A Puzzle For You!!!!

[TuxDave]

Since there's so many questions regarding relativity, I remembered a puzzle my Physics professor proposed to me. I don't quite remember the numbers, but assume they're generally correct.

There is a barn that is goes in 2 meters, before ending in an indestructable wall, when observed from a stationary position. A person is carrying a pole that extends 4 meters in front of him and running at relativistic speeds towards the barn. There's a second person standing next to the barn.

Due to length contraction, the 2nd person sees the first person and his pole extend only 1 meter. So he plans to close the barn doors when the person enters fully into the barn since to him, the guy should fit.

The 2nd guy still sees his pole at 4 meters long since they're both moving at the same rate. However, the barn looks a measely 0.5 meters deep. He figures that he'll run in and crash into the back wall and never enter the barn fully.

What's gonna happen?

 

[thelordemperor]

I'm guessing the guy with the pole smashes into the wall and dies, because either way he can't slow down enough not to.

 

[TuxDave]

Hahaha... excluding death of course. But you're on the right track.

 

[thelordemperor]

Ok serious guess, the guy's actual length is still 4 metres so he hits the walll?

 

[Cattlegod]

Originally posted by: thelordemperor
I'm guessing the guy with the pole smashes into the wall and dies, because either way he can't slow down enough not to.

inertial dampeners

 

[TuxDave]

Originally posted by: thelordemperor
Ok serious guess, the guy's actual length is still 4 metres so he hits the walll?

Well.... he's gonna hit the back of the wall, that's true. But there's a interesting part in relativity that makes it impossible to have perfectly rigid objects. The argument was such that if you had a very long rigid pole and you ran into a wall at reletivistic speeds. Barring death, when the end of the pole hits the wall, your end cannot possible stop right away. That's because if it did, the informatio that the far end hit the pole was transferred to you faster than the speed of light, which is not allowed. So the pole would actually contract like a sponge.

 

[grant2]

Yes I thought objects truly DID shrink as they reached relativistic speeds?

If this were the case though, the pole would be 1m long, enter the barn, have the door closed, and then hit the wall & stop... at which point the pole stretches back to 4m... would it bust through the door that had closed behind it?

A good mind bender!

 

[glugglug]

Originally posted by: TuxDave
Due to length contraction, the 2nd person sees the first person and his pole extend only 1 meter.

BAD MENTAL IMAGE!

 

[TuxDave]

Originally posted by: glugglug

Originally posted by: TuxDave
Due to length contraction, the 2nd person sees the first person and his pole extend only 1 meter.

BAD MENTAL IMAGE!

lol... oops.

 

[Ariste]

Originally posted by: TuxDave

Originally posted by: thelordemperor
Ok serious guess, the guy's actual length is still 4 metres so he hits the walll?

Well.... he's gonna hit the back of the wall, that's true. But there's a interesting part in relativity that makes it impossible to have perfectly rigid objects. The argument was such that if you had a very long rigid pole and you ran into a wall at reletivistic speeds. Barring death, when the end of the pole hits the wall, your end cannot possible stop right away. That's because if it did, the informatio that the far end hit the pole was transferred to you faster than the speed of light, which is not allowed. So the pole would actually contract like a sponge.

Hmm, that's interesting. I never thought of that. So what happens if you have a huge pole stretching through space and you are on one end. You grab the end of the pole and twist it clockwise. Logic says that the entire pole would twist the same way at the same speed, since it is just one continuous pole. But if you cannot transfer information faster than the speed of light, then would the pole not twist at the other end until the information was transferred to it, causing the entire pole to be twisted relative to itself?

Ok, that example is confusing, so now say that you have the same pole extending through space. You, on one end of the pole, push it upwards, causing the other side to go down and the entire pole to spin. Would the pole bend since information cannot be transferred to the other side faster than the speed of light? If the pole was long enough, could the pole bend so much that it would break?

Interesting stuff

 

[TuxDave]

Originally posted by: Ariste

Originally posted by: TuxDave

Originally posted by: thelordemperor
Ok serious guess, the guy's actual length is still 4 metres so he hits the walll?

Well.... he's gonna hit the back of the wall, that's true. But there's a interesting part in relativity that makes it impossible to have perfectly rigid objects. The argument was such that if you had a very long rigid pole and you ran into a wall at reletivistic speeds. Barring death, when the end of the pole hits the wall, your end cannot possible stop right away. That's because if it did, the informatio that the far end hit the pole was transferred to you faster than the speed of light, which is not allowed. So the pole would actually contract like a sponge.

Hmm, that's interesting. I never thought of that. So what happens if you have a huge pole stretching through space and you are on one end. You grab the end of the pole and twist it clockwise. Logic says that the entire pole would twist the same way at the same speed, since it is just one continuous pole. But if you cannot transfer information faster than the speed of light, then would the pole not twist at the other end until the information was transferred to it, causing the entire pole to be twisted relative to itself?

Ok, that example is confusing, so now say that you have the same pole extending through space. You, on one end of the pole, push it upwards, causing the other side to go down and the entire pole to spin. Would the pole bend since information cannot be transferred to the other side faster than the speed of light? If the pole was long enough, could the pole bend so much that it would break?

Interesting stuff

Yup! Nothing is rigid. Everything is essentially a very fast recovering spring... well... supposedly. That's how I learned it. Heh. Oh... then again, I guess we could bring in quantum entangled objects which completely boggles my mind.

 

[Gibsons]

I think anything transmitted though the pole by twisting/striking/pulling it will move at the speed of sound for whatever material the pole is made of. Which could be kinda fast, but not close to the speed of light.

 

[TuxDave]

Originally posted by: Gibsons
I think anything transmitted though the pole by twisting/striking/pulling it will move at the speed of sound for whatever material the pole is made of. Which could be kinda fast, but not close to the speed of light.

In a pole with finite rigidity, yeah, he twisting/bending/whatever will propagate down depending on how rigid the pole is. Given a theoretical "infinite" rigidity, the maximum it can propagate is the speed of light...

 

[DrPizza]

Originally posted by: Ariste

Originally posted by: TuxDave

Originally posted by: thelordemperor
Ok serious guess, the guy's actual length is still 4 metres so he hits the walll?

Well.... he's gonna hit the back of the wall, that's true. But there's a interesting part in relativity that makes it impossible to have perfectly rigid objects. The argument was such that if you had a very long rigid pole and you ran into a wall at reletivistic speeds. Barring death, when the end of the pole hits the wall, your end cannot possible stop right away. That's because if it did, the informatio that the far end hit the pole was transferred to you faster than the speed of light, which is not allowed. So the pole would actually contract like a sponge.

Hmm, that's interesting. I never thought of that. So what happens if you have a huge pole stretching through space and you are on one end. You grab the end of the pole and twist it clockwise. Logic says that the entire pole would twist the same way at the same speed, since it is just one continuous pole. But if you cannot transfer information faster than the speed of light, then would the pole not twist at the other end until the information was transferred to it, causing the entire pole to be twisted relative to itself?

Ok, that example is confusing, so now say that you have the same pole extending through space. You, on one end of the pole, push it upwards, causing the other side to go down and the entire pole to spin. Would the pole bend since information cannot be transferred to the other side faster than the speed of light? If the pole was long enough, could the pole bend so much that it would break?

Interesting stuff

To make more sense of the rigid pole idea, you have to realize that it's made up of atoms, which are made up of nuclei and electrons. What's holding it all together are electromagnetic forces (well, except for inside the nuclei). Anyway, when you move one atom, the atom next to it doesn't react at the exact same instant.. there's a little delay - speed of light and the extremely small distance make this delay incredibly small.

If your idea worked, the length of the pole wouldn't matter... it could be 4 inches long... if both ends rotated "instantly" then information is already travelling 4 inches in less time than it takes light to get from one end to the other.

 

[Ariste]

Well yes, I realize that the pole wouldn't have to be long, but the bend in a 4 inch pole would be completely undedectable (obviously, since poles don't bend every time we move them ). I just used the longer pole as an example because you would be able to see it bend.

 

[Calin]

Originally posted by: thelordemperor
I'm guessing the guy with the pole smashes into the wall and dies, because either way he can't slow down enough not to.

70 kg of something with relativistic speed, hitting an indestructible wall... well, this would equal the total energy of the nuclear weapon stockpile

Calin

 

[jagec]

Originally posted by: TuxDave

Yup! Nothing is rigid. Everything is essentially a very fast recovering spring... well... supposedly. That's how I learned it. Heh. Oh... then again, I guess we could bring in quantum entangled objects which completely boggles my mind.

exactly. You don't need relativity to tell you that a 3-mile long pole will bend a LOT if you try to swing it.

 

[TuxDave]

Originally posted by: jagec

Originally posted by: TuxDave

Yup! Nothing is rigid. Everything is essentially a very fast recovering spring... well... supposedly. That's how I learned it. Heh. Oh... then again, I guess we could bring in quantum entangled objects which completely boggles my mind.

exactly. You don't need relativity to tell you that a 3-mile long pole will bend a LOT if you try to swing it.

Well, what I meant was that, even in a perfect physics world where you can speculate about objects with VERY VERY high rigidity, absolutely rigid objects would violate relativity.

 

[flashbacck]

This is something I've always wonderd. What happens if you have a person at the end of a rope near a blackhole, and you're at the other end, far away, and you try to pull him up?

 

[Geniere]

Assume the black hole had the same mass as the earth. Assume the person tied to the rope was at the same distance from the center of mass of the black hole as he would be at the surface of the earth.

There would be no difference noted when trying to pull the person away using the rope.

There is no property of gravity associated with a black hole that differs from that of the Sun, the Earth, or a baseball. Objects of equal mass have equal gravitational fields.

The event horizon of a black hole with the same mass as the earth would be very small; I recall something on the order of 10 millimeters. Just inside that distance the gravitational attraction is so great that nothing can escape it. As distance from the center of mass increases, the gravitational attraction decreases. At a distance equal to the surface of the Earth, the gravitational force would be the same.

 

[Smilin]

Originally posted by: TuxDave
Since there's so many questions regarding relativity, I remembered a puzzle my Physics professor proposed to me. I don't quite remember the numbers, but assume they're generally correct.

There is a barn that is goes in 2 meters, before ending in an indestructable wall, when observed from a stationary position. A person is carrying a pole that extends 4 meters in front of him and running at relativistic speeds towards the barn. There's a second person standing next to the barn.

Due to length contraction, the 2nd person sees the first person and his pole extend only 1 meter. So he plans to close the barn doors when the person enters fully into the barn since to him, the guy should fit.

The 2nd guy still sees his pole at 4 meters long since they're both moving at the same rate. However, the barn looks a measely 0.5 meters deep. He figures that he'll run in and crash into the back wall and never enter the barn fully.

What's gonna happen?

Is the answer something like THIS?

 

[Cogman]

Hah I knew it. My physics teacher Sucked. We had a problem, with a rod in it. It basicly said if you pushed on one end of the rod how fast was the other end reacting. I said that it would react at the speed of light, everyone else said it would react instantly. My stupid teacher took out a pencil and started wobbling it back and forth betwean he fingers and saying how fast is it reacting, It looks pretty instant to me. I got marked down for that question. But I know I was right And you guys would back me up . (im graduated though, and it really was not work much to my grade, but I know I was right )

 

[TuxDave]

Originally posted by: Smilin

Originally posted by: TuxDave
Since there's so many questions regarding relativity, I remembered a puzzle my Physics professor proposed to me. I don't quite remember the numbers, but assume they're generally correct.

There is a barn that is goes in 2 meters, before ending in an indestructable wall, when observed from a stationary position. A person is carrying a pole that extends 4 meters in front of him and running at relativistic speeds towards the barn. There's a second person standing next to the barn.

Due to length contraction, the 2nd person sees the first person and his pole extend only 1 meter. So he plans to close the barn doors when the person enters fully into the barn since to him, the guy should fit.

The 2nd guy still sees his pole at 4 meters long since they're both moving at the same rate. However, the barn looks a measely 0.5 meters deep. He figures that he'll run in and crash into the back wall and never enter the barn fully.

What's gonna happen?

Is the answer something like THIS?

It's similiar to that puzzle but with the back door always closed. That website doesn't give the solution tho, it merely gives the math that shows the paradox.

 

[Smilin]

Yep it gives the solution to the paradox. Read again.

The Bug-Rivet paradox doesn't have a solution though.

 

[TuxDave]

Originally posted by: Smilin
Yep it gives the solution to the paradox. Read again.

The Bug-Rivet paradox doesn't have a solution though.

From the pole-barn paradox page.

Barn Frame of Reference

The back of the pole enters the barn before the front of the pole leaves, so a 1 ns gate could be closed on both ends, containing the entire pole.

Pole frame of reference

From the pole point of view, the front gate closes just as the back of the pole enters. The surprising result is that the back gate is seen to close earlier from the pole framework, before the front of the pole reaches it. The gate closings are not simultaneous, and they permit the pole to pass through without hitting either gate.

All I see is it's restating the paradox. Lemme read it again carefully. Stupid back and fronts... why can't they use left and right. Argh...

Edit: First of all, that page is kinda weird.

Barn Frame of Reference:
4th Dot. Why is it 32.35+37.04 instead of 32.29+37.04

Pole Frame of Reference:
3rd Dot. It should be t' not t.
4th Dot. It should be t' not t.

Where is the viewer? The left end of the pole or right end.
Front Gate = left side or right side?
Back Gate = left side or right side?

Regardless, I don't see the final evaluation to resolve the paradox. I'll break out the pen and paper tonight.