# Pole and Barn paradox - close the doors for good!

1. Jul 30, 2008

### jtaravens

As I was reading Fabric of the Cosmos, I got stumped at the relativity of simultaneity section. This led me to Google for some additional explanation. I stumbled upon http://www.phys.unsw.edu.au/einsteinlight/jw/module4_pole_paradox.htm" [Broken] which made me think of this question regarding the pole and barn paradox.

I searched around the forum and I didn’t find an answer to my specific question – here goes:

If the person running with the pole appears to the spectator (at a distance) to be inside the barn completely with the doors shut, how can the person running with the pole think that the pole is hanging out of the barn?

I understand how only if the doors are simultaneously shut (according to the spectator) and immediately opened b/c the person running with the pole would not agree with the simultaneous shutting and opening. So to the runner, the first door shuts while the back door is still open allowing the pole to hang out, and then the front door opens while the front of the pole moves out of the barn and then back door shuts. But if both doors are shut, and shut for good, doesn’t it come down to whether the pole is in the barn, or whether the back door came crashing down on the end of the pole? One of my problems is right here: if the doors are closed forever, is the pole in the barn or not? Shouldn’t this be the same for both observers? The pole would either be crushed by the door or not.

If the simultaneity of the doors closing for good is still relative, couldn’t you time the closing so it appears simultaneous to the runner (i.e. have the back door close a bit earlier than the front door)? In this case it wouldn’t be simultaneous to the spectator. But we can still ask if the pole is in the barn or did it get crushed by a door?

I feel like to the runner, the pole is at a static length so it can’t ever be in the barn because it’s too big. This leads me to ask is this just an illusion based on perspectives of when doors are opening and closing and how the pole appears to the spectator (based on length contraction) to pass through the barn. I must be missing something here.

John

Last edited by a moderator: May 3, 2017
2. Jul 30, 2008

### MikeLizzi

True, the runner never observes the pole being completely in the barn. But this fact does not alter anything that must be invariant between reference frames. If the pole is observed to get crushed by the door in one reference frame it will be observed to get crushed by the door in any other reference frame. Likewise if the pole clears the door in one reference frame, it will clear the door in every other.

May I suggets my tutorial on the subject at

http://mysite.verizon.net/mikelizzi/TutorialPoleInBarn.htm

If you have a PC you can actually run the 3d graphics simulation.

3. Jul 30, 2008

### JesseM

If the doors shut simultaneously in the runner's rest frame, in the barn's own rest frame the back door must close later than the front door, not earlier. It'd have to work out so that if the back end of the rod has passed through the front end of the barn before the front door shut (in the barn's rest frame), then that would always mean that by the time the back door shut the front end of the rod would have already had time to pass partway through the front door (assuming the rod continues to move inertially) so the door would get closed on it. Should I try to do the math to prove this or would you rather just take my word for it?

4. Jul 30, 2008

### jtaravens

Well that confuses me a bit - why would the barn's rest frame mean that the back door must close later than the front? While the runner is in the barn, couldn't the back door close before the front door?

I believe my question wasn't so clear. (but no need for mathematics - i'm only a microbiologist so extra math will make my head spin even harder!)

I think this website answers my question
http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html" [Broken]
The site states:
What if the doors are left shut?
If the doors are kept shut the rod will obviously smash into the barn door at one end. If the door withstands this the leading end of the rod will come to rest in the frame of reference of the stationary observer. There can be no such thing as a rigid rod in relativity so the trailing end will not stop immediately and the rod will be compressed beyond the amount it was Lorentz contracted. If it does not explode under the strain and it is sufficiently elastic it will come to rest and start to spring back to its natural shape but since it is too big for the barn the other end is now going to crash into the back door and the rod will be trapped in a compressed state inside the barn.

My interpretation of this is that the pole actually fits in that barn. The spectator sees it in the barn and by shutting the doors for good, you can squeeze the compressed pole in the barn (probably destroyed by strain) for the runner to see too.

MikeLizze- I believe I have a java issue here at work, so I will try later. Thanks!