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May 23, 2022 at 11:12 comment added Professor Sushing What I suggest you do is to consider the scenario in which the crate is half way through the window in the frame of the train, and then Lorenz transform the position of the four corners at that instant on the train into four points in the ground frame, and let us know what you find.
May 23, 2022 at 11:07 comment added Professor Sushing Sorry, I shouldn't have used the word yawing. What I meant was that if you consider your diagram, the distorted square can readily fit through the window provided that it approaches the window at a certain angle.
May 23, 2022 at 10:38 comment added γ Anon I agree that if the crate can pass through in Bob's perspective then it should in Alice's also. I just dont know by which mechanism it can happen. I considered yawing as a potential solution at first, but as said, if the train is Nothbound the crate must yaw counter-clockwise so that the North Western corner isn't more North than Northern edge of the window frame. If the train was going East instead, the crate would have to yaw clockwise so that the South Eastern edge isnt more East that the eastern edge of the window frame. There are also some other problems with yawing.
May 23, 2022 at 9:27 comment added Professor Sushing I think you are missing the point, or I am missing a different one, which is that if you can pass the crate through the window at 90 degrees in the train's rest frame, then it must pass through when viewed from any moving frame. If the crate has to yaw in another frame for that to happen, it is not the case that the crate decides how to yaw- it is that the yawing effect arises in the moving frame according to the speed and direction of motion of that frame, so the change of angle would take care of itself.
May 23, 2022 at 8:52 comment added γ Anon Yes I have Marco. There is no phenomenon that im aware of that will result in the crate yawing counterclockwise from its launch angle, to an angle that would allow it to pass through, and if there was I would have quite a few issues. The biggest is that the crate would require advanced knowledge of the orientation of the window. For instance, the same crate launch velocity and direction could be used on an Eastbound train going 0.5c with South facing windows. This yaw phenomenon would have to now occur in a clockwise direction for the crate to pass through.
May 23, 2022 at 7:42 comment added Professor Sushing It is only too North if it approaches the window at a right angle in the frame in which it is distorted. Have you considered that?
May 23, 2022 at 5:10 comment added γ Anon I've added a picture to the post to clarify Alice's perspective. As you will see, the North Western edge of the crate is too North, even with the Easterly edges of the crate lined up with the window's Northern and Southern edges.
May 22, 2022 at 13:40 history answered Professor Sushing CC BY-SA 4.0