I’m totally new to special relativity and am working through some basic derivations and problems with it for an extra credit activity in a 2nd semester general physics class.

My question is this: say you have an airplane traveling close to the speed of light. It goes through an airplane hangar without changing speed and fits “perfectly” inside it (i.e. it barely fits inside) according to an observer watching from the airplane hangar. The observer knows that the hangar is x distance long so that both the plane and hangar from his point of view are both x distance.

Now from my calculations and just general knowledge you should get that someone in the airplane traveling close to the speed of light views the airplane length as greater than x and the hangar length as less than x correct?

So then, according to the individual within the plane, the airplane doesn’t fit inside the hangar. My question then is who is essentially right about the airplane fitting or not and how does all this get resolved?

My best guess is that both people are correct and their answers to the question “does the airplane fit” do not need to agree.

Also, as a little corollary to this question, what if there were doors at either end of the hangar such that the first one opened precisely when the nose of the airplane came in and closed precisely when the butt of the airplane was in which is also the time the other door opens for the nose of the airplane to leave the hangar again so that the airplane doesn’t smash from the point of view of the observer within the hangar. Again, the airplane wouldn’t fit from the perspective of someone within the plane right? So would the airplane just get wrecked?

I feel like this has got to be a fairly common special relativity question but I had trouble finding something like it online so I apologize if this is a duplicate!

  • $\begingroup$ You use the phrase "which is also the time". According to whom? $\endgroup$ – WillO Nov 5 '17 at 22:16
  • $\begingroup$ Fact: the ladder 'paradox' is so well known in elementary SR that this question should be downvoted since it does not show any research effort (merely stating that you've had trouble finding something like it doesn't mitigate this in any way). Fact: For whatever reason, I can't bring myself to downvote this otherwise well written question. $\endgroup$ – Alfred Centauri Nov 5 '17 at 23:39
  • $\begingroup$ Very impractical and purely theoretical question. Forget an aircraft or hanger, have you first calculated how much energy is needed to accelerate even one kilogram of mass to the minor relativistic speed of one tenth of the speed of light? $\endgroup$ – 0tyranny 0poverty Nov 6 '17 at 0:15
  • $\begingroup$ @AlfredCentauri - Thinking about the problem and solution should be taken as equivalent to research. It seems plain he has been thinking. So no need to feel too conflicted. $\endgroup$ – mmesser314 Nov 6 '17 at 1:46
  • $\begingroup$ "Thinking about the problem and solution should be taken as equivalent to research" - No, that doesn't seem correct to me. $\endgroup$ – Alfred Centauri Nov 6 '17 at 3:11

You have discovered the Ladder Paradox. The resolution of this paradox is in simultaneity of the events. When you say, "fits", you mean that the head and the tail of the airplane both are in the hangar at the same time or simultaneously. However, in special relativity, simultaneity is relative. The events you see as simultaneous do not appear simultaneous to other observers.

The same with the doors closing. If you close both doors simultaneously, other observers would see them closing one after the other. So there is no paradox there. You just need to work through the clock synchronization procedure to be very specific on the order of the remote events.

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  • $\begingroup$ Alright now I’m thoroughly confused. I understand that time is moving slower for the person in the aircraft so that the doors will open/close at a different point in time for them, but how could they not both occur at the same time (even if that time is different than the time observed by the individual in the hangar)?? $\endgroup$ – Liam Cooney Nov 6 '17 at 2:59
  • $\begingroup$ @LiamCooney Because simultaneity is relative. It is well explained here on the example of a moving train and stationary platform: en.wikipedia.org/wiki/Relativity_of_simultaneity $\endgroup$ – safesphere Nov 6 '17 at 4:38
  • $\begingroup$ Yeah I eventually got to relativity of simultaneity thanks :) Took me a bit longer to grasp than the concepts of time dilation and length contraction $\endgroup$ – Liam Cooney Nov 6 '17 at 4:44

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