Train Experiment: Does Simultaneity Depend on Frame of Reference?

[John_M]

About that train experiment. Everyone probably knows the story. For the person on the train, the flash of light hits both ends of the train at the same time. For the person watching on the embankment, the flash of light hits the back end of the train first.

Now, I'm reading a book on SR which words the experiment slightly differently. It says that the flash of light triggers off the doors at either end opening. So, for the person on the train, the doors open simultaneously, whereas for the person at the other end, they do not open simultaneously. From this I'm guessing it must be possible for a flash of light somehow to complete an electrical circuit. I don't know the ins and outs of how this would happen - maybe it isn't even right. I seem to remember something about 'light sensitive diodes' from physics at school about 10 years ago. But still...I'll assume that it's possible.

Let's replay the train experiment with a single, almost instantaneous flash of light. Both ends of the train are wired up to an electrical circuit, which when completed triggers an emergency braking system which stops the train.

To the person on the train, the flash of light hits both ends of the train at the same time, thereby completing the circuit. But in the observer's frame of reference, the flash of light hits each end at different times and so the circuit is never completed.

Is it then correct to state that, to the observer, the train is still going, whereas to the person in the train, it has stopped? I'm guessing everyone will say no to this, so where have I gone wrong?

 

[jcsd]

Where you have gone wrong is to assume that the circuit will work in exactly the same way in both reference frames (note this is different from saying that the laws of physics is different in the two frames as they are infact the same), the answer is simple try as you might to construct such a circuit it can't be done (this will become clearer if you try to model the circuit).

 

[jcsd]

Hmm perhaps saying the circuit works differently is perhaps a tad misleading, anyway remeber that the current does not flow through a circuit instantaneously.

 

[John_M]

Hmm perhaps saying the circuit works differently is perhaps a tad misleading, anyway remeber that the current does not flow through a circuit instantaneously.

The current won't flow through the circuit instantaneously but surely an electrical current, like light, is a form of electromagnetic interaction and will therefore move at the same speed in both frames of reference?

 

[jcsd]

The current won't flow through the circuit instantaneously but surely an electrical current, like light, is a form of electromagnetic interaction and will therefore move at the same speed in both frames of reference?

Think of the current as a single electron flowing around the circuit if you wish, clearly the message velocity is the velocity of the electron and the velocity is not invariant.

Of course you could use some sort of 'optical circuit' using photons so the speed is invariant, however you could not ignore the effects of the Lorentz transformation.

 

[Taibak]

The current won't flow through the circuit instantaneously but surely an electrical current, like light, is a form of electromagnetic interaction and will therefore move at the same speed in both frames of reference?

Not so. That restriction only applies to light and not to other forms of electromagnetic interactions, including current. Moreover, a current is just moving electrons. Since electrons have mass, they can't possibly move at the speed of light.

 

[John_M]

OK...slight error over the electrons then. I dropped physics at GCSE level (But I still find it interesting...)

But would the speed of the electrons really make any difference here? It would only determine the speed at which the message is conveyed to the brake once the circuit has been completed, when the key issue at stake is that, as a result of the relativity of simultaneity, the circuit is completed in one frame of reference but not in the other.

The issue of Lorentz transformations would be relevant to the mechanics of how the circuit works. And I know zero about that. It's just a suggestion, after all.

 

[jcsd]

OK...slight error over the electrons then. I dropped physics at GCSE level (But I still find it interesting...)

But would the speed of the electrons really make any difference here? It would only determine the speed at which the message is conveyed to the brake once the circuit has been completed, when the key issue at stake is that, as a result of the relativity of simultaneity, the circuit is completed in one frame of reference but not in the other.

The issue of Lorentz transformations would be relevant to the mechanics of how the circuit works. And I know zero about that. It's just a suggestion, after all.

The speed of the electron is importnat as there must be communication between the two parts of the circuit which interact with the light in order for them to know the circuit is completed. This communicatio cannot take place instaneously.

What you would actually find happens is that the circuit is completed in both frames even though the flash of light does not hit both ends simulatnaoeusly in both frames. This is due to how times and distances are effected by the Lorentz transformation.

The Lorentz transformation

 

[John_M]

What you would actually find happens is that the circuit is completed in both frames even though the flash of light does not hit both ends simulatnaoeusly in both frames. This is due to how times and distances are effected by the Lorentz transformation.

How would this work??

 

[jcsd]

Well, the exact way it would work, depends on the mechanism used. For example if each end of the train sent an electron to the middle to a device which stops the train if and only if two electrons arrive at it simulataneously.

In the rest frame of the train the flashes strike instanously and the two electron have to travel the same distance, so they arrive at the smae time stoppoing the train.

In the rest frma eof the other observer one end of the train releases it;s electron first, BUT this electron has further to travel than the other electron, so they still reach the middle at the same time stopping the train.

 

[John_M]

The point I was trying to make with my post was as followed: SR means that different truths hold within different frames of reference. The examples people quote are only small, eg a couple of seconds, or a couple of centimetres, either way. But is it possible for those differences, by a sequence of events, to be exaggerated into much greater and more noticeable differences? Something like the 'butterfly effect.'

With respect to your answer, I didn't think an electric current worked like that at all - I thought it was only flowed in one direction ie clockwise or anti-clockwise. Not simply two electrons communicating a message to a central point. I don't really know what I'm talking about here, though. The example I gave is too complicated - it's probably possible to make the same point with a simpler example, involving neither electrons nor Lorentz transformations.

 

[jcsd]

The point I was trying to make with my post was as followed: SR means that different truths hold within different frames of reference. The examples people quote are only small, eg a couple of seconds, or a couple of centimetres, either way. But is it possible for those differences, by a sequence of events, to be exaggerated into much greater and more noticeable differences? Something like the 'butterfly effect.'

The diffeernces oare fram edepednet obeying the Lorentz trasformation slightly. Differemnt frmaes are not like different universes they're just slightly different ways of looking at te same universe.

With respect to your answer, I didn't think an electric current worked like that at all - I thought it was only flowed in one direction ie clockwise or anti-clockwise. Not simply two electrons communicating a message to a central point. I don't really know what I'm talking about here, though. The example I gave is too complicated - it's probably possible to make the same point with a simpler example, involving neither electrons nor Lorentz transformations.

No, of course; I'm trying to use a very basic model to show why the train 'stops' in both frames of reference, you can alter the mechanism if you wish but the fact that SR gives us a self-consisent explantion does not change.