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What's wrong with this so-called paradox?


gib65

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'The train is moving'.

 

It doesn't matter if the train is accelerating or keeping constant speed, it is specified as moving.

 

Just like in Einstein's thought experiment.

 

So how does the observer on the train know he is moving?

 

He doesn't.

 

And what is his (the whole train system) velocity?

 

No specifed.

 

It is a relative velocity, but relative to what?

 

The "stationary" observers external to the train. (Just like in Einstein's thought experiment).

 

This condition is tantamount to specifying an absolute system of reference.

 

No it isn't.

 

So to her the light from the end clocks travels different distances in different times.

 

It must be the same distance as the clocks are equidistant from the centre. Yes, in different times because (from her perspective) the train is moving towards one flash and away from the other. And at the same speed (of light). Hence they must have occurred non-simultaneously.

 

But they were simultaneous for the observer on the train.

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It is interesting that I am the only one who has ventured an opinion on the question

 

Does the clock stop or not?

 

Yet one of those who did not dare answer this question has graced me with a red point.

Edited by studiot
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It is interesting that I am the only one who has ventured an opinion on the question

 

Does the clock stop or not?

 

Yet one of those who did not dare answer this question has graced me with a red point.

 

I thought everyone agreed that the clock stops (as seen from all frames of reference) but people disagree about why (i.e. whether the flashes were simultaneous or not).

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Strange

I thought everyone agreed that the clock stops (as seen from all frames of reference) but people disagree about why (i.e. whether the flashes were simultaneous or not).

 

 

The only reference that I can find is post#14 where pzkpfw thinks the clock stops (apologies if your statememt was meant to be stonger than this).

 

I think it is imperative to establish what would actually happen before arguing about why.

 

Once that is done a properly forumated explanation can be provided to gib65.

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The only reference that I can find is post#14 where pzkpfw thinks the clock stops (apologies if your statememt was meant to be stonger than this).

 

It was: no one has said the clock doesn't stop. For the obvious reason that it does (under any reasonable interpretation of the very slightly ambiguous description). In all frames of reference.

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strange

under any reasonable interpretation of the very slightly ambiguous description)

 

This is a really silly digression.

 

The OP asked specifically, in so many words and in more posts than one if the clock stops or not.

 

The only reasonable interpretation of that is he doesn't know and is not afraid to ask and doesn't claim it as a reasonable interpretation after the event.

 

So can we agree that the middle clock is found to be stopped at the end of the experiment and proceed from there?

Edited by studiot
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1) Does the middle clock stop?

2) What is the correct line of reasoning leading to this conclusion?

3) What is the fault in the reasoning presented in post#1? Note this is the reasoning, not the statement of conditions.

 

Of the three questions the first one is now answered, yes the clock stops.

 

To answer the second and third it is good to point out that analysis and calculations are best done entirely in a single frame of reference and that this is possible in this case since the three clocks are in a common frame.

Mixing information from different frames so easily leads to incorrect conclusions (I'm sure we've all done it).

 

At this point it would be nice to hear from gib65

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To answer the second and third it is good to point out that analysis and calculations are best done entirely in a single frame of reference and that this is possible in this case since the three clocks are in a common frame.

 

The second question is answered by the question defintion (as I, and I think others, understand it): the two flashes occur simulatenously in the train's frame of reference, they travel the same distance to the central clock, at the same speed and so arrive at the same time and stop the clock.

 

The question was: how is this accounted for in the external frame of reference, moving relatively to the train (or, equivalently, that the train is considered to be moving realtively to). As far as I can see, that question has been answered very well by several people.

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strange

The question was: how is this accounted for in the external frame of reference, moving relatively to the train (or, equivalently, that the train is considered to be moving realtively to). As far as I can see, that question has been answered very well by several people.

 

It must be the same distance as the clocks are equidistant from the centre. Yes, in different times because (from her perspective) the train is moving towards one flash and away from the other. And at the same speed (of light). Hence they must have occurred non-simultaneously.

 

So far as I can see your last word on this was to repeat the so called paradox.

 

Which would be (if it were a paradox) why does the middle clock stop if it is observed to receive the flashes non-simultaneously?

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Which would be (if it were a paradox) why does the middle clock stop if it is observed to receive the flashes non-simultaneously?

 

It is the emission of the flashes which is non-simultaneous (as seen by the "stationary" observers).

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At this point it would be nice to hear from gib65

 

It's not so much a paradox as something which seems (to me) to be missing something.

 

In a nutshell, I stated it like this in my OP:

 

 


If everyone has to observe the same events happening, then either a) everyone has to observe that the stop-clock indeed stopped, in which case your assistants would have to conclude that the flashes went off at different times (even though they observed the stop-clocks being synchronized), or b) everyone has to observe that the stop-clocks did not stop, in which case you would have to conclude that the flashes went off at different times (even though you observed the stop-clocks being synchronized).

 

So the clocks start out synchronized, and at the end of the experiment, someone has to conclude that they became unsynchronized. This is not a paradox, but it seems to suggest that somewhere certain laws of physics were violated (I don't think this is actually the case--the laws of physics being violated, I mean--which is why I say something seems to be missing in my understanding). Being initially synchronized and treated them same way throughout the whole thought experiment, you would think that exactly the same things would happen to the two clocks--they wouldn't enter into different states from each other--but they do enter into different states--one clock ends up behind the other--and so it seem (to a novice like me) like the laws of physics were different for one clock than for the other.

 

But I'm gathering that the consensus is that they two clocks are not treated the same--one is placed at the rear of the train and the other is placed at the front--and according to some on this board (and elsewhere--I have this question posted on another science forum), this can result in different effects happening to the two clocks during the acceleration phase of the train's journey (apparently, this is true even for someone on the train). The front clock will appear to run behind the rear clock relative to someone at rest.

 

But this is the part I'm trying to wrap my head around.

 

A few people have said it has to do with the simultaneity of when each part of the train starts accelerating. I don't think this has anything to do with physical lag, by which I mean the fact that an engine at the front of the train will start moving first and all other cars will start to move slightly after (because it takes time for the energy to travel down the length of the train and thereby pull each car)--kind of like how at a traffic light that turns green, not all cars start moving simultaneously but rather one after the other. I don't think this is it because you could just as well have the engine at the rear of the train pushing the other cars.

 

But if we are to say that, relative to an observer at rest, the front of the train starts accelerating first (for whatever reason), then I'm wondering if I understand it correctly. Please tell me if I have this right: suppose that at the moment when the front train starts accelerating, both clocks read 12:00. Then the front train starts accelerating at a rate that pushes the front clock to tick away at twice the rate as the rear clock (relativistically speaking). It takes 5 seconds, according to the rear clock, for the front train to get up to speed and start coasting. At that point the rear clock will read 12:00:05 and the front clock will read 12:0010. (I'm avoiding making both trains accelerating at the same time in order to make things simpler--but I'm sure the same principles would apply even if the rear train started accelerating before the front trains stopped accelerating). Now it's the rear trains turn to start accelerating. It accelerates at the same rate for the same amount of time. This means its clock's rate will be doubled and will end up reading 12:00:15 by the time it starts coasting. However, the front train's clock will not read 12:00:15. Having achieved a high velocity, it's clock will tick away at a slower rate than that of the rear clock while it was at rest. In other words, it will be somewhere between 12:00:10 and 12:00:15. <-- They are out of sync. The rear clock now being ahead will result in its going off (emitting a flash of light) before the front clock.

 

Do I have this right?

 

If so, my only question is: is this a general rule of relativity? That in an accelerating reference frame, things closer to the rear of the reference frame (where "rear" is defined as positions further away from the direction of acceleration) will end up being "ahead" in time relative to things closer to the front, at least once the acceleration has stopped and the system begins coasting? And this, because there is no absolute simultaneity of when each part of the system starts to accelerating, things at the front being considered to start accelerating "first" relative to someone at rest?

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strange

It is the emission of the flashes which is non-simultaneous (as seen by the "stationary" observers).

 

 

Surely both ends of the train (and therefore sources) have the same relative velocity to the stationary observer?

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So the clocks start out synchronized, and at the end of the experiment, someone has to conclude that they became unsynchronized.

Incorrect. In the FRAME that the clocks are synchronized, they STAY synchronized.

In all OTHER frames (in motion wrt the frame above), the clocks are NOT synchronized.

This is because synchronization is a relative phenomenon, i.e. it is FRAME-DEPENDENT.

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Incorrect. In the FRAME that the clocks are synchronized, they STAY synchronized.

In all OTHER frames (in motion wrt the frame above), the clocks are NOT synchronized.

This is because synchronization is a relative phenomenon, i.e. it is FRAME-DEPENDENT.

Can't they go out of sync if they are moved too fast? (twin paradox etc) to be synchronised they might be brought together but then taken to the ends of the train. so they moved along their frame.

Edited by Robittybob1
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They are both in the same frame of reference and so, in that frame of reference, they will remain synchronised.

Each particle within a frame of reference could end up being in another frame of reference. If the clock is moved it moves WRT the original train FoR but the train's FoR stays the same.

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Each particle within a frame of reference could end up being in another frame of reference. If the clock is moved it moves WRT the original train FoR but the train's FoR stays the same.

 

The clocks are stationary at each end of the train. (There is a reasonable synchronization protocol at the start which involves transporting both clocks at the same speed to the ends of the train. But that is all unnecessary as this was all explained pretty clearly by Einstein nearly 100 years ago.)

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Studiot

So to her (the trackside observer) the light from the end clocks travels different distances in different times.

 

Strange

It must be the same distance as the clocks are equidistant from the centre. Yes, in different times because (from her perspective) the train is moving towards one flash and away from the other. And at the same speed (of light). Hence they must have occurred non-simultaneously.

 

Let us examine this exchange carefully.

 

Set aside the issue of simultaneity for just a moment. and measure in the trackside coordinate system.

Call the clocks Cf, Cm and Cr for front, middle and rear.

Let Cf emit a flash as it passes point f and Cr emit as it passes point r on the track.

 

So Cf emits a flash at f which travels back towards Cm, as well as towards the trackside observer.

But Cm in in motion towards f so in the time it takes for Cm to encounter the flash it has shortened the distance and so the trackside observer will see Cm receive the front flash slightly earlier.

 

Similarly whenever Cr emits its flash, simultaneous or not, Cm is in motion away from it so the trackside observer will see Cm receive the rear flash slightly later.

 

So the non-simultaneity does not follow from the Cm being equidistant from Cf and Cr and would be true whether or not equidistance holds. It is a direct consequence of the motion of the train, relative to the track.

Edited by studiot
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So the non-simultaneity does not follow from the Cm being equidistant from Cf and Cr and would be true whether or not equidistance holds.

 

Of course not. Einstein, and the OP, place the obsever (clock) at the center of the train for simplicity.

 

It is a direct consequence of the motion of the train, relative to the track.

 

Of course. The observer on the train says the flashes were emitted simultaneously, the observer on the platform says they were not emitted simultaneously.

 

 

Set aside the issue of simultaneity for just a moment.

 

But that is the whole point of the question!

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Each particle within a frame of reference could end up being in another frame of reference. If the clock is moved it moves WRT the original train FoR but the train's FoR stays the same.

 

But that's not what's happening, so this doesn't apply to the discussion.

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strange

Of course not

 

So you were too hasty in contradicting me.

 

I see this problem as more akin to the extended lifetime of the muon than an Einstinian simultaneity issue.

 

The key to question 2 is to realise that the crucial frame is that of Cm for simultaniety purposes. This happens to be that of the train in this case.

 

@gib65

 

I don't know what you are unsure of and most here have given rather cryptic responses instead of detailed explanations.

 

Your basic experiment description is understandable and I think you realise that most of the analyis is designed to confuse the issue to establish the paradox.

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