3 ms·

My favorite general relativity paradox: A runner is running with a 20m pole at a sufficient velocity so that a stationary observer sees the pole having length 1

by dhosek 5y ago

My favorite general relativity paradox: A runner is running with a 20m pole at a sufficient velocity so that a stationary observer sees the pole having length 10m. The runner runs through a barn which is 10m long. And two people outside shut the doors simultaneously so that the runner is completely enclosed in the barn for a moment. But from the runner's perspective, the barn has length 5m long. What does she see happen when the doors are closed on her?

gridspy 5y ago
How do the two people at opposite ends of the barn agree on when to close the doors as a runner approaches at relativistic speeds? Also, relevant xkcd (what-if) https://what-if.xkcd.com/1/ https://what-if.xkcd.com/1/ Most likely from the runner's perspective the world turns white as they dissolve to plasma prior to reaching the barn.
n3k5 5y ago
> And two people outside shut the doors simultaneously No, they don't. I'd phrase it differently, e.g. “each door is shut for an instant when the end of the pole is just inside the door”. (Also, make it clear that the barn is long enough to fit a 10m pole between the two shut doors.) When you put it as “shut the doors simultaneously”, it's more troll physics than a paradox. Meta-puzzle: figure out how to still imply that the runner is completely enclosed for an instant, without incorrectly insinuating that it is so from her perspective.
deleted 5y ago
[deleted]
contravariant 5y ago
From the frame of reference of the runner the pole will first hit the door at the end of the barn (unless it opens in time), and the door at the front of the barn will only close just after the back of the pole has passed the door. If the doors actually don't open in time then the resolution for the fact that the pole doesn't physically fit is that nothing can be rigid at relativistic speeds. So either the door or the pole or both will deform (violently) to allow the pole to fit inside the barn.
awb 5y ago
At these high speeds and tiny distances, very little would probably be noticeable to a human observer. If any matter collided it would be a catastrophic release of energy evaporating the human. But I think over longer distances there would be a time delay for the light of the explosion to reach the individual, so they would probably the light of a visually warped pole colliding with visually warped barn doors very briefly before disappearing into an explosion.
kazinator 5y ago
Since the two doors are not in the same location in space, there is no absolute "simultaneously". What one frame of reference sees as a simultaneous closure of the doors looks like non-simultaneous closure of the doors in another frame of reference. Simultaneity means that two events coincide in time and space. Different time and/or space means: not simultaneous!
juped 5y ago
This is a special relativity paradox.
- dhosek 5y ago
  D'oh! I know better than to make that mistake and yet "their" it is.

by dhosek 5y ago

gridspy 5y ago

How do the two people at opposite ends of the barn agree on when to close the doors as a runner approaches at relativistic speeds? Also, relevant xkcd (what-if) https://what-if.xkcd.com/1/ https://what-if.xkcd.com/1/ Most likely from the runner's perspective the world turns white as they dissolve to plasma prior to reaching the barn.

n3k5 5y ago

> And two people outside shut the doors simultaneously No, they don't. I'd phrase it differently, e.g. “each door is shut for an instant when the end of the pole is just inside the door”. (Also, make it clear that the barn is long enough to fit a 10m pole between the two shut doors.) When you put it as “shut the doors simultaneously”, it's more troll physics than a paradox. Meta-puzzle: figure out how to still imply that the runner is completely enclosed for an instant, without incorrectly insinuating that it is so from her perspective.

deleted 5y ago

[deleted]

contravariant 5y ago

From the frame of reference of the runner the pole will first hit the door at the end of the barn (unless it opens in time), and the door at the front of the barn will only close just after the back of the pole has passed the door. If the doors actually don't open in time then the resolution for the fact that the pole doesn't physically fit is that nothing can be rigid at relativistic speeds. So either the door or the pole or both will deform (violently) to allow the pole to fit inside the barn.

awb 5y ago

At these high speeds and tiny distances, very little would probably be noticeable to a human observer. If any matter collided it would be a catastrophic release of energy evaporating the human. But I think over longer distances there would be a time delay for the light of the explosion to reach the individual, so they would probably the light of a visually warped pole colliding with visually warped barn doors very briefly before disappearing into an explosion.

kazinator 5y ago

Since the two doors are not in the same location in space, there is no absolute "simultaneously". What one frame of reference sees as a simultaneous closure of the doors looks like non-simultaneous closure of the doors in another frame of reference. Simultaneity means that two events coincide in time and space. Different time and/or space means: not simultaneous!

juped 5y ago

This is a special relativity paradox.

dhosek 5y ago
D'oh! I know better than to make that mistake and yet "their" it is.