# Learning special relativity in my physics class

1. May 16, 2006

### Ajoo

Hi. I just started learning special relativity in my physics class.
The prblem is i don't get this point. My teacher said that 2 inertial frames (A and B) where A moves with speed v relatively to B. He says that two flashes of light F1 and F2 occur when the 2 frames are at the same position. So, he says that an observer in B sees the 2 flashes as simultaneous cause he isn't moving. However A is moving making the distance between him and flash F1 bigger and between him and flash F2 shorter. So he says that from B's point of view F2 occurs before F1.

Well, i don't get this. If the speed of light is constant then A should also see them as simultanious. if the F1's moves towards A at speed c and F2's speed relative to A is also c they should reach him at the same time. Can someone plz explain me this?

BTW, why should we say that A is moving towards F2 and it's not B that's moving towards F1???? I thought it was relative. We can't say if it's A moving away from B or B moving away from A.

Last edited: May 16, 2006
2. May 16, 2006

### JesseM

In A's frame, you're correct that he's not moving towards either of the two points in space where the flashes happened in his frame, and the light beams from both flashes are travelling towards him at the same speed. The key thing is that in A's frame, F1 and F2 did not occur at the same distance from him, so it's consistent for him to judge them to have occurred at different times (for example, maybe in his frame the first flash occurred 0.5 light-seconds away from him while the second occurred 2 light-seconds from him, but the second occurred 1.5 seconds before the first so the light from each reached him at the same moment). This can be explained using the "Lorentz transformation", a set of equations which tells you how the space and time coordinates of a given event in one frame are related to that event's coordinates in another frame, but I can't think of a more intuitive explanation of why this should be true in this particular example...this may not have been the clearest example for your teacher to use. (edit: it looks like Doc Al came up with a good intuitive explanation of why this should be the case)

Instead, here's another example to show why disagreement about simultaneity follows from the fact that each observer assumes light travels at c in all directions in his frame. Suppose I'm on a rocket, and I have two clocks, one at the front of the rocket and one at the back, that I want to synchronize. If I assume that light travels at the same speed in all directions in the rocket's rest frame, then I can set off a flash at the midpoint of the two clocks, and set them to both read the same time at the moment the light reaches them. But now imagine you are in another frame, one in which the rocket is moving forward with some positive velocity. In your frame, the back of the rocket will be moving towards the point in space where the flash was set off, while the front of the rocket will be moving away from it; therefore if you assume light travels at the same speed in both directions in your frame, you will naturally conclude the light must catch up with the clock at the back at an earlier time than it catches up with the clock at the front, since both were at equal distances from the midpoint of the rocket when the flash was set off there. This means that you will judge my two clocks to be out-of-sync if I use the above synchronization procedure, with the back clock ahead of the front clock in your frame.

Last edited: May 16, 2006
3. May 16, 2006

### Staff: Mentor

The relativity of simultaneity

Your description of the situation is not quite clear. Allow me to describe what I think your teacher was talking about.

Imagine two reference frames, A and B. From B's viewpoint, A is moving to the right. Now imagine two flashbulbs at rest in B's frame, located along B's x-axis at x = -L (F1) & x = +L (F2). (Thus the origin of B's frame is right in the middle between those two bulbs.) Let's say that according to B those flashbulbs flash at the same time. Will observers in the (moving) A frame agree that the bulbs flashed simultaneously? Here's a simple argument that shows that they will not. (The argument is simple, but must be followed carefully, step by step.)

Imagine (just for convenience) that a B-frame observer is located at the origin of the B frame. Since the B-frame says that the bulbs flash simultaneously and the light from each flash travels the same distance (L) to get to the origin, the light from both flashes reaches the origin at the same time. (This is a physical fact that observers in any frame will verify.)

Also imagine that the A-frame has an observer located at the A-frame origin. Furthermore, imagine that A-frame observer passes by the B-frame observer at the very moment that the light flashes reach the B-frame origin. Now, as measured by A observers, those light flashes travel at the speed c with respect to the A frame. (According to the principle that the speed of light is the same for all observers.) But the A-frame observers disagree that the light from F1 and F2 travel the same distance. After all, the A-observer is moving towards flashbulb F2 and away from flashbulb F1, so the light from F2 has a longer distance to travel than the light from F1. Since the A-observer (and everyone else) agrees that the light arrives at the same time, he must deduce that flash F2 must have flashed before flash F1. Thus, according to the A-frame, the flashes are not simultaneous. (Simultaneity is frame-dependent.)

Let me know if this makes sense.

I hope the above convinced you that if B observes the flashes as happening simultaneously, then A must disagree. (The key is that the light travels different distances according to each frame.)

If you read through my argument above, you'll see that I say that the A-observer is moving towards flashbulb F2 and away from flashbulb F1. Since these bulbs are fixed with respect to frame B, it makes no sense to say that B is moving towards or away from them. (What you can--and must--say is that the light from the bulbs is moving towards the B-observers. Both the A-observer and B-observer see the light as moving towards them at the same speed c.)

(Looks like JesseM beat me to it! )

Last edited: May 16, 2006
4. May 18, 2006

### Ajoo

Ty both. I think everything is more clear now.