Undergrad Speed of Light in Inertial Ref Frames: Photon Perspective

[Saptarshi Sarkar]

TL;DR

What would be the speed of a photon in a beam of photons wrt another photon in the beam.

According to the 2nd postulate of Special Relativity, speed of light in vacuum is the same in all inertial reference frames.

If I take a beam of photons and see the other photons in the beam from a frame of reference of a single photon, do they look stationary or moving at the speed of light? Also, as the photon is itself moving with the doped how fast would the surrounding seem to move?

 

[Ibix]

As per the second postulate, the speed of light is the same in all inertial reference frames. Therefore an inertial reference frame in which light is at rest is a contradiction in terms. So there is no answer to your question - it is based on a faulty premise, namely that there is such a thing as the "frame of reference of a single photon".

 

[PeroK]

Summary:: What would be the speed of a photon in a beam of photons wrt another photon in the beam.

According to the 2nd postulate of Special Relativity, speed of light in vacuum is the same in all inertial reference frames.

If I take a beam of photons and see the other photons in the beam from a frame of reference of a single photon, do they look stationary or moving at the speed of light? Also, as the photon is itself moving with the doped how fast would the surrounding seem to move?

There are no inertial frames moving at $c$ with respect to other inertial frames. In particular, there is no inertial frame moving along with a beam of photons.

 

[Herman Trivilino]

If I take a beam of photons and see the other photons in the beam from a frame of reference of a single photon,

Imagine chasing that photon in an effort to catch up to it. No matter how fast you chase after it, it will forever recede from you at speed $c$.

 

[Nugatory]

Imagine chasing that photon in an effort to catch up to it. No matter how fast you chase after it, it will forever recede from you at speed $c$.

And anyone watching you chase the flash of light, no matter their state of motion, will find that you are moving at less than $c$ while it is moving at $c$... so no surprise that you can’t catch it.

(Of course @Mister T knows this - the comment is for others reading this thread)