Problem with relativity of simultaneity original exampleby baivulcho Tags: original, relativity, simultaneity 

#1
Feb511, 02:53 PM

P: 3

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? 



#2
Feb511, 03:21 PM

Sci Advisor
P: 8,470

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 nonsimultaneously 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. 



#3
Feb511, 04:08 PM

P: 3





#4
Feb511, 05:04 PM

Sci Advisor
P: 8,470

Problem with relativity of simultaneity original example 



#5
Feb511, 05:36 PM

P: 3

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.




#6
Feb511, 06:04 PM

Sci Advisor
P: 8,470





#7
Feb811, 06:45 AM

P: 304

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.




#8
Feb811, 07:54 AM

P: 3,178

Edit: I now see that I'm not the only one with that preference! :) 



#9
Feb811, 08:31 AM

P: 82

That said, time has passed so maybe tradition needs to give way to accessiblity about a century later. :) 



#10
Feb811, 09:10 AM

PF Gold
P: 4,542

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 colocated, 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. 



#11
Feb811, 09:36 AM

P: 304





#12
Feb811, 09:50 AM

PF Gold
P: 4,542

No, just a more interesting (to me) scenario to consider, since we are considering different scenarios from the OP.




#13
Feb811, 09:53 AM

P: 82

ghwellsjr's example makes sense to me, and I've already been clear that I like Einstein's version.




#14
Jul111, 11:17 AM

P: 163

Ok now suppose that there are 2 extraobservers 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 



#15
Jul111, 11:39 AM

Emeritus
Sci Advisor
PF Gold
P: 5,500

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.




#16
Jul111, 11:40 AM

Mentor
P: 40,907





#17
Jul111, 12:26 PM

P: 163

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 !




#18
Jul111, 01:05 PM

Mentor
P: 40,907

(Note that this is a different scenario than that used by Einstein.) 


Register to reply 
Related Discussions  
relativity of simultaneity help  Special & General Relativity  15  
relativity simultaneity  Introductory Physics Homework  1  
Relativity of Simultaneity  Special & General Relativity  12  
The Relativity of Simultaneity  Special & General Relativity  22 