Relative Simultaneity: Flashlight in Moving Ship

[gmalcolm77]

Yes, it is a what if question, but wouldn't an outside observer see a light?

OK, so let's get rid of the spaceship since we don't need it anyway. A photon traveling at c undergoes spontaneous parametric down-conversion when it runs into a crystal(not moving) and splits into two new photons. Would the two new photons be seen?

 

[Ibix]

An electron traveling at c

Nothing with non-zero mass can travel at c. Rocket, electron, whatever.

 

[gmalcolm77]

Nothing with non-zero mass can travel at c. Rocket, electron, whatever

Sorry, typo corrected.

 

[Ibix]

Sorry, typo corrected.

OK.

OK, so let's get rid of the spaceship since we don't need it anyway. A photon traveling at c undergoes spontaneous parametric down-conversion when it runs into a crystal(not moving) and splits into two new photons. Would the two new photons be seen?

Of course (assuming there's something there to see them).

Edit: The problem with your earlier scenario is two-fold. First that it has a massive object traveling at the speed of light. Second that you are trying to imagine riding along with the object at the speed of light. The second one is impossible, directly from the invariance of the speed of light. The first one is impossible because mass, in relativity, is the modulus of the energy-momentum four-vector. That is zero for things traveling at the speed of light and non-zero for all other things. In other words "has zero mass" and "travels at the speed of light" turn out to be two ways of saying the same thing. Parametric down conversion has neither of these issues, unless you try to imagine riding beside one of the photons.

 

[gmalcolm77]

OK. Great answers, thanks.