My question concerns an aspect of the pole-barn paradox that, to my knowledge, has not been discussed so far. So rejecting the question as "duplicate" is incorrect, in my view. Here is the edited version:

Einstein's 1905 postulates entail that unlimitedly long objects can be trapped, in a compressed state, inside unlimitedly short containers:

"These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. [...] So, as the pole passes through the barn, there is an instant when it is completely within the barn. At that instant, you close both doors simultaneously, with your switch. [...] 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." http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html

One of the comments on the previous version of the question is as follows:

"Note that the pole is not compressed by the Lorentz-FitzGerald contraction, it's compressed by colliding with the back door at 0.866c"

Not true. The compression occurs before colliding - the long object is still flying inside the short container when the doors are closed. That is, the compression is purely relativistic. Then the trapped object will "start to spring back to its natural shape". How much energy will be released if a 1 km object, compressed to 1 cm, restores its original length? Even the question sounds absurd, let alone the answer.

If such trapping is absurd, we have reductio ad absurdum: the absurdity of the logical consequence shows that at least one of the postulates is false. Is trapping unlimitedly long objects, in a compressed state, inside unlimitedly short containers absurd?

  • $\begingroup$ Are you asking if it is possible to compress sufficiently elastic objects? $\endgroup$
    – J. Murray
    Jan 24 at 22:14
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    $\begingroup$ Note that the pole is not compressed by the Lorentz-FitzGerald contraction, it's compressed by colliding with the back door at 0.866c. $\endgroup$
    – PM 2Ring
    Jan 24 at 22:58
  • $\begingroup$ Here's a question from a couple of months ago on this paradox: physics.stackexchange.com/q/597220/123208 $\endgroup$
    – PM 2Ring
    Jan 24 at 23:18
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    $\begingroup$ The two current answers do not address the “trapped in a compressed state” issue that is the crux of the question. But PM2Ring’s comment does. $\endgroup$
    – G. Smith
    Jan 24 at 23:33
  • $\begingroup$ It has been discussed a million times or more . . . the "compressed" pole simply does not exist, it is smeared across time in the barn frame so cannot be trapped. The key word here is simultaneity. $\endgroup$
    – m4r35n357
    Jan 25 at 9:28

The answer to your question is contained in the explanation posted on Baez's website, just as you have linked to it. In short, from the reference frame of a runner following along with the rod as it travels towards the barn, the two barn doors do not open or shut simultaneously, and so there is always room for the rod. Thus there is no paradox.

  • 1
    $\begingroup$ Note that John Baez didn't write this text, he just hosts it. The credited authors are Robert Firth, "SIC" and "PEG". $\endgroup$
    – benrg
    Jan 24 at 23:12
  • $\begingroup$ @benrg, will edit. $\endgroup$ Jan 24 at 23:20

This has nothing to do with elasticity, and the analysis is incorrect. Assuming (and this is absurd) a perfectly rigid pole and that the barn door is infinitely strong so that it can stop the pole dead, then at the time when the front end of the pole hits the barn door, the back end of the pole has not yet entered the barn. As the pole stops, it is found to be too long to enter the barn.

It is clear that in the reference frame of the pole, the front end enters the barn before the back end reaches it. The confusion (paradox) arises from misunderstanding the arbitrary nature of simultaneity in relativity. It is mistake to say that there is "an instant when it is completely within the barn" because in the frame of the pole, this is simply not true.

  • 3
    $\begingroup$ Special relativity does guarantee that the pole can be trapped in the barn given the unrealistic assumption that the barn is impenetrable. The speed of sound is limited to $c$ and a signal traveling even at $c$ can't reach the back end of the pole before the back of the barn does, so the back of the pole can't know to slow down. Therefore there is a time even in the rest frame of (the back of) the pole that it's completely inside the barn. $\endgroup$
    – benrg
    Jan 24 at 23:15
  • $\begingroup$ @benrg, one unrealistic assumption is as bad as two! One can hardly allow the assumption that the barn is not deformed in the impact while disallowing the assumption that the pole is not deformed. If one removes the impact, then in the rest frame of the pole, the front of the pole passes through before the back end. $\endgroup$ Jan 24 at 23:26
  • $\begingroup$ There is nothing unrealistic about assuming that the doors are steel and the pole is marshmallow. You can always make the pole just very slightly longer than the barn, and then it doesn’t have to be moving extremely fast, so the marshmallow does not break the steel. $\endgroup$
    – G. Smith
    Jan 24 at 23:36
  • $\begingroup$ @G.Smith, the marshmallow must be moving very fast for relativistic effects to be significant, and then it will be splattered on the steel. You are just exchanging one unrealistic assumption for another. Of course if it is going slowly enough for an elastic collision it can squeeze into the barn and there is no relativistic paradox. $\endgroup$ Jan 25 at 9:17

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