Undergrad Relative Simultaneity: Flashlight in Moving Ship

[jbriggs444]

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

What color is that sheep again?

 

[gmalcolm77]

What color is that sheep again?

Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?

 

[jbriggs444]

Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?

Not really a helpful way of thinking about it. Your inability to reach one hundred miles per hour is a mere technical challenge, not a logical impossibility.

 

[Ibix]

Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?

That isn't the question you are asking. You are asking how much energy you would use in the run. But a realistic model of you running at 100mph would involve you tearing ligaments and collapsing - so there's no way to answer that question.

Your original question involves asking what happens if you are in a situation where light is both stationary and traveling at 3×10⁸m/s. There can be no coherent answer to a question that doesn't make sense. I realize it isn't obvious that your question isn't coherent. I've explained (post #22) why it isn't, and I'm happy to help you understand that answer. But at some point you need to accept that there is no answer in the terms you want.

 

[nrqed]

Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?

The answer is: it depends relative to what frame your speed is measured and relative to what frame the time to get there is measured.

 

[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.