When is the propagation of an EM wave not reversible?

[univector]

By reversibility, if we turn the direction of the light propagation by 180 degrees, then the new propagation path follows the old propagation path. I suspect that when there is diffraction, the light propagation is not reversible?

 

[jbriggs444]

When you turn the light 180 degrees around, you need to be starting from a diffraction pattern and reproducing the original light. This is, to some extent, the idea behind viewing a holographic image.

Maxwell's equations are time-reversible. Quantum mechanics is as well.

 

[tech99]

The attenuation between transmitter and receiver is the normally same in both direction. This is known as the Rayleigh-Carson Reciprocity Theorem. However, there do exist one-way devices such as directional couplers in waveguide etc and it has also been suggested that non reciprocal transmission might occur in the ionosphere. The latter is not to be confused with the effects of local noise being higher at one end of the path. In such a case, information can be transmitted in one direction better than the other, but the path attenuation is still reciprocal.

 

[Andy Resnick]

Summary:: We know for light rays the propagation can be assumed reversible. But under what condition the light propagation does not follow the reversible principle? What if we consider longer wavelength such as the radio waves? This is important for practical problems such as channel modeling and channel reciprocity.

By reversibility, if we turn the direction of the light propagation by 180 degrees, then the new propagation path follows the old propagation path. I suspect that when there is diffraction, the light propagation is not reversible?

There are nonreciprocal optical elements that typically involve magneto-optical effects or Faraday effect (polarization rotation):

http://physics.mq.edu.au/~msteel/research/nonreciprocal.html
http://przyrbwn.icm.edu.pl/APP/PDF/86/a086z1p20.pdf
https://www.osapublishing.org/jot/abstract.cfm?uri=jot-70-7-525

 

[marcusl]

Radio propagation through the ionosphere is also non-reciprocal due to the Faraday effect. The polarization rotation is very small but it is a source of error in precision mapping and remote sensing measurements such as satellite-based synthetic aperture radar. NASA goes to great lengths to calibrate and compensate for these when making earth-resources measurements.

 

[vanhees71]

Since classical (and quantum) electromagnetism is time-reversible invariant, in principle any solution of the Maxwell equations can be time-reversed, i.e., the time-reversed fields are also a valid solution of Maxwell's equations.

Irreversibility comes however in as it comes into non-relativistic mechanics through the impossibility to prepare the initial time-reversed state. So the practical impossibility to prepare certain states brings in a direction of time and let's us choose the "retarded solution" (in classical Maxwell theory) rather than any other solution.

Take as an example the most simple case of a harmonically oscillating dipole (treated in any good textbook as "Hertzian dipole"). We choose the retarded solution, because it describes outgoing waves. For that we simply have to put the dipole somewhere and switch the AC on, so that the dipole starts to radiate em. waves outwards from its position. This is very simple; just switch on a flashlight and you have something pretty similar (through with good old fashioned lightbulbs you rather emit thermal radiation than a dipole field with it, but the principle for this discussion is the same).

Now think about what's the time-reversed process! Suppose you have the dipole's AC switched on for some time $t$. Then you have an electric field different from 0 in a sphere around it with radius $c t$. To get the time reversed porcess you would have to prepare an electromagnetic field precisely the same as this so generated field but with the wave vectors reversed everywhere such that you get an incoming wave exciting the perfectly time-reversed AC in the dipole. It's pretty obvious that this is very hard if not impossible to achieve, and that's why this situation is never observed in practice.

It's the same as with a gas consisting of some $10^{24}$ particles. Suppose you have filled the gas first in a box separated into two parts by some wall with the gas in only one part and a vacuum in the other. Now you can remove the wall in a reversible way (at least in good approximation). It's obvious what happens: The gas will spread into the entire volume. Since the particles interact practically only through the time-reversible electromagnetic interaction, in principle you can, at some time after taking out the wall, prepare the time-reversed state, and since the equations of motion are time-reversal invariant, all gas molecules will end up at one part of the volume and leaving a vacuum behind. In practice it's of course impossible to do that since you'd have to reverse all the momenta of all the $10^{24}$ particles precisely, and that's impossible.

Also that it comes by chance through collisions between the particle to an exactly time-reversed situation is very unlikely, and that's why we never observe a gas moving completely in one part of the vessel it is confined in and leave a vacuum in the other part. All that happens are some thermal fluctuations of the density of the gas around the quite accurate uniform density of the thermalized state the gas reaches some time (the relaxation time to equilibrium) after taking out the separating wall.

That's also the origin of an "arrow of time" through statistical physics, distinguishing the likely direction of motion towards larger and larger entropy from the unlikely direction of decreasing entropy.

This "thermal arrow of time" (increasing in favor of decreasing entropy) is thus identical with the above discussed "radiative arrow of time" (retarded in favor of advanced solutions of the Maxwell equations). And all these "arrows of time" you can think about are finally traced back to the axiomatically assumed "causal direction of time", which is just assumed in the mathematical structure of spacetime. E.g., in the Minkowski spacetime of SR the part of the symmetry group (the Poincare group) of this spacetime that is continuously connected with the group identity is the proper orthochronous Poincare group, which keeps the direction of time the same when changing from one inertial frame to another. All the other transformations (time reversal and space reflections) do not need to be symmetries to make a relativistic dynamical theory consistent (though electrodynamics and also quantumchromodynamics, which describes the strong interaction among quarks and gluons in fact are both time-reversal and space-reflection invariant), and indeed the weak interaction violates all these discrete additional symmetries (besides time-reversal T and space-reflection symmetry P also charge-conjugation symmetry C, where all particles are changed to the antiparticles as well as CP, PT too; only CPT is still a symmetry, which must be so as long as one considers only local realtivistic QFTs).

 

[er404]

Now think about what's the time-reversed process! Suppose you have the dipole's AC switched on for some time $t$. Then you have an electric field different from 0 in a sphere around it with radius $c t$. To get the time reversed porcess you would have to prepare an electromagnetic field precisely the same as this so generated field but with the wave vectors reversed everywhere such that you get an incoming wave exciting the perfectly time-reversed AC in the dipole. It's pretty obvious that this is very hard if not impossible to achieve, and that's why this situation is never observed in practice.

So the claim in the textbook (Griffiths, D. J. (1999) Introduction to Electrodynamics, 3rd ed., P 425) that the advanced potentials propagate backward in time is wrong?

 

[vanhees71]

Of course it's wrong. By definition nothing ever propagates backward in time. Rather, it's the time reversed state propagating forward in time. In QFT it's also sometimes claimed that Feynman thought antiparticles are particle moving backwards in time. Maybe he wrote such a thing in some popular-science book, but if you look at the formalism, it's quite the opposite: Instead of moving backward in time with negative energy you reinterpret it as moving forward in time (with the opposite charge if the field describes particles with some charge-quantum number). This is achieved by quantizing the negative-frequency modes with creation instead of annihilation operators, such that you get antiparticles moving forward in time having positive energy (Feynman-Stückelberg formalism).

 

[er404]

Feynman held that the advanced waves propagate backward in time from a remote absorber, in order to produce a radiation reaction force at the right moment, which is clearly evident from his papers co-written with Wheeler on the Wheeler-Feynman absorber theory.

 

[jartsa]

By reversibility, if we turn the direction of the light propagation by 180 degrees, then the new propagation path follows the old propagation path. I suspect that when there is diffraction, the light propagation is not reversible?

Single slit diffraction:

If the light that went through the slit is reflected back to the slit and the light that reflected from the screen on which the slit is, is reflected back to the reflection point, then the result is the original light beam reversed.

IOW:

If the screen with the slit does not absorb light, and if we remember to reverse all of the light, then the diffracted and reflected light becomes a narrow beam of light again, if it was a narrow beam of light before it got diffracted and reflected.

 

[vanhees71]

Feynman held that the advanced waves propagate backward in time from a remote absorber, in order to produce a radiation reaction force at the right moment, which is clearly evident from his papers co-written with Wheeler on the Wheeler-Feynman absorber theory.

Yes, but as is also known, this alternative interpretation did not lead to useful physics. Particularly the hoped-for approach to quantization didn't work out.