The Barn Paradox: A Dilemma of Relativity Explained

imagine this scenario this is you this is your garage and this is your friend in the car your garage has these two doors that can instantly close and open when you want and your friend wants to park in your garage but unfortunately he finds out your garage is too small for his car to park seems like an impossible problem to solve but you have the knowledge of special activity and you know that when things are moving they contract due to length contraction so you propose this idea to her friend that he could try to go very very fast so the length of his car contracts and when he's directly inside the garage you close the door your friend doesn't know what you are talking about but he trusts you so he follows along but of course since you are careful you want to just test whether it's possible so you close the door just for a split second so that your friend doesn't crash inside everything went smoothly as it seems you were able to close both doors simultaneously and your friend was truly inside the garage but wait your friend seems to disagree with you he claims he was never fully inside how is this possible well you give this a problem a second thought applying the knowledge of the special activity again and you look at this problem from your friend's perspective for him the length of the car remained the same but moreover everything else got contracted including your garage so you made the problem even worse but how are you able to close the both doors at the same time if your friend could never be fully inside your garage how could you both experience the same event differently now it's time to give it another thought and remember the relativity of simultane ready if there are two events simultaneous for one Observer then in order to preserve the postulates of special relativity these two events can't be simultaneous for the Observer moving relative to him I covered this topic in one of my previous videos so I recommend you to go watch it after this video the doors are like Lightnings therefore even though they were closed simultaneously for you you can't tell the same for your friend so what your friend saw was the right door closed first then opened then the second door closed and opened and this is the resolution of these Paradox right but you can go even further with your questions but if you don't want to be careful and just let the door closed when your friend is inside of course you know that your garage and your friend's car are infinitely firm so you don't have to worry that you cause any damage to your property apart from the fact that your friend is going to probably die from your point of view the car is fully inside and you close the doors car hit the right door and stop since it stops then it must increase in length according to length contraction and this will apply a huge pressure against the doors of your garage from the reference frame of your friend though you close the right door first he hit them and instantly stops and now the second door can't fully close anymore again the same event experience differently by both observers how is this possible to answer this question we have to think of the car on a deeper level we think of this car being made of atoms with the following properties if they are separated with some distance D there is no Force if they come closer together they repel each other and if they are being stretched they attract each other this is a standard property of each material and depending on the strength of this interaction between these atoms we determine the firmness of this material for us the strength is infinite even after smallest deviation since we have an infinitely firm car our car is made of a series of such atoms and we can make the same experiment with this setup but for the sake of Simplicity we can think of it being made of just two the front one and the back one The crucial point to realize here is that these two atoms are causally disconnected and therefore if there is a deviation in one the information about this deviation is spreading with the speed of light therefore from the reference frame of your friend when he hits the right door with the atom on the front the information about this starts spreading with a speed of light but the atom on the back is still moving to the right when this information hits the atom it instantly stops and then the left door is closed now these atoms want to repel each other with an Infinite Strength which creates an infinite pressure on your doors which is consistent with have you as a stationary Observer experience this event so there you have it you were able to park your friend's car in your garage even though it seemed impossible the only price you had to pay was the life of your friend now you see that using just one phenomena of special activity alone like time dilation or length contraction always leads to paradoxes here we use just length contraction and got a so-called ladder Paradox but using relativity of simultaneous from which time dilation can be derived we fixed everything the same thing happens if you use just time dilation you get what is called the clock Paradox but using the length contraction and setting a proper coordinate systems Paradox disappear so this is it for this video thanks for watching if it was informative for you I would really appreciate if you give it a like And subscribe I appreciate it and I see you in the next video

Channel: Physics - problems and solutions

Views: 12,174

Keywords: special relativity, Albert Einstein, length contraction, ladder paradox, barn-pole paradox, special relativity paradox, time dilatation, physics, lorentz transformations, relativity of simultaneity

Id: ceu8-yyd0jI

Length: 6min 45sec (405 seconds)

Published: Thu Sep 08 2022