Does light travel faster than light?

Since the two photons are moving at the same velocity, through the same space, they are in the same frame of reference. Special relativity would not apply.

Remember, relativity is all about relative speeds. So photon 1 is going C1 re a static reference frame and 2 is going C2 = C1 = C re that same reference frame, call it K.

So we have the relative speed between the two photons as W = (C + C)/(1 + CC/C^2) = C is the speed photon 1 sees photon 2 going. [See source.]

Although this is counter-intuitive, it is the correct answer. The fundamental tenet of the special relativity is that the speed of light is always C no matter what the reference frame.

The first statement is correct. The second statement is incorrect. Special Relativity does NOT say "that one photon would 'perceive' that the other photon is traveling at the speed of light". Indeed, neither photon has a frame of reference at all.

Photons travel at c in all inertial reference frames. A photon cannot therefore have its own reference frame, since the phrase "having a reference frame" is short for "the reference frame in which it is at rest." There is no reference frame in which the first photon is at rest, so it can make no measurements at all of the other photon to begin with.

"Does light travel faster than light?"

No, clearly.

"Special Relativity says that one photon would "perceive" that the other photon is traveling at the speed of light, so therefore it is traveling AHEAD of the other photon and not staying next to it."

No special relativity does NOT say that. Light has no frame of reference. Light cannot see light departing at c. Special relativity applies to things that have mass., things that can never reach c.

Acc to theory of relativity of two particles are travelling with same velocity in the same direction their relative velocity is zero. So the photon would not "perceive" dat the photon is travelling ahead of it. Instead it treats as a photon at rest

That's a thoughtful question, and it illustrates the point that Lola is making; photons don't have a reference frame. Another way to look at it is that all points in space and time collapse toward "here" and "now" as you approach lightspeed, which means there is nothing measurable from the photon's "POV", so the photon cannot be said to have a reference frame.

Um, wouldn't it be more prudent to suggest that one photon would "perceive" the other photon as "not moving at all" relative to itself?

The first one