Mowgli

Aha! That makes a lot more sense. Thanks for clearing it up! Well, I think he's saying that the speed of light is a constant in an inertial frame. Later on, he will impose the assumption that it is the same constant for all inertial frames. Coming back to my original question, is this definition of synchronism compatible with (or the same as) the notion of simultaneity?

Is that what Einstein is saying here in this statement? I just don't see it. Here is the statement again. Suppose I have the clock A with me. Then any other clock B will be synchronized with my clock A, because the definition of sycnrhonism is always true.Now consider a clock B in motion with respect to me. It can synchronize with a clock A only if A is moving in tandem with B (in the same inertial frame, ie.) Otherwise the condition tA - tB = t'B - tA cannot be true. Thus B cannot be synchronized to A, in contradiction with the first generalization. Again, consider a clock B in motion with respect to me. Exactly as above, it can synchronize with a clock C only if C is moving in tandem with B (in the same inertial frame, ie.) Otherwise the condition tC - tB = t'B - tC cannot be true. But A is in synch with both B and C.But this is in contradiction with the second generalization. I must be missing something obvious here, can you help me spot it?

But this is exactly what Einstein said in his 1905 paper. I quote from the paper below. Sorry to sound as though I was trying to “trap” you. Believe me, I agree completely with your statement quoted above. I just don't know how to reconcile it with the synchronization assumption (and the subsequent generalizations) above.

If A is in motion... Actually, this is something that I find weird. If B is in motion, A and B are still considered synchronized, but not if A is in motion.

At the core of SR is a definition of what is meant by two clocks being synchronous. Two clocks A and B are assumed to synchronize if a ray of light takes the same time to go from A to B as it will take to go from B to A. Simultaneity, on the other hand, can be defined as follows: two events X and Y are simultaneous to an observer O if light rays from X and Y reach O at the same time (as seen by O's clock.) Are these two definitions compatible? Cheers, Mowgli

Okay, thanks. For an object moving away from the observer, the light flight time effect predicts the following: The time flow appears dilated The length appears contracted The apparent speed cannot be more than the speed of light It takes an infinite energy to accelerate to an apparent recessional speed of c These look suspeciously like the consequences of the coordinate transformation in SR. That's why I was wondering if they could be the same, or at least related... Mowgli

This is the part I haven't understood yet. Suppose I have a clock moving away from me at a constant speed of 0.8c. The clock is programmed to flash every second. I would expect to see the first flash at 1.8 sec (because it is emitted at 0.8c away from me), the second at 3.6 sec and so on. So I would conclude that the time is flowing at the rate of 1/1.8 at the clock. This is the perceptual time dilation. I would be wrong, of course; the first flash won't be emitted one second after the clock leaves me, but 1.67 sec after it leaves me, because of the SR time dilation at the clock. And it will be emitted at a distance of about 1.33c away from me. I will see this flash 3 sec after the clock leaves me, leading me to conclude that the time is flowing at the rate of 1/3 at the clock. So, when SR says that the real time dilation is 1/1.67, am I supposed to observe a time dilation of 1/3 and then deduce from that the time dilation must be 1/1.67? Thanks again, Mowgli.

Thanks for clearing that up, Tom. Since time dilation is the way one clock runs as seen by an observer in a different frame, is it possible to understand it as a perceptual effect? If I have a clock going away from me at a constant speed, it will appear to me to be running slower, due to the light travel time effects. Is the SR time dilation the same as this perceptual effect? Thanks again, Mowgli

Thanks for the explanation, it makes sense now. Only one thing I'm still not clear about though. I thought that the time dilation was always a dilation, whether the coordinate systems were approaching or receding from each other. When Tom applies Lorentz transformation to go from t2' to t2, he gets t2 greater than t2'. Can the time dilation be a time contraction as well? Mowgli

Shall we try a time dilation paradox, again? I have been trying in vain to locate a flaw in the thought experiment below... Imagine a train moving at a constant speed, so that its frame is an inertial frame. At the front end of the train, there is a clock with a trigger mechanism. When the train passes a pole by the track, the clock triggers and records the time reading. There are two poles by the track. Each of them has a similar clock, which triggers when the front end of the train passes it. The clocks on the poles have been carefully synchronized to avoid any ambiguity. The synchronization can be achieved, for instance, by putting the clocks next to each other at the midpoint between the poles and then moving them to the poles at the same speed, accelerating and decelerating in tandem, so that they stay synchronized. As the train passes by, we get four time readings: 1. T1 the time registered when the train passes the first pole, as read by the clock attached to the train, 2. T2 the time registered when the train passes the second pole, as read by the train clock, 3. P1 the time registered by the clock at the first pole as the train passes it, and 4. P2 the time registered by the clock at the second pole as the train passes it. Since T1 and P1 are recorded locally, in the immediate vicinity of the first pole, they should be immune to non-local effects, such as a need to synchronize clocks between their locations. The same argument of locality applies to the second pair of readings (T2 and P2) as well. Once all four time readings are recorded at the respective sites, they are compared. Since the comparison is done at a later point in time, the process of comparison cannot affect the time readings already recorded, even if it involves acceleration or deceleration. (But the necessity for acceleration can be avoided, for instance, by calling the train driver on his mobile phone asking him to read out T1 and T2, and giving him the pole clock readings P1 and P2.) For the stationary observer (staying with the poles), the time interval recorded at the train DT=T2-T1 should be smaller than his interval DP=P2-P1, because the train is in motion, and time dilation applies to its frame of reference. But for the driver moving with the train, the poles are in motion. Each pole clock is dilated, and should be running slower than the train clock. So the difference between their readings should be smaller. DP should be smaller than DT. Since T1, T2, P1 and P2 are four numbers that have already been registered and recorded, DT cannot be both greater and smaller than DP at the same time. Do you think there is a paradox here? If not, which time difference (DP or DT) do you think will be larger? - best wishes, - Mowgli