A question about light

[Jim Beam]

according to relativity, two objects moving toward each other through space in un-acclerated motion have equal right to declare themselves stationary and viewing the other as moving. if two photons are approaching each other at the speed of light, is it not correct for one of the photons to claim its stationary existence while viewing the other approaching at twice the speed of light? If that's a correct assumption, then technically, faster the light travel would a reality. I know i've probably got something wrong, which is why i am asking you all if its a possibility.

[mathman]

When two things are going very fast (relative to a stationary observer), the speed relative to each other is not gotten by simple addition. The general formula is:

u=(v+w)/(1+v*w/c2), where v and w are the individual speeds and u is the relative speed between the two things. Note that for v=w=c, then u=c.

[HallsofIvy]

What mathman said!

In other words, either light ray would "see" the other approaching AT the speed of light.

[Jim Beam]

i knew the light rays would see each other moving at the speed of light, but what i didn't know was why. thanks for the help guys.

[zefram_c]

according to relativity, two objects moving toward each other through space in un-acclerated motion have equal right to declare themselves stationary and viewing the other as moving.
Perfectly true.
if two photons are approaching each other at the speed of light, is it not correct for one of the photons to claim its stationary existence while viewing the other approaching at twice the speed of light?
If you naively plug in u=v=c in the relativistic velocity addition formula, you find the relative speed to be c. However, I would not put too much trust in this result. The reason for that is that a photon cannot claim its own stationary existence. (There has been some discussion here about this issue, do a PF search for a universe containing a single photon.) The "rest frame of a photon" is extremely ill defined from the vantage point of relativity, and no meaningful physics can be done using it. If we try to define it by Lorenz boosting to the photon frame, we find that space is infinitely contracted and time is infinitely dilated. Hence a photon is not aware of its own existence, or the existence of the rest of the universe. It experiences no awareness of either time or space from the moment it is created to the moment it is destroyed (here 'moment' is defined by some inertial massive observer), nor is it aware of the other photon. Hence I don't think that it is physically meaningful within SR to ask what speed does a photon "measure" for another photon - it cannot measure to begin with. But I might be wrong, and in any case if the question of the speed of one photon relative to the answer has a physically meaningful answer, it must be c.