Well, as I said, the example of the light clock only applies to the moment when two inertial frames pass each other. The rest of the experience is a bit different. If you imagine a train coming down the tracks towards you, if it were made of glass, to use your example, and you could see a light clock on it; when it is a long way away, because of the angle, the pulse of light looks as if it is bouncing straight up and down.Viveka wrote: ↑Tue Nov 07, 2017 6:38 pmOkay. I think I have an argument that works:
1, As the embankment observer sees this contraction and dilation of the train moving appreciably close to c, and the train looking at the embankment observer sees this contraction and dilation when moving appreciably close to c. However, how can both be at different rates of ticking on their light-clocks? Embankment>train, and train>embankment. Thus there is a contradiction.
Suppose the pulse of light is up when you first see it. For you to see it, the light from that pulse has to travel a certain distance. By the time the pulse is down, the light doesn't have to travel as far to reach you, because the train is closer to you. But whether the pulse is up or down, the light travels towards you at the same speed. Because the light from the down pulse doesn't take as long to reach you, it arrives sooner than it would have if the train was at rest (relative to you). So your experience of the ups and downs of the light clock are closer together. It looks to you as if the clock is ticking faster than your own. To the person on the train, exactly the same happens if they look at your light clock. In other words, both of you see the others light clock 'ticking' faster than your own.
Once the train has passed you, as the pulse bounces, every time, up and down, the train is further away, so the clock appears to be ticking slower, compared to your own. Again, it doesn't matter whether you are on the train or on the bank, you both see exactly the same. As davidm, myself and others have pointed out, it would only be a contradiction if the claim was that both clocks are in fact ticking slower than the other.
What the example of the 'twins paradox' is meant to demonstrate is that, in fact, one of the clocks is ticking faster than the other. This has been confirmed by experiments such as Hafele-Keating, so if some instantaneous means of communication were possible, then both parties would be able to tell which clock was ticking faster, even though, according to the premises of special relativity, they are getting further apart. But you don't need to posit superluminal communication. Superhuman visual acuity will do the trick. If someone so blessed could have watched the atomic clocks ticking in the Hafele-Keating experiment, from the surface of Earth, they would have seen the clocks on the planes ticking slower than the one in Washington, because that is what they actually did.