Abraham's light momentum breaks special relativity?

[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?

 

[sciencewatch]

Such a medium necessarily has a refractive index of 1.

How come?
The model with an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium but refrative index > 1 is widely used in physics literature.

 

[rpfeifer]

Under some circumstances it may be possible to approximate a medium as having all physical properties identical to the vacuum except for refractive index (and, by implication, the speed of light in the medium). This is not one of those circumstances.

You have to ask how the medium can have a refractive index other than 1, and this necessarily implies other properties which are relevant to the problem at hand (e.g. construction from EM dipoles, which will break homogeneity and which couple to the electromagnetic fields).

It is often possible to say a lot about a material just from these sorts of self-consistency conditions (a good example is the Kramers-Kronig relationship for dispersion in optics, which relates the absorption of a medium to how the real component of refractive index varies as a function of wavelength.)ρ is not from Maxwell's equations - it is the density of the material medium, and v is its velocity. These become highly relevant when you involve the dipole structure of the medium. Their origin is from the continuity equations imposing conservation of mass/energy and momentum.

 

[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.)

The model with an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium but refrative index > 1 is widely used in physics literature. For example,

Tomás Ramos, Guillermo F. Rubilar, Yuri N. Obukhov, Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654 ;

STEPHEN M. BARNETT, AND RODNEY LOUDON, "The enigma of optical momentum in a medium," Phil. Trans. R. Soc. A (2010) 368, 927–939;

M. Mansuripur, Phys. Rev. E 79, 026608 (2009).



Are they all doing wrong things?

 

[sciencewatch]

Under some circumstances it may be possible to approximate a medium as having all physical properties identical to the vacuum except for refractive index (and, by implication, the speed of light in the medium). This is not one of those circumstances.

You have to ask how the medium can have a refractive index other than 1, and this necessarily implies other properties which are relevant to the problem at hand (e.g. construction from EM dipoles, which will break homogeneity and which couple to the electromagnetic fields).

It is often possible to say a lot about a material just from these sorts of self-consistency conditions (a good example is the Kramers-Kronig relationship for dispersion in optics, which relates the absorption of a medium to how the real component of refractive index varies as a function of wavelength.)


ρ is not from Maxwell's equations - it is the density of the material medium, and v is its velocity. These become highly relevant when you involve the dipole structure of the medium. Their origin is from the continuity equations imposing conservation of mass/energy and momentum.

In the total momentum ExH/c**2 + ρv, with ρ the density of the material medium, v the medium local velocity. I can suppose the medium is in the "frozen" state so that ρv=0. Theoretically such a medium is existent and such a model is widely used in the literature, including your colleagues. Obviously, this total mometum is breaking the principle of relativity. To defend your arguments, you have to deny this widely-used physical model.

 

[vgv]

Dear collegues!

I hope following referencies will be interesting for you.

Sincerely

V.G.Veselago

Veselago V G “Energy, linear momentum, and mass transfer by an electromagnetic wave in a negative-refraction medium” Phys. Usp. 52 649–654 (2009)
http://ufn.ru/en/articles/2009/6/i/


Veselago V G, Shchavlev V V "On the relativistic invariance of the Minkowski and Abraham energy-momentum tensors" Phys. Usp. 53 317–318 (2010)
http://ufn.ru/en/articles/2010/3/j/

 

[rpfeifer]

"Are they all doing wrong things?"

No. All of these are good papers. When they talk about an "isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium" they mean one made up of dipoles. When light enters such a medium, the medium inevitably acquires momentum (ρv$\not =$0).

You specified that ρv=0, which I took to imply that your medium was "homogeneous" to the extent that it was not made up of dipoles, and hence did not couple to the light. In retrospect, you probably just made a mistake.

(Think about this: If ρv=0, the material has no momentum. Conservation of momentum then says that the EM wave still has the same momentum as in vacuum. As the total momentum tensor now only reads ExH, momentum conservation tells us that n=1.)

Also please consider that you are being very rude. All your responses are in the form of attacks. Physics is not a personal battle about whose theory is correct - it is about trying to understand how nature works. If something I say doesn't make sense to you, ask me to explain. Better yet, try to work it out for yourself. All your responses have been of the form "YOU ARE WRONG BECAUSE", rather than "Please explain this". If I have made a mistake, it will be obvious when I can't explain something, or when I arrive at a contradiction. Also, I will gladly admit it (because if we found something wrong, that would be interesting and I could probably write a new paper about it). (Note: This has not happened yet during our conversation.)

Example: You could have said "I do not understand why you say this means n=1, when this model is used in papers such as <xxx> with n>1. Please can you explain?"
You said "To defend your arguments, you have to deny this widely-used physical model."
No I don't, I just need to explain what the difference is between the model that you seemed to be talking about, and the model they are using. And please stop trying to turn this into a fight between me and the rest of the world. It isn't.

On that matter, please take a closer look at the first paper you cited: Tomás Ramos, Guillermo F. Rubilar, Yuri N. Obukhov, Phys. Lett. A 375, 1703 (2011); http://arxiv.org/abs/1103.1654
This is an excellent example of how to use the total energy-momentum tensor formalism I am talking about, to show equivalence of Abraham and Minkowski approaches for an Einstein Box.My advice to you is this: Go to university and learn how to solve your own problems. I have just about run out of patience with you. You don't seem to want to learn - you just seem to want a fight.

 

[rpfeifer]

Dear collegues!

I hope following referencies will be interesting for you.

Sincerely

V.G.Veselago

Dear Prof. Veselago,

Thank you for your relevant citations (the consideration of media with negative refractive indices is a particularly interesting subject).

I note that you consider only the electromagnetic portion of the Abraham tensor pair, neglecting the associated material momentum (which propagates along with the wave packet).

Thus, what you say is true and the Abraham EM momentum does not transform as a relativistically covariant object. However, this has no bearing on the usefulness of the Abraham tensor _pair_, as the total momentum p_EM+p_mat does transform as a relativistically covariant object.

Indeed, the main thrust of the current discussion is to try and explain this distinction to one of the posters here, which is why I felt it necessary to post to clarify this point.

Best wishes,
Robert Pfeifer

 

[sciencewatch]

...
You specified that ρv=0, which I took to imply that your medium was "homogeneous" to the extent that it was not made up of dipoles, and hence did not couple to the light. In retrospect, you probably just made a mistake.

(Think about this: If ρv=0, the material has no momentum. Conservation of momentum then says that the EM wave still has the same momentum as in vacuum. As the total momentum tensor now only reads ExH, momentum conservation tells us that n=1.)
...

Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Please kindly indicate: Where is there a problem with this model?

In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there is a mistake in your reasoning:

Because of energy-conservation law, the EM energy density with a medium is the same as that without a medium (vacuum). Thus the ExH/c**2 in a medium must be different from the ExH/c**2 in vacuum:

|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)

Why n =1 must hold?

 

[sciencewatch]

...
Also please consider that you are being very rude. All your responses are in the form of attacks. ..

Example: You could have said "I do not understand why you say this means n=1, when this model is used in papers such as <xxx> with n>1. Please can you explain?"
You said "To defend your arguments, you have to deny this widely-used physical model."
No I don't, I just need to explain what the difference is between the model that you seemed to be talking about, and the model they are using. And please stop trying to turn this into a fight between me and the rest of the world. It isn't.
...

Probably you misunderstood something. I just got surprised that you refuse to accept a widely-used physical model. But I think, my words "To defend your arguments, you have to deny this widely-used physical model." is a real thing you have to do; otherwise the total momentum is not Lorentz covariant. I apologize to you if my words make you uncomfortable.
----------
In pots #85, I asked you:

“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?”

You answered:

“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.)”
“Such a medium necessarily has a refractive index of 1.”

You said a lot for why ρv not =0 for my observed "in the medium-rest frame”. I had thought you intentionally misled me. Sorry.

 

[rpfeifer]

#98:
Good start, much more polite, but then: "there is a mistake in your reasoning" - You're back to trying to turn this into a fight again. Oh well, it was nice while it lasted.

"|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)"

Think about this. You just said the density goes down by a factor of n. At the same time, the wave packet slows down by a factor of n, so the total momentum of the wave packet as described by ExH/c**2 goes down by a factor of n^2. Conservation of momentum says this has to go somewhere. That is, the material is placed in motion with total momentum
∫ |ExH/c**2 in vacuum| x (1-1/n**2) dV
unless the refractive index is equal to 1.
As you can see, you were mistaken in saying I had made a mistake.

You might want to bear in mind that I already spent a long time thinking about these problems when I wrote the review paper - it wasn't just a matter of scrawling down the first thing that came into my head. This is why I keep suggesting: Instead of saying I've made a mistake, ask me to explain to you. As well as being more polite, you'll look a lot less sloppy and/or possibly foolish.

#99:
"I apologize to you if my words make you uncomfortable."
You don't "make me uncomfortable". You just insult me. Important difference.
Now it seems to me that you are using a false apology to imply that
(i) your arguments are effective, and
(ii) I am taking them personally, and hence am worried.
Neither of these is true, but I am taking your insulting manner personally (of which this is another example) and I would appreciate an apology for that. Actually, never mind, I'm getting a bit arrogant here myself. Just try not to be so confrontational in future, OK?

"in the medium rest frame"
The rest frame before or after a light pulse enters the dielectric?
Typically, this refers to the rest frame before the light enters the dielectric. In this frame the dielectric is then placed in motion.

 

[rpfeifer]

I'll just expand on my last comment a bit.

"I may have misunderstood you there: You may have wanted to discuss a system where the dielectric is initially in motion, then stops when the light pulse enters it."
Total momentum is also conserved in this instance, as the momentum transferred from the light to the block is sufficient to stop its initial motion. Again, however, you cannot consider the Abraham EM density in isolation, as you have to also consider how the momentum which is transferred to the block propagates. The Maxwell stress tensor tells us that it is not instantaneously spread over the entire block: It has to propagate as some sort of matter wave. Thus, in that frame the momentum of the block behaves like this:

Before the pulse enters it:
Total momentum: Nonzero. Locally: Uniformly ρv$\not=$0.

Once the pulse has entered it:
Total momentum: Zero. Locally: Takes the form of a matter wave, i.e. <ρv(x)>=0 but ρv(x)$\not=$0 for most x.
Here, v(x) represents the velocity of the medium at point x (where x is a point within the medium).
Note that for a bounded wave packet propagation of the associated matter wave is made more complicated as you must take into account ongoing interactions as the edges of the packet propagate through the material. Yet another explanation as to why you cannot consider the EM and material portions of the momentum density separately, and thus why it doesn't matter that the Abraham EM density (in isolation) doesn't transform covariantly: You never encounter it in isolation.

By the way, do you feel that we have answered your original question yet? I ask because we do now seem to be talking about something only tangentially related (i.e. whether the framework in RMP79 is consistent, rather than whether the Abraham EM expression is inconsistent with SR).

 

[sciencewatch]

#98:
...
"|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index)"

Think about this. You just said the density goes down by a factor of n. At the same time, the wave packet slows down by a factor of n, so the total momentum of the wave packet as described by ExH/c**2 goes down by a factor of n^2. Conservation of momentum says this has to go somewhere. That is, the material is placed in motion with total momentum
∫ |ExH/c**2 in vacuum| x (1-1/n**2) dV
unless the refractive index is equal to 1.
As you can see, you were mistaken in saying I had made a mistake.
...

Please pay attention to the model: Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving.

In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there are two mistakes now in your reasoning:

(1) The field momentum should be DxB (instead of ExH/c**2) in a medium,
(2) Under the energy conservation, the EM energy density with a medium is the same as that without a medium (vacuum). Thus the ExH/c**2 in a medium is different from the ExH/c**2 in vacuum:

|ExH/c**2 in a medium| / |ExH/c**2 in vacuum| =1/n (refractive index) ----- (1)
---
Momentum flus conservation:

With a medium, momentum flux = DxB*(c/n)=n**2 *(ExH)/c**2 *(c/n) = n *(ExH)/c ----(2)
Without a medium (vacuum), momentum flux = ExH/c**2 * c = ExH/c -----(3)

Using Eq. (1), we find Eq. (2) = Eq. (3), the momentum-flux conservation.
----------------------
Why n =1 must hold?

 

[Dale]

Observed in the medium-rest frame, the dielectric is not moving.

The medium rest frame is non-inertial.

 

[rpfeifer]

"Please pay attention to the model: Suppose that there is a plane wave propagating in an isotropic, homogeneous, non-conducting, no-loss, non-dispersive, ideal medium. Observed in the medium-rest frame, the medium material momentum should be zero and the refractive index can be assumed to be >1. Observed in the medium-rest frame, the dielectric is not moving."

OK, how did this EM wave get into this dielectric? When it entered, it set up a wave in the dielectric, which is still there. That is, <ρv(x)>=0 but ρv(x)$\not=$0. And this dipole matter wave couples to the EM field.

If you do not allow for the entry of the wave into the medium at some point in the past, then the situation you describe is unphysical (e.g. infinite dielectric). This even applies to a plane wave (for which it is necessary to assume that the beam is "turned on" gradually at t=-∞, but I will not attempt to explain details of boundary conditions at infinity to you here. If interested, look it up).

"In your arguments, in such case you think the field momentum = ExH/c**2, the same as in vacuum because the material momentum is zero, resulting in refractive index n=1. However, there are two mistakes now in your reasoning:"

*rolls eyes* Here we go again.

(1) You assert the Minkowski momentum. However, for conservation of angular momentum the total momentum multiplied by c must equal the Poynting vector plus the material energy flux, i.e.
c x (p_EM+p_mat) = ExH/c+ρcv.
Note that neither the Poynting vector nor the material energy flux have ever been under debate in the controversy. These are the S terms in $T^{\mu\nu}$.

If we use the Minkowski momentum, then we have to have a "material" momentum of
ρv+ExH/c^2-DxB.
Do you like having a material momentum density which contains E, H, D, and B? Does this make sense to you? Sure, it might not contribute to momentum transfer, but it doesn't describe the movement of matter any more.

(2) "Under the energy conservation, the EM energy density with a medium is the same as that without a medium (vacuum)."

Don't be ridiculous. The wave packet is packed into a smaller volume, so the energy density goes up. Exactly the same as happened with momentum. If you're thinking about a plane wave, which is infinite, it still has this compression. To see this, remember that a plane wave may be infinite, but it still propagates. Therefore, consider a "chunk" of wave just about to enter the dielectric. Work out what happens. You'll see it gets compressed.

"Using Eq. (1), we find Eq. (2) = Eq. (3), the momentum-flux conservation."

There are mistakes in your working. If you fix them, you might end up with a derivation of the Minkowski momentum density - which then violates conservation of angular momentum.

If you eventually managed to fix that, you would have the material given in RMP79.

You are retracing the steps of hundreds of physicists before you. This is why literature reviews exist: To show what has already been done. Go away and read the literature. Start with all the citations in RMP79. M∅ller is particularly relevant here.

----------------------
"Why n =1 must hold?"

Because the argument I gave above is valid, and the one you gave was based on two mistakes.

 

[rpfeifer]

The medium rest frame is non-inertial.

Thanks, Dale, very elegant. Yep, you can construct a co-ordinate frame using GR in which space--time as you know it is rippling gently back and forth rather than the atoms of the medium.

That would be very silly, but in a good way. (The physics would be 100% correct, and absolutely no practical use whatsoever!) Nice one!

Being a GR solution, the maths involved are, of course, way beyond those presented in RMP79 (and would involve a stress-energy tensor for spacetime in the adopted co-ordinate frame, which would (by definition of the frame) couple to the EM tensor).

I doubt that sciencewatch had such a solution in mind.

(Note for junior physicists: The phrase "co-ordinate frame" has a special mathematical meaning. It comes from differential geometry, and refers to a very specific type of mathematical object, which people usually first encounter as the set of objects e^a_\mu(x) in tetrad-formalism GR.)