“Open” magnetic field lines is another concept that Dr. Scott condemns (”The Electric Sky”, page 118; “D.E. Scott Rebuts T. Bridgman: Open Magnetic Field Lines'', pg 11), but like so many other of his claims, he is, at best, playing semantic games. In principle, magnetic and electric field lines can extend to infinity, however, in most cases we wish to examine, we don't want or need to consider the behavior at infinity. Is Dr. Scott saying that any time you want to visualize something with a magnetic field, you must represent the entire universe?
In any real analysis, we have to draw the boundary somewhere. This can leave field lines cut-off. Particles can still flow along these lines. In general, they will connect to field lines from another field of a more distant source. In the case of magnetic dipole fields, these 'open' lines generally occur near the poles. If Dr. Scott claims these lines don't exist, is he claiming that charged particles cannot travel out from these regions? Where do the charged particles go?
The recognition that magnetic field lines can never end is acknowledged by many researchers by enclosing the term 'open' in quotes. I will use that convention here.
Dr. Scott's obsession with 'open' field lines also reveals an hypocrisy on his part. It's as if he wants to treat them as 'real', in need of being drawn 'complete'. But Dr. Scott's claim gets even stranger when we begin to explore his justification that 'open' field lines violate Maxwell's equations [Scott 2007]. Specifically, Scott claims that field lines must be closed to satisfy the Maxwell Equation,
But magnetic field lines are not 'real', they are representations of a vector field designed as mere guides to directions of charged particle flow, representing the direction of the vector field at that point. When we draw a field line as complete between two points, say A and B, (See Figure 1 at below) we are saying that we expect the particles moving outward from point A will eventually arrive at point B. If a field line is 'open', such as for point C, we don't expect the particle to ever return to the original system, such as point D, but connect to magnetic fields from other more distant sources. Dr. Scott's insistence on closed magnetic field lines makes such systems of plasmas permanently CLOSED to any kind of charged particle transfer.
Figure 1: An exploration of closed and 'open' field lines. The red field lines close back on the source object for the field. The blue field lines are 'open', connecting to more distant field sources which we don't show in this graphic.
The Maxwell equation,
, is true everywhere in a magnetic field. This is a consequence of what is called the Divergence Theorem and is related to the observational evidence that there are no (known) magnetic monopoles (source points of magnetic flux) and it means that the net magnetic flux passing through a closed surface is zero: the same amount of magnetic flux passes into the surface as passes out of it. This condition demands no other constraint!
In fact, the simplest set of 'open' field lines, a constant magnetic field, where the field lines extend from points at 'negative infinite distance' to 'positive infinite distance', trivially satisfies the divergence condition. Dr. Scott's claim that 'open' field lines violate the divergence condition for magnetic fields is false by trivial counter example! An undergraduate physics major taking a year course in electromagnetism should immediately recognize Dr. Scott's statement as a gross error.
The really embarassing part is that Dr. Scott managed to get this fundamentally erroneous claim into the IEEE Transactions on Plasma Science, a journal that is supposed to be peer-reviewed! This wasn't an obscure paragraph in the paper. A large section of the paper was devoted to arguing this statement. The journal allowed a blooper like this through? What does that say about the quality of the peer-review process for this journal?
But let's cut Dr. Scott some slack. Maybe Dr. Scott relying on the divergence condition was actually a typo (a really big typo). Perhaps Dr. Scott really meant to invoke the other Maxwell equation related to magnetic field structure, Ampere's Law:
There is no requirement that the path be closed when defining magnetic field lines, only that if the path is closed, by Stoke's Theorem, it will specify some characteristic of the current and electric field passing through the surface enclosed by the path.
While drawing field lines as closed loops will guarantee that
As an additional check, I've examined a number of papers written in the past 100 years on the development of electromagnetism and on magnetic fields and field lines, many written by leaders in the field, including works by Alfven, Vasyliunas, Stern, Swann, and Falthammar, and have found no support for Scott's statements that field lines cannot be 'open'. Many of these researchers use the concept themselves. If Dr. Scott wishes to continue making this particular claim, he needs to provide more documentation than "Don Scott Says So". Professionals with a stronger background in electromagnetism than Dr. Scott (or me), disagree with him.
Update: January 4, 2015: W.D. Clinger on the International Skeptics Forum has pointed out a nuance in this argument of how magnetic field lines can end at magnetic null points (i.e. reconnection sites).
Contrary to Dr. Scott's claims in “The Electric Sky”, 'Open' field lines do not violate Maxwell's Equations!
References
[1] D. E. Scott. Real Properties of Electromagnetic Fields and Plasma in the Cosmos. IEEE Transactions on Plasma Science, 35:822–827, August 2007. doi: 10.1109/TPS.2007.895424.
6 comments:
Scott's IEEE paper mentions that:
"The notion that magnetic field lines can be open ended is impossible to reconcile with Maxwell's simple and universal
equation ∇B = 0"
Is this the statement you say is the "fundamentally erroneous claim into the IEEE Transactions on Plasma Science"?
If not, which statement?
The erroneous claim is that field lines cannot be open.
That div(B)=0 allows a constant field which is all open field lines is part of the evidence that the claim is wrong.
And just to be clear, we're saying that the erroneous claim is that field lines can not be open (1) in reality, or (2) represented as open.
Option 1 implies that the universe may include open field lines? Option 2 is a matter of convenience?
div(B)=0 by itself says the lines can never have an endpoint. This means either closed or infinite.
If you make the domain the entire universe then conditions change. If the Universe is finite, there may be an additional closure condition, but it is not part of Maxwell's equations. If the Universe is infinite (a popular idea in Plasma Cosmology) then then lines may be forever open.
However, since Scott's examples of his claim are always in regards to finite systems (geomagnetic field, solar magnetic field, etc.), he appears to have an issue with option 2 as well. The 'open' field lines of the Sun may connect to other 'open' field lines of the general galactic magnetic field, or even other stars, but they don't connect back to the Sun.
As I state above, professionals recognize that 'open' field lines almost certainly eventually connect to something so they often enclose the term in quotes.
"div(B)=0 by itself says the lines can never have an endpoint. This means either closed or infinite."
since div(B)=0 is false when div is infinity I would think that means magnetic field lines are closed, at least technically.
"The 'open' field lines of the Sun may connect to other 'open' field lines of the general galactic magnetic field, or even other stars, but they don't connect back to the Sun."
That would make them closed. Closed is closed. A north connects to a south and vise-versa. No matter if it is another star, planet etc...
Physicists are funny, You don't have an issue with magnetic fields that extend to infinity when it suits; but you hold fast to the conviction that space is electrically neutral? It's all gravity baby! all that magnetic field flying around space but no current is moving? lol... really.
Clearly Anonymous does not understand the mathematics of electromagnetism and resorts to playing word games trying to change the definitions of the scientific terms.
The ‘div’ in div(B) = 0 is a differential operator (Wikipedia: Divergence) so saying 'div is infinity' is a statement which makes no mathematical sense. Div(B)=0 means that all 'flows' going into a volume, go out of the volume, there are no field line ‘sources’ within the volume. This is contrary to electric fields and classical gravitational fields, where the 'flow lines' of the vectors connect on charges and masses respectively, so div(E) and div(g) can be non-zero.
Changing the definition of a ‘closed’ field line does not make it valid. A field line being ‘closed’ does not mean connecting to a body. As noted above, a field line does not ‘connect’ to a body as a magnetic field line has no source (divergence-less). A closed field line means it connects to itself, like a circle or loop. Magnetic fields lines do not even need to ’connect’ to the current sources. The magnetic lines of force around a straight wire form loops around the wire. The do not need to even connect to it.
Wikipedia: Field Line
MIT: Visualization of Fields and the Divergence and Curl
Space is electrically neutral in general. Electric fields can form in areas with strong gradients in plasma density, temperature, or gravitational influence, which are commonly boundaries between different regions (solar wind and magnetosphere, stellar ‘surfaces’, etc.) (see Real Electric Universe). These fields are hypothesized to be the sources of the ‘seed currents’ that start a magnetic field by mechanisms such as the Biermann battery (Wikipedia).
Magnetic fields can exist in regions with no net current. A photon, consisting of oscillating electric and magnetic fields, can continue to propagate until it is absorbed, scattered, etc. LONG after the current that created it has stopped. That’s how an antenna works. This is because Maxwell’s equations have an extra term, sometimes called the ‘displacement current’ created by a changing electric field. This ‘displacement current’ can exist in regions where a REAL current is not flowing (Wikipedia: Maxwell’s Equations). Once a magnetic field gets started, it can persist for a very long time under the right conditions, even when J=0.
The commenter, like so many Electric Universe supporters, has a very incomplete understanding of electromagnetism. And also like so many cranks, instead of learning the facts, they just make stuff up thinking that their ‘notions’ must be correct.
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