Non-existence of the B field
- From: RP <no_mail_no_spam@xxxxxxxxx>
- Date: Sat, 25 Oct 2008 19:27:17 -0700 (PDT)
Just a continuation of a previous discussion. I'd like to give it a
fresh new direction, however. Again I'll post the links to a summary
of Purcell's model [Schroeder] of the B field as a superposition of
opposing enhanced E fields.
http://physics.weber.edu/schroeder/mrr/MRR.html
http://physics.weber.edu/schroeder/mrr/MRRnotes.pdf
In addition, I'll provide some notes [Ganley] relevant to the previous
discussions, from about the same year that Purcell's book was
circulated.
http://www.hep.princeton.edu/~mcdonald/examples/EM/ganley_ajp_31_510_62.pdf
The above is a purely algebraic formulation of the subject as it was
known at that time, i.e., circa 1960.
In the Ganley article it is noted that the longitudinal and transverse
forces transform as follows:
F_t = F_t' / gamma
F_ x = F_x',
where t and x indicate the transverse and longitudinal vector
components respectively.
The primed frame is rest frame, thus, given two point charges
initially at rest and lying on the yz plane, motion of the system
along x results in a reduction of the force between these charges by a
factor 1/gamma.
Thus settles the previous debate about a pair of point charges at rest
wrt each other as viewed from a frame of reference in which the system
is in motion.
But Schroeder, conversely, derives an increase in the transverse force
on his charged plates by the inverse of this factor, i.e., by a factor
of gamma. What gives?
Well, to be fair, Schroeder's charged plates contract in length, and
the line density of charge is thus increased via Lorentz/Fitzgerald
contraction, by a factor gamma. The point charges in the above
argument do not of course have lengths to contract.
The contraction of the plates, which do have extension, gives rise to
the increase in transverse force per unit area by a factor gamma.
However, we should be able to see that what this increase in charge
density accomplishes is an exact cancellation of the transverse
reduction in force produced by purely relativistic considerations, as
noted by Ganley, occurring between the point charges that compose the
charges on the two plates. In other words, there should be no change
in the force per unit area of these plates when transforming from one
frame to the other.
This latter result is derived by Ganley using a similar argument
involving parallel conductors in motion along their lengths.
Schroeder's premise for a transverse force increase is thus
obliterated. But as I had noted in the previous thread, it was already
logically disconnected from the increase in transverse force
postulated to occur between counter flowing point charges.
But, though Ganley seems to be winning the debate thus far, he then
goes and applies a magnetic force to his two point charges in order to
account for the reduction in force observed. Is this step necessary?
The answer is no, it isn't. What is it's source? This convention, that
permeates modern treatments of classical electrodynamics, does nothing
more than allow us to retain the Coulomb force unaltered, which is
supposedly required in order to conserve charge.
I suppose the requirement of retaining Coulomb's Law intact would
depend upon how "conservation of charge" is defined. I would tend to
disagree with Ganley's stance on this. The "charge", being a number of
electrons (particles), wouldn't be non-conserved if we were to allow
for an alteration to Coulomb's Law to account for the effect of
relative motion of the charges. Ganley's, and all of modern physics,
stance on this is thus a matter of convention only. This magnetic
force that is arbitrarily prescribed thus has its entire existence
based in convention. In my estimation the Coulomb equation is simply
incomplete, and thus incorrect. The same results would follow either
way, at least mathematically, (and does) but the conceptual models
involved in the two approaches are not insignificant. Later I hope to
show how the classical view is the more cumbersome of the two, and
lends only to confusion about various electronic effects that are
actually quite simple when using the alternate approach of a variable
Coulomb force.
_______
The magnetic force applied to the two moving point charges in Ganley's
example, is representative of a "lack" of Coulomb force, rather than a
force in and of itself. This differentiates it from the force
provided by the B field surrounding a conductor, as in Purcell's
example, which is representative of enhancements to the Coulomb field
rather than reductions of it.
The Purcell type of "magnetic" field represents additional E fields
superposed over the Coulomb E fields, and the Ganley type of
"magnetic" field represents negative E fields superposed over the
Coulomb E fields. This in my estimation is no small difference, and
the obvious solution is that neither type of magnetic field exists,
there is only velocity dependent E fields in their stead. Nor is the
relative speed involved in this reaction that of a charge or system of
charges wrt some arbitrary observer, but rather it is the transverse
speeds of the interacting charges wrt each other. Frames of reference
really have nothing to do with the interaction of charges. They would
continue to interact in the same manner in the complete absence of
observers. Isn't this what the PoR is all about after all?
The final conclusion of all of this, I believe, is that convention has
historically placed sensibility in the back seat. I have derived the B
field from just such a variable E field of the components of charge in
parallel conductors, and at one time the paper was published to the
web. After changing internet services I simply never bothered to put
it back up. It was incomplete anyway, so it doesn't seem a priority to
place it back on the web, not to mention its fair resemblance to
Wilhelm Weber's theory, which is already widely available on the web.
For what it's worth, Weber had already derived the relation E=mc^2,
and the constant c before Maxwell/Lorentz was published, and long
before Albert Einstein derived the same relationship.
What I discovered was that my version of Weber's model, because it
involved up to it's final point only magnetostatic and electrostatic
systems, where propagational delays are negligible, it is, in that
state of affairs both Galilean and Lorentz invariant. Further
considerations of relativity will be applied to it, and hopefully I'll
be able to present a more consistent form of Purcell's model. I
already have a significant amount of material in hand but it is
admittedly very difficult to rewrite an entire chapter of science
history.
Until then, maybe I have at least provided something to talk about.
I'm surprised, actually, at the number of regulars who are unfamiliar
with Purcell.
.
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