Simple Question On Relativity

[bisclavret]

I got this simple problem from a physics forum and surprisingly a lot of PhD holders were not able to answer it despite the fancy lingo they were using..Try this..

A train runs at a speed approaching the speed of light. If you are inside the train and the headlights are turned on, would you see the light in front of the train?

[Delta]

You see light from reflection, so if it hits something (the road, air particles, etc) the light is coming at you, so of course you see it. Maybe I misunderstand the question.

[LSD]

A train runs at a speed approaching the speed of light. If you are inside the train and the headlights are turned on, would you see the light in front of the train?

Not immediately, but eventually (obviously depending on the differential between the train's speed and C).

[bisclavret]

Ok, you are inside the train, the windshield is transparent, the train is travelling in a vacuum(let's pretend for argument's sake), and although objects with mass could not travel at the speed of light but can anly approach notoriously(in physics textbooks) the speed of light let's just say the train also travels at the speed of light, again for argument's sake. If you are looking through the windshield and the light projected from the headlight bulbs(?) has no chance of hitting anything and reflecting in vacuum, will you see the light in front of the train?

[bisclavret]

You see light from reflection, so if it hits something (the road, air particles, etc) the light is coming at you, so of course you see it. Maybe I misunderstand the question.


Lets ignore the light-reflecting-on-something-for-you-to-see-it rule. I guess if it hits something then you see that something and not the light beam(?). Anyway, lets think for a moment that you got one of those honey I shrunk the kids gadgets and you got small and went inside the headlights.(how's that for compromise?)

[LSD]

et's just say the train also travels at the speed of light, again for argument's sake. If you are looking through the windshield and the light projected from the headlight bulbs(?) has no chance of hitting anything and reflecting in vacuum, will you see the light in front of the train?

No, because that would require that the light beam move faster than C which is a physical impossibility.

In that (obviously impossible) scenario, the lightbulbs would appear to be off, even though they were on.

[ComradeRed]

Yeah, it would be visible to the observer inside the train because the train is not yet at the spped of light! That is to say, it is less than the speed of light :)

But that's not the relativistic answer :P

You have to create the relativistic velocity vector for it (after the Lorentz contraction, assuming the train was 99/100 times the speed of light in its velocity, the light would still travel what appears to the observer on the trains at the speed of light -- the trippy part of relativity).

So to an observer in an inertial frame, it appears the light is moving faster than the speed of light, but in reality it is moving at the speed of light according to the reference frame that is moving :)

I hope that made sense...

[bisclavret]

No, because that would require that the light beam move faster than C which is a physical impossibility.

That was my first guess but the mod (who finally intervened in that forum of eggheads) said that the speed of light is constant in all inertial frames of reference. You are moving with the train and relatively the train is stationary in your frame of reference so you should be able to see the beam. An outside observer that is stationary relative to the moving train would not see the beam though. At least LSD, you didn't have to define what mass is and even the nature of a photon before answering, No, which is what the eggheads did. Im also seeing Comradered's response just now(but there is no now in relativity) below which is more precise. Comradered is Comradered. :)

[RebelDog]

Originally posted by [email protected] 4 2006, 08:25 PM
I got this simple problem from a physics forum and surprisingly a lot of PhD holders were not able to answer it despite the fancy lingo they were using..Try this..

A train runs at a speed approaching the speed of light. If you are inside the train and the headlights are turned on, would you see the light in front of the train?
I think you are trying to ask if you could approach the speed of light, would you see a light beam travelling at the differential of your speed and c (speed of light)
ie, you travel at 10miles p/h less than the speed of light, would you then observe light travelling at 10miles an hour. The answer is no. C is a constant of the universe, it travels always at the same speed no matter what speed the observer is travelling at.
Light will always travel toward you at and away from you at the same speed (about 186,000miles p/h) your speed makes no difference. C travels at the same speed for all observers.

It is hard to imagine this being true but it is a rock solid fact. Your question is very like the thought experiment Einstein used to solve the puzzle.

[bisclavret]

The answer is no. C is a constant of the universe, it travels always at the same speed no matter what speed the observer is travelling at.

You have to remember though that it depends on your frame of reference. If you are in the train, then the train and thus the headlight bulbs are stationary relative to you, so to maintain the premise that C be constant for all inertial reference frames, you should see the light beam as though the train were not moving at the speed of light. If on the other hand, you are outside the moving train and stationary relative to it, you will not see the light beam since both the light beam and train are travelling at the same speed.

[RebelDog]

Originally posted by [email protected] 5 2006, 01:34 PM

The answer is no. C is a constant of the universe, it travels always at the same speed no matter what speed the observer is travelling at.

You have to remember though that it depends on your frame of reference. If you are in the train, then the train and thus the headlight bulbs are stationary relative to you, so to maintain the premise that C be constant for all inertial reference frames, you should see the light beam as though the train were not moving at the speed of light. If on the other hand, you are outside the moving train and stationary relative to it, you will not see the light beam since both the light beam and train are travelling at the same speed.
The speed of c does not depend on your frame of reference, that is why it is a constant. It is the same speed at all frames of reference. What differs for the observers is time. The light from the train will travel toward and away from you at c, the trains speed has no effect on c. The headlights will appear as normal for the person on the train and the person stationary relative to the train.

[ComradeRed]

Hey genius, the constant c is the speed of light in a vacuum IN AN INERTIAL REFERENCE FRAME!!!

Only there is it the same, but mess with those two parameters and it changes! :o

Otherwise it would be a constant.

In absolute spacetime, you would be correct that irrespective of the velocity of the observer, the speed of light would be constant. That's why relativity is so revolutionary, it gives reason to discard absolute spacetime (it's also why General Relativity had to come into being -- with absolute spacetime gone, what does gravity look like? :huh:).

[RebelDog]

Its analogous though.

[ComradeRed]

No, my point is that the train thought experiment is supposed to be heuristic and was disposed of later by Einstein because it failed explaining relativity properly (although it beautifully explained the Galilean transformation).

He drew the conclusion of the Lorentz transformation as the more proper relativistic transformation (he quipped later on that it was like the train analogy without the train). But if this were so, then there would be no "maximum velocity" unless it is in certain conditions (the speed of light in a vacuum IS different than the speed of light out of a vacuum).

This itself challenges absolute spacetime, as is implied to exist in your explanation (that was one of the reasons why it was so revolutionary); and this is merely special relativity, mind you(!).