Relativity
In Einstein’s thought experiment a train traveling a light speed reaches a stationary observer on a platform. It is known that the observer sees the back of the train arrive first. Does the observer also see the sides of the train to be reversed and the left side to be on the right and vice versa? Or does the observer see the train to be back to front, upside down and inside out? Cheers
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Peter Stiphout
3 years, 7 months ago
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Hey Peter, can you say some more to set up this thought experiment so we're on the same page?
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In regards to the light speed train being viewed by a stationary observer on a platform. Over decades of reading on the subject I came across some interesting work carried out by mathematicians/ physicists. Amongst which was a maths proof which was accepted that the back of the train was seen by the observer to arrive first. Another also accepted provided math proof that the observer would also see the passengers to be on the outside of the train. As such the train was seen to be inside out. The work was carried out by highly qualified and respected mathematicians/ physicists whose names I cannot recall. My own thoughts on the matter lead me to believe that the observer would also see train to be upside down and I seek further information. Unfortunately I have all the maths and physics skills of a Wombat. I hope this helps and please do not hesitate to contact me if more is required. I think the note I sent in on a Quantum string quandary is equally interesting. Cheers
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Hmm, I am not aware of this inside out result. Shapes can stretch and deform differently to different observers, but can't change their topology (in other words, make an object turn inside out or in this case, put the passengers outside the train). That's because the Lorentz transformation (the function that maps one observer's coordinates onto another's) are continuous, and maintain the relative orientation of coordinates.
Regarding the observer on the platform, are you sure that you're not thinking about the following:
?
You should definitely include a reference to what you're talking about, because what you've written isn't actually true. First off, a train can't go the speed of light relative to any observer simply because it has mass. I know this sounds pedantic and overall unimportant, but it really does matter. But let's imagine the train was, in our reference frame, travelling extremely close to the speed of light, heading directly towards us, in a vacuum (nothing to stop it) and with some light nearby to illuminate it (we want to see it). What would we see?
A fully correct answer would probably leave you bored, as the sum of all the "observable" effects would essentially make the train completely indecipherable, possibly even effectively unobservable. Here's a list of such "observable" effects:
Length Contraction: All objects travelling with some finite velocity are automatically length-contracted along their line of motion. On top of that, their observed lengths are scaled by a factor dependent on their direction of motion relative to you. For a train travelling straight at you, you can divide the front face of the truck into a bunch of small sections. Only the center will be travelling directly towards you, while all the other parts will be pointing slightly away from you. The net result will be an extremely fisheye looking front of the train. (Not reversed in any way though) If we were looking at it lengthwise though, the train would looked like a completely compressed accordion. It would be entirely compressed along its direction of motion.
Doppler Shift: A similar shift happens to the observed wavelength of light being emitted by anything travelling with a finite velocity. For a train travelling infinitesimally close to the speed of light, you literally wouldn't see anything. All of its light would be shifted out of the visible spectrum and into the high-energy gamma ray spectrum (which would totally toast you in a flash, but let's ignore that). We actually want to see the train though, so let's suppose it's going fast enough to look "weird", but slow enough for us to still be able to see it. Then the center would looking blue-er/violet-er, with the edges looking more normal.
Time Shift: Let's not ignore the fact that the train is travelling near the speed of light, so you probably wouldn't see anything at all. It would zip past you in the blink of an eye, ripping you to atomic shreds. But that's boring, so let's suppose you could speed up your internal processes enough to actually see what was going on. What you would see is a warped train coming at you with all of its internal processes slowed down significantly.
So no, no reversal of the train. That would only happen if the train were travelling faster than speed of light, which can't happen. If it were possible though, the train "reversing" would be the least paradoxical of observable effects. Here's a clip discussing a few of these effects.
Another way of imagining the light speed train is to imagine a rectangular box in equatorial orbit around a much greater gravitational mass. Does the box begin to spin relative to its direction of rotational orbit. If so in what direction (s) . Now increase the gravitational mass of the object around which the box orbits. Say to a black hole. The box is accelerated to light speed. Assuming the box is almost indestructible but can be flattened out like a piece off cardboard before being folded into a box. Does the box then become an inside out version of its former self? As seen by a stationary observer does the box appear to be back to front and upside down? Cheers
Many generalizations need to be made to find a relatively normal answer. We'd have to consider the train to be indestructible, and that there is nothing inside. Very interesting!