Monday, June 15, 2009

Scott Rebuttal. II. The Peratt Galaxy Model vs. the Cosmic Microwave Background

When the Electric Universe crowd wants to haul out real scientific work to lend credence to their claims, they often like to talk about the galaxy formation model proposed by Anthony Peratt at the Los Alamos National Laboratory[1,2,3].

In Peratt's model, galaxies form at the intersection of large-scale (many megaparsecs long) Birkeland currents. This model had the interesting feature that it formed objects that resembled spiral galaxies and they exhibited rotation profiles similar to those observed for spiral galaxies, without the need for dark matter needed in the standard Big Bang cosmology. These characteristics were observed in both plasma experiments and in particle simulations.

So why isn't the Peratt model the accepted model for galaxy formation? Because galaxies are not defined by rotation curves alone. Peratt's model made a number of other predictions that failed significantly.

The Birkeland currents, by definition, have magnetic fields parallel to their direction of flow. These currents will also will generate their own magnetic field, just like any other current. However, the field along the path of the current needs to be much stronger than the self-generated field or the stream will be unstable. The electrons will trace out circular or helical paths due to the magnetic field as they move along the current stream. But in circular motion, the electrons will accelerate, and therefore radiate. This radiation is called cyclotron (in the non-relativistic case) or more generally, synchrotron radiation.

So these Birkeland currents will be expected to emit synchrotron radiation. Dr. Peratt calculated just how much they would be expected to radiate and obtained values of energy output on the same order of magnitude as the measured flux of the cosmic microwave background radiation[4].

But there was a problem. Cyclotron emission for electrons of a fixed energy emits energy in discrete spectral lines corresponding to the cyclotron frequency and harmonics (integer multiples). The cosmic microwave background is a broad smooth blackbody curve, very different from the sharp line spectra of cyclotron radiation.

But we don't expect the electrons to be monoenergetic nor the magnetic field their in to be completely uniform. Peratt assumed a 'bithermal' electron velocity distribution, where the mean electron motion would correspond to one temperature along their direction of motion, but another temperature perpendicular to their direction of motion. [Note that the commenter 'Anaconda' in this thread (link) dismisses the use of 'thermal synchrotron' distribution because I could not demonstrate it had been seen under laboratory conditions. I assume he would condemn Peratt for invoking thermal synchrotron radiation as well. Actually, 'thermal synchrotron radiation' relies on the correctness of two concepts: the Poynting vector definition of electromagnetic energy, and Maxwell's equations. It basically says that the radiation flux from a collection of particles, emitting incoherently, is the sum of the fluxes of radiation from individual particles.]

With a distribution of electron energies and magnetic field strengths, the peaks of the synchrotron radiation broaden into 'bumps'. Peratt found that by assuming the CMB was created by the sum of the emission of many of these current streams, the shape of the CMB spectrum could be matched over frequencies up to 100GHz. But he needed many filaments to do this, about 10^31[4].

Peratt's model clearly requires synchrotron emission from the current streams powering the galaxies and his own calculations show that instruments such as COBE and WMAP have sufficient sensitivity to see them.

Peratt reports that the mean lengths of these current streams must be on the order of 350 MEGAPARSECS. This means that the currents driving the nearer galaxies, such as M31 & M33 should be clearly visible in the raw WMAP data, before the foreground processing is even performed!

So we look up the coordinates of M31 & M33. From the SIMBAD astronomical database, we find

M31 RA: 00 42 44.31 dec:+41 16 09.4 ICRS 2000. Galactic: 121.1743 -21.5728
M33 RA: 01 33 51.02 dec:+30 39 36.7 ICRS 2000. Galactic: 133.6107 -31.3306

Here's a snapshot of the M31 and M33 superimposed on the WMAP CMB map using Google Earth in Sky mode. (click to enlarge)

We can also check out the nearby Virgo cluster of galaxies.

Where are the current streams to power these galaxies!? The streams for these nearer galaxies and clusters should lie over all the other more distant streams. At a distance of 600,000 pc for M31, a 350Mpc long filament should appear to be 2*arctan((350e6 pc/2)/0.6e6 pc) or 180 degrees across. Even if not strictly linear, this structure should show up! Where is it? All we see are random blobs, more consistent with noise (and consistent with the Big Bang interpretation) than current streams.

Why should I , or anyone else, believe these galactic-scale currents exist when Peratt's own predictions for them fail?

Peratt own calculations demonstrated that the flux from these currents was comparable to the intensity of the cosmic microwave background radiation [4] and he even expected to see a ''”spaghetti” of radiating filaments surrounding the viewer'[5].

I have heard reports that in addition to the current streams not being visible, the Peratt model had serious difficulty reproducing the fluctuations of the CMB at the level detected (10^-5), though I have yet to find where this result may have actually been published.

Perhaps the synchrotron radiation is being beamed?

This happens in pulsar emission, so it could be happening in the current stream and is not beaming directly towards us? There are several problems with this scenario:
  1. Synchrotron radiation is beamed in the direction of motion. In the case of electrons moving in circular orbits, the beam sweeps out a full 360 degrees in the plane of motion, much like the headlight of a motorcycle moving around a circular track. The emission could be confined to a plane, but the plane would be aligned with it's normal (perpendicular) vector along a circle around the current stream. The beaming would still sweep over all directions outbound from the current stream.
  2. To explain the galaxy distribution, these currents must be pointed all over the sky in random directions. This means the plane of the electron motion will be randomly distributed as well. The odds that we are out of the coverage of all these emitting electrons becomes slim.
  3. Peratt only needs 30keV electrons to generate the galaxies in his models. This makes the electrons non-relativistic, so the beam of light emission is very broad, not narrow as would be the case for relativistic electrons. The emission would be strong in many directions so beaming is not a problem.
Why Don't We See the SDSS Filaments in WMAP?

In his rebuttal (link, The WMAP Map, page 10) to my previous paper (link), Dr. Scott tries to deflect this criticism of the Peratt model by asking why don't we see the filaments of galaxies reported in the large-scale galaxy surveys such as 2dFRS or SDSS against the CMB maps (see Large-scale Structure of the Cosmos).

In mainstream cosmology, these filaments are NOT due to electric currents. Computer simulations of structure formation are perfectly capable of forming filamentary structures without the need for them to be powered by currents. You can see for yourself the results of some of these simulations at the website for “Simulating the joint evolution of quasars, galaxies and their large-scale distribution”. This group even makes their simulation code, called Gadget, generally available so others may evaluate it.

In dark matter cosmologies, these filaments are NOT expected to be strong sources of emission over a broad range of wavelengths such as synchrotron radiation. In order to be seen by WMAP, these filaments would need to have sufficient emission or absorption in the radio frequencies observed by WMAP. Since these filaments would be largely atomic hydrogen, their major emission and absorption in radio would occur at a frequency of 1.420 GHz (wavelength = 21 cm). This frequency, as well as others frequencies of emission and absorption expected by atomic hydrogen, are well outside the frequency of WMAP observations (23-94 GHz). Atomic hydrogen is largely transparent in the WMAP frequency range[6].

WMAP CMB is produced by a combination of measurements from FIVE all-sky maps. The raw input data is available as well. Some high-level image products the the input bands (23-94 GHz) are available here. Note that neutral hydrogen, detected in the intergalactic medium due to its absorption in the Lyman alpha line, is transparent in these radio wavelength bands. Other sources of foreground emission can be accounted for as well, as we can see in these foreground datasets. Free electrons, such as needed for Peratt's currents, show up in the synchrotron radiation maps and the free-free (bremsstrahlung radiation) maps.

The WMAP frequency bands were chosen to for a region near the minmum of microwave emission by galaxies. The yellow bands in the figure below (K, Ka, Q, V, W) represent the frequency coverage of WMAP.

Courtesy of WMAP. Used with permission.

Other Questions About the Peratt Galaxy Model

There are a host of additional problems with the Peratt model which I cannot find addressed anywhere.
  1. What powers these cosmic-scale Birkeland currents? What is the origin of the EMF that drives them? Are there any laboratory or theoretical models that such currents of such size and magnitude could be driven by turbulence?
  2. With a mean length of ~350 Megaparsecs for Peratt's filaments, the ends of these filaments should be visible in our current galaxy surveys so we should be able to see the source of the EMF and magnetic field which maintain them. Not only do we not see any objects that could fulfill this role, even Don Scott admitted that they did not know the source of these Birkeland current systems. These invisible, physics-defying current sources must be far more complex than single weakly interacting particles proposed as Dark Matter. Because their predicted emission is well within the sensitivity of our present day instruments, these invisible current sources are a far larger problem for EU than Dark Matter is for the standard cosmology.
  3. With currents driven by 30 keV electrons in Peratt's simulations, this is more than enough energy to ionize intergalactic neutral hydrogen (ionization potential = 13.6 eV). Recombination (electron and proton reforming the hydrogen atom) will emit photons at these energies, in the ultraviolet. Cosmological redshift could move this emission into the visible range for galaxies at high redshift (z>4) values. More distant and sensitive surveys should see these currents in the range of optical emission!
I'd like to thank some members of the WMAP team for their helpful input.

July 12 Update: Added labels

  1. A. L. Peratt, W. Peter, and C. M. Snell. 3-dimensional particle-in-cell simulations of spiral galaxies. 1990.
  2. W. Peter and A. L. Peratt. Synchrotron radiation spectrum for galactic-sized plasma filaments. IEEE Transactions on Plasma Science, 18:49–55, February 1990.
  3. A. L. Peratt. Plasma and the Universe: Large Scale Dynamics, Filamentation, and Radiation. Astrophysics & Space Science, 227:97–107, May 1995.
  4. W. Peter and A. L. Peratt. Thermalization of synchrotron radiation from field-aligned currents. Laser and Particle Beams, 6:493–501, August 1988.
  5. A. L. Peratt. Electric space : evolution of the plasma universe. Astrophysics & Space Science, 244:89–103, 1996.
  6. J.P. Wild. The Radio-Frequency Line Spectrum of Atomic Hydrogen and its Applications in Astronomy. Astrophysical Journal, vol. 115, p.206. 1952.

Sunday, June 7, 2009

Some Preliminary Comments on Crothers' Relativity Claims

The work of Stephen J. Crothers has been promoted heavily by the Electric Universe advocates, as one of their 'experts' on issues of Special & General Relativity. There is even a section of his papers on the plasmaresources site. Mr. Crothers' main page on this site, The Black Hole, the Big Bang, and Modern Physics', provides some strange reading.

This is a preliminary examination of some of Mr. Crothers' papers. It is by no way complete, but there are enough interesting errors in the works I've examined so far to make a few comments. I've concentrated on the paper “On Certain Conceptual Anomalies in Einstein's Theory of Relativity”[4], with some supplemental reading of references [1,2,3].

Crothers seems to take particular issue with the concept of black holes in general relativity. However, it appears most of his complaints are non-issues if it is impossible for an infalling observer or particle to actually cross the event horizon. I know of no astrophysical processes involving black holes that actually require infalling material to cross the event horizon[6], though I have seen this description used in press releases. If the singularities in the Schwarzschild metric at the center and at the event horizon are not reachable by an observer, then Crothers issues are largely moot. In some older literature, stars collapsing to the Schwarzschild radius were often called 'collapsed stars' which might be a more technically correct way to describe these objects. I have my own favorite 'black hole paradox' which demonstrates that the idea popularized in the media and science fiction of falling through the event horizon probably cannot occur.

Each section of "On Certain Conceptual Anomalies in Einstein's Theory of Relativity"[4] states some conclusion backed by claims which are at best weak, and in a number of cases, scientifically wrong. Here's a few I found that can be described with a minimum of mathematics.

[4, Section 2]: “Misconception: that Ricci=0 fully describes the gravitational field”

I find several problems in this section, as Mr. Crothers attempts to justify this statement.

1) The issues attributed to the statement describing "the perceived source of the field in terms of its center of mass" is a red herring. Newtonian gravity has a similar issue in that the exterior field of a spherical shell of mass is identical to the field of a point mass at the center of the spherical shell, a location where there is no actual mass. So what is Mr. Crothers' point?

2) The statement that one needs two line elements to describe the metric for the interior and exterior of the mass is somewhat strange. The 'two' line elements cover two non-overlapping, but continuous ranges of the independent variable, r, and therefore the elements are considered to be a single function, the function being described as piecewise. This is standard knowledge, in which case, why does Crothers mention it at all. Perhaps he does not understand it?

3) Mr. Crothers makes a fair number of his claims based on the concept of an 'incompressible fluid' in relativity. However, an 'incompressible sphere of fluid' is not a valid concept in relativity. In terms of the equation of state, incompressible means

where \rho is the fluid density and P is the fluid pressure. This means it no amount of change in fluid pressure will change the density of the fluid. This could also be inverted to read

But this term is directly related to the speed of propagation of disturbances in the matter, AKA the speed of sound. The general expression for the speed of sound in a fluid, c_s (not to be confused with the speed of light), is

Therefore, it is trivial to see that a truly incompressible fluid must have an infinite speed of sound. This is in violation of the principle that there is a limiting speed for signal propagation in relativity.

The mathematics does not stop one from combining these contradicting concepts, but the results and conclusions from such an analysis cannot be trusted. I found the reference to an early paper where Schwarzschild explored this problem historically interesting, but the paper was largely ignored after the realization of this contradiction. Modern researchers use more realistic equations of state, derived from nuclear experiments or theory, when dealing with compact objects. There have been some examinations of ways to treat incompressibility in GR[5], but Mr. Crothers does not use this.

[4, Section 3]: “Misconception: that General Relativity permits point-masses”
This section seems to rely on the bizarre claim that things permitted in General Relativity do so in violation of Special Relativity. This is backwards and misses the point of the distinction.

1) Special relativity is 'special' because it is limited to the 'special 'case of observers in uniform relative motion. General Relativity is the more 'general' theory, permitting non-uniform motion (accelerating) observers. Special relativity is a subset of General Relativity. In general relativity, the metric can have the very general form:

where x_i represents generalized coordinates. Due to the symmetry of the metric tensor, these 16 functions reduce to 10 independent functions.

Special relativity is limited to the much simpler Minkowski metric,

which simply means that the g_mn terms are constants limited to values of 0, 1, and -1. All solutions in special relativity are solutions in general relativity.

This suggests that Mr. Crothers does not understand relativity at all. Any conclusions based off the notion that SR is a more fundamental theory than GR, is immediately suspect.

2) Point masses are used in Newtonian gravity and point charges are used in electromagnetism. This idealization is convenient for modeling systems where the range of motion is much larger than the dimensions of the objects. This assumption essentially says that tidal effects, due to a finite object size, are negligible.

In “A brief history of black holes”[2], Crothers makes a related bizarre claim:
Even the electron has spatial extent, according to experiment, and to quantum theory.
Crothers gives no reference for this claim and it is simply wrong. I haven't done quantum electrodynamics (QED) since the late 1970s, but QED treats electrons as point particles. An experimental upper limit of about 1e-22 m has been placed on the electron's size from scattering experiments. This is far smaller than the classical electron radius of 2.8e-15 m obtained by equating the total electrostatic energy to the electron rest mass. References to the papers on this work can be found at Wikipedia: Electron-Fundamental Properties

But even mathematically, this makes no sense. Infinitesimals, a mathematical entity that is as small as it needs to be, down to a point, are the foundation of calculus which forms the mathematical underpinnings of modern physics & engineering. One technique, Green's Functions, builds the fields of extended objects by integrating (essentially summing) the fields of point sources, represented as a Dirac Delta Functions. Point sources are the foundation of much of mathematical physics.

[4, Section 7]: "Misconception: that "Schwarzschild's solution" is Schwarszshild's solution"

I found this historically interesting, and I'll probably examine that aspect of it further. However, it is irrelevant to the physics whether Schwarzschild said anything about black holes.

It is not clear whether Crothers totally denies the validity of relativity or is promoting an alternative interpretation or another theory entirely.

I found nothing in Crothers writing on the experimental implications of his claims beyond his claimed non-existence of black holes. Mr. Crothers needs to explain why we get experimental agreement in spite of his claimed flaws in relativity? There is plenty of experimental evidence of the validity of general relativity (pulsar timing, accretion disk doppler profiles, GPS) [7,8].

  1. S.J. Crothers. On the vacuum field of a sphere of incompressible fluid. Progress in Physics, 2:76–81, July 2005.
  2. S.J. Crothers. A brief history of black holes. Progress in Physics, 2:54–57, April 2006.
  3. Stephen J. Crothers. On line-elements and radii: A correction. Progress in Physics, 2:25–26, April 2007.
  4. Stephen J. Crothers. On certain conceptual anomalies in einstein’s theory of relativity. Progress in Physics, 1:52–57, January 2008.
  5. F. I. Cooperstock and R. S. Sarracino. General relativistic incompressibility. Nature, 264:529–531, December 1976. doi: 10.1038/264529a0.
  6. K. Thorne, R. Price, and D. MacDonald. “Black Holes: The Membrane Paradigm”. Yale University Press, 1986.
  7. Clifford M. Will. The confrontation between general relativity and experiment. Living Reviews in Relativity, 9, 3 2006.
  8. Scott Rebuttal. I. GPS & Relativity, April 3, 2009