# Observers moving at the speed of light (Relativity)

I'm a high school physics teacher, but unfortunately I do not have a lot of experience with physics outside of a few courses I took in university - none of which dealt with relativity or quantum physics. As a result, I'm at a bit of a disadvantage when trying to teach concepts I'm not entirely comfortable with. And relativity is not exactly the easiest concept to throw together. As a result, I'm looking for some help.

Here is the problem. I have the following question from a test bank:

Three observers located at A, B and C are watching two starts located close to Observers A and C. Both stars explode simultaneously. Explain how observer C will see the stars explode if C is moving toward A at the speed of light. (I hope the following diagram works)

Code:
*                                           *
A                     B                 <-- C
The answer in the test bank is the following:

-Observer C will see star A explode when he interacts with that light moving toward him (no problems here)
-Observer C will not see star C explode until he stops and the light "catches up" with him (????)

Based on my limited understanding of relativity, shouldn't the light from exploding star travel towards observer C at the speed of light, regardless of his velocity? And so shouldn't the light reach him? I could understand if he were in a non-inertial frame of reference, but he's not. He's traveling at a constant velocity, as is the light, so it should catch up to him at the speed of light.

Shouldn't it?

## The Attempt at a Solution

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There is more than one error with this problem that make it unanswerable as asked. The first is that the stars supposedly explode simultaneously. There is no such thing as absolute simultaneity. You need to specify what frame of reference this "simultaneous" explosion takes place in. Observers at different locations will have different interpretations of what is simultaneous. And neither is more "correct" than the other.

Second, observer C cannot be "moving at the speed of light". It is impossible for anything with a rest mass greater than zero to be accelerated to the speed of light. Now, it might be better to word this that observer C is observed by observers A and B to be moving towards them at a speed that is near the speed of light. Of course the opposite is true, C will observe A and B approach him at near the speed of light.

Now back to your simultaneity issue. There are three observers and all three would have a different definition for a simultaneous explosion. If it was simultaneous to A that means B would see the explosion of the star near C long before he saw the explosion of the star near A, in fact there would be a time gap that would be the same as it takes for the light to get from A to C between the two explosions. What C would observe would depend on what fraction of the speed of light he was going and how big his head start was. Without solid numbers I would not even want to try the transform. But assuming he was very very close to the speed of light and he was placed right he could go at a speed so that the events were simultaneous for him too. He would need a slight head start so that the light from the star exploding near his starting point collided with the light from the star exploding near A.

And to clarify, light always travels at c relative to you, and in all directions. There is no absolute zero motion, nor motion, all you can do is to define distance and motion as relative to something else.

Let's see if we can try to fix the problems with the way the question is worded.

In order to fix the simultaneity problem, let's say that according to Observer B the two stars explode simultaneously.

I'm now trying to work around the issue of the observer having mass. Is it possible to ignore mass in this situation? Can we say that the observer C has a mass of 0? What I'm trying to determine, in the end, is if I am moving at the speed of light would I ever see that star explode?

tiny-tim
Homework Helper
welcome to pf!

hi yetiboy! welcome to pf! Three observers located at A, B and C are watching two starts located close to Observers A and C. Both stars explode simultaneously. Explain how observer C will see the stars explode if C is moving toward A at the speed of light. (I hope the following diagram works)
i'm sorry, but this question is rubbish an observer cannot travel at the speed of light (and no, there's no such thing as an observer of mass zero, the Lorentz transformation simply doesn't work for v = c)

which site did you get this question from?

(btw, there's no simultaneity problem, the observers all have the same velocity so they all agree on simultaneity, even though of course they have to back-calculate from the times they see things )

Would you believe this actually came from a textbook test bank? Nelson Physics 12, a high school textbook.

No wonder this has been such a pain to try to figure out. Isn't it wonderful that the creators of a textbook don't actually understand the concepts. Should I really be surprised?

Thanks for all of your help, I appreciate it.