is sometimes the custom to not plot the zero frequency bin.
Another problem one encounters in the transition of Fourier transforms on functions to DFT and FFTs on discrete data points is the problem of aliasing. In the case of Fourier transforms on functions, we can generally find that the transform has a no-zero amplitude at frequencies that can range from zero to infinite (and negative infintity). This happens even if the original function is non-zero over a finite range of time. But what happens in the DFT and FFT where there is a maximum frequency (the Nyquist frequency) that can be analyzed? The answer is that the power from those frequencies above the Nyquist frequency get aliased into frequencies below the Nyquist frequency. This means that some of the power measured at a given frequency is not necessarily from that frequency and care must be exercised in the interpretation.

Extending the Fourier Transform to Three Dimensions

We examined the one-dimensional Fourier transform above. However, we can expand the tranform from 1-dimension to 3-dimensions. This is easier when done using the wave number, k, because it acts as a 3-dimensional vector.

Using the wave number, we express the represents the direction of the wave with k = 2pi/lambda * direction vector, or

With a 3-dimensional form of the wave number vector, we can define the phase as the projection of the wave number vector on the direction vector,

With this definition of the phase, the Fourier Transform can then be extended to three dimensions as

with the inverse transformation defined as

where the integration is performed over the volume of the system.

This is the proper 3-dimensional form of the Fourier transform that preserves the orthogonality characteristics (that the 'waves' identified are linearly independent). I shall show in a future post that the radial form used by many quantized redshift supporters is NOT equivalent to this form and therefore cannot reliably identify periodicites in a 3-dimensional space.

The Fourier transform can also be extended to 4-dimensions (spatial + temporal) where the function is integrated over a volume and time. The term in the complex exponential term becomes wt-k*x, which is an invariant in relativity. This form is used heavily in electromagnetism in design of antennas and waveguides.

Next, we explore the power spectral density of some known datasets.

Next Weekend: Playing with the PSD

Quantized Redshifts. III. How is Fourier Series Related to the PSD?

2011-02-05T18:52:00.001-05:00

Continuing with the introduction to Fourier analysis...

The amplitude of each term satisfies a relationship with the original function called the Parseval equality (Wikipedia).

Mathematical Note: some readers may not have the mathematical background to make sense of some f the symbols used in this equation or others in this blog (and particularly this series of posts). The vertically stretched 'S' on the left hand side of the equation is the calculus symbol for integration (wikipedia), basically a method of summing little chunks of 'area' under a smoothly varying function. The funky-looking 'E' on the right side of the equation is the Greek letter Sigma, and represents summation of a series of values (wikipedia). On a personal note, it was curiosity about these symbols when I was in the eight-grade that motivated me to learn calculus on my own. It's value extends far beyond science and mathematics.

Physically, we can think of this as an expression of conservation of energy, that the total energy in the signal, the square of the amplitude of the function, f(x), must be equal to the total energy in each frequency composing the signal. If we plot the square of amplitude of each frequency (an^2+bn^2), we obtain a plot which is the equivalent of the power spectral density (PSD).

Note that the PSD for the square wave displays power not just in the zero frequency bin, but also has smaller peaks of power at higher frequencies in between frequencies of zero power! Beyond the fact that the square wave repeats with a wavelength of 20, why would it have these additional peaks?! It is our first clue that one must be very careful when interpreting the PSD.

We'll examine a few more cases, such as the sawtooth wave, were the Fourier coefficients are computed to be

A plot like those above yields:

Click to Enlarge

Due to the sharp discontinuity at L=20, we observe a small overshoot that is part of the Gibbs phenomenon.

Let's also look at the half-sine (rectifier) wave with Fourier coefficients

Click to Enlarge

Notice that in all these graphs, there is power in frequencies other than the zero (no frequency) bin. With appropriate scaling, one would see there are non-zero amplitudes for values of n up to infinity.

Are the frequencies real?

One should be careful to define what one means by 'real'. I'd be inclined to define 'real' in this case as if the frequencies found are representative of the underlying physical mechanism for forming the original signal as opposed to an artifact of the sampling. And since all non-zero signals exhibit some sampling, there will always be sampling artifacts in the resulting PSD.

The Fourier series demonstrates that there is an alternative way to represent almost any finite function. In many ways, it is as indistinguishable as saying that you could represent the number 10 by 3+2+5 or 4+6. Think about the way you do pen-and-paper arithmetic, especially subtraction and division, and you'll realize these alternative representations are done all the time. The Fourier series becomes useful by providing an additional set of mathematical 'tricks' which may facilitate solving some other problem.

For example, in the case of the half-sine (rectifier) example above, such as signal is usually generating by running a sine wave signal (such as A/C) through a non-linear device like a rectifier, which chops off the negative (reverse) part of the current. In this case, the signal does not have to be formed by a summation of the frequencies in the Fourier series (though that would be an alternative way to form it). In this case, I would be inclined to say the frequency components of the signal are not 'real', but simply an alternative representation.

But suppose you're examining a process where you expect to have some regular structures or variation? Then the peaks might tell you more about the structure under examination, but one must exercise extreme care.

The major point of this section is to introduce the fact that non-zero power in the frequency bin of a given signal profile is NOT evidence of a real frequency indicating some intrinsic structure. I will demonstrate more examples of this in the coming sections.

More online Fourier resources

Models were generated using Python v2.6, v2.7, numpy 1.5, scipy 0.8. Plots generated using matplotlib 1.0.0

Next Weekend: The Fourier Transform, FFT and PSD, Oh My!

Publication delay

2011-01-29T07:06:00.000-05:00

The recent east coast snow storms have played havoc with our power and internet access and this has set me back in progress in the redshift quantization posts.

I'm pushing back releases by one week while I try to finish our cleanup and await a more stable power and internet access.

Sorry for the inconvenience.

Posts of Interest on Other Blogs...

2011-01-26T19:59:00.007-05:00

I recently discovered Rob Knop's Galactic Interactions blog on Scientopia.org. Dr. Knop has several posts of potential interest to followers of this blog.

Velikovsky: Worlds in Rectal Defilade
How I know “plasma cosmology” is wrong
One of Astronomy’s pet crackpot theories: non-cosmological quasar redshifts. I found this article of special interest for the figure summarizing the work of Tang and Zhang.

Another nice piece from science history that covers topics relevant to this blog (thanks to Physics & Physicists: Dark Energy and Dark Matter - The "Placeholders" of Our Time
for drawing my attention to this article).

Insert discovery here: the role of placeholders in science

Enjoy!

Quantized Redshifts. II. The Fourier Series

2011-01-22T18:06:00.071-05:00

The Tools
The mathematical tool commonly used in reports of redshift quantization is the power spectral density (PSD) (Wikipedia). You've seen simple versions of the PSD in the form of a graphic equalizer in computer applications such as iTunes. Sound engineers use a graphic equalizer to adjust audio power in multiple frequency bands (Wikipedia). While the PSD is an excellent tool for identifying well-defined frequencies, broadband signals which cover many frequencies, require considerably more effort to interpret. To understand this requires a bit more exploration of just what the PSD is and does.

History
Charles Fourier was the father of what we now call the set of transformations that bear his name. Why did Fourier develop these transformations? Fourier was working on the problem of heat transfer, examining solutions of the equation (Wikipedia).

For very simple cases of conduction between two planar surfaces, the solution to the equation seemed intractable. But Fourier decided to approach the problem in a standard reductionist way - can the big problem that is unsolvable be broken down into a set of simpler problems that can be solved by the existing techniques. Because the heat transfer equation was a differential equation of 2nd-order, one possible set of simpler solutions might be a weighted sum of sines and cosines. Fourier explored the idea that any function f(x) in a range of position, x, from -L to +L, might have an alternative representation as a sum of sines and cosines. In mathematical notation, this is written,

where n is an integer ranging from one to infinity. Fourier found that this equation would be true if the coefficients, an, and bn, were given by the integrals:

The technique provided the means for Fourier to re-write the heat transport equation into a sum of 2nd-order differential equations where the individual terms did have simple solutions. Then the method would allow him to recombine the simple solutions into the complete solution to the problem.

Caveat: Care should be exercised as some sources define a0 and the normalization of an and bn different than defined here. So long as a consistent set of series and coefficients are used, there should be no problem.

Fourier Series: Frequencies Everywhere!
The technique would prove to be incredibly powerful, and would open the door to the more generalized methods of orthogonal functions (wikipedia). These techniques would become very important for solving the more complex equations that would be developed for electromagnetism (Maxwell's Equations) and quantum mechanics (Schrodinger Equation).

But the Fourier series has another implications important for our story

All functions of a finite range could be expressed as a sum of sine and cosine waves. The cosine wave is equivalent to a sine wave shifted in phase by 90 degrees (pi/2 radians).

Caveat: I say 'All functions', but there are some limitations, called Dirichlet conditions (Wikipedia). However, it is easy to see that in a practical sense, it means that almost any function that can represent a physical system will have a Fourier Series.

Let's look at a function and its Fourier series.

We'll start with a square wave (Wikipedia). The square wave can be expressed mathematically as

and graphically, we'll show two periods of the wave.

From the 'recipe' above, we can compute the Fourier coefficients for this profile, a & b:

We plot the amplitude of these coefficients, using different colors for the sine and cosine components. The dot represents the actual amplitude of the coefficient (vertical axis) for a given integer, n (the horizontal axis).

In this example, we see that for the cosine terms in blue, only the first coefficient, a0, is non-zero. All other cosine terms are zero. The sine terms, in red, are very different - we see that the even frequencies are zero and the odd frequencies are non-zero.

As a check on our result, and to illustrate that the Fourier series really does work, we can plug these coefficients into the Fourier series and add them up and see how they compare to the original function. To examine how the result behaves when we include more terms, we'll use multiple colors to distinguish the curves with a different number of terms. The black curve is the original square wave. The cyan curve is constructed from only two terms, red includes four terms, blue includes eight terms, and green is 32 terms..

Click to Enlarge

Notice that the more terms we include, the more closely the series value matches the original function in black. There is only one discrepancy, and that is the Gibbs phenomena (wikipedia) visible at the top of the square where it turns down. This occurs at strong discontinuities in the function. The more terms we include, that overshoot will get narrower in width, but it is an unfortunate artifact of the discontinuity in the square wave.

Next Weekend: The PSD connection

Quantized Redshifts. I. Introduction

2011-01-15T17:52:00.014-05:00

In the previous post, I examined the claim that the SDSS galaxy survey visibly exhibits symmetry that places the Earth in a favored position. The claim did not hold up very well to some very simple visual tests (see Delusions of Geocentric Quantization...).

This is the first of a series of posts dealing with claims of 'quantized' redshifts of extragalactic objects (galaxies and quasars) using the power spectral density (PSD), a popular tool for searching for frequencies in data. Redshift quantization is often claimed as a means for dismissing the Big Bang as a cosmological model and is commonly invoked by supporters of Plasma Cosmology and/or Electric Universe as well as various flavors of creationism (CreationWiki). Not all creationists support claims of redshift quantization, most notably Reasons To Believe is an Old-Earth Creationism (OEC) group that accepts much of Big Bang cosmology. See also RationalWiki & Wikipedia

The power spectral density (PSD, Wikipedia) is a popular analysis tool for temporal (time series) and spatial datasets. At one time it was performed in analog circuits with wide frequency bins using band-pass filters for such applications as audio signal analysis. While once a very computationally-intensive technique for digital signals, the development of the Fast Fourier Transform (FFT) combined with the speed and memory of modern computing hardware, has made the PSD relatively easy to compute. Unfortunately, many who have access to the PSD make the mistake of assuming that it blindly 'finds frequencies' in datasets. They don't take the time to understand what the PSD actually does with a dataset.

It would be nice if there were a comprehensive tutorial with detailed demonstrations of what types of datasets work well with the PSD as well as what types of artifacts are created by poorly chosen sampling and other misuses, but I have yet to find one. Most researchers working with this tool, myself included, have had to discover these problems for themselves, by generating test datasets of known content and processing them through the PSD. Then one discovers just how easy non-periodic processes can create peaks in the PSD that can be misinterpreted as real frequencies.
The PSD has had popular use in time-series and one-dimensional spatial analysis. There is a well-defined extension for computing the PSD in 3-D space. It is tempting to reduce 3-D spatial datasets to 1-D for their simplicity, but if done, one must be careful to transform the coordinates correctly, lest errors and artifacts be introduced.

For most of those researchers reporting redshift periodicities with the radial technique, you find many of them do most of their work in areas other than cosmology - so they don't take the time to learn the nuances of the technique on the data they are using. They often seem to have a MatLab or IDL toolbox that generates an FFT and they use it without experimenting with what their process does to signals of KNOWN content.

Now for some quick overview questions.

Would 'quantized redshifts' be evidence against the Big Bang?

Possibly, but not definitively.

If the quantized redshifts were a property of the light as it propagated over cosmological distances, there are scenarios where it would not impact actual cosmological structure.

The serious impact for Big Bang cosmology would be if the quantization represented the actual distribution of galaxies in concentric shells around the Milky Way galaxy. Such structure formation would be very difficult to reconcile with current known physics.

Are 'periodicities' the same thing as 'quantization'?

No.

The action of gravity is expected to create large scale structures in Big Bang cosmology, with density enhancements and voids created by gravity attracting material from one region to collect it to form structure. This can create create regions with preferred size scales just as water waves have preferred scales in bodies of water. We have actually observed the enhancement predicted by Big Bang cosmology as it has propagated from the cool spots of the cosmic microwave background into the large galaxy collections we observe today. See Baryon Acoustic Oscillations are NOT 'Redshift Quantization'

Most of those who try to deny Big Bang cosmology evidence have been attempting to hijack the terminology, trying to claim that the periodicities actually observed are the same as quantization. In this way, they can cite mainstream cosmology references as evidence for their claims. From a Christian perspective, such willful distortion of the professional use of the term could be considered equivalent to bearing false witness (Wikipedia: Ten Commandments).

Do Periodicities imply geocentrism or galacto-centrism?

No.

Structure formation limits homogeneity (the uniformity or smoothness of the distribution of matter in the cosmos) to particular size scales. When compared to the large scale, these inhomogeneities are so small that they do not significantly violate the conditions of homogeneity for Big Bang cosmology any more than the existence of mountains is a killer for the 'round earth' theory (see Wikipedia : Flat Earth Society, The Flat-out Truth). See also Testing the Homogeneity of Large-scale Structure with the SDSS Data and The scale of homogeneity of the galaxy distribution in SDSS DR6)

In cosmology, homogeneity is defined at a cosmic scale value, often designated by the variable, a, defined over all space, which increases with cosmic time, which I will represent with the Greek letter, tau. When we do observations, we see a galaxy at distance, d, we are sampling the cosmos at time tau-d/c (due to the curvature of space, this relationship is not strictly true and as a result, there are several different measures of distance in cosmology - wikipedia). Therefore the density distribution and structure will appear to change with distance due to this sampling effect.

In addition, one of the beauties of the power spectrum technique used for identifying structure in these datasets is that while it can identify periodicities in a system, it does so without regard to any 'center' for those periodicities. Note that even the periodicity of the baryon acoustic oscillations identified in the SDSS data (see Baryon Acoustic Oscillations are NOT 'Redshift Quantization') of about 500 million light years is not obviously visible in the SDSS data. In the SDSS sample from the previous post (Delusions of Geocentric Quantization...), the graphic is about 500 million light years in radius and should contain about two oscillations across its diameter. Can you visibly identify it? If so, where is it's center? Use the methods outlined in the previous post.

My Goals for this series of posts

The basic topics I plan to cover in this series of posts (and some of these will require more than one post) are

An introduction to Fourier Series and its extension to the Fourier Transform, the FFT, and the PSD
Explore the PSD produced with ideal data as input
Explore what happens to the PSD when noise is introduced into the data
Discuss some common misuses of the PSD
Problems created in the PSD by radially sampling a 3-D dataset
More experiments with the PSD, demonstrating some specific claims found in creationist literature

I've scheduled these at about one post per week, with perhaps a short digression in between some posts. I think I've got these split out in just about reasonable chunks suitable for blog posts, but I will no doubt miss some nuances. There are a substantial number of graphs and equations that need to be installed via the Blogger interface, which is not really ideal for these types of communications. Let's see how it goes...

Next: The Fourier Series and its Applications

Delusions of Geocentric Quantization...

2011-01-08T17:00:00.000-05:00

In a couple of comments sections of this blog (links), Mr. Rick DeLano claims that, despite evidence to the contrary, he SEES periodicities in some of the skymaps produced by such groups as the Sloan Digital Sky Survey (SDSS). In particular, he mentions skymaps such as those available at the SDSS at links like the one reproduced here.

Click for larger version

I suggested Mr. DeLano conduct an exercise with this graphic to test his statement but I find no evidence that he has actually done so. A LOT of bad science is driven by researchers claiming they 'see' something in a dataset that can't be objectively identified (see Pathological Science, Pareidolia). Persistence in pursuit of these claims has destroyed more than a few careers.

Since Mr. DeLano is unwilling or unable to make any actual effort to validate his claim in an objective way, I will examine the claim in detail here, performed the test which I described to him.

Let's examine the issues in several steps to make sure we have a reasonably complete understanding of the data we are examining.

What does the SDSS plot represent in its projection from a 3-dimensional space?

I have taught several astronomy classes and occasionally found that students unfamiliar with the ways in which 3-D datasets are sometimes projected into a 2-dimensional page genuinely do not understand what they are seeing.

The SDSS plot is a 'slice' of the sky 1.25 degrees above and below the celestial equator. In this case, the two-dimensional plot of galaxies on the sphere of the sky is projected in to the third dimension with the value of the redshift, z, which is a proxy for the distance of the galaxy from the observer. Once extended into three dimensions, a slice is cut through the sphere, creating a circular plane on which we will project a small amount of data above and below the slice.

Click for larger version

In this construction, the Earth is in the center of the sphere is represented by the blue dot in the center of the plot. The pie-slice shaped regions marked in yellow are areas where data could not be collected because the Milky Way obstructs too many of the more distant objects. This map represents a very small section of the entire sky visible from Earth, so one needs to exercise caution when extending anything 'seen' in this dataset to the entire sky.

What is meant by 'quantization' in the rigorous scientific sense?

Historically, describing a physical quantity as 'quantized' has meant that it has discrete measured values. In atomic physics, the energy levels of atoms are described as quantized because they would correspond to a fixed energy in each state. In the case of a hydrogen atom, the electron energy levels were proportional to 1/n^2, where n is an integer, 1,2,3,4,... Intermediate values, such as energies corresponding to n=1.2 or 5.7, are never observed.

For redshifts to be 'quantized', they would have to only occur at certain discrete values. For example, if redshifts were quantized in steps of z = 0.02, we would expect to only see galaxies with redshifts that were integral multiples of this value. For a quantized redshift of z=0.02, we would only find galaxies on the green circles surrounding the Earth in the graphic below.

Click for larger version

In the plot above, there is not even the suggestion of alignment of galaxies along these curved lines. Note that Hartnett & Hirano, using power spectral analysis (Galaxy redshift abundance periodicity from Fourier analysis of number counts N(z) using SDSS and 2dF GRS galaxy surveys) reported redshift periodicities at z = 0.0102, 0.0246, and 0.0448. All of these values, and their integral harmonics, should be visible in this graphic as well-defined walls of galaxies confined between the green circles. As I will illustrate in the coming posts, many different things can create peaks in power spectra.

Yet we see many of these 'walls' of galaxies cutting across the green circles, in violation of the claim that the distribution is spherically symmetric around the Earth.

Here's some structures I've identified in the SDSS map. None of them exhibit an Earth-centered symmetry.

Click for larger version

What is meant by 'periodicity' in the rigorous scientific sense?

Substances that support wave-type motions, such as gases and fluids, can support various periodic behaviors, both in time and space. In fact, Fourier analysis was developed to mathematically handle just these types of physics problems. The superposition of these wave motions will create density enhancements in otherwise uniform gases and fluids.

Is there structure in the SDSS survey?

Absolutely! Modern cosmological simulations predict a pattern of clumping under gravity (including some energy loss by radiative processes in the plasma, which forms due to the energy release of the collapse). Here is a snapshot from one of the modern simulations (see more at Simulating the joint evolution of quasars, galaxies and their large-scale distribution) which exhibit some similarity to a collection of soap bubbles, where the bubbles enclose 'empty' voids with membranes and filaments of soap and water.

It is possible to identify a number of apparent cross-sections of 'bubbles' in the structure. I mark just a few in the graphic with light-blue ovals, but many more, with overlaps can clearly be identified. These are like the slices through many of the cosmological simulations

Click for larger version

This is a slice through the data incorporating distances inferred from the galaxy's redshift value.

What happens when you look through the data in directions perpendicular to this, if you were to see these galaxies projected on the sky at night? Does it retain a similar bubble-like structure? Here's a sample from the NYU value-added catalog.

This is how the SDSS galaxy distribution would look if we could see it projected on a section of the sky about 100 degrees x 60 degrees in area. The animated gif steps through the data at different values of redshift, z. We see structures, very similar to the filaments and bubbles in the SDSS projection in z, out to about z = 0.2, suggesting that the structures we observe look the same from at least two very different directions. Beyond z = 0.2, the galaxies become too sparse to identify any structure.

Astronomy Picture of the Day also recently posted a release of the 2MASS survey that plotted one million galaxies on the sky. I leave it as an exercise to the reader to identify structures (walls & bubbles) in this map. The structures revealed in this map resemble those in the SDSS survey in angle and z plotted above, consistent with the idea that the universe is homogeneous.

Does the structure in the SDSS surface exhibit a high degree of symmetry around the Milky Way Galaxy?

There is a selection effect created by the fact that observers look outward from the Earth radially and this places us in the center of the data, with everything else scattered beyond that. These plots only go out to z = 0.14 (or about 0.14*(3e5 km/s)/(72 km/s/Mly) = 580 million light years). You can obtain a more accurate distance using the cosmology calculator at Ned Wright's Cosmology Tutorial site. The SDSS survey extends far beyond this. To use this aspect of the geometry to claim the Earth is the center of the Universe is as bizarre as standing on a mountaintop, noticing that your view extended equally in all directions around you, and then declaring YOU are the center of the universe.

So I've tried to identify the 'concentric/geocentric structures' claimed by Mr. DeLano and others, but no objective tests seem to support the claim. This suggests that the 'concentric structures' are a form of pareidolia and only exist in the mind of the observer who wishes them to exist.

As I have demonstrated above, this was a very simple set of tests, which I performed with very simple, and freely available, graphics tools. Yet Mr. DeLano was unable, or unwilling, to do it himself. Why?
Annotations installed in SDSS graphics using Inkscape.

Initiating Power-up for the 2011 New Year...

2011-01-01T07:49:00.000-05:00

What a 6 weeks...

Numerous parties, both hosting and attending
A funeral that involved a few hundred miles of 2-way travel, some through lake-effect snow
Some (minor) snowstorms at home
A small and mildly disruptive home repair/remodel
I organized a presentation by Dr. John Mather (wikipedia) for NCAS and had lunch with Dr. Mather & Dr. Robert Park (wikipedia). The presentation is available online at YouTube.
My new computer system is almost completely configured. I've run a few compute-intensive simulations on it as testing for the redshift quantization project.

And through all this I managed to make a lot of progress on my To Do list.

Project 1: The Quantized Redshift tutorial is largely complete. Four of the articles, with graphics, are currently staged, with more to come. I expect to release one per week.
Project 2: The GPS project is a little less developed since it has a number of sub-components that I want the capability to address
Project 3: Five Lagrange Points don't exist in geocentrism. Pretty far along due to it's simplicity, but it still requires a fair amount of background material. However, Mr. Delano's arrogance has provided an interesting opportunity and I'll give this some time to develop.
Project 4: For the Michelson interferometers operating in space, I've received a reply from the instrument team. I will start assembling more detailed documentation about what we know from these spacecraft.
Project 5 & 6: Hardly touched these two.

An important note to potential commenters:
Any comments made to the current series of posts which is addressed in a future article will not be released until the future article is released so I can appropriately link it as a response. I already have several additional posts addressing currently pending comments and I plan to hold them as well.

I've been thoroughly enjoying this time away from weekly posting. I have made an incredible amount of progress on material that I have been wanting to develop into tutorials that would be appropriate for classroom use. Since I now have a backlog of material on quantized redshifts that still need to be converted to blog posts. I expect to release them about once per week but that frequency may slow as I catch up to material still under development.

Teachers should free to e-mail me with suggestions of specific topics on this site that you'd like to see developed into material more suited to classroom use.

Holiday Hiatus...

2010-11-19T19:56:00.003-05:00

As the holidays approach, a number of other family responsibilities have arisen which severely limit my ability to do weekly updates to this blog. I also have a number of blog-related projects which are almost complete yet are being delayed by an increasing number of comments which I am dealing with though the comment system which limits the use of graphics and equations. Many of these comments will be far easier to refute with some of the demonstration projects I've had under development. I'm tempted to avoid significant postings again until I'm ready to release Project 1 (described below). There may not be significant activity here again until January 2011.

Some of these projects are, in order of highest to lowest priority:

Redshift quantization demonstration: This has applications to many creationist and plasma cosmology claims. I've made considerable progress on this and am now concentrating on some of the introductory material needed to explain why just about ANY non-zero distribution produces a power spectrum with 'peaks'. Basically, I start with simple distributions WITHOUT periodicities installed in the data and show they generate peaked power spectra similar to those reported by supporters of redshift quantization. Then I do the test that redshift quantization supporters never do - actually install the reported periodicities in the data and demonstrate just how different the power spectra appear. This project will probably be a long series of posts which I have started mapping out.
GPS relativistic corrections: Definitely needed considering how many relativity deniers in the Electric Universe and creationist communities make totally false claims about the size of the relativistic corrections in the GPS system.
The Physics of Lagrange Points: More than the Inverse Square Law. I've done a lot of work on this recently in my day job, so I should assemble it while it's fresh in my mind.
Follow-up to instrument teams on the Michelson interferometers operating on-board satellites: Michelson interferometers are routinely used for precision wavelength measurements. I've even used one in undergraduate physics optics labs. Another problem created by the geocentrists claiming c is really c+v is for high-frequency resonance cavities in space, of which there are many!
N-body code demonstration: I already have a really nice demonstration code that does non-interacting particles in electric and magnetic fields. I even have the interface generating output to nice renderers like POVray to generate movies. My next step is to install particle interactions and to expand the for gravitational simulations and gravito-electromagnetic simulations.
Particle-in-Cell (PIC) simulation: This is a follow-on to the N-body code. I also have a need for a generalized capability for this in my day job.

I'd like to make the codes for doing this generally available, but after the flack from the "ClimateGate" code (Guardian.co.uk: If you're going to do good science, release the computer code too) I'm trying to upgrade my coding habits to install regular unit testing, etc. rather than using comments to control test cases. I'm better than many scientists when it comes to programming (I had a decade of business programming experience before I went into science), but I do need to adopt some of the newer programming tricks, even for my hobby projects.

I'm also in the process of configuring a new multi-core desktop computer system which will be more dedicated to simulation runs (running these codes on a laptop just sends the cooling fans into overdrive). It's a real headache to get everything installed 64-bit so I'm currently in a configure-build-test-delete-change configure-... cycle. I'll probably post some configuration details on the blog so others can possibly reproduce the work AND see that this work does not always require high-end supercomputing resources (a common complaint by pseudo-scientists is whining that they can't test their ideas because they are blocked from access to the types of resources of professionals).

I will probably post responses to some existing comments on the site but new comments will be let through as I have time to deal with them. Those who insist on posting their long tomes, usually poorly referenced, which often trigger the Blogspot posting bug, may find themselves waiting a while.

If you want to follow any sparse activity without repeatedly visiting the site, you can subscribe to the post and comments feeds via RSS (links in left sidebar under "Subscribe To").

Happy Holidays! (just to piss off the fundamentalists and militant atheists bothered by those things :^)

Reading: "Cauldrons of the Cosmos" by Rolfs & Rodney

2010-11-12T19:52:00.001-05:00

My my original studies for my Ph.D. were in nuclear astrophysics, it has been a while since I last really explored the topic in terms of what we know about the atomic nucleus, and what that knowledge tells us about the cosmos. For this blog, I decided to 'recharge' my nuclear physics background since nuclear physics comes up often in creationists and electric universe claims.

To do nuclear astrophysics, one must have a broad understanding of both nuclear physics (how the atomic nucleus works) and astrophysics (to understand the types of environments where energies are sufficient that the nuclear structure can undergo change). In graduate school, my nuclear astrophysics classes were taught by the man that wrote the book. In this case, Principles of stellar evolution and nucleosynthesis, by Donald Clayton.

However, Don Clayton's interests were in later stages of stellar nucleosynthesis, the formation of the heavier elements. In situations I deal with, crank claims usually try to claim few to no nuclear reactions are taking place in stars. For that case, I needed a book that placed more emphasis on the nuclear reactions earlier in the star's life. It would be even better if I could find a book that covered the status of experimental verification of stellar nuclear reactions.

The book I found which did an excellent job of covering these two topics was

C. E. Rolfs and W. S. Rodney. Cauldrons in the cosmos: Nuclear astrophysics. 1988.

This book presented a lot of material on theoretical and experimental nuclear astrophysics, and a number of items I had not seen covered to the level of detail before.

Going Backwards to Go Forwards
One of the major difficulties in doing experimental nuclear astrophysics is that it is very difficult to reproduce stellar interior conditions in Earth laboratories. But sometimes nature provides a 'back door' on the process. We have yet to find a violation of the principle of microscopic reversibility - that all atomic and subatomic reactions can run backwards and forwards. If we can have the reaction

A + B -> X + Y

then

X + Y -> A + B

is also possible. As in chemistry, there are physical principles we can use to mathematically relate the reaction rates in the forward and reverse reaction.

Photodisintegration, where a high-energy photon 'breaks' a nucleus into smaller components, is very hard to measure. It requires a high density of high-energy photons that is very difficult to produce in a lab but easy to occur at the center of a million kilometers of hydrogen (for an example where the lab is reaching the capabilities of the stellar environment, see 'Out There' Astrophysics Impacts Technology (again)). In some of these cases, we can measure the capture cross-section of the particles created in the original reaction and then compute the photoionization rate using quantum mechanics (pg 148).

Similarly, the very important triple-alpha reaction (wikipedia), where three helium nuclei (alpha particles) collide to form a carbon nucleus, be examined by exploring the reaction from the opposite direction (pg 282):

Proton+Proton Reaction
One nice part of Rolfs and Rodney text is the level of detail it covers on the theoretical AND experimental aspects of nuclear reactions in stars, starting with the proton-proton chain and covering the individual reactions. The reaction at the base of the chain,

has never been observed under laboratory conditions. The reason why is that the coulombic repulsion between two protons at stellar core temperatures is too large to be overcome by the classical mechanical means of overcoming an energy barrier. However, quantum mechanics gives the process a very small probability of the two protons tunneling through the coulombic barrier to interact (the same process used with electrons in the tunnel diode). The tunneling probability is LOW. At a temperature of 10,000,000K, this probability is 9e-10 (pg 155). Yet even with this low probability, there is so much hydrogen at the center of the Sun, at sufficient density, that the interaction rate makes up for this low probability and accounts for the energy release we measure from the Sun.

In terms of measuring this reaction rate in the laboratory, the calculation on pg 334 puts this in perspective. The total cross-section for the reaction at a lab energy of 1 MeV is about 1e-47 cm^2. With a proton beam of 1 milliamperes on a THICK target of pure hydrogen with 10^23 atoms/cm^2 in the beam, the time between reactions would be 1 MILLION YEARS. This experiment is clearly impractical to do with current technology.

If the proton+proton reaction had a much higher reaction probability, sufficient for us to measure in current laboratories, then the reaction rate at the centers of stars would be so high that stars would have burned out long ago.

While there are very few nuclear reactions which we can measure in the laboratory at relevant stellar energies, the practice is calibrate the data to the cross-section computation in the energy ranges where we can measure, and then extrapolate this function to lower energies. The advantage of this is that any other interactions which could influence the reaction rate would increase the reaction cross-section (pg 189).

Over 100 pages of the book (pg 190-327) is devoted to descriptions of experimental nuclear astrophysics techniques.

Once some of the techniques are described, the book goes into more detailed explorations of nuclear reactions with more complex nuclei heavier than helium. There is discussion of the nuclear reactions around Be7, which decays via electron capture. This creates the interesting effect that the beryllium-7 nucleus is stable, while the beryllium-7 atom is not. This is because the electron wave-function in the innermost electrons has a significant amplitude in the nucleus itself, increasing the probability of electron can react with the protons for the inverse-beta decay reaction (pg 346):

This effect from electrons suggested that for beta-decays, the CHEMICAL environment could influence the nuclear decay rate - a fact that was explored experimentally in 1947(ref) and realized theoretically by Bethe & Pierels in 1934 (1934Natur.133..689B). The neutrino from this reaction, since it is a branch of the proton-proton chain, is also discussed as a means of testing the reaction (pg 364). This reaction is also an important step in the formation of neutron stars (link).

Modern experiments with this method of altering radioactive decay rates have occasionally been invoked by Young-Earth Creationists as evidence that nuclear decay rates could have been significantly higher in the past (See Accelerated Radioactive Decay According to Answers in Genesis)

The theoretical and experimental work around more complex reactions is explored as well. I was surprised to find how many of the heavier nuclei experiments so important for described the steps of stellar reactions beyond hydrogen and helium burning actually have significant laboratory experiments behind them.

Because researchers don't have the resources to explore EVERY possible nuclear reaction hypothesized to occur in stars, they must rely on nuclear models to compute the structure of the nuclei of interest and then compute the cross sections of the reaction of interest. One model that has found successful use is the Hauser-Feschback statistical model which can be used to compute an energy-averaged cross-section for nuclei were there are many resonances (pg 432). While these models are used for reactions where we don't have data, they are often tested and calibrated by applying them to reactions where we can obtain experimental data (pg 434).

Pages 493-495 covered some of the early ideas (about 1988) for solving the solar neutrino problem which was still unsolved at that time.

Stellar Composition Effects
One of the other interesting applications in the book was a discussion of limiting cases in stellar composition. In a simple case of a chemically homogeneous star, the structure is largely determined by the mean molecular weight, mu. This value can be approximated in atomic mass units, by the equation

mu= 1/(2X+0.75Y+0.5Z)

where X is the mass fraction of hydrogen, Y is the mass fraction of helium, and Z is the mass fraction of every element with an atomic mass greater than helium, often referred to as 'metals'. Since everything must add up to 1.0, we require that Z = 1-X-Y. In the text, the authors examined two interesting limiting cases, a star of all iron (Z=1, X=Y=0) and all hydrogen (X=1, Y=Z=0). In the early 1900s, it was believed that stars were largely iron due to the large number of iron lines in the Sun's spectra. However, once astronomers understood how spectral lines were formed, largely through the work of Cecilia Payne, it was eventually understood that they were largely hydrogen. In the example, we see that the mean molecular weight of an all hydrogen star is mu=0.5, while for an all iron star it is mu=2.0. In terms of gas pressure, this means that the iron star must have about four times higher pressure than a hydrogen star to maintain hydrostatic balance (pg 96).

Applications
One of my motivations for reading this book was to refresh my nuclear physics background but also to explore possible alternative sources of information for dealing with the cranks that claim the Sun and other stars are not nuclear powered. While the book is now over 20 years old, it directed me to some of the earlier research in experimental nuclear astrophysics from which I was able to track more modern work and updates via ADS.

One of the most useful items I found was the computation of what was required to produce the proton+proton -> deuteron reaction in the laboratory. While various cranks like to claim that the failure to produce the reaction in the laboratory is a failure of nuclear astrophysics, the facts paint a different picture. It is not that researchers tried to produce the reaction and failed, but they probably have never tried to produce that reaction specifically because it had such a low probability at the energies available in the Sun's core. There have been many experiments in the late 1930s to the 1950s colliding protons together over a broad range of energies (refs).

While this twenty-year old book provided an excellent overview of stellar nuclear reactions, I suspect significant revision of some experimental results will take place as the National Ignition Facility (link) enables these reactions to be explored at significantly higher densities.

GPS, Relativity & Geocentrism

2010-10-29T21:46:00.010-04:00

This is in response to Rick DeLano comments on GPS and relativity, originally posted in the comments of John Hartnett's Cosmos. 1. Introduction.

For this analysis, I will define Physical Geocentrism as a system which claims that the Michelson-Morley experiment (MMX) makes the Earth a fixed, motionless frame of reference. This seems to be consistent with the claims Mr. DeLano makes in his earlier comments and below.

Just how well tested is relativity?

DeLano: "We are only now beginning to be in a position to determine whether the behavior of “c“ is as predicted in non-Earth reference frames."

False.

We've pretty much had the capability since space flight - and especially interplanetary flight. We've been able to measure newer predicted relativistic effects since the 1960s, such as the Shapiro Delay (Wikipedia)

In addition, there are currently at least two satellite instruments flying in space, moving relative to the Earth, AND to the object they're imaging, where the optical configuration used is similar to the Michelson-Morley experiment. The system is used for precision Doppler velocity measurement. They use 'c' for the velocity of light when removing Doppler effects from the spacecraft velocity relative to the target.

As high-bandwidth transmissions become common in space, we will have to include the relativistic effects there as well to keep precise timing. Physics Today: Time dilation seen at just 10 m/s.

But Doesn't GPS Use Geocentric Coordinates?
The GPS system uses several different coordinate systems, including an inertial system with an orientation fixed to the distant stars. Computations transform to a geocentric system when needed to compute locations physically on the Earth. For more details and references, see Scott Rebuttal. I. GPS and Relativity.

DeLano: "The early evidence is shockingly unsupportive of Relativity (JPL time correction built into GPS software, for example, which renders “c“ constant in only one frame. Hint: it ain't the solar system barycenter)."

That can only be a credible statement to an audience that knows NOTHING about relativity.

According to relativity, provided you do ALL your calculations in a given frame, you can always use 'c' as the speed of light in that frame.

That is what frame-independence of the speed of light MEANS.

If you transition between reference frames you must do the appropriate relativistic transformation and then do all your calculations based on measurements in THAT frame. Then you can use 'c' in that frame as well.

If You Want to Know About GPS, Read the Spec!
But here is the real killer for the claim of no relativistic effects in the GPS system. Back during the system's development, the contention over the reality of relativistic effects was so severe, a frequency synthesizer was installed to alter the system clock frequency to the relativistically-corrected value - just in case. Neil Ashby describes how the required clock synchronization could not be achieved until the corrected synthesizer was turned on (see General Relativity in the Global Positioning System by Neil Ashby). A copy of the original paper, from 1978, describing the launch and initial testing of the first GPS satellite, is available online: INITIAL RESULTS OF THE NAVSTAR GPS NTS-2 SATELLITE.

Today, the relativistic correction is described in the GPS specifications. It's available at the Navigation Center of the U.S. Coast Guard, under GPS References, see Interface Specification (IS-GPS-200E, 8 June 2010). The relativistic corrections are described in Sections 3.3.1.1 and 20.3.3.3.3. (Note that the USCG site layout has changed so these links are different than the earlier article.)

So I ask the question, could Physical Geocentrists have built a working GPS system?

But the implications of an absolute reference frame like Physical Geocentrism requires goes far beyond what is covered here.

Coming Soon: More technology implications (more things that would NOT work if Physical Geocentrism were valid) AND APPLICATIONS (what WOULD work if Physical Geocentrism were valid) of Physical Geocentrism!

Dealing with Creationism in Astronomy

Geocentrism vs. the Barycenter

Another Big Bang Prediction Confirmed. More Headaches for the Infinite Age Cosmologies

"Are You Smarter Than a 17th-Century Geocentrist"

Electric Universe Fantasies & Heliopause Electrons

"The End of the World as we Know It" with Stuart Robbins

Doin' Real Science: Simulating Particles

I'm Still Here...

Pseudoscience and the Technomystic II

Pseudoscience and the Technomystic

Electric Sun, Electric Comets & 'Conspiracies'

Reading: "Cosmical Electrodynamics" by Alfven & Falthammer

Tidbits on Extrasolar Planets and Polonium Halos

Electric Universe Apologetics, or, With Friends Like These...

Geocentrism's "Quantized Planetary Orbits"

Miscellaeous News: Adam & Eve, Creationism in the classroom

Setterfield, SED (Stochastic Electrodynamics), and NASA

Geocentrism: Laser Ranging Experiments

Goodies from my Recent Excursions

Miscellaneous Links on Geocentrism & Relativity Denial

Stupid Geocentrist Tricks

Electric Universe: Measurement of the Electric Current in a Kpc-Scale Jet

Heliocentrism's 'Vested Interests'...

Challenges for Electric Universe 'Theorists'

Polonium Halos

Geocentrism: Ubiquitous Aberrations

What The Electric Universe 'Theorists' Won't Tell You...

Geocentrism: Failing More Basic Physics...

Geocentrism: Failing Basic Physics...

Balticon 45

A Science Event in the Maryland/D.C. Area

Quantized Redshifts XI. My Designer Universe Meets Some Data and What's Next...

Links of Interest

Upgrading my Scientific Toolbox

Geocentrism: Does NASA use Geocentrism?

Quantized Redshifts. X. Testing Our "Designer Universe"

Apology to Dr. Hartnett

Quantized Redshifts. IX. Testing the Null Hypothesis

Mathematical Interlude: Pseudo-Random Number Generators

Quantized Redshifts. VIII. An Uncommon Power Spectral Density "Blooper"

Quantized Redshifts. VII. Common Power Spectral Density "Bloopers"

SpaceMath @ NASA

Quantized Redshifts. V. Exploring the PSD with Simple Datasets

Quantized Redshifts. IV. The Fourier Transform, FFT & PSD

Quantized Redshifts. III. How is Fourier Series Related to the PSD?

Publication delay

Posts of Interest on Other Blogs...

Insert discovery here: the role of placeholders in science

Quantized Redshifts. II. The Fourier Series

Quantized Redshifts. I. Introduction

Delusions of Geocentric Quantization...

Initiating Power-up for the 2011 New Year...

Holiday Hiatus...

Reading: "Cauldrons of the Cosmos" by Rolfs & Rodney

GPS, Relativity & Geocentrism