Consider a man who is 1 metre in width and is running (at relativistic speeds) towards a pothole in the ground which is also 1 meter in width.

In the reference frame of the man it appears as though the pothole is moving towards him and as a result should shrink in size and therefore he will run over it.

In the reference frame of the pothole it seems as though the man is running towards it and so should shrink and then fall through the pothole.

How would one resolve this apparent contradiction as it is not plausible that the man will fall through the pothole in one reference frame and not fall through in another.

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    $\begingroup$ This is just the "man falling into a grate" variation of the ladder paradox: en.wikipedia.org/wiki/… $\endgroup$ – tparker May 16 '17 at 18:09
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    $\begingroup$ If he is running close to the speed of light and can't even jump over a 1 meter pothole that is pathetic. $\endgroup$ – Señor O May 16 '17 at 18:17
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    $\begingroup$ Also of interest is the fact that his legs must be moving relativistically relative to him. When you run, your leg is moving exactly the opposite velocity of your body (relative to you) when in contact with the ground, and ~twice your velocity relative to the ground when bringing them forward. $\endgroup$ – Señor O May 16 '17 at 18:20

In the reference frame of the man it is easy to step over even a wide pothole, because the wide pothole is not wide in the man's frame.

Quite interesting is that in the pothole frame the step frequency approaches zero as the running speed approaches the speed of light.

So in the reference frame of the pothole it seems as though it takes a long time for the man to take one step. The man moves a long distance during a long time, in other words one step takes the man a long distance forwards.

If one footprint of said man is next to a milestone that says 2 miles and the next footprint is next to a milestone that says 4 miles, then all observes agree that the length of stride of the man is the same as the distance between the two milestones.

  • $\begingroup$ Downvoted after the Community user bumped this to the homepage because as far as I can tell you are stating that the man passes over the hole without incident, which is incorrect: as Rindler (“Length contraction paradox,” 1961) notes, there is no doubt that the grate’s description of events must be correct; and this must inform us when we try to see the world from the man’s perspective. $\endgroup$ – CR Drost Jun 18 '19 at 21:44

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