Is the asymmetry mentioned in 1905 SR paper fully removed?

[Dale]

How long will it take until you accept reading that the "Kinematical" part of Einstein's paper deals with observable quantities whereas the "Electrodynamical" part exclusively relates to non-observable quantities?

I don't know the distinction you are drawing here, but it is not relevant to the topic of this thread. The topic of this thread is the asymmetry mentioned in the first paragraph and illustrated by the specific example of a magnet and conductor in that same paragraph. The Kinematical and Electrodynamical parts come later and use their own separate examples where needed.

The two cases of that first paragraph's example are related by a boost. The Lorentz transform is a boost. Therefore it is reasonable to use the Lorentz transform to remove the asymmetry discussed there.

If you want to discuss other scenarios that you believe are NOT related by a boost then I am glad to do so, but it is clear that the scenario in the first paragraph is a boost. Do you disagree about that specifically?

Obviously Einstein refers to "observers" and measuring devices ("rods" and "clocks") in the Kinematical part of his paper

Obviously. Which is why I discussed them in post 33 (paragraph beginning "Furthermore"), even though they are not relevant for the asymmetry example in the first paragraph of Einstein's paper.

 

[Sugdub]

I don't know the distinction you are drawing here, but it is not relevant to the topic of this thread...Obviously. Which is why I discussed them in post 33 (paragraph beginning "Furthermore"), even though they are not relevant for the asymmetry example in the first paragraph of Einstein's paper.

Before concluding in his §6 that the asymmetry has been removed, Einstein invokes the transformations for x,y,z,t arrived at in §3 and applies them to two expressions of Maxwell's equations respectively matching the cases evocated in the moving magnet and conductor paradigm. Obviously he considers that the equations derived in his §3 are relevant to resolving this asymmetry. The fact that these equations properly connect both cases was known before 1905, but so far the Lorentz transformation appeared to be a postulate. By referring to the outcome of §3, Einstein attempts to provide an in-depth justification, based on more general postulates, for the efficiency of the Lorentz transformation. This shows the relevance of the "Kinematical" part in respect to removing the asymmetry at stake.
Whether Einstein actually succeeds is however disputable. Let's come back to the nature of the "asymmetry": the explanation given for the observed current appears to be non-symmetrical (an electric force on the one hand, an electromotive force on the other hand), whereas the problem to be resolved is defined in a fully symmetrical way (two symmetrical descriptions of the relative motion between the magnet and the conductor). So the "asymmetry" referred to by Einstein points to a logical anomaly, insofar a non-symmetrical conclusion (different causes for the current) cannot be inferred from fully symmetrical hypotheses.
There are two ways to resolve this anomaly: either re-formulate the conclusion so that it becomes symmetrical, or re-formulate the hypotheses so that they contain an asymmetry which triggers the asymmetry in the conclusion. I can't see that any of these alternatives has been met.

 

[GregAshmore]

Whether Einstein actually succeeds is however disputable. Let's come back to the nature of the "asymmetry": the explanation given for the observed current appears to be non-symmetrical (an electric force on the one hand, an electromotive force on the other hand), whereas the problem to be resolved is defined in a fully symmetrical way (two symmetrical descriptions of the relative motion between the magnet and the conductor). So the "asymmetry" referred to by Einstein points to a logical anomaly, insofar a non-symmetrical conclusion (different causes for the current) cannot be inferred from fully symmetrical hypotheses.
There are two ways to resolve this anomaly: either re-formulate the conclusion so that it becomes symmetrical, or re-formulate the hypotheses so that they contain an asymmetry which triggers the asymmetry in the conclusion. I can't see that any of these alternatives has been met.

Where Sugdub says "different causes for the current", I have said, "different quality of the force". The one cause for the two forces (which result in the two currents) is the magnetic pole. The difference in quality has to do with the integral of the work done over the path of the moving conductor not being [reducible to] a scalar. (Sorry for any mangling of the mathematical principle.) That difference in quality still exists under SR. Einstein chooses to call the electromotive force an auxiliary concept, but to me it seems to be just as much an asymmetry as always, given that the mathematical nature of the asymmetry is still present under SR. UNLESS the path integral problem goes away with the use of the Faraday tensor, in which case even Einstein's auxiliary concept goes away.

 

[Dale]

Whether Einstein actually succeeds is however disputable.

Whether or not 2+2=4 is also disputable. Even though the math clearly demonstrates that one side of the argument is wrong, that fact does not prevent the dispute from happening. So it is here.

Mathematical fact 1: Maxwell's equations are not invariant under Galilean transforms.
This is an asymmetry.

Mathematical fact 2: Maxwell's equations are invariant under the Lorentz transform.
The asymmetry is resolved.

So the "asymmetry" referred to by Einstein points to a logical anomaly, insofar a non-symmetrical conclusion (different causes for the current) cannot be inferred from fully symmetrical hypotheses.

The hypothesis (Maxwell's equations) is not fully symmetrical under the Galilean transform. The asymmetry can be inferred since the Galilean group is not a symmetry group of Maxwell's equations.

There are two ways to resolve this anomaly: either re-formulate the conclusion so that it becomes symmetrical, or re-formulate the hypotheses so that they contain an asymmetry which triggers the asymmetry in the conclusion. I can't see that any of these alternatives has been met.

Or the third way, find a different symmetry that the hypothesis does have.

 

[GregAshmore]

Mathematical fact 1: Maxwell's equations are not invariant under Galilean transforms.
This is an asymmetry.

Mathematical fact 2: Maxwell's equations are invariant under the Lorentz transform.
The asymmetry is resolved.

That is not the asymmetry to which Einstein refers in the introduction. He speaks of the asymmetry with regard to energy. The mathematical condition which causes the symmetry of energy is built into Maxwell's equations. Because it is built into Maxwell's equations, it continues to exist when those equations are transformed from frame to frame in SR. Except, Einstein points out, for the rest frame of the charge, where the v cross B term is zero.

If the mathematical asymmetry were eliminated by making Maxwell's equations invariant under the Lorentz transform, there would be no point in Einstein instructing us to transform the field to the rest frame of the charge to determine the force on the charge, nor would there be any reason to assert that the electromagnetic force in other frames is an "auxiliary concept", rather than an asymmetry.

 

[Dale]

That is not the asymmetry to which Einstein refers in the introduction. He speaks of the asymmetry with regard to energy.

The EM fields are governed by Maxwells equations. All asymmetries of classical EM phenomena are asymmetries of Maxwells equations.

 

[ObsessiveMathsFreak]

I'm actually reading through this at the moment, so I'll throw my hat in here for a second. Here's the summary of the paper's position after the derivation of the transformation rule between EM fields in the stationary and moving reference frames

If a unit electric point charge is in motion in an electromagnetic field, there acts upon it, in addition to the electric force, an “electromotive force” which, if we neglect the terms multiplied by the second and higher powers of v/c, is equal to the vector-product of the velocity of the charge and the magnetic force, divided by the velocity of light. (Old manner of expression.)

To my understanding, this is basically a summary of the method of using the Lorentz force $\mathbf{F} = q ( \mathbf{E} + \mathbf{v} \times \mathbf{B}$ to calculate the force on a moving charge.

After this the paper adds

If a unit electric point charge is in motion in an electromagnetic field, the force acting upon it is equal to the electric force which is present at the locality of the charge, and which we ascertain by transformation of the field to a system of co-ordinates at rest relatively to the electrical charge. (New manner of expression.)

This was probably clearer in the original German. As far as I can understand, this viewpoint says that the (electric) force on a moving charge is just given by the electric field on it $\mathbf{F}' = q \mathbf{E}'$, but this electric field $\mathbf{E}'$ is the one measured in the moving frame(present in the locality... ascertained by transformation).

Einstein later states that "... [the] electric and magnetic forces do not exist independently of the state of motion of the system of co-ordinates." So you can't talk about the force on charge (in your frame) as being composed of bits of this or that. You must transform into the frame of the charge and measure fields and forces there(then presumably transform the force/acceleration back to your frame).

He also says that this resolves the paradoxes/problems with Homopolar/Faraday generators. It's a very great pity that he didn't spell this out explicitly though.

 

[Dale]

So you can't talk about the force on charge (in your frame) as being composed of bits of this or that.

That isn't what he said. He said you can't talk about the force on the charge as being composed of bits of this or that without specifying the frame. Once you have specified the frame you can talk about the composition just fine. The electric and magnetic forces are frame-variant quantities.

 

[Sugdub]

The electric and magnetic forces are frame-variant quantities.

Although this statement is true, it could well be misleading. We should note that a change of reference frame is something rather general which aims at connecting an infinite set of reference frames. But the forces at stake have only been defined for two very peculiar frames, not for the general case.
Let's come back to the issue at stake. The electric theory assumes that the conductor is in absolute rest and its "v" parameter stands for the absolute velocity of the magnet. Conversely, the magnetic theory assumes that the magnet is in absolute rest and its "v" parameter stands for the absolute velocity of the charges alongside the x axis. Both expressions of the force cannot be physically reconciled by connecting their mathematical expression through a Lorentz transformation which assumes that neither the conductor nor the magnet is in absolute rest and that "v" stands for their relative velocity. The assignment of different "names" to the different definitions for the "v" parameter would make it obvious. Here we are dealing with different physical definitions for "v" which cannot be all valid at the same time.

 

[Dale]

The electric theory assumes that the conductor is in absolute rest and its "v" parameter stands for the absolute velocity of the magnet. Conversely, the magnetic theory assumes that the magnet is in absolute rest and its "v" parameter stands for the absolute velocity of the charges alongside the x axis.

What is "the electric theory" and what is "the magentic theory"? There is just one classical theory on electricity and magnetism: Maxwell's equations. It covers both electricity and magnetism and does not assume that a magnet or conductor or anything else is at absolute rest.

Honestly, I don't know where you are getting this garbage, but it does make some of your other statements make more sense. Garbage in, garbage out.

 

[GregAshmore]

I'll sign out here. I did learn something, so I thank all who participated.

 

[Sugdub]

The same for me. We had enough signs of misbehaviour under stress.

 

[Dale]

The same for me. We had enough signs of misbehaviour under stress.

This is an amusing parting comment. I suppose that my pointing out your fallacious arguments and incorrect premises is "misbehavior under stress" in your book. The correct behavior would be to simply marvel at the unfathomable wisdom of your fallacies and swallow your premises?

Anyway, if you ever wish to continue the conversation you are certainly welcome back. But I will continue to point out where your arguments fail.