Why do we know all photons have same speed as the speed of light?

[snorkack]

Do we know? Are you sure? Because I have no idea.

Diffraction of light is due to photons of different frequency having different speed. But it always looks due to interaction with medium.

That doesn't make any sense to me. How would that suggest a rest mass of photons?

Because of the relation
E²=p²c²+m²c⁴
Assuming zero m, it simplifies as
E=pc
It approaches E=pc when E>>mc²
But it would change and the speed of particle would fall as E approaches mc². And the speed would have no lower bound.

Compare photon with neutrino. Since neutrinos are hard to observe and low energy neutrinos especially so, it is hard to measure neutrino speed. Indeed, even though some neutrinos have rest mass as shown by oscillations, we do not have evidence that they all do. But in contrast to low energy neutrinos, low energy photons are easy to observe - longwave radio waves! And they do not show evidence of medium independent, vacuum dispersion which photon rest mass would cause.

 

[lomidrevo]

Diffraction of light is due to photons of different frequency having different speed.

No, it isn't. @Lord Jestocost alredy mentioned in above post that "different speed" is only apparent. I also suggest to read the Feynman's lecture linked by him, it explains why.
Btw. to describe refraction or diffraction of light you can safely stay within domain of classical EM field theory, no need to complicate life by jumping to QED and talking about photons.

Because of the relation
E2=p2c2+m2c4
Assuming zero m, it simplifies as
E=pc
It approaches E=pc when E>>mc2
But it would change and the speed of particle would fall as E approaches mc2. And the speed would have no lower bound.

I am not sure what you are trying to do here. I hope you know that "speed of light is the same constant for all observers" is a postulate of special relativity. You just cannot use the results of SR (like $E^2 = p^2c^2 + m^2c^4$ ) to try to "simulate" how it would be if constancy of speed of light is violated. The theory is build on this fact. The equations would not be valid if $c$ could vary. According to SR, for light you get exactly $E = pc$, point.

 

[snorkack]

I hope you know that "speed of light is the same constant for all observers" is a postulate of special relativity.

You could just as well call it a "postulate of special relativity" that speed of neutrinoes is the same constant for all observers. Except, oops, neutrinoes oscillate... which doesn´ t actually affect special relativity. Special relativity merely requires a special maximum speed to exist, and does not require any particles to actually travel at that speed - whether it is all neutrinoes, one of three neutrinoes, no neutrinoes but all photons or not photons either (but only gravitons) - SR is unaffected.
However, if any photons inherently, in vacuum, traveled slower than light like most neutrinoes do, the problem is that it would mess up electromagnetic fields, especially at the low frequency end. Therefore we can verify that light travels exactly at speed of light, not only approximately at the speed of light like most neutrinoes.

 

[vanhees71]

Neutrinos are not massless. They are quite complicated critters too ;-)).

 

[Dale]

At this point the question in the OP has been answered. So we will close this thread rather than go off on more tangents. @fxdung in the future please try to not hijack your own thread. Keep the discussion to the question in the OP and try to actually respond to the other participants instead of hammering us with a barrage of new questions