Lienard-Wiechert potentials

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I recently got a copy of Purcell's very excellent Electricity and Magetism book. In the chapter about moving charge, he states without proof that the electric field due to a moving charge points at where the charge is now, as if there is instantaneous action at a distance. This is of course necessary for length contraction to work.

After much digging about, I uncovered that this radial electric field, and a flattening of the same field (aka length contraction) is explained by the Lienard-Wiechert potentials, using retarded potentials.

The question is, if retarded Coulomb potentials moving in a medium (some preferred frame) explain relativistic effects and also explains the magnetic field (as Purcell shows), why is it preferred to believe there is no medium propagating this information?

Of course we cannot detect this absolute reference frame, but such a medium may help us understand the nature of matter. And is a medium not implied by general relativity (a naive question, as I'm not well versed on this).

Thanks.
 

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  • #2
Dale
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if retarded Coulomb potentials moving in a medium (some preferred frame) explain relativistic effects and also explains the magnetic field (as Purcell shows), why is it preferred to believe there is no medium propagating this information?
You answered your own question:
we cannot detect this absolute reference frame
You are also free to believe in unicorns, Santa Claus, etc., but they cannot be detected and are not necessary for explaining any known physical observations so they are omitted from modern physical theories.
 
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So, we can't detect the absolute frame, so for that reason you might banish the medium to the North Pole. But just because you can't detect it doesn't mean it ain't there.

But how do we explain all these waves? What's waving? The presence of waves would appear a strong motive to keep a medium in the picture.
 
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Dale
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But just because you can't detect it doesn't mean it ain't there.
If you cannot detect it then even if it is there it doesn't matter. It has no physical consequence, if it did, then you could detect it. In other words, you will never make an incorrect physical prediction by assuming that an undetectable entity doesn't exist.

But how do we explain all these waves?
With Maxwell's equations. No medium is needed or implied.
 
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Maxwell's equations can be derived from Coulomb's law and postulates of relativity (choose your version of relativity here, as both are fine); check out Elliott, Relativity and Electricity, IEEE Spectrum, 1966, for a nice example. Maxwell's eqs are only descriptive of the behavior of these waves. The waves (both electric and magnetic) are caused by Coulomb potentials propagating outward from a charge. What are they propagating in?

That's like explaining how a tsunami travels from a fault line to the shore by writing down the wave equation - it describes it but doesn't explain it what it propagates in. What's the medium it travels in? Are you ok with the notion that there are waves that mysteriously travel in the absence of a medium?
 
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Dale
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Maxwell's equations can be derived from Coulomb's law and postulates of relativity
Sure, but then you start with the premise of no medium, which is a premise I assumed that you did not want to start with.

What are they propagating in?
Why would you assume they are propagating in anything? There certainly is no evidence to that effect.

Are you ok with the notion that there are waves that mysteriously travel in the absence of a medium?
Completely.
 

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