Special Relativity - Paradox?

[Guest]

Here are some basic laws of relativity

1) At relativistic speeds (close to the speed of light), a length contraction occurs in the direction of motion (ie. a man running at 0.9c would be seen to get very skinny - he WOULD not shrink height-wise though).

2) The laws of Physics apply in all inertial frames, no matter how fast you are travelling.

Here's the problem.

There is a barn in a field. The barn is 5m long inside and has one end open. At the other end there is a brick wall.

A polevaulter is carrying a 6m pole infront of him, running towards the barn at a relativistic speed, u.

An observer watching this sees a Lorentz length contraction and hence the pole (and the man) are seen to shorten, and he sees the man with his pole run into the barn withouth any problems.

However, the man running at relativistic speeds doesn't actually know he's running at this speed, he thinks the barn is coming towards him at a relativistic speed! Because of this, he sees the length between himself and the barn shorten, and also the length inside the barn shorten (to less than 5m). He himself is carrying a 6m pole, so before he even reaches the entrance to the barn he is stopped by the brick wall.

How can 2 different things happen in these 2 inertial frames?

Can this paradox be solved?

Thanks,

Tom

[quigley0]

Yes! But, not by me. :)

Does this have anything to do with the "to get somewhere, you have to cross have the distance, and then half the remaining distance - Therefore you never get there" kinda thing?

[Guest]

Nothing at all :-)

Ive kind of figured out the solution. It's to do with Time Dilation

[Dave Veteran]

So this isn't a topic about my cousin in the basement?

The "special" one.

[raid517]

Here are some basic laws of relativity

1) At relativistic speeds (close to the speed of light), a length contraction occurs in the direction of motion (ie. a man running at 0.9c would be seen to get very skinny - he WOULD not shrink height-wise though).

2) The laws of Physics apply in all inertial frames, no matter how fast you are travelling.

Here's the problem.

There is a barn in a field. The barn is 5m long inside and has one end open. At the other end there is a brick wall.

A polevaulter is carrying a 6m pole infront of him, running towards the barn at a relativistic speed, u.

An observer watching this sees a Lorentz length contraction and hence the pole (and the man) are seen to shorten, and he sees the man with his pole run into the barn withouth any problems.

However, the man running at relativistic speeds doesn't actually know he's running at this speed, he thinks the barn is coming towards him at a relativistic speed! Because of this, he sees the length between himself and the barn shorten, and also the length inside the barn shorten (to less than 5m). He himself is carrying a 6m pole, so before he even reaches the entrance to the barn he is stopped by the brick wall.

How can 2 different things happen in these 2 inertial frames?

Can this paradox be solved?

Thanks,

Tom

586685196[/snapback]

Sure it can be solved!!! (This is where reading about the history of science can come in handy, as it is basically just a rehash of a thought experiment that Einstein did himself in order to try to explain special relativity ro the great unwashed masses such as me).

The ideas behind Einstein's theories of relativity aren't exactly easy to test. To overcome this, Einstein developed a number of thought experiments to try and explain the ideas of relativity to people who find such ideas difficult to grasp. One of these is the the pole vaulter pardox which delves into the idea of the length contracion of an object as it moves with a speed near the speed of light.

The idea of a length contraction, as you move with a speed near the speed of light, can lead to a number of interesting paradoxes. One of the more interesting, as you pointed out is that of the barn and the pole vaulter. To understand this better, perhaps we should reframe your question?

Imagine that a pole vaulter is carrying a pole a bit longer than that of a nearby barn. The pole vaulter would like to store his pole in the barn.

A friend of his is taking Astronomy 123 and has read today's lecture. He therfore proposes to his friend, who is an incrediby fast runner, that is he were to run really fast, the length of the pole would shrink, and therefore would easily fit inside the barn. Having not read the class notes, the pole vaulter agrees to this idea and starts running. What happens?

From the viewpoint of the pole vaulter's friend, who is standing in the same reference frame as the barn, there's no problem, and the pole fits inside the barn.

From the viewpoint of the pole vaulter, however, who is running at a speed of 0.99 times the speed of light, it is the barn which shrinks, and there's no way his pole will fit inside.

So once again, we are confronted by your apparent paradox.

So what really happens? Can the pole be stored in the barn or not?

The answer, like most of the answers to apparent paradoxes within special relativity, comes when the two people try to compare their experiences. That is, when they re-enter each other's reference frame.

In this case, the pole vaulter will continue running until he (or the pole) runs into the wall of the barn (ow!), or pulls his 'stop on a dime' running technique. Either way, at that point he leaves the reference frame he had been in, the one in which the pole fits inside the barn, and re-enters the reference frame in which the pole is too large for the barn. At this point, both he and his friend have to agree that his friend's idea was not a great one.

Bummer!

So really there is no confict because at either stage both the pole vaulter and his friend (and the barn wall) are all going to be forced to agree that running at the barn wall at 0.99% the speed of light was not the smartest thing he could do, since the outcome from everyone's perspective is always going to end up being the same (since at some point both observers are always going to be forced to enter the same frame of reference).

Put another way there are only two possible outcomes to this paradox, either the pole vaulter stops dead (at which point he enters the same frame of reference as his friend), or he crashes into the wall (at which point he enters the same frame of reference as his friend). In both cases the outcome (and causality) are preseved in that the pole breaks and does not fit in the barn.

End of paradox!

I hope this helps. :)

GJ

Edited October 17, 2005 by raid517

[neowin_hipster]

lol, nice pics.

[raid517]

Mmm.. maybe not hight art, but they serve a purpose... :p

GJ

[vincent]

Great explanation raid, this and the link in my sig helps.

[Guest]

The paradox works, however each person in the different frames interprets the scenario differently due to time dilation. If the man crashes into the wall fram, he must crash into the frame in the other (einsteen's first postulate), therefore there is only the argument between the two people as to whether he crashes BEFORE he enters the barn or AFTER.

Sorry if that didnt make sense - im a bit drunk.

[ev0|]

Sorry if that didnt make sense - im a bit drunk.

586687408[/snapback]

Please come back after you've sobered up then, nobody wants to talk relativity effects with a drunk, don't you know. :wacko:

[raid517]

Lol, true, Einstein's special relativity is hard enough to grasp when you are sober, so if only one thing is certain it is that that you will definitely not understand it when you are drunk!

But in any case to a degree you are right (if I understand what it is you are trying to say). In both instances the outcome will be the same. If the pole vaulter runs at the barn at non relativistic speeds, either he must stop before hitting the wall, or he must continue until he hits the wall and the pole will break. At relativistic speeds, his options are identical. Either he must stop before he hits the wall, or he must continue to the wall, at which point the pole will break.

If he stops then he and his friend must agree that running into a barn with a pole that is too long to fit in the barn is a silly idea. If he continues into the barn and hits the wall, he and his friend with have to agree similarly. Clearly in both instances the causal outcome are identical.

The only thing open to dispute is exactly *when* either of these events occurred. But since 'when' (and time in general) as Einstein's equations showed us is a relative (and fairly fluid) thing, it is possible to two different observers in two different inertial frames to have a different perspective on this. (Although again both answers will always invariably converge at a single point, so that it is always possible for he and his friend to agree exactly when the pole hits the wall. It is only while the pole vaulter maintains relativistic speeds that any dispute arises).

GJ

[Guest]

The paradox works, however each person in the different frames interprets the scenario differently due to time dilation. If the man crashes into the wall fram, he must crash into the frame in the other (einsteen's first postulate), therefore there is only the argument between the two people as to whether he crashes BEFORE he enters the barn or AFTER.

The paradox works, however each person in the different frame interprets the scenario differently due to time dilation. If the man crashes into the wall in ONE frame, he must crash into the frame in the other (Einsteen's first postulate), therefore there is only the argument between the two people as to whether he crashes BEFORE he enters the barn or AFTER. <-- Sobered up version.

[raid517]

Can you explain what you mean when you say that 'the paradox holds'? Do you mean that you still envisage that there is a problem? Clearly the 'when' of it is neither here nor there as time in special relativity is not considered a fixed quantity, so different things in different inertial frames can appear to happen at different points. But the fact remains that the outcome will always be the same, regardless of which particular inertial frame you are travelling in, because regardless of your velocity, the laws of physics (and of long sticks banging into walls) will always be the same, regadless of your velocity.

It is a tricky idea to grasp for sure and I wish I could explain it better.

Perhaps if someone could find a video it might help?

GJ

[Guest]

I bought this up with my Physics Lecturer this morning in tutorial - We've been asked to think about this problem a little more - I tried to explain about the effect of Time Dilation but he wasn't really buying it, so Im going to read up a bit on it and try and come up with a solid solution. Thanks for all your ideas guys :-)

[raid517]

Well now you are confusing me too.... It is true that I don't quite see where your paradox is and in exactly what sense you are invoking time dilation in this.

In essense the only perspective that is accurate is that of the pole vaulter - because clearly if he runs at relatavistic and/or non relatavistic speeds, the outcome is always going to be the same, he and his pole will not fit in the barn.

Both before and after the experiment, he and his friend will have no option but to agree on this.

GJ