A relativity problem (train & platform)

  • Thread starter Ookke
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  • #26
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JesseM said:
If the train passes the front of the platform in one frame, it must pass it in all frames. Different reference frames cannot disagree about local events which occur at a particular time and spatial location, like one object passing arbitrarily close to another.
No problem. The point is that if the train passed the front of the platform it passed the front of the platform. It doesn't go backwards when Ooke slams on the brakes to end up not passing the front of the platform.

Edit: sorry, I get what you mean now. I was thinking whole trains and whole platforms. Apologies. Perhaps we should resurrect the collision to guarantee local events. A platform ending with buffers perhaps?
 
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  • #27
JesseM
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Farsight said:
The train is 100m long passing a platform apparently 10m long. If it stops instantly, every part of it stays where it was.
Ookke didn't say it stopped instantly. If it did, though, it would indeed have to stretch. In these sorts of thought-experiments it's always easier to think about a set of separate objects representing the front, back and middle of the train which accelerate according to some predetermined schedule, with no rigid structure connecting them. So if they each stopped instantly in the frame where they were originally at rest before accelerating, that would mean the object representing the back stopped before reaching the platform, the object representing the middle stopped at the center of the platform, and the object representing the end stopped after passing completely by the platform.
 
  • #28
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Farsight said:
Factual? Ooke's passenger can't admire the countryside. For one it's going by a bit fast, it's foreshortened, and the only light he'd see would be a blue shifted blob straight ahead. If he tossed a sweet wrapper out of the window it would just keep going until it hit something like a nuclear bomb.
Yes and? :smile:
The point is that he passed the end of the platform. And I fully agree with JesseM that there can not be any ambiguity about this from the perspective of another frame.

If you claim that it could not be determined then how do you claim it could be determined that the train stops in the middle? :wink:

Farsight said:
The train is 100m long passing a platform apparently 10m long. If it stops instantly, every part of it stays where it was. So it would have to stay ten times as long as the platform, which is really 1km long.
Sorry Farshight but you are completely wrong about this. In no single scenario would the train become 1km long.

JesseM said:
Ookke didn't say it stopped instantly. If it did, though, it would indeed have to stretch.
It does, but not to 1km.
 
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  • #29
JesseM
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Farsight said:
No problem. The point is that if the train passed the front of the platform it passed the front of the platform.
Only if you assume the train stays rigid in its own instantaneous rest frame at each moment, the "Born rigidity" condition I mentioned above. If you don't impose this condition, then the train need not stay 100 m long after it comes to a stop. If you do impose this condition, I don't think you'd see any backwards motion, you'd just see the back, middle and front of the train decelerate over three different finite periods of time, with the back end taking longer to come to rest than the middle, and the middle taking longer than the front, all coming to rest at the same moment in the platform's frame. I believe all three ends would come to rest after passing the far end of the platform, since I think the front end is already more than 100 m past the end of the platform when it begins to decelerate in the platform's frame, but I'd have to check the math to make sure of that.
 
  • #30
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Whoa. I'm NOT saying the train ends up 10km long. I'm saying that's not factual, but is an illustration of where the looseness of the thought experiment takes us. And I'm saying that if the train stopped in the middle of the platform the front of the train DID NOT pass the front of the platform.

Don't be rude, MeJennifer.
 
  • #31
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Farsight said:
Whoa. I'm NOT saying the train ends up 10km long. I'm saying that's not factual, but is an illustration of where the looseness of the thought experiment takes us. And I'm saying that if the train stopped in the middle of the platform the front of the train DID NOT pass the front of the platform.

Don't be rude, MeJennifer.
I am not sure anymore what you are saying :smile:

Does the train pass the end of the platform: YES
Does the train get longer when it decellerates from the perspective of the frame of the platform: YES
Does the train get longer when it is stoped than the length as measured in the train's restframe: NO

Do you agree?
 
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  • #32
JesseM
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Farsight said:
Whoa. I'm NOT saying the train ends up 10km long. I'm saying that's not factual, but is an illustration of where the looseness of the thought experiment takes us. And I'm saying that if the train stopped in the middle of the platform the front of the train DID NOT pass the front of the platform.
If the train does not remain rigid, then the train can elongate, and it definitely will if each part accelerates instantaneously. And if you add something like the Born rigidity condition, the train must accelerate over an extended period, so even if the middle of the train begins to accelerate at the moment it passes the middle of the platform, it may not stop until it has passed the end of the platform.
 
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  • #33
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Yes of course I agree MeJennifer. Sorry if I wasn't very clear but please reread my posts. Thank you for that Jesse.
 

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