Hmm… crazy-assed logical leaps. CALLs. I like that - “Einstein makes CALLs”. I might start using that deliberately.
Anyway, I’ve finally got round to Einstein’s book on relativity, at the behest of several posters on this forum. Actually, I’ve got to say, it’s pretty damn good at explaining things in a simple way.
However, his early assumptions leave an uncomfortable taste in the mouth.
So, from Section Nine, “The Relativity of Simultaneity”…
Einstein describes a train moving along at a constant velocity. Lightning strikes the embankment at points A and B. Midway between these two points is point M, which, at the time of the strike, also happens to be point M’ on the train.
Clearly, a person standing at the side of the tracks at point M would see the strikes from A and B at the same time, since he is midway between them.
Albie can take it over from here. This is how he describes what an observer sat at M’ on the train would see:
He then goes on to say that this shows that time has no meaning independent of the state of motion of a body, i.e. that it has no absolute significance. He concludes that the time interval between two events depends on the motion of the observer. From here, of course, the rest of his theory moves on smartly.
BUT - I have a major problem with this statement. Perhaps I’m missing something obvious, in which case I’d be grateful if a smarter brain can put me straight. If so, you have permission to mock me spectacularly.
So here goes:
[list=1]
[li] Since we know that the observed speed of light is always the same (in a vacuum) no matter what the speed of the observer, wouldn’t beams of light from A and B - which after all, originate as if they were also from points A’ and B’ on the train - reach the observer at M’ simultaneously? Relative to him, they travel the same distance, and so must take the same length of time. Therefore, simultaneity is not dependant on the motion of the observer, which contradicts what the great guy says in the above passage.[/li]
[li] OK, let’s pretend that the observer really can hasten towards a beam of light, i.e. that the speed of light is not constant independent of the observer. Perhaps Einstein was just picking on light waves to make a point. In this case, the observer on the train will see the flash from B before the flash from A. But this does not mean that the flash from B happened before the flash from A - it just means that the observer was not at the midpoint when he observed the first flash.[/li]
[li] Expanding on point 2, perhaps Einstein is pointing out that the apparent simultaneity of the flashes depends on your movement. Relative to the embankment (which we will pretend is totally stationary, i.e. the Earth is not moving), the flashes are observed simultaneously. Relative to the train, B is observed before A. However, if we are now allowing passengers to “catch up” with light, then the observer at M’ could detect that he is moving relative to the light sources (from the fact that he is “catching up” with light from B, and “riding ahead” of light from A). So, the passenger could calculate that he observed the light from B when he was x miles from the source of B; therefore B occurred at such-and-such time. Also, he observed the light from A when he was y miles from A; therefore A occurred at another calculable time. He would conclude that A and B occurred simultaneously, relative to the sources.[/list=1][/li]
So, as far as I see it - if the speed of light really is constant, then simultaneity of events is independent of motion, and so time does have an absolute significance.
On the other hand, if we ignore the constant value of c for a second, then the proof given above that the time between events is dependant on the observer is clearly crazy: no matter how the observers are moving, they can agree on the position of the source and the speed of the source relative to a given “zero”, and thus can agree on the timing of the events from these sources.
Right - what have I missed? Please commence laughing in my face.
