In special relativity the relativity of simultaneity is explained with the following example. We have one frame of reference - a train moving from left to right with constant speed v relatively to the embankment, and second frame of reference - the embankment itself. On the embankment there are points A and B and their midpoint M. On the train there is the point M'. When M and M' meet each other, two lightnings strike both A and B. The observer on the embankment sees that the two flashes of light meet at the midpoint M. But since the train is moving and the point M' with it, M' moves towards B and therefore the observer on the train will see that the beam from B will arrive first at point M' and after that will arrive the beam from A. And so simultaneity is relative - for one observer the two events are simultaneous, but for the other they are not. But lets imagine for a moment that when the points M and M' coincide we put points A' and B' on the train which coincide respectively with A and B. So it is the same whether we say the beams start at A and B or at A' and B' - at the moment of the lightning strikes, those points coincide with each other. Lets imagine the people on the embankment and those on the train are aware of the experiment that is taking place. What is the point of view for the people on the embankment? They know that the speed of light is constant c in every direction, and therefore when the point M and M' meet they begin to wait for the two flashes of light and expect the light beams to meed at their midpoint M - the light needs equal time to travel the equal distances AM and BM. So they are right for themselves. Now lets consider the point of view of the train passengers. They know about the principle of relativity and so too expect the speed of light to be constant c in every direction. At the moment when point M and M' meet, the people start to wait for the flashes too. They know that point A' and B' are equally distant from the point M', because when M and M' coincide(and the flashes occur) - A and A', and B and B' coincide too(whether we take length contraction into account or not shouldn't matter because the important thing here is that the length A'M' is equal to B'M' according to the train passengers - according to them A and B are equally distant from M, and M' and M coincide at that moment with or without length contraction). So knowing that A'M'=B'M' and expecting the speed of light to be the same both from A' to B' and from B' to A', they would expect the light to cover the distances A'M' and B'M' for the same time, and therefore meet at point M'. What prevents the passengers from making such conclusions, and not be surprised when the two flashes don't meet at their midpoint M'? What is the difference between the train and the embankment - surely we can say that the train is stationary and the embankment is moving relatively to it with velocity v, so when the flashes occur at points A' and B', the point M will be moving towards A' and the people on the train will expect that for the people on the embankment the flashes won't be simultaneous. So is this difference in the way the two beams arrive at points M and M' real - for the people on the train the beams will meet at some other point? Or it is only a matter of relative conclusion - the observer on the embankment will expect the beams will meet only on his midpoint, and the observer on the train will expect the same thing?
But this argument only makes sense if the train observers for some reason assume both strikes happened simultaneously in their own frame--why should they do that, a priori? Einstein wasn't proposing that the embankment observers would just assume a priori that the strikes happened simultaneously in the embankment frame, he was including that as a fact unique to this particular physical scenario. There's nothing odd about the notion that two lightning strikes at equal distances from a given observer (in this case the train observer) might happen at different times in the observer's frame, in which case that observer will see the light from them at different times. If I'm sitting in my house for a week, and on Monday I see the light from a strike 1 mile to my North, and on Friday I see the light from a strike 1 mile to my South, I'm obviously not going to think that both strikes happened simultaneously and therefore be puzzled by the "paradox" that I saw the light from them at different times, I'll just conclude that one strike happened Monday and the other happened on Friday. Of course you could imagine a different physical scenario than the one Einstein proposed, one where the strikes do happen simultaneously in the train frame, but this would mean they happen non-simultaneously in the embankment frame so the observer at M doesn't see the light from each one at the same time. In any specific physical scenario, there's going to be some specific fact about which frame the strikes were simultaneous in and which they weren't.
That is exactly what I want you to imagine - that they are aware of the experiment. Because the flashes of lightning occur just when points M and M' coincide, therefore both observers can experience that moment equally well, and will know that two beans of light are traveling(from point A and B for the embankment and from A' and B' for the train) towards their middle points, and can begin to wait for the beams of light to arrive. Isn't it only natural for both of them to expect the beams to cover the equal distances from the front to the middle and from the back to the middle for the same time?
What do you mean by "in the moment" though? In the train frame, the distance between A and B is shorter than the length of the train (i.e the distance between A' and B') because of length contraction, so the moment that A and A' coincide happens earlier than the moment that B and B' coincide. No, in both frames the light beams meet each other at the position of M--all frames must agree about local facts confined to a single location in space and time, like when two objects meet one another. Of course in the train frame M is moving, and at the time the two light beams meet M is closer to the back of the train (B') than to the front (A'). Not if the strikes happen at different moments! Suppose the distance from the end of a train to the middle is 5 light-seconds, and one strike hits the front end at t=30 seconds, and then another strike hits the back at t=32 seconds. In that case, if each beam travels at c so it takes 5 seconds to move 5 light-seconds, naturally the light from the front strike will reach the center at t=35 seconds, and the light from the back strike will reach the center at t=37 seconds. That can't happen, as I said all frames must agree about local events. For example, suppose there was a bomb at the center of the train with light-sensors on both sides, programmed to explode if it detects flashes of lights on each side at the same moment--if different frames could disagree about whether the bomb explodes that would obviously be a pretty serious problem! Again, why do you think there's a problem with the train observer just saying the lightning strikes themselves happened at different moments, so that's why the light from each one reached him at different moments?
So you mean that in the original Einstein's example when it is said "Just when the flashes of lightning occur, the point M' coincides with the point M....", it is meant that when the points coincide the flashes occur but only for the observer on the embankment - so the whole example is described from the embankment observer's stand point. For the observer on the train first occurs the flash at B then the points M and M' meet each other and after that the strike at A occurs - and what the passenger describes(first flash from B and then that from A) is logical consequence of the the sequence of the events. So my confusion came from the way the example is described from like a third(distant) point of view. The conclusion is that when we describe something in the theory of relativity we describe it either from one frame of reference or from another - never from some murky outside third view point.
Yes, any statement about simultaneity (which includes any statement about one event happening 'when' another event is happening at a different location) is meant to be from the embankment frame's view. Of course local events, like the fact that the lightning strikes the front at the same position and time that A and A' coincide, are true in both frames. I thought A was the front of the train and B was the back? Either way, in the train frame first the front of the train coincides with the front point on on the track (which I was calling A), then later M and M' coincide, then later the back of the train coincides with the back point on the track (which I was calling B). Yes, that's right, any description involving frame-dependent facts such as simultaneity or length can only be from the perspective of a particular frame.
I never liked this example (although I think that it was formulated by Einstein himself). I think it is confusing and hard to understand. To understand the relativity of simultaneity, it is much easier to imagine a light being turned on in the middle of the train. The light reaches the front and the back of the train simultaneously, according to an observer on the train. But according to an observer on the embankment, the light will reach the back of the train before it reaches the front of the train, because according to such an observer, the light that reaches the back of the train will have travelled a shorter distance than the light that reaches the front of the train, since train is moving, according to this observer.
Yeah, personally I find it easier to inverse the scenario and give the example of a light bulb in the middle of the train. That avoids such unlikely pure chance events. Edit: I now see that I'm not the only one with that preference! :-)
At the time, it would have been a very intuitive explanation (I think it still is) given the prevalence of commuter rail, and the often unique experience associated (Which train is moving)? I can see why the mind would drift in that direction, and I think it's unfair to dismiss it because it's not instantly grasped by all. That said, time has passed so maybe tradition needs to give way to accessiblity about a century later. :)
Suppose we have two light sources, one moving in the middle of the moving train and one stationary in the middle of the station platform and they both flash when they are co-located, will the light on the train reach the ends of the train simultaneously according to an observer on the train and will the light on the platform reach the ends of the platform simultaneously according to an observer on the platform? Of course the answer is yes. Now repeat the experiment with one of the light sources failing to flash. Is anything different? Of course the answer is no. To me, this is a much more interesting scenario to analyze.
No, just a more interesting (to me) scenario to consider, since we are considering different scenarios from the OP.
Ok now suppose that there are 2 extra-observers put at B` and A` ends of the train. They are instructed to send light signals once their detectors are stroke by the lightening. Then the light signals from both ends go to a mirror in the middle of the train ( where the middle observer is there) and reflected back to B` and A` where they can register them and record the times of arrival. In that particular case, the recorded times of final arrival of the signal will be equal for both B` and A` simply because the light from B` takes shorter time to reach the middle mirror but compensates that by taking longer time after reflection relative to A`. So both B` and A` observer will agree that both lightening events happen at the same time same like the conclusion of the embankment observer. However, there will be a definite disagreement with the middle observer M` who still insists that B` happens ahead of A` So the final conclusion for all the observers in the train is that the train is moving in the direction of B`. This can simply solve the puzzle. However, as we learnt from Mickelson experiment, that no such way to know that the inertial FOR is moving because the laws of physics and c remain invariant. This makes new paradox. It also undermines the weakness of Einstein`s hypothesis that the simultaneity is a relative thing because: 1) it assumed that the whole calculation is made from the embankment observer point of view 2) it does not give clear definition of what does detecting an event means relative to different observers apart from using just light signal to detect the events
This thread is from February. Please don't post in old threads like this. If there is something you want to discuss that you think was not addressed, please start a new thread.
No. Recall that the lightning strikes are simultaneous only in the embankment frame, but not in the train frame. The observers on the ends of the train will detect the lightning strikes at different times (per their clocks) and thus send their light signals out at different times. Sure, but that's because your assumption that A' and B' detect the lightning strikes at the same time is incorrect.
The assumption I made that A` and B` are simultaneous is based on a though experiment I proposed when a reflecting mirror put in the middle of the train. Remember that Einstein`one was also a thought experiment. The strikes of lightening seen on A` and B` happen at the same time for the stationary observer but the calculation based on detecting them relative to M` is also based on the stationary observer`s point of view. And for my model with 2 observers located at the 2 ends of the train, their observation should coincide after receiving the reflecting signals. I did not propose that A` and B` are simultaneous or not, I just flow with the experiment. There is no preference to assume that the simultaneity should be observed according to M` while it could be recorded using 2 observers A` and B` and then they can use a conventional communication channels to share their results regarding the time of recording the signals !
I don't see your point. If train observers A' and B' detect the arrival of the reflected light at the same time (according to their clocks) then there's no way that observer train observer M' (at the middle of the train) could have seen light from A' and B' arrive at different times. Note that we are merely discussing observations made from a single frame--that of the train--so relativity hasn't even entered the picture yet. (Note that this is a different scenario than that used by Einstein.)
We are discussing the interpretation of observation made in train FOR based on the consideration of the stationary observer according to the laws of optics and light transmission. Remember that the whole process started when lightening strikes the 2 ends of train at the same time as seen by the external observer. The problem is that when you regard the ordering of events is due to interpretation of M`, the 2 ends-observers will disagree with M` either after recording their observation from the reflected light from M`-mirror or after communication by conventional channels for instance,,, There is one way out for that,,,,,, is to accept the fact that the train is moving in direction of B` ( which contradicts the relativity principle)
OK, so now you're back to Einstein's example: The lightning strikes at the ends of the train are simultaneous according to the platform observers. Good. No, none of the train observers disagree. All their observations are consistent with the lightning striking the ends of the train at different times (per their clocks). For some reason, you think that observers A' and B' will detect the lightning at the same time; not so. Of course the train is moving. Why do you think that contradicts the relativity principle?