Long train falling through gap in track

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Einsteins relativistic train in tunnel paradox. There is a video on YouTube with this title. Towards the end of the video one person sees the length contracted train fall into the gap. The person on the train seems to see it become like a fluid that flows into the gap*. How can the train behave like this

* i gather that this because the train is not completely rigid

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Why the hell is the Wagner necessary? I remember as a student dealing with this paradox in the following form: a rod of length x moves along its length across the top of a table which is of course infinitely thin and with no friction. In the table is a slot of length x plus dx, a tiny amount so that the rod will just fit into the slot and fall through it when dropped onto the slot.

An observer at rest on the table will see the rod contracted, so when it moves over the slot, it will fall through it. But an observer moving with the rod will see the slot contracted, so the rod will be too long and not fall through the slot. How to reconcile these?

The principle is that whatever happens at rest will also happen at speed. If the rod falls through the slot at rest, it will fall through at speed (given the obvious impossible Gedankenexperimente conditions). Even though the observer on the rod sees the slot as too small, the ends of the rod still meet their respective ends of slot at the same time. I make this purely as a confident assertion because I am not longer able to dredge up the maths to prove it, but I well remember doing it many decades ago, and convincing myself that this was the case. I certainly would not have been able to do it with all that music in the background.

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Posted (edited)

Why the hell is the Wagner necessary? I remember as a student dealing with this paradox in the following form: a rod of length x moves along its length across the top of a table which is of course infinitely thin and with no friction. In the table is a slot of length x plus dx, a tiny amount so that the rod will just fit into the slot and fall through it when dropped onto the slot.

An observer at rest on the table will see the rod contracted, so when it moves over the slot, it will fall through it. But an observer moving with the rod will see the slot contracted, so the rod will be too long and not fall through the slot. How to reconcile these?

The principle is that whatever happens at rest will also happen at speed. If the rod falls through the slot at rest, it will fall through at speed (given the obvious impossible Gedankenexperimente conditions). Even though the observer on the rod sees the slot as too small, the ends of the rod still meet their respective ends of slot at the same time. I make this purely as a confident assertion because I am not longer able to dredge up the maths to prove it, but I well remember doing it many decades ago, and convincing myself that this was the case. I certainly would not have been able to do it with all that music in the background.

Yes I watched with the sound off.

But I wasn't convinced either by the proposed events or the proffered explanations.

I am particularly suspicious of this comment

The principle is that whatever happens at rest will also happen at speed.

.

Isn't that contradicted by the observed fate of cosmic pi mesons?

Edited by studiot

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This is a miserable video that works ok on the explanation of relativity of simultaneity (the first half).

The second half tries to introduce the notion of Born rigid motion and is a disaster. Imagine that the train had many wheels, all powered. Then , instead of being "pushed" in one point (in the back), it will move like a rigid rod, with no "compression". The explanations from "Adam's point of view" , fail miserable now , because the train no longer behaves like an accordion. The first case (the train hitting the front door of the tunnel while compressing against the "infinitely rigid" front door) is not only self-contradicting (there are no "infinitely rigid" objects in relativity) but also unphysical: the train will get deformed in Adam's frame while it goues through the tunnel unscathed in Sarah's frame. The "professor" screwed up royally.

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Posted (edited)

This is a miserable video that works ok on the explanation of relativity of simultaneity (the first half).

The second half tries to introduce the notion of Born rigid motion and is a disaster. Imagine that the train had many wheels, all powered. Then , instead of being "pushed" in one point (in the back), it will move like a rigid rod, with no "compression". The explanations from "Adam's point of view" , fail miserable now , because the train no longer behaves like an accordion. The first case (the train hitting the front door of the tunnel while compressing against the "infinitely rigid" front door) is not only self-contradicting (there are no "infinitely rigid" objects in relativity) but also unphysical: the train will get deformed in Adam's frame while it goues through the tunnel unscathed in Sarah's frame. The "professor" screwed up royally.

Yeah. Slow as it was, it went from reasonably good to horrible at almost the speed of light...

The train falling through the gap was especially bad. That happens (of course) in neither frame.

Edited by J.C.MacSwell

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"That happens (of course) in neither frame"

What does happen then

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"That happens (of course) in neither frame"

What does happen then

The at rest length of each car being longer than the gap, and given the geometry shown...depending on alignment it bridges and continues or hits the other side...there is no relativistic speed at which it will fall through. It is not 100.00000% rigid but it does not lose the rigidity that it has, never mind fall (accelerate downward) like that in that amount of time.

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Posted (edited)

"That happens (of course) in neither frame"

What does happen then

The train will get over the gap. It might get a little bump against the leading wheels. The whole example originates from a very bad idea from the book by Taylor and Wheeler. Shows that even famous physicists mess up at times.

One very strong criticism against the scenario is that it attempts to use SR IN THE PRESENCE of GRAVITATIONAL FORCE. This is embarrassing.

Edited by zztop

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There are plenty more criticisms that can be levelled against that vid.

The front of the train hits the unbreakable door huh?

And then what ?

Well it stops.

Stops, you say?

Well yes it is at rest relative to the track.

So what is the train length now as seen by the bloke on the train v the train length as seen by the girl on the track?

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There are plenty more criticisms that can be levelled against that vid.

The front of the train hits the unbreakable door huh?

And then what ?

Well it stops.

Stops, you say?

Well yes it is at rest relative to the track.

So what is the train length now as seen by the bloke on the train v the train length as seen by the girl on the track?

That reminds me of the joke: "What is the last thing that goes through a bees mind when it hits the windshield?"