In what direction does length contraction occur?

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Consider a train traveling at a relativistic velocity, with three observers. One inside the train, and two outside the train traveling at different velocities with respect to it. Say there is a finish line of sorts at a certain point. All observers will agree when the train reaches the line.

Does this mean that length contraction occurs, in layman's terms, with the back of the object contracting toward the front?
 

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  • #2
tiny-tim
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Consider a train traveling at a relativistic velocity, with three observers. One inside the train, and two outside the train traveling at different velocities with respect to it. Say there is a finish line of sorts at a certain point. All observers will agree when the train reaches the line.

Does this mean that length contraction occurs, in layman's terms, with the back of the object contracting toward the front?
Hi Flexo! :smile:

When the question says "All observers will agree when the train reaches the line", it means that they set their watches to the same time (probably zero) when the front of the train crosses the line.

They could equally well set their watches to the same time when the back crosses the line.

Or when the middle crosses the line.

Or the train could be extended, with the extra portion at the front.

There is nothing special about the front of the train.

In layman's terms, the length is observed to contract all over. :smile:
 
  • #3
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Hi Flexo! :smile:

When the question says "All observers will agree when the train reaches the line", it means that they set their watches to the same time (probably zero) when the front of the train crosses the line.

They could equally well set their watches to the same time when the back crosses the line.

Or when the middle crosses the line.

Or the train could be extended, with the extra portion at the front.

There is nothing special about the front of the train.

In layman's terms, the length is observed to contract all over. :smile:
It seems to me that the two moving observers would set their watches to zero at different times if the train contracted from both directions. Is this just a problem with my visualization?
 
  • #4
tiny-tim
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It seems to me that the two moving observers would set their watches to zero at different times if the train contracted from both directions. Is this just a problem with my visualization?
Sorry … yes it is! :smile:

They can set their watches to zero at whatever times they choose.

If they're moving at different speeds relative to the train, then there will be a different time, t = 1, say, when the back crosses the same line (another line) for both of them.

So if they use another pair of watches, set 1 unit behind the first pair, then by your same argument, the contraction is now towards the back! :smile:
 
  • #5
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Sorry … yes it is! :smile:

They can set their watches to zero at whatever times they choose.

If they're moving at different speeds relative to the train, then there will be a different time, t = 1, say, when the back crosses the same line (another line) for both of them.

So if they use another pair of watches, set 1 unit behind the first pair, then by your same argument, the contraction is now towards the back! :smile:
It seems strange that observers will agree on a time that any point on the train reaches the line.
Say the train has numbers from 1-1000 in large print on either side of it. Each of these numbers is placed such that it reaches the finish line 1 nanosecond after the last. Both observers set their clocks to t=0 when 1 crosses the finish line. Are you saying that both observers will agree on the time that any given number crosses?
 
  • #6
tiny-tim
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Are you saying that both observers will agree on the time that any given number crosses?
No, I'm saying that the railway company can draw 1000 numbered lines on the ground, and both observers can re-set their watches so as to agree on the time that any particular number n on the train crosses line n. :smile:
 
  • #7
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No, I'm saying that the railway company can draw 1000 numbered lines on the ground, and both observers can re-set their watches so as to agree on the time that any particular number n on the train crosses line n. :smile:
It seems to me that no contraction is occurring in this scenario, because the observer seeing the train as going faster would observe less time between number n crossing line n.
 
  • #8
tiny-tim
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It seems to me that no contraction is occurring in this scenario, because the observer seeing the train as going faster would observe less time between number n crossing line n.
Not following you. :confused:

There is always an observed contraction of an object moving relative to the observer.
 

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