Abraham's light momentum breaks special relativity?

[Dale]

Why the fiber-recoiling experiment [Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; ] cannot be explained by the Minkowski’s formulation since the Minkowski's and Abraham's formulations have equal rights?

Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.

In fact, to me it seems obvious that the fiber will be pushed regardless of the formulation. We know the momentum of the light as it exits, so by conservation of momentum we know the total momentum in the fiber is a net push. How you partition that into light and matter momentum is arbitrary.

 

[sciencewatch]

Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done.

The arguments you provide:
(1) Total momentum = light momentum + matter momentum;
(2) The total momentum is the same (unique), no matter whether the light momentum is described by Abraham’s or Minkowski’s formulation (or even how to partition the total momentum into light momentum and matter momentum is arbitrary);
(3) The result of measurements or fiber recoiling only depends on the total momentum.
require the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. I hate to but I have to say that, your arguments have some basic logical problem.

 

[sciencewatch]

Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.

I don't know what this sentense exactly mean. But to my best knowledge, any reported light-momentum-in-medium experiments cannot be explained by both Abraham’s and Minkowski’s formulations at the same time.

 

[Dale]

However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign.

No, it didn't. I already rebutted the assertion in this story in post 61.

 

[Dale]

But to my best knowledge, any reported light-momentum-in-medium experiments cannot be explained by both Abraham’s and Minkowski’s formulations at the same time.

Then please re-read the review article I posted at the beginning of this discussion in post 3, you clearly did not understand it.

 

[sciencewatch]

Then please re-read the review article I posted at the beginning of this discussion in post 3, you clearly did not understand it.

Following your suggestion, I have re-read the review article [Rev. Mod. Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 ]. The main conclusions in the article are copied below:

1(In I. INTRODUCTION). We therefore hope this paper will increase awareness that the controversy has been resolved, and that predictions regarding measurable behaviors will always be independent of the electromagnetic energy-momentum tensor chosen, provided the accompanying material tensor is also taken into account.

2(In XI. CONCLUSION). The original Abraham-Minkowski controversy, over the preferred form of the electromagnetic energy-momentum tensor in a dielectric medium, has been resolved by the recognition that division of the total energy-momentum tensor into electromagnetic and material components is arbitrary. Hence the Minkowski electromagnetic energy-momentum tensor, like the Abraham tensor, has a material counterpart, and the sum of these components yields the same total energy-momentum tensor as in the Abraham approach.

3(In XI. CONCLUSION). On these grounds, all choices for the electromagnetic energy-momentum tensor are equally valid and will produce the same predicted physical results, as has been demonstrated for a wide range of specific examples...

4(In XI. CONCLUSION)… We have discussed the realization that any electromagnetic energy-momentum tensor must always be accompanied by a counterpart material energy-momentum tensor, and that the division of the total energy-momentum tensor into these two components is entirely arbitrary.
-------
I think, the arguments you provide:
(1) Total momentum = light momentum + matter momentum;
(2) The total momentum is the same (unique), no matter whether the light momentum is described by Abraham’s or Minkowski’s formulation (or even how to partition the total momentum into light momentum and matter momentum is arbitrary);
(3) The result of measurements or fiber recoiling only depends on the total momentum.

have well outlined the conclusions given in the review article.

Your arguments require both the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. Therefore, your arguments have a serious logical problem.

You suggest me to re-read the review article, because I “clearly did not understand it”. I guess, you mean I did not understand the following article’s statement:

“On these grounds, all choices for the electromagnetic energy-momentum tensor are equally valid and will produce the same predicted physical results, as has been demonstrated for a wide range of specific examples...”

Indeed, I did not understand what this statement exactly means. In my understanding, Abraham’s and Minkowki’s formulations are apparently not compatible, except for in free space, and the same experimental observation cannot be explained by both two formulations. If you know some experiment do can be explained by the both formulations at the same time, please kindly give specific information.

As I have indicated, your arguments have two problems:

(1) The Abraham’s momentum is not compatible with the principle of relativity;
(2) The property of equal rights assigned by your arguments is apparently broken by experimental facts [ http://physics.aps.org/story/v22/st20, Phys. Rev. Lett. 101, 243601 (2008) for example], and such arguments are not self-consistent logically.

In view of above, I would say that, it is premature to conclude “the controversy has been resolved”.

 

[rpfeifer]

Hello. I'm going to reply to this thread in a few parts. First of all, I will address the original question (Is p_A=hbar*w/n*c consistent with special relativity?), then I'll comment on the fibre experiment of She, Yu, and Feng, respond to a few other points raised in this thread, and finally I'll reply to post #66, which is about the review paper Rev. Mod. Phys.79:1197-1216 (2007), henceforth RMP79.

To begin with the original question (I will use units in which hbar=c=1, for convenience):
If k is the momentum in vacuum and p is the momentum in a medium, people often call
p=nk
the Minkowski formulation, and
p=k/n
the Abraham formulation. This is a gross oversimplification. To understand the flow of energy and momentum in a material, you cannot work with p alone. You need to use the energy-momentum tensor, made up of p (momentum), u (energy density), sigma (stress tensor) and S (Poynting vector). When dealing with electromagnetism, it is customary to further divide each of these into p_EM and p_matter, u_EM and u_matter, etc.

When you put these together in the correct way (as described in RMP79 Eq. (7)), and add together the EM and matter components, you get the total energy momentum tensor, T. Unless you're working on black holes or something, where general relativity will be required, then conservation of energy and conservation of momentum ABSOLUTELY REQUIRE that T is consistent with special relativity. However, they say nothing about individual quantities such as p_EM.

You can also put together a 4-vector (u_EM+u_matter, p_EM+p_matter)^T which also behaves correctly under special relativity. However, what about the p in p=k/n and p=nk?

You have probably figured out by now that these are just p_EM. You can make any change you like to p_EM and still be consistent with special relativity, so long as p_EM+p_matter remains the same.

Historically, a lot of people did what the original poster did, and asked questions like
"Is p_EM(Abraham)=k/n consistent with special relativity?" (Answer: NO)
"Is p_EM(Minkowski)=nk consistent with conservation of angular momentum?" (Answer: NO)
"Can p_EM(Abraham) explain this experiment?" (Answer: Yes for some, no for others)
"Can p_EM(Minkowski) explain this experiment?" (Answer: Yes for some, no for others)

The sensible question to ask is:
"Can T explain this experiment?"
Once you specify the properties of your materials, there is only one choice for T. I would like to say that again: There is only one choice for T. There is no T(Minkowski) or T(Abraham). It is uniquely fixed by conservation laws, and by special relativity.
Fortunately, the answer to the sensible question is: YES.

Hopefully things make more sense to you now.

By the way, if you're wondering where the Abraham and Minkowski formulations come into it, if T is fixed, well:
We can write down something we'll call T(EM, Minkowski) (for example). It looks like
( u_EM(Minkowski) S_EM(Minkowski) )
( p_EM(Minkowski) -σ_EM(Minkowski) )
but then T is given by T(EM,Minkowski)+T(matter,Minkowski):
( u_EM(Minkowski) S_EM(Minkowski) ) + ( u_matter(Minkowski) S_matter(Minkowski) )
( p_EM(Minkowski) -σ_EM(Minkowski) ) ( p_matter(Minkowski) -σ_matter(Minkowski) ).
Given that T is fixed, you can work out what the matter terms are. You can do exactly the same for T(EM,Abraham). Same T (it has to be, according to conservation of energy, conservation of momentum, and special relativity), and that means same behaviour.

Incidentally, you might be wondering if we can measure, say, p_EM directly and tell if it is the Abraham or Minkowski version. The short answer is: No, the mathematics of the energy-momentum tensor tells us this is impossible. Any experiment will only measure the total p, p_EM+p_matter, which is the same for Abraham and Minkowski (it has to be, as it is a part of T).

 

[rpfeifer]

Next, I will quickly comment on how this applies to the experiment of She, Yu, and Feng (Phys. Rev. Lett. 101, 243601 (2008)).

Although these authors do not publish their calculation, I suspect it went something like this:
For Minkowski, p=nk. A photon leaving a medium loses momentum, and the medium gains it, so the medium moves in the same direction as the photon.
For Abraham, p=k/n. A photon leaving a medium gains momentum, and the medium loses it, so the medium recoils.
She, Yu, and Feng observed a recoil, and concluded this meant the Abraham momentum was correct.

Let me show you why this is a problem: Read about the experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), summarised in Sec. IV.B of RMP79). As before, we say:
For Minkowski, p=nk. A photon leaving a medium loses momentum, and the medium gains it, so the medium moves in the same direction as the photon.
For Abraham, p=k/n. A photon leaving a medium gains momentum, and the medium loses it, so the medium recoils.
Ashkin and Dziedzic observed the medium moving in the same direction as the photons. Surely that means the Minkowski momentum is correct? We have reached a contradiction!

(In other words, this approach is internally inconsistent :) )

This isn't really surprising - the behaviour of the system is really described by T, and if we insist on splitting this into EM and matter parts, that's 32 separate parameters! (16 if we don't split it.) The momenta we have been using, p=nk and/or p=k/n, are only three of these 32 parameters (specifically p_EM). We've been ignoring over 90% of the physics! No wonder our results were inconsistent.

Gordon analysed the situation studied by Ashkin and Dziedzic in more detail in Phys. Rev. A 8, 14 (1973), and showed that both the Abraham and Minkowski formulations give the same result. It's quite a complicated calculation (and he uses Gaussian units, not SI, which makes things more difficult to follow for the younger generation of physicists), but the main point is this: There is NO WAY to get the correct result just from p=nk and p=k/n. I suspect She, Yu, and Feng fell into the same trap (though, unless they provide their calculation, there is no way to know for sure). A full analysis of their experiment in the Minkowski formulation would be a good exercise for a postgraduate classical field theory class.

However, we don't need to do this to know that their conclusion is wrong. Why do I say that? Because physics depends only on T, and there is only one choice for T (for a given dielectric material). I'll put a bit more historical context on this in my next post, and also respond to #66.

 

[rpfeifer]

Before I respond to #66, here are a few brief responses to some of the other posts:

Note - In my posts, to keep things clear I will only use EM to mean "Electromagnetic", never "Energy-Momentum".

Answer to #7:
Yes: In relativistic electrodynamics, there are no equations which depend explicitly on p_EM or p_matter (only on p_total, in T). Therefore, p_EM can be whatever it likes, even if it is not relativistically covariant. T is what matters; p_EM is a fiction. Sometimes it is a convenient fiction, and sometimes it is one which leads us astray. I have tried to provide some guidelines on this in Phys. Rev. A 79, 023813 (2009) (arXiv:0902.2605v2).

Comment on #14:
"Light momentum is a measuable physical quantity; theoretically there should be a correct formula to calculate, in my opinion. If both Abraham's and Minkowski's formulas are correct, then n=1 must hold."
No - momentum transfer is a measurable physical quantity. However, you have no way of ensuring that only the light transfers momentum (except by doing your experiment in vacuum, without any dielectric materials present, in which case it is indeed true that n must be exactly 1).

Answer to #30:
"For the photon, mass-energy equivalence: mass=energy/c**2=hbar*w/c**2 really has nothing open to question?"
In a medium, you have both photons and excitons (corresponding to the EM and material portions of the energy-momentum tensor).

Comment relating to #48:
In an explicitly SR formulation of EM, p_EM does not appear (except in the combination p_EM+p_matter). Thus p_EM can tell us nothing about the validity or otherwise of SR. Thus, 'Abraham’s momentum “is no contraindication to SR”'.

Comment on #57:
Some clarification is required here. You can measure "p_total while some light is passing through". This is not the same as measuring p_EM. DaleSpam may have meant the former, but many readers may have mistaken this for the latter.

 

[rpfeifer]

Response to #66:

As one of the authors of Rev. Mod. Phys.79:1197-1216 (2007), henceforth RMP79, I would like to point out that there are three very good examples of experiments which can be explained by both formulations at the same time, and which are reviewed in this very paper.
1) The experiment of Jones and Richards (later improved on by Jones and Leslie) in Proc. R. Soc. London, Ser. A 221, 480 (1954), Proc. R. Soc. London, Ser. A 360, 347 (1978), and Sec. IV.A of RMP79. In this experiment a photon reflects off a pivoting mirror suspended in a dielectric fluid. On first inspection the experiment appears to support the Minkowski formulation, but (as pointed out by Jones and Richards in the above citation, and again by Jones in Proc. R. Soc. London, Ser. A 360, 365 (1978), it is equally well explained by the Abraham formulation with appropriate accompanying material momentum tensor. This is also explained in Sec. VIII.C.1 of RMP79.
2) The experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), and Sec. IV.B of RMP79) in which a laser beam exiting a fluid causes the surface of this fluid to bulge outwards. A detailed treatment is provided by Gordon in Phys. Rev. A 8, 14 (1973) (note - he uses Gaussian units, which may cause confusion in readers accustomed to SI units).
3) The experiment of Walker, Lahoz, and Walker Can. J. Phys. 53, 2577 (1975), also Sec. IV.C of RMP79, in which angular momentum is transferred to a rotary pendulum. This experiment initially appears to support the Abraham formulation, but is also correctly described by the Minkowski formulation when the appropriate material momentum tensor is included.

In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by
(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.
This leads to two important conclusions:
(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).
(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.

In your post you stated "such arguments are not self-consistent logically", but there is nothing in your post which supports this statement (you have not presented any internal contradictions in the formulation presented in RMP79). Perhaps you meant "If Phys. Rev. Lett. 101, 243601 (2008) can only be explained by the Abraham momentum, then RMP79 is incorrect"? If so, then please carefully consider points (i), (ii), (a), and (b) above, and also post #67, as these demonstrate why _any_ experiment can be explained in terms of either the Abraham or the Minkowski formulation. If you meant something else, perhaps you can clarify?

I would just like to point out that all the examples I have provided were in RMP79, which you claim to have read. May I suggest that instead of reading superficially through the text, you work through the paper instead, making sure you understand the origin of each equation? You will probably need at the very least:
(i) A copy of Jackson's Classical Electrodynamics (1999)
(ii) Access to journals through a good university library, national library, or equivalent.
If you do this, I can more or less guarantee that all your questions will be answered.

Regards,
Robert Pfeifer
(Many thanks to DaleSpam for doing a great job, and already answering most of these questions elsewhere in the thread - it's great to see that my review paper has been read and appreciated! Hopefully by putting everything in one place like this, we can bring this thread to a close. Sciencewatch, I hope this answers your questions.)

 

[rpfeifer]

SR has only been around for a hundred years, geometry and algebra was tried and tested for thousands...

Oh, and finally, a comment for John232:
SR is geometry. That's all it is (and it's very nice, too). Specifically, it is the geometry of Lie Group SO(3,1) (X) R⁴, also known as the Poincare' group. That's why you won't be able to use SR to falsify SR: It's a self-contained, self-consistent mathematical structure. There's always the possibility that SR is only an _approximate_ description of the universe in the absence of significant gravitational effects, but the experimental constraints on this are very strong (and getting stronger - there are research groups which make careers out of testing this).

If you want to learn more about that, you'll need a good background in multidimensional calculus (grad, div, curl, Stokes' theorem, stuff like that) and tensor calculus/notation, and then I'd recommend courses in Riemannian geometry and Differential geometry, or spending a few months working through a book like Frankel's "The Geometry of Physics" (a very nice book, but watch out for the errata!).

 

[sciencewatch]

Response to #66:
...
In fact, the main thrust of Sec. VIII of RMP79 is that once the material properties of the dielectric are specified, the total momentum tensor is uniquely determined by
(i) consistency with special relativity, and
(ii) conservation of linear and angular momentum.
This leads to two important conclusions:
(a) No valid combination of EM and material energy-momentum tensors can break special relativity. If you are using a combination of tensors which appears to break this, then your choice of tensors is incorrect (usually, the material tensor is incorrect or missing). Note that I have never yet seen a fully relativistic formulation of the material counterpart tensors written down anywhere in the literature - even those given in RMP79 are valid only for media moving at v<<c, though the full expressions could be obtained from Eqs. (33)-(34).
(b) As the _total_ energy-momentum tensor is uniquely fixed by (i) and (ii) above, any division into components necessarily yields the same total tensor, and thus the same physical behaviours. That is, Abraham and Minkowski correspond to the same T, and thus the same physics.
...

Why is the Abraham’s momentum not compatible with the relativity for plane waves in a medium?

To support the compatibility of Abraham’s momentum with the relativity, your strong argument is that the total tensor is Lorentz covariant. However, this is not enough.

The total tensor is constructed from electromagnetic (EM) field–strength tensors in a covariant form. The Lorentz covariance of EM field–strength tensors is a sufficient condition to keep Maxwell equations invariant in form, but it is not a sufficient condition to keep the covariance of momentum-energy 4-vector. For plane waves in a uniform medium, the wave vector and frequency constitute a Lorentz covariant 4-vector [Phys. Lett. A 375, 1703 (2011), Eq. (A7); http://arxiv.org/abs/1103.1654 ], and according to the special relativity, the photon momentum and energy must constitute a covariant 4-vector. However, the Abraham’s momentum and the photon energy cannot constitute a covariant 4-vector. That is why I say the “Abraham’s light momentum breaks the special relativity”.

 

[sciencewatch]

Response to #66:

... there are three very good examples of experiments which can be explained by both formulations at the same time, and which are reviewed in this very paper.

1) The experiment of Jones and Richards (later improved on by Jones and Leslie) in Proc. R. Soc. London, Ser. A 221, 480 (1954), Proc. R. Soc. London, Ser. A 360, 347 (1978), and Sec. IV.A of RMP79. In this experiment a photon reflects off a pivoting mirror suspended in a dielectric fluid. On first inspection the experiment appears to support the Minkowski formulation, but (as pointed out by Jones and Richards in the above citation, and again by Jones in Proc. R. Soc. London, Ser. A 360, 365 (1978), it is equally well explained by the Abraham formulation with appropriate accompanying material momentum tensor. This is also explained in Sec. VIII.C.1 of RMP79.

2) The experiment of Ashkin and Dziedzic (Phys. Rev. Lett. 30, 139 (1973), and Sec. IV.B of RMP79) in which a laser beam exiting a fluid causes the surface of this fluid to bulge outwards. A detailed treatment is provided by Gordon in Phys. Rev. A 8, 14 (1973) (note - he uses Gaussian units, which may cause confusion in readers accustomed to SI units).

3) The experiment of Walker, Lahoz, and Walker Can. J. Phys. 53, 2577 (1975), also Sec. IV.C of RMP79, in which angular momentum is transferred to a rotary pendulum. This experiment initially appears to support the Abraham formulation, but is also correctly described by the Minkowski formulation when the appropriate material momentum tensor is included.
...

Please support the property of equal rights assigned by your arguments.

The interpretations for these experiments you enumerated are not easy to understand; even the authors themselves, who did the experiments, cannot easily understand them, with minds often changed. How to convince ordinary readers?

The fiber-recoiling experiment [Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; ] is widely recognized as a very clear visual experiment. The authors of the experiment insist that it should support the Abraham’s formulation. In my understanding, the Abraham’s and Minkowski’s formulations are not compatible, and this experiment cannot be explained by the Minkowski’s. According to your arguments, however, this experiment also can be explained by Minkowski’s formulation. So, please give your explanation to support the property of equal rights assigned by your arguments.

 

[Dale]

Your arguments require both the Abraham’s and the Minkowski’s formulations to have equal rights, which means that, a specific experiment, which can be explained by Abraham’s formulation, also can be explained by Minkowski’s formulation. However, all reported experimental observations (http://physics.aps.org/story/v22/st20, for example) have already broken the property of equal rights that your arguments assign. Therefore, your arguments have a serious logical problem.

I already answered this in posts 59 and 61. This experiment does not break the "equal rights" in any way, as I have already told you multiple times.

In order to break the "equal rights" you would have to demonstrate:
1) That the result is explained by Abraham's momentum
2) That the result is not explained by the total momentum

The authors did 1) but did not even attempt 2) including never calculating the total momentum tensor. Personally, I think it is patently obvious that 2) is false. This experiment does not break the "equal rights" argument, as I have already explained several times. Please come up with something new, this is getting repetitive.

the same experimental observation cannot be explained by both two formulations. If you know some experiment do can be explained by the both formulations at the same time, please kindly give specific information.

This is false. Specific examples are given in the review article showing how several different experiments can be explained by both.

 

[Dale]

(Many thanks to DaleSpam for doing a great job, and already answering most of these questions elsewhere in the thread - it's great to see that my review paper has been read and appreciated!)

Welcome to PF with a particularly good string of posts! I hope you will stick around for conversations on other topics as well.

 

[sciencewatch]

I already answered this in posts 59 and 61. This experiment does not break the "equal rights" in any way, as I have already told you multiple times.

In order to break the "equal rights" you would have to demonstrate:
1) That the result is explained by Abraham's momentum
2) That the result is not explained by the total momentum

The authors did 1) but did not even attempt 2) including never calculating the total momentum tensor. Personally, I think it is patently obvious that 2) is false. This experiment does not break the "equal rights" argument, as I have already explained several times. Please come up with something new, this is getting repetitive.

Your Post-59 answer is “fiber recoiling obviously depends on the total momentum, which is the same for Abraham and Minkowski.”

According to your answer, the fiber recoiling can be explained by both Abraham’s and Minkowski’s formulations at the same time. However, the authors of the experiment, She, Yu, and Feng clearly claim:

“From the experiments described above, we believe that the phenomenon observed is due to the force exerted by the outgoing light. The nature of SF movement cannot be explained by Minkowski momentum. Minkowski momentum predicts a pull force, which pulls the whole SF to one side for asymmetric refraction [see Fig. 2(j)] or pulls it straight for direct transmission.” “In conclusion, our experiment and analysis suggest that Abraham momentum is correct.” [See: Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; ]

Obviously, your arguments are not consistent with the above authors’ claim, and you did not give any explanations why the above authors’ claim is wrong. Accordingly, your conclusion “This experiment does not break the ‘equal rights’ in any way” is not well grounded.

--------
Your post-61 answer is “Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.” ----- Sorry, I don’t understand what you exactly mean.

 

[rpfeifer]

Response to #72:

The brief answer to your question "Why is the Abraham’s momentum not compatible with the relativity for plane waves in a medium?" is because there is absolutely no reason for it to be compatible on its own (without a material counterpart). This is explained in RMP79.

To expand at greater length:

"Abraham's momentum" has nothing to do with special relativity. Let me distinguish clearly between:
(i) The Abraham-style EM and material energy-momentum tensors
and
(ii) The Abraham momentum.
Using the Abraham momentum to perform a calculation is not the same as using the Abraham-style tensors.

Abraham's momentum (n/k) is not compatible with special relativity on its own, as you have pointed out. This says absolutely nothing about whether the Abraham-style EM and material tensor pair are compatible with special relativity.

I do not assert the compatibility of "Abraham's momentum" with SR, only the compatibility of the Abraham-style tensor pair. You need to appreciate this distinction, as your objections all arise from confusing these two.

Physics is written in terms of the Abraham-style tensor pair ((i), above) or the Minkowski-style tensor pair (the equations are the same - I know; I've written them out; you should too). Using the "Abraham (or Minkowski) momentum" ((i) above) in a calculation is never anything more than a shorthand (and it is frequently a faulty one, as demonstrated in post #68, above).

Once you understand this, you will see that arguing about the lack of Lorentz covariance of the Abraham momentum is pointless: Yes, it is not covariant. No, this does not indicate a problem with SR, or with the Abraham momentum. It is simply irrelevant.

 

[rpfeifer]

Response to #73:

Supporting the properties of equal rights:
(1) See Proc. R. Soc. London, Ser. A 221, 480 (1954) and Proc. R. Soc. London, Ser. A 360, 365 (1978) (both cited in RMP79).
(2) See Phys. Rev. A 8, 14 (1973), as cited in RMP79.
(3) See Israel, Phys. Lett. B 67, 125 (1977) and Obukov & Hehl in Phys. Lett. A 311, 277 (2003). Both are cited when discussing this experiment in RMP79. Off the top of my head I think the tensors in O&H might differ slightly to the ones given in RMP79, but as I recall, this does not affect the proof.

You will note that all of these papers were clearly cited in RMP79 as providing the demonstrations you were looking for. When asking questions about matters discussed in the review paper RMP79, please have the courtesy to first check RMP79 to see if your questions are already answered in there.

Of course, all three experiments also follow from the general demonstration given in RMP79 (which, in turn, is based on arguments presented in these, and other, papers). That's the point of giving a general demonstration. Once it's done, you don't need to bother proving every individual case any more. Unfortunately, you don't seem to have understood the general demonstration, and I'm not going to go through every experiment ever done, to explain how it works.

Regarding the fibre recoil experiment, you are asking me to repeat myself. Specifically:
(i) The method apparently used to show this experiment was incompatible with the Minkowski momentum is flawed, and leads to a logical contradiction (see post #68). Thus you have no reason to claim that the experiment is incompatible with the Minkowski momentum (unless you have performed a better calculation than the one described there, in which case please post your calculations so we can discuss them).
(ii) The universal demonstration of equivalence presented in RMP79 applies to this experiment.

In summary, you have no reason to state that the Minkowski momentum does not work in this experiment (the only argument I am aware of which leads to this conclusion is trivially shown to be flawed, as described in #68) and a very good reason to believe that it does work (the general demonstration of equivalence in RMP79, in which you have not yet successfully found a fault - your objections, including the question in #72, seem to be based on a misunderstanding, which I have addressed in #77).

Now we have cleared up that misunderstanding, you may find that the evidence leans towards equivalence of the two formulations. Also note that my post #77 above is a direct answer to your original question .

 

[rpfeifer]

Response to #76:
I have answered the physics questions in this post in my response to #73.

Regarding your comment "Sorry, I don’t understand what you exactly mean" in response to DaleSpam, may I suggest the following:
Re-read the sentence carefully. Work it out clause by clause if you have to. It makes sense. If you're reading too quickly to understand what this sentence means, you're probably reading too quickly to be thinking about our responses.

 

[rpfeifer]

In #73 you asked: "The interpretations for these experiments you enumerated are not easy to understand; even the authors themselves, who did the experiments, cannot easily understand them, with minds often changed. How to convince ordinary readers?"

This is a good question. Regrettably, sometimes the answer is:
Explain to that ordinary reader that if they want to understand, they need to take a course in tensor calculus, a postgraduate course in electromagnetism, learn about Gaussian units, read Jackson's book pretty much from cover to cover, and then read and work through all the calculations in my paper, also reading as many of the citations as they need to in order to achieve this.
If you want it easier than that, well, I'm afraid that's the easy way. (Easier than working it out using only papers published before 2007, I think! )

People often want an explanation in words. That's fine, but when you argue with the words, the answer is usually "The words are an incomplete description. Here is the maths." That seems to be what is happening here - but you keep on ignoring the maths and going back to the words.Oh, by the way, since you said "even the authors themselves, who did the experiments, cannot easily understand them", I'll just comment on that - my experience is that active theory experts in this field do now seem to agree on this matter (recent examples: S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010)). It used to be that the information was scattered. Now that it's all collected together, it no longer seems to be under debate among theorists - though there have been a few lovely papers coming out tying up loose ends. In time, hopefully, experimentalists such as She et al. (the fibre team) will become aware of this, and will stop making misleading statements suggesting that it is still Abraham vs. Minkowski rather than, as we now know, Abraham <3s ("hearts") Minkowski.

(footnote: The agreement of experts doesn't make something true - but you would be well advised to make sure you understand the consensus opinion before trying to prove it wrong!)

 

[rpfeifer]

Sciencewatch: In light of the above, time to put your money where your mouth is (metaphorically speaking).

Instead of just claiming that other peoples' work is wrong, please show us some proof. That is, please demonstrate (i.e. using formulae) a mathematical contradiction, or give a mathematical calculation predicting a behaviour which disagrees with experiment, arising as a consequence of these alleged errors.

Here are two of your claims I would like to see mathematical evidence for:

A)
You have asserted that the fibre experiment distinguishes between the Abraham and Minkowski momenta (the Abraham momentum explains it and the Minkowski one doesn't). I am not aware of any valid argument which shows this. Please demonstrate.

(Note: In #68 I presented an invalid argument, then shot it down. As far as I know, this is the only argument which produces that claim, and it is incorrect. If you can provide a better argument, I would welcome it.)

B)
You have also claimed that "Abraham momentum breaks SR", meaning the following:
(1) The Abraham EM momentum is not covariant.
(2) If the Abraham EM momentum is valid, then this means SR is wrong.
I agree with (1). I do not agree with (2).

In RMP79 I provide a framework which allows both the Abraham and Minkowski momenta to be valid at the same time, and which is consistent with SR. This is a constructive disproof of (2) (i.e. I not only show that (2) is wrong, I also explicitly demonstrate the opposite).

Your objections to RMP79 all indicate that you do not understand the mathematics involved (or possibly, the physics).

If you wish to disprove the framework given in RMP79, please do so by either (i) demonstrating a theory-destroying intrinsic mathematical flaw in RMP79, or (ii) demonstrating that RMP79 makes a prediction (i.e. a specific, calculated result) which disagrees with an experiment.

(Also see S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010), among others.)

C)
If you have a third option, please feel free to pursue that instead. I look forward to seeing your maths. Not just words.Why am I asking you to do this? Because this thread is starting to sound increasingly like
S: "You're wrong!"
D&R: "No we're not, and we have maths! Here it is."
S: "Yes you are!"
D&R: "No we're not, and we still have maths! Here it is again."
etc.

The balance is easily redressed: You just need to provide some maths in favour of your argument. (Note that proving the Abraham EM vector is not independently covariant doesn't count: I already agree with that. You would have to show that there cannot exist any material four-vector which makes the total vector covariant (a ridiculous claim), or you would have to show that the Abraham EM vector MUST be independently covariant. Note that SR does NOT require this, as explained in RMP79.)

 

[sciencewatch]

Sciencewatch: ...
Instead of just claiming that other peoples' work is wrong, please show us some proof. That is, please demonstrate (i.e. using formulae) a mathematical contradiction, or give a mathematical calculation predicting a behaviour which disagrees with experiment, arising as a consequence of these alleged errors.
...
In RMP79 I provide a framework which allows both the Abraham and Minkowski momenta to be valid at the same time, and which is consistent with SR. This is a constructive disproof of (2) (i.e. I not only show that (2) is wrong, I also explicitly demonstrate the opposite).

Your objections to RMP79 all indicate that you do not understand the mathematics involved (or possibly, the physics).

If you wish to disprove the framework given in RMP79, please do so by either (i) demonstrating a theory-destroying intrinsic mathematical flaw in RMP79, or (ii) demonstrating that RMP79 makes a prediction (i.e. a specific, calculated result) which disagrees with an experiment.

(Also see S. Barnett, Phys. Rev. Lett. 104, 070401(2010), and C. Baxter and R. Loudon, J. Modern Optics, 57, 830 (2010), among others.)
...

In fact, there is no need to do math calculations for identifying basic concepts.
Now let me check some of your arguments starting with the principle of relativity.

In your review paper, you repeatedly claim:

“… division of the total energy-momentum tensor into electromagnetic and material components is arbitrary.”
“… the division of the total energy-momentum tensor into these two components is entirely arbitrary.”
[See: Rev. Mod. Phys.79:1197-1216 (2007); http://arxiv.org/abs/0710.0461 ]

My questions are:

1. According to the principle of relativity, the propagation direction of light momentum (electromagnetic field momentum) should be parallel to the wave vector for a plane wave, observed in any inertial frames. In your division of the total energy-momentum tensor, is this principle of relativity taken into account?

2. Since the division is arbitrary, there must be a division that makes the electromagnetic field momentum perpendicular to the direction of the wave vector. Do you think it is physical for the electromagnetic field momentum of a plane wave to be perpendicular to the wave vector?
--------
Can I say your arbitrary division is “a mathematical contradiction” or “intrinsic mathematical flaw”, or at least something related?

 

[rpfeifer]

1. No. As you would see from the maths, according to the principle of relativity the propagation direction of total momentum should be parallel to the wave vector for a plane wave observed in any inertial frame. This only holds for the EM component on it own when in vacuum. Consequently:
"In your division of the total energy-momentum tensor, is this principle of relativity taken into account?"
Yes.

2. What I (or you) "think" based on gut feeling is irrelevant. The mathematics tells us that this is
(i) permissible
(ii) irrelevant
and
(iii) not in conflict with the principle of relativity.

You have just proven my point: You need to stop arguing with words and start arguing with maths. Better yet, you need to stop thinking with words and start thinking with maths. Then you will understand the situation. Until then, you will keep tying yourself in knots.

You conclude: 'Can I say your arbitrary division is “a mathematical contradiction” or “intrinsic mathematical flaw”, or at least something related?'
Answer: Clearly not.

Hint: To do so, you would need to start by writing some maths... (perhaps you do not understand the meaning of the phrases "a mathematical contradiction" and an "intrinsic mathematical flaw"? These are things which can only be shown using mathematics. Sometimes words can be used to indicate the presence of such a flaw, but these words always translate directly into mathematics. The words which you have been using do not translate into mathematics consistent with physics as we know it. That is why I have asked you to start expressing yourself in maths. If you do so, it will stop you from making careless mistakes like you did just now. Right now you're just showing that you do not understand the physics because you do not understand the maths. That is why your word-based intuitions keep leading you astray.

If you don't start producing some maths, you are wasting my time. I have explained why your word-based arguments are nonsense, but you don't accept that. Unless you start doing physics (hint: physics is done using maths), I see no point in engaging in further armchair philosophy.

(Note: I'm sure philosophers recognise the annoying nature of "armchair philosophers" as well - people who have just read Cliff's Notes on Wittgenstein and suddenly think they know everything about philosophy from Kant to Aristotle...)

 

[Dale]

According to your answer, the fiber recoiling can be explained by both Abraham’s and Minkowski’s formulations at the same time. However, the authors of the experiment, She, Yu, and Feng clearly claim:

“From the experiments described above, we believe that the phenomenon observed is due to the force exerted by the outgoing light. The nature of SF movement cannot be explained by Minkowski momentum. Minkowski momentum predicts a pull force, which pulls the whole SF to one side for asymmetric refraction [see Fig. 2(j)] or pulls it straight for direct transmission.” “In conclusion, our experiment and analysis suggest that Abraham momentum is correct.” [See: Phys. Rev. Lett. 101, 243601 (2008); http://physics.aps.org/story/v22/st20 ; ]

Obviously, your arguments are not consistent with the above authors’ claim, and you did not give any explanations why the above authors’ claim is wrong. Accordingly, your conclusion “This experiment does not break the ‘equal rights’ in any way” is not well grounded.

The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.

As I mentioned above, in order to disprove the Minkowski momentum they need to do more than just demonstrate Abraham's momentum, they need to demonstrate that their results are consistent with the Abraham's momentum and also that the result does not depend on the total momentum. As the review article shows, any phenomenon which depends on the total momentum can be explained by both. They did not examine that so they cannot make their claim.

Consider a system or free-body diagram consisting of the tip of the fiber. On one side there is a momentum flux of the EM wave in free space, on the other side there is a momentum flus of the EM wave in the fiber as well as the material momentum tensor. Those two terms together are the total momentum. In steady state, the conservation of momentum requires that momentum flux of the light be equal and opposite of the total momentum flux, and therefore the bending of the fiber depends on the total momentum.

Therefore, while this experiment does show that Abraham's momentum is correct, it does not show that Minkowski's momentum is incorrect. I think it is very obvious that this experiment depends on the total momentum.

Your post-61 answer is “Simply because the authors of the study did not perform such an analysis does not mean that it cannot be done. Again, an experimental confirmation of Abraham is not an experimental contradiction of Minkowski.” ----- Sorry, I don’t understand what you exactly mean.

I am sorry you don't understand. I have explained several times in the clearest manner I know how. Both Minkowski and Abraham can be true, they do not contradict each other. I hope that is clear enough.

 

[sciencewatch]

...
If you don't start producing some maths, you are wasting my time. I have explained why your word-based arguments are nonsense, but you don't accept that. Unless you start doing physics (hint: physics is done using maths), I see no point in engaging in further armchair philosophy.
...

Please tell me: What is the total momentum for a uniform plane wave in the medium-rest frame? According to the Eqs. (40)-(43) of your review article [Rev. Mod. Phys.79:1197-1216 (2007), http://arxiv.org/abs/0710.0461 ], the total momentum is ExH/c**2 (=Abraham’s momentum density vector) in such a case; am I right?

 

[rpfeifer]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)

 

[sciencewatch]

The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.

As I mentioned above, in order to disprove the Minkowski momentum they need to do more than just demonstrate Abraham's momentum, they need to demonstrate that their results are consistent with the Abraham's momentum and also that the result does not depend on the total momentum. As the review article shows, any phenomenon which depends on the total momentum can be explained by both. They did not examine that so they cannot make their claim.
...

I think, She, Yu, and Feng, the authors of the experiment [Phys. Rev. Lett. 101, 243601 (2008)] have the best position to answer your challenge: “The author's claim is unsubstantiated. In their entire article they never once calculated the total momentum tensor. Therefore, they make the claim without any correct justification.”

I am sorry Physical Review Letters published such unsubstantiated claim.

 

[sciencewatch]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.

In an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium, ρv=0, right? Then the total momentum is ExH/c**2=Abraham's momentum density vector. Right?

 

[rpfeifer]

Such a medium necessarily has a refractive index of 1.

 

[sciencewatch]

No. It is ExH/c**2 + ρv.
You cannot ignore the material medium. It is carrying some of the momentum flux.
(Actually, this is a momentum density. You have to integrate this over the whole of the (infinite) plane wave to get the momentum.)

ρ is what in Maxwell equations?