Question

A. How does the speed of light in a vacuum change when observed from two different frames of reference?

b. Which frames of reference must be studied using general relativity?

c. A stationary observer sees a clock on a train that is traveling at nearly the speed of light. Describe how the passage of time on this clock compares with the passage of time on an identical clock that the observer is holding. Write 2 - 3 sentences explaining your reasoning.

Answer 1

a) It is absolute, so it does not change.

b) Inertial ones.

c) Inside the train the time will slow down relatively to the outside clock. So if one travel at nearly the speed if light for 2 hours on his clock, for outdoor observers it will look like 3 hours.

Answer 2

a) The velocity of the light is invariant, this means that is always the same independent of the frame in which you are looking.

b) Inertial frames, this means that the frame is "not accelerating" (it can be fixed in place or moving with constant velocity)

C) When you are in the train, you are in the same frame than the clock, so you will no see nothing interesting, now, if you are outside of the train you will see a time dilation, this means that each "tick" of the clock is slightly longer than the one that the observer is holding. This happens because of the invariance of the speed of light, a way of seeing it is the next:

Suppose that the clock works sending a light signal, it travels a distance "d", it rebounds in a surface and comes to a receptor, when the photon hits the receptor, a "tick" of the clock is recorded, which would mean that a second has passed.

If the clock is still, the photon travels the distance d two times at a velocity c, so the "tick" of the clock is each "2d/c" seconds.

Now, in the moving clock, the distance that the photon moves is slightly higher (because now it also moves with the clock) suppose that this distance is D, so now the time is "2D/c", which will be bigger than the one that we had before.