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In some contexts e.g. on Wikipedia it is defined as a matter of happening . In others(e.g. as defined by Einstein in his book "Relativity the special and general theory") it is defined as a matter of observation.
Both definitions are distinct from each other. In case of Wikipedia's thought experiment two events $A$ and B(reaching of light at the back and front of train) are declared not simultaneous without observing them.
acc. to the Einstein's definition events can be empirically dissimultaneous only if they are observed to be dissimultaneous. So A and B are not dissimultaneous as par the criteria imposed by Einstein.

Are A and B (as explained on Wikipedia's experiment) are dissimultaneous in platform's frame, if yes then explain how these will be observed dissimultaneously.

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First, to be clear, events are points in spacetime that exist independent of any coordinate system as is the interval associated with two events.

So, we can say, without introducing a coordinate system, that the interval associated with two events is timelike, lightlike, or spacelike

In the timelike case, we can say that one event is later than the other, i.e., there is a separation in time between the events with one event after the other. It is possible to assign identical spatial coordinates to these events, i.e., they can be co-located in a coordinate system.

For the spacelike case, we can say that the two events are spatially separated and it is possible to assign identical time coordinates to these events, i.e., the events can by co-located in time (simultaneous) in a coordinate system.

Thus, one cannot say that two events are simultaneous in an absolute way.

Only by introducing a coordinate system (reference frame) do we add the necessary structure to discuss if two events are simultaneous according to some (but not all) coordinate systems.

Simultaneity is relative; it is in "the eye of the beholder".

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Simultaneity depends on the frame of reference. The statement that two events are simultaneous in a reference frame is just the statement that in the time coordinate of the two events in that frame are the same. This definition in general depends on the reference frame.

However, there are two exceptions where whether or not the events are simultaneous is the same in all reference frame. The first exception is when the events occur at the same place and the same time in some reference frame. Then it occurs at the same place and time in all reference frames. So they events are simultaneous in all reference frames.

The other exception is when, in some reference frame, you can get from the first event's space-time coordinates to the second event's space-time coordinates moving slower than the speed of light. In this case the events will never be simultaneous in any reference frame. To see this, imagine a person moving at constant speed from one event to the other. Now imagine going to a frame where the events are simultaneous. The person would need to be in two places at once, but this is impossible.

The example on the wiki of the light bulb turning on in the train is an example where simultaneity does depend on reference frame. In the reference frame of the train the two events are simultaneous, but in other reference frames the events will not be simultaneous.

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    $\begingroup$ How can we prove two events aoccured at same time without observing them? $\endgroup$
    – user31782
    Feb 24 '14 at 13:14
  • $\begingroup$ I suppose you can't prove that they happened at all without observing them at least indirectly. I don't see what that has to do with the question though. $\endgroup$ Feb 24 '14 at 15:39
  • $\begingroup$ This has to do with my question. Your definition of simultaneity is a bit incomplete, more precisely is different from that of the Einstien's. In wiki's experiment events $A$ and and $B$ are declared to dissimultaneous without observing them. My question is how to use both the definitions to show that $A$ and $B$ are not dissimultaneous in platform's frame? $\endgroup$
    – user31782
    Feb 24 '14 at 16:08
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    $\begingroup$ @Anupam, I think you need to understand the "observing" in SR doesn't mean "seeing". Think of a reference frame as a framework of rods and synchronized clocks. To establish if two events are simultaneous in this reference frame requires only recording the readings of the clocks co-located with the events. (cont.) $\endgroup$ Feb 24 '14 at 23:58
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    $\begingroup$ (cont.) From the Wikipedia article "Observer (special relativity)": Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured. Speaking of an observer in special relativity is not specifically hypothesizing an individual person who is experiencing events, but rather it is a particular mathematical context which objects and events are to be evaluated from. The effects of special relativity occur whether or not there is a sentient being within the inertial reference frame to witness them. $\endgroup$ Feb 24 '14 at 23:59
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Simultaneity is a convention in special relativity, not an observation. The Einstein clock synchronization procedure is one way of defining a plane of simultaneity in space-time; however, special relativity can be (and has been by, e.g., John Winnie in 1970) reformulated with a wide range of allowable clock synchronization schemes with no effect on the things you can actually measure. Einstein himself emphasized in the 1905 paper that this was a matter of definition, not empirical fact.

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  • $\begingroup$ I am referring to the definition given in article $VIII$ "ON THE IDEA OF TIME IN PHYSICS" in the book "Relativity the special and general theory." Concisely the definition is : "Two events occured in space are simultaneous if and only if they are observed to be simultaneous. $\endgroup$
    – user31782
    Feb 25 '14 at 12:01
  • $\begingroup$ That article explicitly emphasizes that what you are taking as the definition of simultaneity is a chosen convention. It is based on a postulate about the (immeasurable) one-way speed of light which "is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity." $\endgroup$
    – user27578
    Feb 25 '14 at 17:55
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[...] as defined by Einstein in his book "Relativity the special and general theory") it [simultaneity] is defined as a matter of observation.

Einstein's literal prescription can be read for instance here: http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I#Section_8_-_On_the_Idea_of_Time_in_Physics

To summarize in my own (hopefully carefully enough chosen) words:
Some particular indication (e.g. "being struck by lightning, $A_s$") of one particular element of a railway embankment ($A$) and some particular indication (e.g. "being hit by a thunderbolt, $B_h$") of some other particular element of a railway embankment ($B$, which was and remained at rest wrt. $A$) are called

  • "having been simultaneous to each other" if there exist an particiant ($M$) who was and remained "middle between" $A$ and $B$ and who observed $A$s indication $A_s$ and $B$s indication $B_h$ in coincidence;

  • "having been dissimultaneous to each other" if there exist an particiant ($M$) who was and remained "middle between" $A$ and $B$ and who observed $A$s indication $A_s$ and $B$s indication $B_h$ not in coincidence, but in sequence ("first one, and later the other"; regardless of which "first");
    or else, if $A$ had seen $B$s indication $B_h$ before, or at latest in coincidence with, stating its own indication $A_s$;
    or else, if $B$ had seen $A$s indication $A_s$ before, or at latest in coincidence with, stating its own indication $B_h$;

  • or otherwise there is at best only circumstantial evidence about simultaneity or dissimultaneity of $A$s indication $A_s$ and $B$s indication $B_h$.

In case of wiki's thought experiment [ http://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment ] two events A and B (reaching of light at the back and front of train) are declared not simultaneous without observing them.

In the thought experiment as described in the Wikipedia article there are relevant elements of the train being explicitly considered and named ("the front and back of the traincar"); and the "one observer midway inside a speeding traincar" is obviously meant as the "middle between the front and back of the traincar", and thus capable of contributing observations for determining whether and which indications of these two "ends of the traincar" were simultaneous or dissimultaneous to each other.

But there are no corresponding particular elements of the "platform" being named; and there is apparently no consideration given to the "other observer standing on a platform as the train moves past" having been "middle between" particular elements of the "platform", and thus capable of contributing observations for determining whether and which indications of any such elements of the "platform" might have been simultaneous or dissimultaneous to each other.

(In fairness: there is a similar shortcoming in Einstein's (related, though not quite equal) discussion of http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I#Section_9_-_The_Relativity_of_Simultaneity -- where the two "places of the embankment, $A$ and $B$" are explicitly named and $M$ is the "middle between $A$ and $B$"; but "ends" or corresponding "elements of the train" are not explicitly and distinctly named, making it difficult to identify and address "$M'$" explicitly as a "middle between" particular participants.)

Are events in this experiment simultaneous if observed?

It has been noted (correctly) in other answers already that "one cannot say that two events are simultaneous in an absolute way".
Simultaneity or dissimultaneity are not attributes of pairs of entire events; because each event may always involve several distinct participants (such as "the front of the traincar" and some particular element of the embankment, passing each other) who were not at rest to each other.
(That's "what simultaneity is not", or "what dissimultaneity is not", respectively.)

Instead, as indicated above, and as apparent in Einstein's definition, but unfortunately not explicitly verbalized by Einstein:
Simultaneity or dissimultaneity are attributes of pairs of indications of individual distinct participants who were at rest to each other (such as two "places of the railway embankment"; or two "ends of a train").

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  • $\begingroup$ "Are events in this experiment simultaneous if observed?". I corrected it, it is "Are events in this experiment simultaneous if observed in platform's frame?" $\endgroup$
    – user31782
    Mar 14 '14 at 8:24
  • $\begingroup$ Anupam: "Are events in this experiment simultaneous if observed in platform's frame?" -- Such a formulation is awfully close to being improper. (Such as talk of "lifetime of a muon in the frame of some racetrack" instead properly of invariant "lifetime of a muon"; or "length of a train in the frame of the embankment" instead properly of invariant "length of the train" as well as invariant "distances between railway ties"; or "mass of a proton in the frame of some accelerator" instead properly of invariant "mass of a proton" ...) Unfortunately, your formulation is indeed often used. $\endgroup$
    – user12262
    Mar 19 '14 at 22:46
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Sure, flash lights sent within the train cannot be observed by the observer on the platform. Nobody (or no device) can see light that is not sent directly to its eyes (receiver). Observer on the platform can see light sent within the train only if it is resent to him after it travelled locally (i.e. unseen directly from the platform).

Therefore, there will never be any problems with simultaineity. Both flashes reach the ends of the train simultaneously as registered by local (travelling) devices, and nobody on the platform can see them directly. There is no way to see the flashes reach the ends of the train dissimultaneousy.

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  • $\begingroup$ bright magus: "Nobody (or no device) can see light that is not sent directly to its eyes (receiver)." -- That's surely correct. However, it is generally assumed in the thought-experiments of RT that any events (and all separate indications of the various participants in any one event) are perfectly visible; giving off sufficient "light" to be seen and recognized by multiple observers (who are not necessarily at rest to each other). Yes, RT may be generalized by weakening this idealization. But whether your argument relates to the OP's question is dubious. $\endgroup$
    – user12262
    Apr 15 '14 at 22:23
  • $\begingroup$ There were the times when "it was generally" assumed that the world was supported by four elephants. Nowadays, as you say, there are people who claim they can see the invisible. Now, to make sure, are we still in the physics domain? (Are you going to keep chasing me all over the forum? If you do, you might want to produce something more challenging.) $\endgroup$ Apr 15 '14 at 23:03
  • $\begingroup$ bright magus: "[...] chasing me all over the forum?" -- You must be referring to our previous correspondence there. Well, someone better; since the "drive-by community" apparently wouldn't point out to you that even 1905 "the accelerations are measured in the stationary system K" $\endgroup$
    – user12262
    Apr 16 '14 at 5:09
  • $\begingroup$ user12262: Get a grip: you can see light from lightning, because there are multiple rays that get scattered (and that's real physics). However, rays you see then are not the ones that travelled from the source to the place of striking. You still can't see the rays that made the whole route (unless they got reflected after). So please, if you get a kick from watching the invisible or stopping the time and seeing a change in speed... have fun ... $\endgroup$ Apr 16 '14 at 7:41

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