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## Question

Suppose there is a stick moving at high velocity (close to the speed of light or at least high enough for relativistic consideration). The stick is 1m long, it's velocity is constant and it is moving on a perfectly flat surface.

Now suppose it approaches a hole also 1m wide.

In the stick's frame of reference it is standing still and the hole is moving towards it at constant speed, due to the laws of relativity the length of the hole will contract making the stick longer than the hole thus allowing it to pass straight over.

In the hole's frame of reference the opposite is true and so the stick contracts making it fall through the hole.

Obviously both cannot be true so what is the outcome of this situation?

NB it's been a while since my relativity days and I've done this fairly quickly so please excuse any technical errors in this post. The general problem though is genuinely from a book on relativity and does have an accepted solution.

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At that speed, the stick would fly over the hole. Relativity is just an abject view. The hole doesn't really shrink, neither does the stick. They both remain the same length. If the stick were going considerably slower, it would fall in the hole.

Realistically, a stick can't travel that fast on its own, so I'd say it would never fall in the hole because its wheels are too big.

Edited by Llam4
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At that speed, the stick would fly over the hole. Relativity is just an abject view. The hole doesn't really shrink, neither does the stick. They both remain the same length. If the stick were going considerably slower, it would fall in the hole.

Realistically, a stick can't travel that fast on its own, so I'd say it would never fall in the hole because its wheels are too big.

Relativity isn't an abject view, no inertial frame is any more applicable than any other, so the lengths do change.

We're assuming here that whatever would cause the stick to fall in the hole is strong enough so that if it fits it falls in

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At that speed, the stick would fly over the hole. Relativity is just an abject view. The hole doesn't really shrink, neither does the stick. They both remain the same length. If the stick were going considerably slower, it would fall in the hole.

Realistically, a stick can't travel that fast on its own, so I'd say it would never fall in the hole because its wheels are too big.

AFAIK (which isn't very far...) there is some debate over whether or not length contraction is observable. LHC should be able to sort that out.

With respect to the question... I think the frame of reference situation was sorted out by general relativity... and the up shot was that its the object that is moving with respect to the rest of the universe that gets shrunk. So (ignoring other factors) the stick would do the shrinking.

I could, of course, be wrong.

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Relativity isn't an abject view, no inertial frame is any more applicable than any other, so the lengths do change.

We're assuming here that whatever would cause the stick to fall in the hole is strong enough so that if it fits it falls in

They'd both have a 1m long object flying at them at the same speed, meaning they'd both contract to the same size. Since there's apparently a strange force that can shove a stick flying near light speed into a hole its own size in a nanosecond, the stick would fall in the hole.

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In the stick's frame of reference it is standing still and the hole is moving towards it at constant speed, due to the laws of relativity the length of the hole will contract making the stick longer than the hole thus allowing it to pass straight over.

I'm not Einstein on this, but from the stick's frame of reference, the hole is getting closer, doesn't this mean the length of the hole increases (looks bigger) ???

Just a question...

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AFAIK (which isn't very far...) there is some debate over whether or not length contraction is observable. LHC should be able to sort that out.

With respect to the question... I think the frame of reference situation was sorted out by general relativity... and the up shot was that its the object that is moving with respect to the rest of the universe that gets shrunk. So (ignoring other factors) the stick would do the shrinking.

I could, of course, be wrong.

Length contraction is a known observed phenomenon.

[Edit: Or not. I think a physics teacher lied to me. After doing a little more research, I see that you are correct - it's observability is still in question.]

As far as frame of reference, the point is that it is all relative to what reference you are considering. If you are saying "with respect to the universe" then both the stick AND the hole are moving (the hole is on some plant which is presumably spinning and revolving around a star, which is in turn revolving around the center of it's galaxy, etc...) You must define which point of reference you are referring to. So, if you are sitting on the stick (not going to happen, but let's pretend) you would think you were sitting still and the hole was moving, therefore the hole would shrink. If you are sitting next to the hole, you would think you were sitting still and the stick was moving, thus the stick shrinks. Both are correct.

I've heard this one before, although typically it's stated that when at rest the stick is BIGGER than the hole. Nonetheless, for a sufficiently high speed the stick will appear to contract to fit into the hole.

But it's been way too long since I took a modern physics course, and this is as much as I remember. What the actual outcome of this situation is, I can't say for certain.

I would say that the stick falls in the hole.

As far as the hole sees it, the stick simply is too short and falls in.

As for the stick's perspective, the front end will dip down into the hole and strike the wall. The stick cannot stop instantly (this would require information travelling faster than the speed of light - the front end "knows" that it hit the wall and can stop, but the back end doesn't "know" this yet so it tries to keep traveling. Another way to look at this is that the force of stopping cannot be applied instantly everywhere on the stick) thus the stick cannot be infinitely rigid, and therefore will bend or compress until it fits in the hole and comes to rest.

Edited by dwilly
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Suppose there is a stick moving at high velocity (close to the speed of light or at least high enough for relativistic consideration). The stick is 1m long, it's velocity is constant and it is moving on a perfectly flat surface.

Now suppose it approaches a hole also 1m wide.

In the stick's frame of reference it is standing still and the hole is moving towards it at constant speed, due to the laws of relativity the length of the hole will contract making the stick longer than the hole thus allowing it to pass straight over.

In the hole's frame of reference the opposite is true and so the stick contracts making it fall through the hole.

Obviously both cannot be true so what is the outcome of this situation?

NB it's been a while since my relativity days and I've done this fairly quickly so please excuse any technical errors in this post. The general problem though is genuinely from a book on relativity and does have an accepted solution.

Hmm, If a stick is traveling at the speed of light (299,792,458 m/s) then I would doubt there would be enought time for it to fall in to the hole in just 1/299,792,458 of a second.

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Length contraction is a known observed phenomenon.

[Edit: Or not. I think a physics teacher lied to me. After doing a little more research, I see that you are correct - it's observability is still in question.]

As far as frame of reference, the point is that it is all relative to what reference you are considering. If you are saying "with respect to the universe" then both the stick AND the hole are moving (the hole is on some plant which is presumably spinning and revolving around a star, which is in turn revolving around the center of it's galaxy, etc...) You must define which point of reference you are referring to. So, if you are sitting on the stick (not going to happen, but let's pretend) you would think you were sitting still and the hole was moving, therefore the hole would shrink. If you are sitting next to the hole, you would think you were sitting still and the stick was moving, thus the stick shrinks. Both are correct.

I've heard this one before, although typically it's stated that when at rest the stick is BIGGER than the hole. Nonetheless, for a sufficiently high speed the stick will appear to contract to fit into the hole.

But it's been way too long since I took a modern physics course, and this is as much as I remember. What the actual outcome of this situation is, I can't say for certain.

I would say that the stick falls in the hole.

As far as the hole sees it, the stick simply is too short and falls in.

As for the stick's perspective, the front end will dip down into the hole and strike the wall. The stick cannot stop instantly (this would require information travelling faster than the speed of light - the front end "knows" that it hit the wall and can stop, but the back end doesn't "know" this yet so it tries to keep traveling. Another way to look at this is that the force of stopping cannot be applied instantly everywhere on the stick) thus the stick cannot be infinitely rigid, and therefore will bend or compress until it fits in the hole and comes to rest.

I think the problem you would have with measuring length contraction would be with the old uncertainty principle, you can't definitely no the position and momentum of an object and you need both to measure it. Just top of my head like.

I thought like you guys when I first saw this to be fair that the stick would just whizz right over the top. Maybe I should have left out the specific lengths as obviously they imply it happens well quick the point is merely that they are the same length so we could say they're say 1000000000m. Don't have the book it's from with me but I'll post the answer given there later.

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it won't fall when moving near the speed of light.

Not owing to the requirement of a nearly infinite momentum change to do so,

but owing to the fact the stick must lose its relativistic speed to encounter the hole.

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I am curious to the alignment of the stick to the hole (width or forward facing), and if there is 'normal' gravity as the conditions...

Was it a black hole ?? I suspect not

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I am curious to the alignment of the stick to the hole (width or forward facing), and if there is 'normal' gravity as the conditions...

Was it a black hole ?? I suspect not

Like so:

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But I think this paradox is due to a confusion with the frames of reference. Looking at things only from the stick's point of view makes the hole smaller, while the stick stays the same. Loooking at things only from the hole's perspective makes the stick smaller and the hole stays the same.

However, in order for these objects to interact, I believe you need to consider a joint frame of reference, which must be a union of the two perspectives. So either they both shrink, or they both stay the same, depending on your frame of reference. The result is, if the stick fit at velocity zero, it will fit at relativistic velocities.

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Stick travels near light speed, with enough "gravity" to counteract velocity instantly and pull it into a hole of the same size? That's an awful lot of energy to dissapate in a hurry. BIG boom. Bye-bye relaity?...

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Suppose there is a stick moving at high velocity (close to the speed of light or at least high enough for relativistic consideration). The stick is 1m long, it's velocity is constant and it is moving on a perfectly flat surface.

Now suppose it approaches a hole also 1m wide.

In the stick's frame of reference it is standing still and the hole is moving towards it at constant speed, due to the laws of relativity the length of the hole will contract making the stick longer than the hole thus allowing it to pass straight over.

In the hole's frame of reference the opposite is true and so the stick contracts making it fall through the hole.

Obviously both cannot be true so what is the outcome of this situation?

NB it's been a while since my relativity days and I've done this fairly quickly so please excuse any technical errors in this post. The general problem though is genuinely from a book on relativity and does have an accepted solution.

If it falls in the hole when the two objects have no relative motion, it will fall in when the stick is moving at (nearly) c, just not all at once. This is a variation of the "ladder paradox." It's much easier for you to google it than for me to try and explain it.

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