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GR8677 #71
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Special Relativity$\Rightarrow$}Relativity!

The order of the door opening depends on which reference frame one is in. Whether or not one actually put the relativistic cake in one's mouth to have performed the motion of eating the cake... is all relative.

Observe this table summarizing the results of some trivial calculations of rest lengths,

$\begin{eqnarray} ........... own frame & & other's frame\\ car........ 5 m & & 3m \\ garage..... 4 m & & 2.4m
\end{eqnarray}$

So, the car fits in the garage in the garage's frame (the car is $3m$ and the garage is $4m$). But, in its own frame, the car is much too big to fit in the garage (car is $5m$ and the garage is merely $2.4m$). Which frame is right? Relativity puts equal footing to either, and thus one shall never know. Be an agnostic, and one just might live a happy carefree life.

Alternate Solutions
 torturedbabycow2010-02-14 17:50:06 dogsandfrogs explained it pretty well. Once you've calculated both lengths in both reference frames, you'll see that whether the car "fits" in the garage also depends on the reference frame. (Which cuts out (A) and (C) immediately.) What this means is that the order of the doors opening/closing ALSO depends on the reference frame, since we're told that they do so automatically as soon as each end of the car passes. This seems like it might be an issue for causality, but it isn't. (To be pedantic, it's not true that the order of putting-cake-in-mouth and eating-cake is relative - no matter what frame of reference you are in, putting-cake-in-mouth always comes first. Only when the second event is outside the "light cone" of the first can the order of events be reversed based on reference frame, since they're not causally related and it doesn't "matter" which one goes first. :P And that's why there's not really a paradox.)Reply to this comment
whereami
2018-04-09 02:01:42
special relativity doesn\'t really change how things are, i think. It only supplies you with different coordinates of space and time. In this case no matter what frame you choose, the doors will be opened/closed at the moment when it is perceived to be needed to be opened/closed. \r\nIf you don\'t believe this you can calculate for both frames. \r\nAnswer is E bytheway.
gear3
2013-09-24 09:34:36
I think D is the right answer.
At first,in the garage frame,the length of the car is 3m. We assume when the car's head goes to gate A, we close both gate A and B instantly AT THE SAME TIME.
Then, in the car frame, the garage is shorter than the car. When gate A hits the car's head, it closes,but gate B doesn't close(you can calculate it yourself.I just state the process).Then the car crashes, but you should notice the car's tail won't be damaged AT THE SAME TIME because the impact need time to go to the tail and its maximum speed is c. The garage's speed is 0.6c.
Anyway, although gate A is closed ,gate B isn't. After a few time, when gate B is closed the whole car is damaged in the garage.
Special relativity never violates the law of causation.
 dochang2017-10-17 18:12:32 Nope. E is indeed correct. Try solving the problem with a Minkowski diagram. It becomes immediately evident that after transforming from one reference frame to another, the simultaneity of the closing and opening of the doors is no longer preserved. Causality is also preserved because in both reference frames, the presence of the car causes the doors of the garage to open and close.\r\n
torturedbabycow
2010-02-14 17:50:06
dogsandfrogs explained it pretty well.

Once you've calculated both lengths in both reference frames, you'll see that whether the car "fits" in the garage also depends on the reference frame. (Which cuts out (A) and (C) immediately.) What this means is that the order of the doors opening/closing ALSO depends on the reference frame, since we're told that they do so automatically as soon as each end of the car passes.

This seems like it might be an issue for causality, but it isn't. (To be pedantic, it's not true that the order of putting-cake-in-mouth and eating-cake is relative - no matter what frame of reference you are in, putting-cake-in-mouth always comes first. Only when the second event is outside the "light cone" of the first can the order of events be reversed based on reference frame, since they're not causally related and it doesn't "matter" which one goes first. :P And that's why there's not really a paradox.)
 Almno102010-11-12 00:37:13 Imagine if you had a cadillac that could go the speed of light. Parking that thing would be rough.
justguessing
2009-09-26 09:03:33
i believe the paradox arises from the fact that garage doors just dont open at the speed of light. It's takes like at least ten seconds.
 sher2010-01-07 11:11:34 it is very confusing
OrrinJelo
2009-08-06 17:16:57
So the answer is E? Can anyone explain this better?
 dogsandfrogs2009-10-07 09:25:30 Yes, the answer is E. Think of both reference frames: In the frame of the car, when it is passing through the garage, the car is 5 meters and the garage is 2.4 meters. Obviously in this frame the car is not contained within the garage at any point. In the frame of the garage, the garage is 4 meters, and the car is 3 meters as it is passing through. In this frame, the car is short enough to be fully contained within the garage, with an entire meter to spare. Because the car is in the garage and not in the garage depending on your choice of frame, there is no unique answer.
 shak2010-07-31 21:34:13 Thank you Dogsandfrogs
 Setareh2011-10-26 11:26:21 I loved your comment Dogsandfrogs..

You are replying to:
I think D is the right answer. At first,in the garage frame,the length of the car is 3m. We assume when the car's head goes to gate A, we close both gate A and B instantly AT THE SAME TIME. Then, in the car frame, the garage is shorter than the car. When gate A hits the car's head, it closes,but gate B doesn't close(you can calculate it yourself.I just state the process).Then the car crashes, but you should notice the car's tail won't be damaged AT THE SAME TIME because the impact need time to go to the tail and its maximum speed is c. The garage's speed is 0.6c. Anyway, although gate A is closed ,gate B isn't. After a few time, when gate B is closed the whole car is damaged in the garage. Special relativity never violates the law of causation.

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