Is the asymmetry mentioned in 1905 SR paper fully removed?

[Dale]

Your last reply won't convince those who followed our debate.

I think that is making a pretty big assumption about the disposition of those following the debate.

I challenge the view that the transformation derived by Einstein in the "kinematics" part of his 1905 SR paper could actually account for a boost: the transformation he derived does not respond to a change of reference frame.

The transformation he derived is a single-parameter linear transform which maps lines of constant position in one frame to lines of constant velocity in another frame. That is a boost, by definition. Simply look at the equation at the end of section 3, it is clearly a boost.

However you now become aware of the unavoidable consequences of that discovery and you want to escape. You should feel free to retract your initial support to my analysis. No need to argue, it's much better to play it honestly.

The thing I was supporting was your understandable confusion over the use of "observers" in SR as a shorthand for a reference frame. It isn't even relevant here since there are no observers mentioned at all in the scenario under discussion, as I already pointed out with a verbatim quote of the entire paragraph in question.

 

[Sugdub]

The thing I was supporting was your understandable confusion over the use of "observers" in SR as a shorthand for a reference frame.

We might be close to identifying the root cause of our divergence of views. Indeed Einstein believed he could derive the Lorentz transformation in response to a change of reference frame steered by the relative velocity between two description frames. It is therefore not surprising if he raises the equations you refer to. Having achieved this derivation he could then invoke SR and its Lorentz transformation to justify the equivalence of both descriptions of the EM field resulting from his analysis of the moving magnet and conductor problem. His strategy in the 1905 SR paper is clear.
However, as already pointed out, a change of reference frame can only account for a change of description for the same realm, it is a pure mental act which cannot trigger, predict or explain the change of any physical quantity directly observable such as space or time quantities. Let's assume with Einstein that the relative speed between two measurement devices be accountable for the change of value of directly observable physical quantities (please note that I'm no longer referring to "observers"). It would mean that the state of motion of these devices is objectively different, that one objectively moves faster than the other … and this would breech the principle of relativity of motion. Had SR been conceived as a theory only dealing with mental descriptions without any observable consequences, it could lead to a transformation steered by the relative speed between two description frames with the caveat that this transformation could not apply to any directly observable physical quantity. It could however be invoked in support to the EM paradigm since this only deals with mental descriptions of non-observable physical quantities.
Conversely, in the "kinematics" part of his 1905 SR paper Einstein clearly referred to a change of directly observable physical quantities, namely space and time quantities. Such changes must be traceable to a change in experimental conditions. As demonstrated above, the relative speed between two measurement devices cannot account for such a change, hence the need for an additional hypothesis which sets an objective difference in experimental conditions: one device is at rest in respect to the target object whereas the second is in relative motion in respect to it. This has two consequences which Einstein did not spot: first the transformation to be derived cannot respond any longer to a "change of reference frame" since the relative speed between the measurement device and the target object changes from nil to v; second the parameter which steers the transformation must be the one which accounts for the change in experimental conditions, namely the relative speed between the second measurement device and the target object and no longer the relative speed between both measurement devices. These consequences are unavoidable if one wants to develop a theory which affects space and time quantities.
The "kinematics" part of Einstein's paper is a mix of both approaches, but I'm afraid physicists cannot have it both ways: they are just incompatible.

 

[Dale]

Let's assume with Einstein that the relative speed between two measurement devices be accountable for the change of value of directly observable physical quantities (please note that I'm no longer referring to "observers"). It would mean that the state of motion of these devices is objectively different

The paragraph in question also made no reference to any measuring devices. The fallacy you are committing is called the "strawman fallacy". You are having trouble attacking Einstein's actual position, so you add things that he didn't put in there and attack those additions. It is rather transparent.

I agree that two situations, one where a given measuring device is at rest wrt a given object and one where the same measuring device is in motion wrt the same object are not related by a boost. I agree, but point out that it is completely irrelevant to the scenario under consideration. Please try to make a non-fallacious argument.

Furthermore, when talking about reference frames or observers in terms of a system of physical clocks and rods, each reference frame has its own set of clocks and rods. So a Lorentz transform does not change the relative velocity of any clock or rod to any other object, it simply changes which set of clocks and rods is considered stationary. That is a boost.

The mathematical FACTS are thus: Both a Galilean transform and a Lorentz transform are boosts (i.e. single parameter linear transforms mapping lines of constant position to lines of constant velocity). Maxwell's equations are not invariant under a Galilean boost, which is an asymmetry. Maxwell's equation are invariant under a Lorentz boost, which is a symmetry.

If you don't like Einstein's presentation, that is fine; you don't even need a logical reason to dislike it, which is good since you don't seem to have one. However, your dislike of the presentation doesn't alter the math of SR one bit, nor does it reflect on its validity at all.

 

[ghwellsjr]

Taylor has the first chapter of the older 1965 editio of "Spacetime Physics" available for dowload at his website:

http://www.eftaylor.com/special.html

Probably not enough to get the complete story, but enough to see if you like the book.

Potential buyers of Spacetime Physics should be aware that there is a huge difference between the first and second editions. They are really different books. So if you look at the first chapter of the first edition in the link above and you don't like it, that doesn't mean you won't like the second edition. Conversely, if you do like it, and you decide to save some money by buying a used copy of the first edition, you should not think you are merely buying an older version of the second edition. When most people are recommending Taylor and Wheeler, they are referring only to the second edition. Your best bet is to find a library that has both or at least the second edition if you want to evaluate it before you buy it. But whatever you do, if you see just a copy of the second edition and like it, don't buy the first edition or you'll be sadly disappointed.

 

[Sugdub]

The paragraph in question also made no reference to any measuring devices.

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?
Sugdub: "… in the "kinematics" part of his 1905 SR paper Einstein clearly referred to a change of directly observable physical quantities, namely space and time quantities."
Einstein's SR paper: I-Kinematical part; §1 Definition of simultaneity... "If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B."
I-Kinematical part; §2 On the relativity of times and Lengths … "By means of stationary clocks set up in the stationary system and synchronizing in accordance with §1 the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated “the length of the rod." … "We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks."
I-Kinematical part; §3 Theory of Transformation of Co-ordinates …. "We now imagine space to be measured from the stationary system K by means of the stationary measuring-rod, and also from the moving system k by means of the measuring-rod moving with it; ... Further, let the time t of the stationary system be determined for all points thereof at which there are clocks by means of light signals in the manner indicated in §1 …."

Obviously Einstein refers to "observers" and measuring devices ("rods" and "clocks") in the Kinematical part of his paper and he compares two different experimental scenarios leading to different values of observable quantities. The root cause of this argument is that you were so far unable to read / admit that the "Kinematical" part refers to observable quantities whereas the "Electrodynamical" part exclusively refers to non-observable quantities. The same transformation cannot fit to both paradigms since Electrodynamics must deal with a change of reference frame whereas Kinematics cannot do so.
Hence my question: what is the rationale for invoking SR and its Lorentz transformation for resolving the EM problem at stake?
II-Electrodynamical part; §6 Transformation of the Maxwell-Hertz Equations for Empty Space..."If we apply to these equations the transformation developed in §3, by referring the electromagnetic processes to the system of co-ordinates there introduced, moving with the velocity v, we obtain the equations..."
Capito?

 

[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.