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I was wondering whether a relativistic torpedo which is a futuristic cannonball measuring 1m in diameter could fit a small circular cracks on the surface of an energy shield with a diameter 10% smaller. Note that any contact with the energy shield would cause the torpedo to detonate prematurely! So I am wondering could the torpedo moving at fractional speed of light pass through the gap due to length contraction or I should write romance instead?

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    $\begingroup$ Length contraction is in the direction of movement, not across it. See the famous thought experiment with the relativistic ladder fitting in a shorter barn. $\endgroup$
    – AlexP
    Dec 9, 2023 at 6:53
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    $\begingroup$ Please don't write about romance involving relativistic length contraction and hole-fitting. $\endgroup$ Dec 9, 2023 at 10:14
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    $\begingroup$ To be honest, if it's moving at relativistic speeds, it's going to fit through the hole. Not due to any size changing shenanigans but more brute force and ignorance. $\endgroup$ Dec 9, 2023 at 17:54

2 Answers 2

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thou shall not pass!

Length contraction happens in the direction of motion, not isotropically.

If your bullet move such that it has a Lorentz factor of 0.1, that will apply only to the direction of the motion. Since the hole diameter will likely be transverse to that, the projectile won't pass.

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  • $\begingroup$ Plus, from the frame of reference of the torpedo, the rest of the universe appears to undergo length contraction and the torpedo stays the same length. So the torpedo would actually be less able to fit in small spaces from its frame of reference, compared to when it was stationary. $\endgroup$
    – causative
    Dec 9, 2023 at 23:39
  • $\begingroup$ Pretty sure that any projectile moving at relativistic speeds is gonna be passing any obstacle. It just may not fit the way OP imagined it :D $\endgroup$
    – Davor
    Dec 10, 2023 at 16:57
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I'm building on L.Dutch's answer, which I up voted

The problem here is that length contraction is one-dimensional along the vector of motion. That means that even if your torpedo contracts all the way to zero length, you still have a disk with a 1 meter diameter. This doesn't help you. No matter the orientation, you're trying to push a 1 meter object through a less-than-1-meter opening.

What you need is something that contracts in two dimensions! That way the torpedo would narrow and fit through the opening.

The only problem is that there's no way to do that, that we know of.

I'll throw a question out to our Celestial Mechanics. I thought length contraction was an optical thing — something that was seen by the observer but was NOT an actual shortening of the physical object. Unfortunately, someone inside the torpedo using a measuring stick to measure the length of the torpedo would always measure a meter in length because either the physical contraction didn't occur or the stick is contracted along with the torpedo. So... physical contraction or observed optical contraction? Kinda curious.

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    $\begingroup$ The ladder paradox address the apparent or physical question. Yes, a ladder longer than a barn but travelling at relativistic speed will fit inside the barn. But only from the point of view of the owner of the barn. From the point of view of a traveller riding the ladder, it is the barn which is length contracted, so that for them it the barn appears even shorter, and the ladder will most definitely not fit. All in all, it comes down to the relativity of simultaneity. $\endgroup$
    – AlexP
    Dec 9, 2023 at 23:10
  • $\begingroup$ the ladder will not fit, but the doors will not be closed at the same time from the perspective of the ladder. i would say lorenz contraction is neither physical contraction nor observed optical contraction, but a (real) relativistic effect - a third category. $\endgroup$
    – ths
    Dec 11, 2023 at 11:08

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