The Speed of Light and of Galilean Relativity - Comments

[Laurie K]

There is no need to even talk about photons in special relativity, photons are not present.

That would make it very hard to solve SR based relativistic rolling wheel problems, especially for solutions with "optical appearance" plots.

Photons are not small billiard balls. Regardless, the events of emission and detection exist in all frames - they are not coordinate dependent. Any other statement borders on misinformation.

I tend to agree with you on this one. Have you ever wondered what happens, 'optical appearance' wise, between emission and detection in a de Sitter double star type experiment with a constant c?

The following diagram shows the photon paths, emitted from 2 rotating sources, that travel directly to an observer at c over one complete rotation. These photons exist at the time of the observation as long as the sources continued to emit during the previous complete rotation and the emitted photons were not blocked or distorted. The observation point is stationary wrt to the center of the sources plane of rotation and the photon paths are shown for the observer being at various different angles 0, 45, 60, 90 degrees to the plane of rotation. The color of the paths reflects the shift at the point of emission, for each quarter, which is then kept consistent as the photon travels through to the observer.

The speed of light is kept constant because the distance between the 2 emission start points 1,0 3,0 and the observer will always be the same regardless of the angle of the observer to the plane of rotation of the sources or the angular velocity of the sources themselves. This distance will always equal 2 * Pi * r * c/v after one complete rotation of the sources for both sources angular velocities<c.

 

[vanhees71]

Usually when in wanna-be modern textbooks about classical phenomena photons are used you can as easily also use the more consistent and correct description of classical electrodynamics. What's called a "photon" in such cases is often just "ray optics" (i.e., the eikonal approximation) or just kinematics of the wave-number four-vector $(k^{\mu})=(\omega/c,\vec{k})$. Whatever is shown in your diagrams are no photon paths. There is not even a position observable for photons. Maybe it shows "light rays" in the proper sense of the eikonal approximation, but that must not be thought of as "photon trajectories".

 

[Orodruin]

That would make it very hard to solve SR based relativistic rolling wheel problems, especially for solutions with "optical appearance" plots.

There is no need to talk about photons in this respect. Just as there is no need to talk about photons when doing classical ray optics. Actually, calling the world line of a classical massless particle in SR a "photon path" is a huge misnomer. See also the reply by vanhees71.

 

[Dale]

I try to consistently use the term "light pulse" when I am talking about classical flashes of light. Especially if I am neglecting diffraction and other complications.

 

[Laurie K]

Whatever is shown in your diagrams are no photon paths. There is not even a position observable for photons. Maybe it shows "light rays" in the proper sense of the eikonal approximation, but that must not be thought of as "photon trajectories".

I was originally wondering how a simple geometric rotating observational model would work on galactic scales and if the apparent changes in shift along the way could appear within the optical Depth of Field of our astronomical observations.

This is how the light rays, if you like, were plotted for the 45 degree plot vanhees71. The observer is at the point where the photons arrive after one complete rotation of the source(s) and the 'light rays' shown are for the photons still in transit between the source(s) and the observer.

After one quarter of rotation photons from the start point 1,0 have traveled directly towards the observer and reach point 1, 1 while their source moves to position 4,0. Accordingly the photons emitted from start point 3,0 travel to point 3,1 while their source moves to point 2,0. All other photons emitted from their sources (heading directly towards the observer) are spread between points 4,0 & 1,1 and 2,0 & 3,1 respectively.

After two quarters of rotation the photons that arrived at point 1,1 have traveled to point 1,2, the photons at 4,0 traveled to point 4,1 and the source has moved to point 3,0 so the newly emitted photons are spread out between 3,0 and 4,1. The photons that arrived at point 3,1 have traveled to point 3,2, the photons at 2,0 traveled to point 2,1 and the source has moved to point 1,0 so the newly emitted photons are spread out between 1,0 and 2,1.

After three quarters of rotation the photons at point 1,2 have traveled to point 1,3, the photons at 4,1 traveled to point 4,2, the photons at point 3,0 traveled to point 3,1 and the source is at 2,0. The newly emitted photons are spread out between 2,0 and 3,1. The photons at point 3,2 have traveled to point 3,3, the photons at 2,1 traveled to point 2,2, the photons at point 1,0 traveled to point 1,1 and the source is at 4,0. The newly emitted photons are spread out between 4,0 and 1,1.

After one complete rotation the photons at point 1,3 have traveled to the observer at point 1,4, the photons at 4,2 traveled to point 4,3, the photons at point 3,1 traveled to point 3,2, the photons at 2,0 traveled to point 2,1 and the first source is back at its start point 1,0. The newly emitted photons are spread out between 1,0 and 2,1. The photons at point 3,3 have traveled to the observer at point 3,4, the photons at 2,2 traveled to point 2,3, the photons at point 1,1 traveled to point 1,2, the photons at 4,0 traveled to point 4,1 and the second source is back at its start point 3,0. The newly emitted photons are spread out between 3,0 and 4,1.

 

[Laurie K]

Actually, calling the world line of a classical massless particle in SR a "photon path" is a huge misnomer.

The diagrams are not of world lines but more like the Optical Appearance plot used by Øyvind Grøn in the Fig 9 part C plot in his paper "Space geometry in rotating reference frames: A historical appraisal". http://areeweb.polito.it/ricerca/relgrav/solciclos/gron_d.pdf

 

[Orodruin]

The diagrams are not of world lines but more like the Optical Appearance plot used by Øyvind Grøn in the Fig 9 part C plot in his paper "Space geometry in rotating reference frames: A historical appraisal". http://areeweb.polito.it/ricerca/relgrav/solciclos/gron_d.pdf

This does not change the fact that calling them photon paths is a huge misnomer.

 

[haushofer]

It's a bit late, but I missed this reply. In my language they have the saying "better sometime than never", so here it goes.

Can you be more explicit? I wasn't aware that there was such a thing. Maxwell's equations are Maxwell's equations; they are Lorentz invariant, not Galilean invariant.

My point was, that when you want to consider elecotromagnetism in the non-relativistic limit (such that you obtain equations that are Galilei-covariant), the time derivatives of both fields drop out. Levy-Leblond (Nuovo Cimento B 14, 217-234) showed that these equations correspond to the limit c --> oo of the Maxwell equations. For an arxiv-link, see e.g.

https://arxiv.org/abs/1303.5608