You can view the relatsically train as a sinlge rigid object as long as it’s not accelrating, the problem as phrased doesn’t involved accelrtation which makes it simpler as accelration breaks the symmetry of the situation. The back and the front aren’;t causally connected as an action on the front won’t instaneously effect the back. Yes you can assume the doors close instaneously as it doesn’t matter in this apparent paradox.
You can imagine that the framer sets up a computer exactly at the midway point in the barn which sends two light pulse in either direction to trigger the doors when the train is fully in the barn (or just before in order to take into account the time the pulse takes to travel to the door), so from the farmer’s point of view they both shut at exactly the same time. Now consider the train travelling at a relativistic speed and how it views this light pulses. So imagine now, at the time the front of the train reaches the front door, the point on the train that was level with the computer when the pulses were emitted. According to relativity from it’s point of view both pulses must of travelled at c, but it’s moved some distance since the pulses were emitted, so from it’s point of view (and indeed the whole train as it is in the same refernce frame) the front door will close before the second as it now has less distance to travel.
From the point of view of a staionery observer the train will fit in the barn, from the point of view of the train it won’t.
I should of made this clearer in the above explanation: From the point of view of the train it is sitting still and it’s the barn that is travelling at a relatvistic speed.
The premise seems to be relying on a signal sent trhough the barn and thus the people on the train see things differently than the computers/people in the barn do.
Does it change anything if you go back to my original idea that the whole thing is timed? That is, you have two computers, one at each end of the barn, controlling the door there. Each computer has hyper-accurate clocks and we tell them to shut the doors at time X. We now send our train hurtling down the tracks at near light speed and time it such that the train will be ‘inside’ the barn at the precise moment (time X) the computers tell the doors to shut. Does this make any difference to ‘catching’ our train inside the barn now? I assume caclulations to see this sort of timing would be possible (even if the actual details of setting up the experiment would be difficult).
[sub]If this is too much of a hijack at this point let me know and I’ll restart this in another thread.[/sub]
Yes the same explanation still works when you have two clocks ‘staionery’ 100% accurate clocks as in order to agree with the time in the farmers reference frame then they must make the doors close at the same time as the two pulses of light would of in the above example.
Imagine trying to put a plastic tube in a cardboard box where the box is slightly shorter than the tube. You can’t put it in straight, but if you rotate it at an angle it will fit.
Now imagine the barn as a four-dimensional box where the fourth dimension is time. And the train is the tube. When you accelerate the train, its frame of reference rotates with respect to the barn. The full length is still there, but some if it is in the time dimension instead of in XYZ. Now the tube fits in the box.
To a stationary observer the train looks like it got shorter. To someone on the train it looks like the only part of the train is in the box at a time. Both are accurate 3-D descriptions of the 4-D reality.