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Two lightning bolts striking either end of train


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#1 Tir21

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Posted 9 January 2017 - 02:15 PM

Simultaneity - Albert einstein and the theory of relativity. This video says that the person on the train will see lightning from front of the train first. But what if we take it that the train is stationary and the earth is moving below the train.

How could we tben explain the passenger on the train seeing the front bolt first
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#2 Lord Antares

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Posted 9 January 2017 - 02:31 PM

The speed of lights moves at a certain speed, however large. So of course it will be seen sooner by someone who is closer to the lightning bolt. Of course, this difference is imperceptable by humans and they would both agree to seeing it at the same time, but we are talking about technicalities, right?

Maybe I'm missing something because you haven't provided the video. There's not enough info to discuss more.


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#3 Tir21

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Posted 9 January 2017 - 02:39 PM

Thanks heres the video
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#4 swansont

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Posted 9 January 2017 - 02:40 PM

Simultaneity - Albert einstein and the theory of relativity. This video says that the person on the train will see lightning from front of the train first. But what if we take it that the train is stationary and the earth is moving below the train.

How could we tben explain the passenger on the train seeing the front bolt first

 

 

The conclusion from relativity is that strikes are not simultaneous in the train's frame if they are simultaneous in the earth's frame.


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#5 VandD

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Posted 11 January 2017 - 02:52 PM

 

 

The conclusion from relativity is that strikes are not simultaneous in the train's frame if they are simultaneous in the earth's frame.

Yest, but I think Tir21 wants to know how the thought experiment runs from the train passenger point of view. That's a different story.

I'll give it a try:

 

@Tir21

Very good question, Tir21.

Let's first start with Einstein's setup before jumping to your question. .

-The embankment observer sees both bolts simultaneously. For him, in his frame of reference, both lightning bolts happened simultaneously( lights from the bolts travel same length).

-The train passenger does not see both bolts simultaneously.

Why does this mean for him both bolts didn't happen simultaneously?

 

If one would state (as is often the case) it is because he moves toward the front bolt, we could throw in maybe also for the train observer both bolts happened simultaneously, but he only SEES the light from the events at a different moment in time because he moves towards the light coming fron the front bolt and thus sees that one first... No relativity of simultaneity in that scenario!

 

But in fact he does't see them simultanously because when he meets the embankment observer no lighting bolt occurs:

1. first the front bolt occurs (before the train passenger meets the embankment observer), 2. then both observers meet. No lighting bolt occurs.

3. Finally the rear bolt occurs, after both observers separated a split second ago.

(Note: in train frame both light will travel dame distance to train passenger)

 

Look at it this way: when train passenger and embankment passenger meet, both bolts happen simultaneously for the embankent observer. Now, IF both bolts would ALSO happen simultaneously for the train passener when both observers meet, then the train passenger HAS to SEE both bolts also simultaneously, because in his frame the lights travelling from the simultaneous events also travel same distance (not necessarily same distance as in embankment frame, but that is irrellevent because only the front and rear distance in the train frame is important for the train observer analysis!), and hence would reach him simultaneously. But.... because the train observer sees both bolts not simultaneously he concludes: "For me (in my frame), lighting bolts occuring simultaneously when I and embankment observer meet can not be correct".

We know the train passenger indeed does not see the light from both bolts simultaneously, because that's what's experimentally observed bij the embankment observer. Receiving light from one bolt after recieving light from the other bolt are two different events. And that cannot change for the train passenger.

 

 

Now we get to your question: a thought experiment from the train passenger's point of view for simultaneous lighting bolts in the embakment frame.

Both bolts occur simultaneously in the embankment frame. Lights from the bolts do not reach the train passenger simultaneously (=two events). That's what he will physically experience and observe. Your question now is: how could the train passenger EXPLAIN seeing the front bolt first?

Train passenger knows the set up: in embankment frame both bolts occur when both observers meet. And lights hit embankment observer simultaneously (=one event).

Now train passenger he reasons as follows. "IF they ALSO occur simultaneously for me when I meet embankment observer, then they are also at same distance from me, hence both lights from bolts HAVE TO reach me simultaneously. But the lights from the bolts do NOT reach me simultanously. It can only be because for me (in my frame), lighting bolts occuring simultaneously when I and embankment observer meet can not be correct"

 

Is there another option?

The train observer might think for him both bolts DID occur simultaneously, but both lighning bolts were not at the same distance from him... hence both lights do not reach him simultaneously...

But that's not a valid option. Because it would mean

the three events

1/ front lightning bolt

2/ both observers meet

3/ rear lightning bolt

occur simultaneously in train AND embankment frame, but the embankment observer considers both observers halfway between the two simultaneous lightning bolts, whereas the train observer considers both observer NOT halfway between simultaneous bolts...

You might think it's a valid option, but there is no theory to explain it.

 

-------

Your question might be: if we consider the train at rest end the embankment moving, why does the train passenger knows he will not NOT see both bolts simultaneously (lights from the bolts not reaching him simultaneously)?

Or better formulated, why HAS IT to be that way (not seeing them simultaneously)?

The only 'thought experiment' reasoning we can make is: he and the embankment observer know it happens that way, because in the embankment frame the bolts reaching the train observer are two different events and they can not melt together into one event in the other frame.

And the best way to find out is doing the experiment. Both lights from bolts will and do not reach the train observer. But as a thought experiment one has also to wonder why ;-).


Edited by VandD, 11 January 2017 - 02:58 PM.

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#6 swansont

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Posted 11 January 2017 - 03:15 PM

Yest, but I think Tir21 wants to know how the thought experiment runs from the train passenger point of view. That's a different story.

 

 

Perhaps a different story, but it had better end up with the same answer.


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#7 geordief

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Posted 11 January 2017 - 03:51 PM

My take on this is that simultaneity only occurs when two events are separated by zero space and zero time (a rare occurrence).

So, by my definition ,in this particular scenario neither observer can say that the 2 events are truly "simultaneous"

They can only claim they are simultaneous in so far as they respectively observe them as such,which is why they disagree.

If events are truly "simultaneous" according to my "higher" standard ,all observers will agree (perhaps trivially?)
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#8 swansont

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Posted 11 January 2017 - 04:15 PM

My take on this is that simultaneity only occurs when two events are separated by zero space and zero time (a rare occurrence).

So, by my definition ,in this particular scenario neither observer can say that the 2 events are truly "simultaneous"

They can only claim they are simultaneous in so far as they respectively observe them as such,which is why they disagree.

If events are truly "simultaneous" according to my "higher" standard ,all observers will agree (perhaps trivially?)

 

 

That's not the relativity take on it. Same place and same time are required for an unambiguous determination. Same time depends on your frame if the events are not co-located. Hence the relativity of simultaneity.


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#9 geordief

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Posted 11 January 2017 - 04:54 PM

That's not the relativity take on it. Same place and same time are required for an unambiguous determination. Same time depends on your frame if the events are not co-located. Hence the relativity of simultaneity.


Well my take was no doubt simplistic and not particularly useful or helpful here (just a special case I guess)

Edited by geordief, 11 January 2017 - 04:55 PM.

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#10 zztop

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Posted 11 January 2017 - 05:30 PM

Well my take was no doubt simplistic and not particularly useful or helpful here (just a special case I guess)

Two events are separated by the amount of time \Delta t and by the space \Delta x in frame F.

In frame F', the two events are separated by the time interval \Delta t'=\gamma(\Delta t -v \Delta x/c^2).

 

Now, if the events are simultaneous in F, it means that \Delta t=0.

 

This means that , in frame F', the events are separated by the time interval:

 

\Delta t'=-\gamma v \Delta x/c^2.

 

You can have \Delta t'=0 if \Delta x=0.

 

Another way of looking at it is : if \Delta x=0 then \Delta t'=\gamma\Delta t , so, in this PARTICULAR case,  simultaneity is preserved across frames of reference.


Edited by zztop, 11 January 2017 - 05:32 PM.

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#11 VandD

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Posted 12 January 2017 - 09:17 AM

My take on this is that simultaneity only occurs when two events are separated by zero space and zero time (a rare occurrence).


Two events separated by zero space and zero time are a contradiction in terms. Two events mean space separation and/or time separation. You cannot melt two events into one.
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#12 geordief

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Posted 12 January 2017 - 11:22 AM

Two events separated by zero space and zero time are a contradiction in terms. Two events mean space separation and/or time separation. You cannot melt two events into one.

Well ,we can as a limit and from an observer's frame of reference can't we?

 

But I have agreed it is of little consequence.


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