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Aug7-08, 02:45 PM
Sci Advisor
P: 8,470
Quote Quote by jtaravens View Post
Greene gives an example of you and “Chewie” both sitting on a couch. Chewie is 10 billion light years away. Ignoring rotations of planets and stuff, if both you and Chewie are stationary then you two can say you experience the same now. HOWEVER, if Chewie gets up and walks at about 10 mph away from you – his now will be about 150 years before yours. If Chewie walks towards you – his now will be about 150 after you. (I may have mixed up the moving toward=after your now; moving away = toward your now but regardless….)

I can’t wrap my head around this. I understand (pretty well for a non-physicist) general time dilation effects and the basic ideas of relativity. But I can’t figure out how and why the angle of the “slice through the spacetime loaf” changes forward 150 years or back 150 years by Chewie moving towards or away from you. Is this just an extrapolation of the moving train with two people shooting at each other when a flash occurs on the train and the observers on the train say the shots occur at the same time and the stationary observers (off the train) say one fired before the other?
Yes, the moving train thought-experiment illustrates why, if each observer assumes that light always moves at c in their own frame, then different observers must disagree about simultaneity, hence slicing the loaf in different ways (each 'slice' represents a set of events which are all simultaneous in a given frame). As a simple example, if I'm at the exact middle of a train car and I set off a flash there, and there are two detectors at either end, then if I assume light moves at c in both directions in my rest frame, I must conclude that the two events of the detectors going "click" happen simultaneously. On the other hand, if you are on the tracks and see the train car moving forward, you'll see the detector at the front of the train moving away from the point where the flash was set off while the detector at the back is moving towards that point, so naturally if you assume light moves at c in both directions in your rest frame you'll conclude that the light must have caught up with the back detector before the front one, so the click of the back detector happened at an earlier time than the click of the front one.

Of course nothing forces you to assume that light moves at the same speed in all directions in every frame, you'd be free to pick a set of coordinate systems where light had different speeds in different directions. But the physical appeal of this assumption is that when you do design each observer's coordinate system based on the idea that light moves at c in every coordinate system, you'll find that when you express the equations representing the fundamental laws of physics in terms of each coordinate system, they end up obeying the same equations in each of these systems--this is a symmetry in the laws of nature known as "Lorentz-invariance". If you made a different assumption about the speed of light in different directions, the equations would be different in different coordinate systems.