Chubykalo and Vlaev's basic mistake

Juan R. González-Álvarez keeps touting this paper as "proof" that there are "instantaneous interactions" in classical electrodynamics:

Chubykalo and Vlaev, "Necessity of Simultaneous Co-existence of
Instantaneous and Retarded Interactions in Classical
Electrodynamics", Int. J. Mod. Phys. A14, 24, p3789-3798 (1999).

J.D. Jackson issued a criticism (hep-ph/0203076, Int.J.Mod.Phys. A17 (2002) 3975-3979). Chubykalo and Vlaev responded (physics/0205041v1, unpublished).

In both the original paper and in their reply C&V make the same clear and obvious mistake, one which Jackson pointed out. C&V claim

d|R|/dt0 = -c (I use ASCII d where they use \del)

[Here |R| is the distance to the observation point from
the source position at the retarded time t0.]

Jackson points out this is inconsistent with the next equation in the original paper (between eq. 15 and 16), and the the correct value is:

d|R|/dt0 = - R.V/|R| (R and V are bold)

[R is the 3-vector from source to observation point and V is
the 3-velocity of the source evaluated at retarded time t0.]

It is easy to see that Jackson is correct and C&V are wrong: Consider the source charge moving perpendicular to the line connecting source and observation point. For this case, |R| is unchanging, and d|R|/dt0 MUST be zero. Jackson's formula gives this value, C&V's formula does not.

To compute this explicitly, at time t0+dt0 we have:
R(t0+dt0) = R(t0) - V dt0 (sign from direction of R)
|R(t0+dt0)|^2 = R(t0)^2 - 2 R.V dt0 + V^2 dt0^2
Subtracting |R(t0)|^2, dividing by dt0, and taking the limit:
d|R|^2/dt0 = -2 R.V
But
d|R|^2/dt0 = 2 |R| d|R|/dt0
and Jackson's result follows.



The other problem was pointed out by Jackson, and completely ignored by C&V in their response: Just before eq (11) in the original paper, C&V state "\phi and A must not depend on x,y,z,t explicitly". This is nonsense -- those potentials QUITE CLEARLY have an explicit dependence on x,y,z,t (and also an implicit dependence via the retarded time t0). Jackson points out that their omitting this explicit dependence was offset by a different mistake in computing the fields, but there's no offsetting mistake in verifying Maxwell's equations. So their conclusion that the fields don't satisfy Maxwell's equations is wrong, and Jackson shows this.

In their conclusion, C&V state that one must include both the implicit and explicit dependence on x,y,z,t. Well DUH! Of course one must do so! Indeed, their original (incorrect) claim was due to their omitting the explicit dependence! But the fact that the potentials and fields have explicit dependence on t is not any sort of "instantaneous interaction" -- x,y,z,t are the LOCAL place and time of the observation, and have nothing whatsoever to do with the source. As I said before: there is no place in this paper where any property of the source is evaluated at t, EVERY evaluation of source quantities is at t0, the RETARDED time; so there is no "instantaneous interaction" between source and observation.

[I suppose there is "instantaneous interaction" between the
observation at x,y,z,t and the fields at x,y,z,t, but this
is not what one would call "instantaneous interaction", this
is part and parcel of what one means by "field". And it
certainly is not "instantaneous action at a distance", which
is what virtually all readers of their paper's title would
think.]


Bottom line: there is no problem with the usual formulation of classical electrodynamics, the fields derived from retarded L-W potentials _DO_ satisfy Maxwell's equations [*], and there is no "instantaneous interaction" in this paper, except in the title. Both C&V's and Juan R. González-Álvarez's claims to the contrary are wrong.

[The fact that their 6-year old response remains unpublished
is indicative, but not definitive. Check out citations to
C&V's paper and see that Jackson and I are not alone
in criticizing fundamental aspects of Chubykalo's papers...]

[*] Of course the zillions of successful products designed
using retarded L-W potentials are a pretty solid refutation
of claims that they are wrong.


Tom Roberts
.

Relevant Pages

  • Re: Chubykalo and Vlaevs basic mistake
    ... In both the original paper and in their reply C&V make the same clear ... Jackson points out this is inconsistent with the next equation in the ... Jackson points out that their omitting this explicit dependence was ... there is no "instantaneous interaction" between source and observation. ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... Nowhere does the paper present any alternate formulation, only L-W potentials are used, with ALL SOURCE QUANTITIES EVALUATED AT THE RETARDED TIME t0. ... AT MOST what they have established is that the conventional notation is inadequate to express the subtleties of differentiating a retarded-time function of the source trajectory with respect to the implicitly-defined retarded time, and relating it to the coordinate time of the point at which the fields are to be evaluated. ... notation for its "partial" derivatives. ... THAT is what an "instantaneous interaction" would involve, not their subtleties about differentiating with respect to implicitly-defined variables. ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... Juan R. González-Álvarez wrote: ... than the retarded time t0. ... --- Uncle Al to Tom Roberts in sci.physics.research Feb 2008 ... Rather than quoting somebody else's insult, why is it you cannot show any "instantaneous interaction" in their paper? ...
    (sci.physics.relativity)
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