I'm having trouble reconciling two different versions of the Pole and Barn paradox.

Version 1: Consider a pole 10 m long and a barn 5 m long with a front and rear door. A runner carrying the pole (frame S') moving with respect to the barn and a farmer (frame S) runs into the barn. The farmer will see that the pole fits into the barn if the runner is moving at a speed:

gamma = Lp/L = 10/5

v = 0.866c

But according to the runner, the barn is moving towards him. The barns length contracts to:

L = Lp/gamma = 5/gamma = 2.5 m

How is it possible for a 10 m pole to fit in a 2.5 length contracted barn? Basically by drawing a spacetime diagram it becomes apparent that the pole doesn't fit. From the farmers frame, the front of the 5 m length contracted pole gets to the rear door of the barn simultaneously as the end of the pole enters the front door. But in the runners frame, these events are not simultaneous and the pole does not fit into the barn (the front end of the pole leaves the back door before the end of the pole enters the front door).

Version 2: Consider the same situation, but the rear door is replaced with an armor plate. From the farmers frame, when the pole fits into the barn, he shuts the front door (in the next instant, assuming the pole doesnt break, the pole must bend or break through the armor plate). From the runners frame, the front end of the pole hits the iron plate, with 7.5 m of the pole still outside of the barn. If information travels down the pole at speed of light c, it would take 10/c to reach the back of the pole. The barn on the other hand must reach the back of the pole in 7.5 / (0.866*c), which is less time than the time it takes for the info to travel down the pole. Thus, the runner is in agreement with the farmer, and the 10 m pole is contained within the 2.5 m barn.

Question: How is it that the pole fits into the barn in version 2, but not in version 1?

Question: My book says, as a part of version 2, "since this is relativity, the runner must come to the same conclusion in his rest frame [as the farmer] as the 2.5 m barn races towards him at v = 0.866c." But in version 1, the runner didnt come to the same conclusion?

"Basically by drawing a spacetime diagram it becomes apparent that the pole doesn't fit."

Depends whose frame you draw it in.

Remember, all inertial frames are equally valid. The resolution of the paradox is that both answer really are correct because you are asking about the relative timing of space-like separated events (the front of the pole leaving the bard and the rear of the pole entering the barn) and they do not have a uniquely defined time order.

But the second version is illustrating a different point: that all frames can agree on the answer to the question "Is the rear of the pole inside the barn when it learns that there has been a collision?".

That questions concerns a single space time event (news of the collision reaching the rear of the pole), and so all observer can agree that this happens within the barn.

There are no "two versions" of the thought experiment, there is only one version, and every observer must ultimately agree about the question whether the pole is fully contained within the barn in the asymptotic future even though the different observers disagree about "what is out there" at a specific moment of time $t$ or $t'$.

And yes, be sure that the pole will be caught, as explained in Part 2, at least when the doors are robust enough to prevent the pole from getting through. From the farmer's viewpoint, it's obvious why the pole may get caught. From the pole's viewpoint, it doesn't fit at one moment – as argued in Part 1 – but it doesn't mean that the pole won't be caught. As clarified in Part 2 (and these considerations about the speed of the propagation of the information is overlooked in Part 1), the information about the front end of the pole that just hit the solid enough door is spreading at most by the speed of light (more realistically, by the much slower speed of sound) and the rear end of the pole continues to move, thus shrinking the length of the pole, and at some moment, the pole fits into the barn and the rear door closes, too. From the farmer's viewpoint, the doors may get closed simultaneously, but simultaneity is relative in relativity, so in the pole's reference frame, the front door closes before the rear door does.

If the doors are too soft and the pole is able to penetrate through them, both observers will agree that the barn won't get caught and will continue to move.

• Before this question was asked I would have agreed that there was only one version, but I would have asserted that the singular version was the one where the pole passes freely through the barn and the question is "Is the pole every fully contained in the barn?", to which the correct answer is "There is no unique answer." It is only today that I have heard of this variant in which with pole is crushed on the far door. – dmckee Jan 26 '14 at 8:07
• I think it is a thought experiment and it's clear that the real questions we want to add are questions that can be settled experimentally or operationally - that's the point of thought experiments. "Is the pole fully contained at one moment?" is a question whose answer depends on the inertial frame, and it is hard - and frame-dependent - to answer this question experimentally. The really clear question everyone understands is whether the pole gets caught, and this is a different question than the previous one (though in some frames, the answer to that question follows from the prev. answer). – Luboš Motl Jan 26 '14 at 8:12
• But otherwise, I think that one should still say that it is the same thought experiment because what's happening is the same process, the same arrangement of objects in the spacetime. Like in any thought experiment, one may ask different questions, and lots of intermediate smaller questions that help us resolve the big ones, and so on, but I think it is just conceptually wrong to say that there are two thought experiments if the processes are absolutely identical. – Luboš Motl Jan 26 '14 at 8:14
• In every thought experiment, the real question is whether some theoretical paradox or shocking prediction will manifest itself experimentally, in a way that may be detected and that has clearly visible practical implications. "Pole isn't fully contained within the barn according to the pole's frame at some moment" is not such a practically visible result of the experiment; it is an intermediate theoretical consideration whose practical consequences are being studied by the thought experiment - that's why the thought experiment was designed. – Luboš Motl Jan 26 '14 at 8:18
• All I can say is that the freely moving version appears in a lot of US texts, and it seems to serve an important pedagogical point, because by the time you get to it the students have forgotten that you showed them the relativity of simultaneity on day one: too much focus on the mechanics of getting the Lorentz transform and the consequent effects on time and distance intervals. – dmckee Jan 26 '14 at 8:29

Please leave both barn doors open and take a picture when the runner and the pole are completely inside. The fortitude of the pole or the doors are nonsensical to this paradox.

What is important is that the concept of simultaneity in different inertial reference frames are different.

What the observer at rest relative to the barn sees is, the runner and the pole both contracted, completely inside the barn at the same instant "simultaneously" when a picture is snapped.

What the runner sees is that the barn is contracted, and the light from the photoflash illuminates the front of the pole / front barn door and the back of the pole / back barn door at times that are just different enough so that the event that is furthest away in the direction of motion occurs first. The lining up of the front end or back end of the pole with the barn doors are no longer simultaneous.

• Now have a picture taken by an observer riding a cart moving parallel to the pole at the same speed. The situation reverses. This is all about the relativity of simultaneity. Nothing else. – dmckee Aug 12 at 17:01

The universe actually follows general relativity which extremely closely follows special relativity because the speed of light is so fast. Time also ticks faster at higher heights but by such a tiny amount that an object moving at 0.5 c at a height of 5 m will have much more time dilation from speed than time contraction from height.

According to special relativity, the pole will be enclosed in the barn because information can't travel faster than light. In fact, a shock wave only travels at 12 km/s in the material with the highest speed of sound of any material, diamond. I read on a web page that I can't find anymore that the speed of sound in diamond is 12 km/s.

According to my answer at https://www.quora.com/If-a-car-runs-at-the-speed-of-light-will-the-headlights-work/answer/Timothy-Bahry, the universe might not actually follow general relativity and there might actually be a material that a shock wave can be sent through faster than light and indeed if a poll of that material enters a barn of a strong enough material at a high enough speed, the collision actually will send information through the poll back through time in Earth's frame of reference preventing the back end from entering in the first place before the door was going to close, and if you are are about to set up an experiment that sends information from one point in space-time faster than light in one frame of reference then in another frame of reference into its own past light cone, it will nucleate the destruction of the universe at the speed of light before you actually get a chance to send information from a point into its own light cone and as soon as you reach a point that's at the edge of its own past light cone, space will disappear where you are.

I think the scenario where both doors close while the pole moves through the barn, has nothing to do with the laws of special relativity, but more with newtons laws - compensating for the laws of special relativity. As the pole comes to an abrupt stop, it will compress to the previous observed length within the barn, converting the energy of movement into kinetic energy what will cause shrinkage. After it stops, it will resume its original length, and bend in order to fit the smaller space. We can not fool the physical laws of nature.

## protected by Qmechanic♦Mar 30 '17 at 2:27

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