Oh no! Not another question about SR! Maybe somebody can explain the following thought experiment! There are two lightposts and two people inbetween the lightposts. L1|----------|P1--->|--------|P2 |----------|L2 Light is being emitted from lightposts at L1 and L2. P2 is stationary with respect to L1 and L2. P1 is moving towards P2. Now then, because P1 is travelling in the same direction as the light from L1, the light will cover less distance for P1 than for P2, therefore in order for the speed of light to remain constant time will pass more slowly for P1 than for P2. But, P1 is travelling in the opposite direction to the light coming from L2. Therefore, the light will cover more distance for P1 than for P2, and in order for the speed of light to remain constant time will need to pass more quickly for P1 than for P2. Therefore, time for P1 is passing both more slowly and more quickly than for P2. For example: let's assume that light is travelling 10 miles/min. P1 is travelling 5 miles/min towards P2. After 1 minute for P2, light from L1 will have travelled 10 miles for P2, but only 5 miles for P1, therefore 30 seconds will have passed for P1. 10 miles/1 min = 5 miles/30 seconds. After 1 minute for P2, light from L2 will have travelled 10 miles for P2, but 15 miles for P1. Therefore 1 minute for P2 is equal to 1 minute and 30 seconds for P1. 10 miles/1 min = 15 miles/1.5 minutes. Therefore, 1 minute for P2 is equal to both 30 seconds and 90 seconds for P1!
Hi Zeno, It's a bit more complex than that... The distances involved are also different for P1 and P2, and even the timing of the lights is different. I'll do up a little animation for you when I have some time.
Hi Zeno, If you are interested in learning SR, then I would recommend that you learn how to do the Lorentz transform algebraically and that you learn how to draw spacetime diagrams geometrically. For me, the spacetime diagrams were particularly important for getting a more-or-less intuitive understanding of SR. In this case, the key is to remember that there are 3 elements of SR: time dilation, length contraction, and relativity of simultaneity. Most confusions stem from remembering the first two, but forgetting the third. Basically, if L1 and L2 are flash bulbs and if L1 and L2 flash simultaneously in P2's rest frame, then L1 flashes before L2 in P1's rest frame. -Dale
Thanks for the replies. But, I would like to point out a few things. First of all, relativity of simultaneity does not apply because one can assume that the person at P1 doesn't start moving towards P2 until after both light flashes have been emitted. Also, if we keep the time the same for both people and only change the distances involved, then we end up with another paradox involving lengths. If we change both time and distance in order to keep the speed of light constant then we end up with a paradox involving both time and distance.
In that case, P1's rest frame is an accelerating, and the constant speed of light rule doesn't apply.
Sorry Pete but this seems just a dodge. Since this is a hypothetical gendankin the acceleration can be made instantaneous to some velocity. It doesn't change the ultimate conclusion according to SR but your answer isn't actually a valid one to make.
Thanks for your opinion, Mac, but you're wrong. Instantaneous acceleration is still acceleration. if P1's velocity changes, instantaneously or not, then the speed of light is not constant in P1's frame..
I strongly encourage you to actually go through the exercise of working out the Lorentz transforms in each scenario that you are suggesting. The Lorentz transform is the formal mathematical framework of SR and it ensures that SR is completely self-consistent. So there are no actual paradoxes in SR. -Dale PS Relativity of simultaneity always applies, though sometimes observers agree on which events are simultaneous. Just like length contraction and time dilation always apply and sometimes observers agree.
Now that yo hve once again opened your mouth and made false statements, lets see you demonstrate mathematically just how it is that "during??" an instantaneous acceleration where t = 0 that you hve any comparative veloicties. :bugeye:
Sure. In that instant, the light pulse position jumps in P1's rest frame. It moves a non-zero P1-frame distance in zero P1-frame time. The speed of the light pulse in that instant = distance/time = value/zero = infinite. Ridiculous? Sure. But no more ridiculous than instantaneous acceleration.
