# Abraham's light momentum breaks special relativity?

1. Oct 18, 2011

### sciencewatch

The Abraham's photon moment p_A=hbar*w/n*c is not Lorentz covariant, but it has been confirmed by several experiments. For example, G. B. Walker and D.G. Lahoz, Nature 253, 339 (1975); W. She, J. Yu, and R. Feng, Phys. Rev. Lett. 101, 243601 (2008).

The special relativity is flawed or the experiments were not correctly observed?

2. Oct 18, 2011

### yoron

You lose me here?

"An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame (this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame).

This condition is a requirement according to the principle of relativity, i.e. all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference."

Are you saying that the Abraham effect, in where the photon is seen to lose momentum entering a medium is inconsistent? It's been tested and seems to be correct, as far as I know? If you are referring to the way, if seen as a wave, the 'momentum' increase, as the wavelength is found to decrease, then that is correct too. The problem only exist if you want radiation to be only' one', or the other.

Or, is it something else you mean?

3. Oct 18, 2011

### Staff: Mentor

4. Oct 18, 2011

### sciencewatch

Let me re-state my question.

For a plane wave in an isotropic, homogeneous, non-conducting medium, the wave vector k and the frequency w constitute a wave 4-vector (k,w/c) which is Lorentz covariant, where |k|=n*w/c with n the refractive index. Sine the Planck constant hbar is assumed to be a Lorentz invariant. Thus hbar*(k,w/c) is a Lorentz covariant momentum-energy 4-vector. The Minkowski's photon momentum is defined as p_M=n*hbar*w/c = hbar*|k|, and we say the Minkowski's momentum hbar*k is Lorentz covariant, as the space component of hbar*(k,w/c).

However, the Abraham's momentum p_A=hbar*w/(n*c) does not have such property, that is, it is not Lorentz covariant, unless in free space. But some experiments strongly support Abraham's formulation. Is the special relativity flawed? or the experiments were not correctly observed?

5. Oct 18, 2011

### sciencewatch

This is a good review paper.

It is mainly talking about various EM and material tensors which are used to obtain various momentum and energy conservation equations.

In principle, Maxwell equations support various momentum conservation equations; however, this is an indeterminacy. It is the indeterminacy that results in the question of light momentum in a medium.

6. Oct 19, 2011

### Staff: Mentor

Yes, and the answer doesn't really matter. What matters is that the total energy and momentum is conserved and covariant. You can break that total momentum up into parts which are not covariant, but that does not challenge SR in any way.

7. Oct 19, 2011

### sciencewatch

"You can break that total momentum up into parts which are not covariant, but that does not challenge SR in any way."

Do you have any theoretical grounds that support "partial momentum" is not Lorentz covariant?

8. Oct 19, 2011

### Staff: Mentor

No, I was just going by your claim in the OP that it is not covariant. Do you have reason to doubt your own claim? I do not.

9. Oct 19, 2011

### sciencewatch

1. "by your claim in the OP that it is not covariant" --- What does it mean for "OP"?

2. My reason is:

For a plane wave in an isotropic, homogeneous, non-conducting medium, the wave vector k and the frequency w constitute a wave 4-vector (k,w/c) which is Lorentz covariant, where |k|=n*w/c with n the refractive index.

Sine the Planck constant hbar is assumed to be a Lorentz invariant. Thus hbar*(k,w/c) is a Lorentz covariant momentum-energy 4-vector. Because hbar*w/c is the photon's energy, hbar*k must be the photon's momentum according to the relativity covariance. Thus only the Minkowski's photon momentum is consistent with the relativity, while the Abraham's momentum is not.

10. Oct 19, 2011

### Staff: Mentor

OP = Original Post or sometimes Original Poster

Yes. And since the choice between them is arbitrary I would recommend using Minkowski's momentum if you are doing relativistic problems.

11. Oct 20, 2011

### sciencewatch

However some experts of relativistic electrodynamics insist that the wave 4-vector be Lorentz covariant, but the light momentum may take Abraham's momentum. Does that mean the special relativity has some flaw? For example, see: T. Ramos, G. F. Rubilar, and Y. N. Obukhov, Phys. Lett. A 375, 1703 (2011), http://arxiv.org/abs/1103.1654 .

12. Oct 20, 2011

### Staff: Mentor

Not at all. A similar thing happens with gauges. There are many different possible choices for gauges. For example Coulomb or Lorentz. Both are equally valid but the Coulomb gauge is not covariant. No big deal.

13. Oct 20, 2011

### sunroof

There also have experiments with a high credibility to support Minkowski momentum,e.g.

Campbell, G.K., Leanhardt, A.E., Mun, J., et al, "Photon Recoil Momentum in Dispersive Media", Physical Review Letters. Vol94, issue 17, 2005, pp.170403

Wang Zhong-Yue, Wang Pin-Yu, Xu Yan-Rong (2011). "Crucial experiment to resolve Abraham-Minkowski Controversy". Optik 122 (22): 1994–1996.

14. Oct 21, 2011

### sciencewatch

Choice of gauges and choice of light momentum formulations are different things.
Gauge is a kind of math tool, while light momentum is a physical reality.

Without using Lorentz gauge or Coulomb gauge, one still can solve EM problems. The solutions to Maxwell equations do not deppend on the choice of gauges.
Without Lorentz gauge, covariant EM-field strength tensors also can be set up.

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.

15. Oct 21, 2011

### sciencewatch

Minkowski's momentum is Lorentz covariant, and it is supported by the Fizeau running experiment.

16. Oct 21, 2011

### John232

Sometimes, I wonder if special relativity is even compatible with itself. If you take d'/t', you don't get v. They are inversely related to the lorentz, so you would then get a different velocity than the original that determined the amount of spacetime dialation in the first place. I vote for a misassigned t' variable.

17. Oct 21, 2011

### pervect

Staff Emeritus
In special relativity (or rather in the MInkowski space-time of Special relativity), v always equals dx/dt, so I don't know what your problem is. Offhand, I'd guess you were, in fact, using a missagned 't' variable from the wrong frame, not realizing or having some sort of mental block about 't' being frame dependent.

Note that this remark doesn't apply to GR, because in GR coordinates are general and don't necessarily directly represent distances (or times). This is somewhat similar to the way that lattitude and longitude on the Earth's surface are coordinates, and don't represent distances until you apply the metric.

18. Oct 21, 2011

### John232

If you look at a geometrical view of SR, there is no reason why velocity shouldn't equal d'/t', since it would equal c. You can pythagreom theorom the equation for t' and d', but then you can't get the original value back that you tried to solve to correct getting the constant value c. d'/t' doesn't give you back c like it should. It would be similair to checking your answer that c is indead the same, the goal of assigining d' and t' in the first place.

19. Oct 21, 2011

### John232

If t'=t sqr(1-v^2/c^2), and L' = L sqr(1-v^2/c^2), then the lorentz portion would cancel and then L'/t' = c. The difference between the time dialation equation is exchanging the time variables, t and t'. The way it is L'/t' does not equal c.

20. Oct 21, 2011

### John232

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