Special Relativity Train Scenario

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Discussion Overview

The discussion revolves around a thought experiment involving a train and a tunnel, exploring concepts of length contraction in special relativity. Participants examine the implications of building a shorter tunnel based on the relativistic speed of the train, and whether such a scenario could be practically realized.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes that if a train moving at relativistic speed (0.8c) is observed by a stationary engineer, its length appears contracted to 5m, suggesting a shorter tunnel could suffice.
  • Another participant argues that tunnel lengths are typically determined by physical constraints rather than the speed of objects passing through, questioning the practicality of the scenario.
  • References to the "pole-barn paradox" are made, indicating a related thought experiment that may provide further insight into the discussion.
  • A participant acknowledges the impracticality of the scenario and suggests that tunnel height might be a more relevant constraint, although they struggle to formulate a scenario utilizing this aspect.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of constructing a shorter tunnel based on relativistic effects, with some agreeing on the theoretical possibility while others emphasize practical constraints. The discussion remains unresolved regarding the applicability of the thought experiment in real-world scenarios.

Contextual Notes

Participants note limitations in the scenario, such as the lack of practical implementation and the focus on length rather than height, which may not accurately reflect real-world engineering considerations.

kasha
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Assume there is an engineer who built a tunnel, tunnel length is 10m, and we have a train its length is also 10m...so the tunnel can encompasses the entire length of the train.

But if we assume that train is a light express train, it always comes through the tunnel at relativistic speed, let's say train speed = 0.8c, relative to the observing engineer.
So the civil engineer who built the tunnel, watches the train gets shorter due to special relativity (Train length relative to the standing engineer is 5m).

Does it make sense to say: since the train crosses the tunnel at relativistic speed close to the speed of light, so the engineer can build a shorter tunnel (length 5m) and tunnel can still encompasses the full length of the train?!? Engineer has saved money on the lower cost shorter tunnel.!
 
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If the only constraint on the tunnel length is that the entire train has to fit into the tunnel at some instant of time in the tunnel's rest frame, then yes, the tunnel could be built shorter if the train were guaranteed to be moving at relativistic speed. However, I don't see how any actual tunnel would have this as its only constraint. Tunnel lengths are determined by what must be tunneled through, not by what's going to be passing through the tunnel.
 
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You may want to google for "pole-barn paradox" - the path you're on is going to take you there pretty quickly.
 
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PeterDonis said:
If the only constraint on the tunnel length is that the entire train has to fit into the tunnel at some instant of time in the tunnel's rest frame, then yes, the tunnel could be built shorter if the train were guaranteed to be moving at relativistic speed. However, I don't see how any actual tunnel would have this as its only constraint. Tunnel lengths are determined by what must be tunneled through, not by what's going to be passing through the tunnel.

You are right...there is no actual implementation of my scenario. Tunnel Height is more realistic constrain than the tunnel length. but couldn't come up with a scenario that would utilize the Tunnel Height, because the tunnel height would be unchanged relative to the train operator since the train moves on the x-axis whereas the tunnel's height is y-axis.

Thanks a lot
 
Nugatory said:
You may want to google for "pole-barn paradox" - the path you're on is going to take you there pretty quickly.

Oh wow...never heard of that paradox, but that makes much more sense than by training fitting in a tunnel :-)

Got all the answers I was looking for: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/polebarn.html

Many Thanks
 

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