Relativity of simultaneity

[vulgarian]

Hi.

 

Im having troubles getting this concept, and it would be really useful if someone can help to clarify my understanding...

 

Referring to Einsteins thought experiment involving the train and two flashes of lightning hitting the track:

 

The reason for these events being simultaneous on the platform, but not on the train, is because the light takes a finite amount of time to reach the observation point. During this time the train has advanced towards one event and away from the other, therefore one flash will hit the observer on the train before the one chasing it. An explanation of this phenomenon introduced the relativistic length of the train, but this does not seem to be important since the extra length with respect to the platform's reference frame should still be balanced and the observation points of the train and platform should still both be midway between the two events when they occur - it seems purely the motion of the train against the finite speed of light that results in the apparent difference of observations.

 

If this is so, how can one say that the event is not simultaneous from the trains reference frame (surely it is just the mechanics of the observational method that makes the events appear to occur at different times).

Following from this line of thought another method of conducting the experiment would seem to indicate that the events occur at the same time from both reference frames:

 

At each point where the lightning strikes, a device is placed (one on each end of the platform and one on each end of the train - though the length may have to be decreased on the train to account for the relativistic length due to its velocity). The devices are arranged so that observation points and event points all align spatially when they occur.

 

Inside the device is a waterclock (or decaying atom) that is triggered by the heat of the lightning stike. Checking the progress of the devices on the platform confirms that the events were simultaneous. The two devices on the train should also be equal, even if the ones on the train are less advanced than the ones on the platform due to time dilation, the events were still simultaneous.

 

Sorry if this is a bit long-winded, im just trying to iron out the wrinkles in my understanding of this. Thanks for bearing with me!

[swansont]

Not sure if I follow all of your scenario, but

 

The devices are arranged so that observation points and event points all align spatially when they occur.

 

If this involves lining up multiple points on the train with corresponding points on the ground, you can't make this work. If someone on the ground thinks they all line up from the train's length contraction, someone on the train will disagree since the train station will be length contracted.

[vulgarian]

Thanks swansont.

 

I guess what i am getting at is that the relative non-simultaneity of the reference frames seems to me to be a case of perception, much like a supersonic jet passing overhead, and that if light was not used to determine simultaneity then both reference frames would agree on the events occuring at the same time - albeit at different amounts of time ago. So instead of observing the rays of light from each event (which the observational velocity can skew), each event initiates an timing mechanism which can be checked once the train has stopped and isnt travelling at some reality warping velocity!

 

Not sure if I follow all of your scenario, but

If this involves lining up multiple points on the train with corresponding points on the ground, you can't make this work. If someone on the ground thinks they all line up from the train's length contraction, someone on the train will disagree since the train station will be length contracted.

 

Blimey this is wierd. So if, when the train is stationary, it is the same length as the platform, and A', M', and B' all align with A ,M, and B. But during the experiment it is to be travelling at c/2 when the events strike and the observervers coincide, so before the experiment the distance between the sensors is reduced by lorentz's dialation factor for c/2, then the points wont align at the time of the experiment?

[swansont]

Thanks swansont.

 

I guess what i am getting at is that the relative non-simultaneity of the reference frames seems to me to be a case of perception, much like a supersonic jet passing overhead, and that if light was not used to determine simultaneity then both reference frames would agree on the events occuring at the same time - albeit at different amounts of time ago. So instead of observing the rays of light from each event (which the observational velocity can skew), each event initiates an timing mechanism which can be checked once the train has stopped and isnt travelling at some reality warping velocity!

 

They will disagree on the accuracy of the timing mechanism, and/or the mechanisms will disagree if one is on the ground while the other is on the train.

 

Blimey this is wierd. So if, when the train is stationary, it is the same length as the platform, and A', M', and B' all align with A ,M, and B. But during the experiment it is to be travelling at c/2 when the events strike and the observervers coincide, so before the experiment the distance between the sensors is reduced by lorentz's dialation factor for c/2, then the points wont align at the time of the experiment?

 

Right. If the front of the train lines up, the rear won't.

[vulgarian]

I really appreciate your help here but im still struggling.

 

Right. If the front of the train lines up, the rear won't.

This is raising more questions im afraid! I've knocked up a paint picture to clarify what is in my mind... To me it seems if the dialation is accounted for before the experiment by moving the train sensors so that they line up when at speed. Then when the train tears by, a snapshot from the platform will show an elongated train with sensors lined up, while a snapshot from the train will show a compressed platform with sensors lined up.

 

Ive obviously got the wrong end of the stick somewhere, because following this logic, the observer on the train could just say "Wait a minute! Im am stationary and the platform is moving by me at a great speed, and should therefore appear to be longer, and the observer on the platform could say i am whizzing past a stationary train which should appear to be compressed!"

 

 

They will disagree on the accuracy of the timing mechanism, and/or the mechanisms will disagree if one is on the ground while the other is on the train.

 

Yeah im taking it for granted that the time that will elapse between the event and observation will differ between the devices on the train and on the platform. Im not sure what you mean by accuracy. Im thinking whatever relativistic effects occur due to the velocity, the sensors on the train will still be balanced and thus agree on the time of the event. (unlike if light is used to detemine simultaneity)

[Sisyphus]

 

This is raising more questions im afraid! I've knocked up a paint picture to clarify what is in my mind... To me it seems if the dialation is accounted for before the experiment by moving the train sensors so that they line up when at speed. Then when the train tears by, a snapshot from the platform will show an elongated train with sensors lined up, while a snapshot from the train will show a compressed platform with sensors lined up.

 

It's never elongated. In the rest frame of the train, the platform is compressed. In the rest frame of the platform, the train is compressed. (Your second picture is wrong.) You are correct that it does not matter which is considered to be moving. All the observations between them are symmetrical.

 

I don't really understand what you're describing with the timers, but rest assured there is no way to rig them to make it work. Events which are simultaneous (at different locations) in one reference frame simply are not simultaneous in any other reference frame. It's not just a matter of perception.

[Janus]

This how events occur according to the embankment observer:

 

 

The same events according to the train observer: