Compatibility of Classical Electromagnetism & Relativity

[MrBlank]

TL;DR Summary

There is no relativistic charge increase in classical electromagnetism. Special relativity appears to require relativistic charge increase.

Physicists consider classical electromagnetism and special relativity to be compatible.

If classical electromagnetism is assumed to be (otherwise) correct then the experimental evidence is interpreted as showing that there is no relativistic charge increase.

It is well known that there is energy in electric fields. This is true even in classical electricity. This can be shown by considering capacitors.

Consider a point charge at rest. It has an electric field. There is energy in its electric field. In special relativity there is mass-energy equivalence. Therefore, there is mass associated with the electric field.

Now consider the point charge to be moving at a constant, non-zero, velocity. In both classical electromagnetism and special relativity, the electric field is length contracted in the direction of the velocity. In special relativity, there will be a relativistic increase in the mass associated with mass in the electric field. There will be a corresponding increase in the energy of the electric field. This increase in energy in the electric field is equivalent to a (relativistic) increase in the charge.

This implies that classical electromagnetism and special relativity are not compatible.

Is there an error in what I have written?

 

[Dale]

In special relativity, there will be a relativistic increase in the mass associated with mass in the electric field.

No. Mass is a relativistic invariant. There is no increase in mass.

There will be a corresponding increase in the energy of the electric field

There is indeed an increase in the energy but ….

This increase in energy in the electric field is equivalent to a (relativistic) increase in the charge.

This does not follow. There is also energy in the magnetic field which does not require additional charge.

Relativity does not predict an increase in charge. Charge is a relativistic invariant.

 

[Vanadium 50]

You've been writing "relativity gets it wrong" posts for years, without success. It would probably have been worth spending the time getting to know SR forwards, backwards and sideways before undertaking this. You will discover there is no mathematical inconsistency, so no thought experiment can disprove it. (A real experiment is another issue)

Probably the most fundamental error you make is that you are discussing moving charges but only considering electric, not magnetic fields. So you're not even starting from the right place.

 

[pervect]

Classical electrommagnetism is totally compatible with special relativity. What it's incompatible with is non-relativistic classical mechanics. More precisely, classical electromagnetism is only compatible with classical mechanics in a frame in which the speed of light is c. This boils a rather technical argument about something physicisits call "covariance" to a form that is hopefully accessible.

Because velocities add in classical mechanics, there is only one special frame in which the speed of light can be c. In some frame moving with a velocity v_e, the speed of light according to classical mechanics would have to be c + v_e or c - v_e, making the two theories incompatible. This was the situation people accepted back in the days before Einstein proposed special relativity.

Before special relativity, it was a real mystery why the Earth, where we frequently use Maxwell's equations, should be such a "special" frame. Special relativity fixes the issue by making Maxwell's equations correct in all frames of reference, modifies classical non-relativistic mechanics to do so.

The rest of your argument is apparently based on a misunderstanding of special relativity. While we can certainly help with that, if you're interested, the conditions on which I personally would be interested is if you're actually looking for an explanation, as opposed to have already made up your mind and basically interested in pushing your own point of view rather than listening. Possibly others are more interested in arguing the point - I've been down the road too many times to be terribly interested personally.

I can also point at "The Ultimate Speed" for some experimental evidence of why classical mechanics is known to be wrong. See the video , or look up the associated peer-reviewed paper. There are certainly papers that discuss more precise tests - there are many such papers. The main merits of the approach in this video is that it's aimed at a more general audience.

 

[Sagittarius A-Star]

It is well known that there is energy in electric fields. This is true even in classical electricity. This can be shown by considering capacitors.

Correct.

This increase in energy in the electric field is equivalent to a (relativistic) increase in the charge.

No. The following paper shows a charged capacitor, moving in frame $S$ in the direction of the electric field. The energy of the electric field is, because of length contraction, decreased by the factor $\gamma$, compared to the capacitor's rest frame $S_0$. What also must be taken into account is, that the sides of the capacitor must provide pressure to counterbalance the tension of the field, to hold the plates apart. Then for the whole capacitor, including the field, it follows the familiar law "energy =$\gamma$ × rest-energy". This results with invariant charge.

A simple relativistic paradox about electrostatic energy
...
Abstract
A charged parallel-plate vacuum capacitor moves uniformly through an inertial frame. Its field energy alone does not transform according to the familiar law "energy= $\gamma$ × rest energy." However, when the stresses in the supports are taken into account, the entire system does satisfy this relation.

Source:
https://www.researchgate.net/public...lativistic_paradox_about_electrostatic_energy

 

[Mister T]

This increase in energy in the electric field is equivalent to a (relativistic) increase in the charge.

There are lots of ways of increasing the energy without increasing the charge.