# B Einstein's Train Thought Experiment

#### DavidMCR

Summary
Seeking some answers on Einstein's thought experiment
So I got this from an article on wikipedia that covers Einstein's train thought experiment:

A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by Daniel Frost Comstock in 1910[13] and Einstein in 1917.[14][12] It also consists of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past.

A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back of the traincar at the same time.

For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times.

Q: Why would an observer inside the moving train, relative to the platform, view the flash of light reaching both ends of the traincar at the same time? Does that not suppose the train to be motionless?

If light travel takes time, then would he not (in theory) first see the light emanating from its source, spreading out, reaching one side before the other? The person on the platform notices the light at a different point in time since it takes longer to reach his eyes, but if the light were to be produced halfway between both observers then both would perceive it at the same time.

Does the speed of light change if one were moving?

The second paragraph makes more sense to me than the first; I don't see why the first observer would see the light strike both ends at the same time, if he is moving ...

Just wanted to ask before I move on.

Related Special and General Relativity News on Phys.org

#### Nugatory

Mentor
You ask "Does that not suppose the train to be motionless?". As far as the guy in the train is concerned, the train IS motionless while the ground is moving in the other direction. Whenever two things are in constant motion relative to one another, we can consider either one to be at rest and the other one moving - this isn't Einstein/relativity stuff, it's true in classical physics as well and was first formalized centuries ago by Galileo (google for "Galilean relativity"). So we can analyze the problem as if the train is motionless and the earth is moving, or the other way around, and neither is more right than the other.

It's tempting to say that the earth is "really" at rest, that there's something special and more real about the frame in which the surface of the earth is at rest - but consider that the surface of the earth is moving with the earth's rotation, the earth is moving around the sun, the sun is orbiting the center of the galaxy, the galaxy is drifting through space.... the earth is only "at rest" if you happen to standing on its surface and moving along with it. Or if you want, you can imagine that you are an astronomer on Mars watching the experiment through a powerful telescope. Now both the train and the ground are moving (earth and mars are moving at many kilometers per second relative to one another), just at different speeds, and the question of which one is "motionless" never arises.

#### Ibix

Q: Why would an observer inside the moving train, relative to the platform, view the flash of light reaching both ends of the traincar at the same time? Does that not suppose the train to be motionless?
Yes. That's the principle of relativity - you can always regard yourself as motionless.

Put it another way - the platform is on a planet, turning at up to a thousand miles an hour, orbiting at about twenty kilometers per second. Why would you think of that as motionless?

#### DavidMCR

Ok, so things move relative to something else (for how else could we tell it's in motion, right?).

I want to add something, just bear with me -- gotta get some grub.

#### DavidMCR

This is fascinating to me though

#### Borg

Gold Member
Instead of a train, consider two spaceships that both think that they are at rest and being passed by the other. Can you say who is moving and who isn't? As far as the occupants of each ship is concerned, they are at rest with respect to their own ship.

#### DavidMCR

So motion, or lack thereof, is relative. Does that mean if we could ascertain the boundaries of the physical universe then we could (in theory) determine the speed and direction of everything in relation to everything else? I mean if we, for instance, assume the universe as shaped like a box, for example.

The speed of light is a constant, right?

If I start off, stationary (relative to the fixed speed of light) beside a light source, at starting point A, and immediately set off at 50% the speed of light, and simultaneously that light producing source emits a beam heading off in the same direction, then that light beam will continually cover 50% more distance, right?

What if I were to then strike a match while going at 50% the speed of light, would that ray of light go 50% faster or 100% faster relative to my position?

What I'm getting at is this: does light get affected if its source is already moving?

I'm not maybe being too clear; let me know!

#### DavidMCR

Instead of a train, consider two spaceships that both think that they are at rest and being passed by the other. Can you say who is moving and who isn't? As far as the occupants of each ship is concerned, they are at rest with respect to their own ship.
That makes sense. I think I get this quite well. This reminds me of when one is flying high in an airplane, you have the illusion that you're not travelling that quickly, which is due to the draw distance; if you we passing more closely the terrain would appear to move rapidly in the opposite direction.

#### Borg

Gold Member
You should get away from the ground analogies. You keep thinking of the train as being the moving object when the reality is that you can't say who is actually moving.

For the spaceship example, they could pass really close such that they appear to 'move' rapidly. The distance illusion has no bearing in the problem.

#### PeroK

Homework Helper
Gold Member
2018 Award
What I'm getting at is this: does light get affected if its source is already moving?

I'm not maybe being too clear; let me know!
The speed of light is independent of the motion of the source. Light travels though vaccum at $c$ in all inertial reference frames. It doesn't matter whether the source of the light was moving in your reference frame when the light was emitted.

#### PeroK

Homework Helper
Gold Member
2018 Award
That makes sense. I think I get this quite well. This reminds me of when one is flying high in an airplane, you have the illusion that you're not travelling that quickly, which is due to the draw distance; if you we passing more closely the terrain would appear to move rapidly in the opposite direction.
The aeroplane is a good example. You have the same situation if you were on a rocket. There is no concept in physics of absolute motion.

#### Ibix

Does that mean if we could ascertain the boundaries of the physical universe then we could (in theory) determine the speed and direction of everything in relation to everything else?
There is no such thing as far as we are aware - so there is no theoretical basis on which to answer this question.
If I start off, stationary (relative to the fixed speed of light)
This doesn't make sense. You can be stationary with respect to a person or a planet or some physical object, but stationary relative to a speed? You can say "I was stationary next to a lamppost", but "I was stationary next to 60mph" is nonsense.
at starting point A, and immediately set off at 50% the speed of light, and simultaneously that light producing source emits a beam heading off in the same direction, then that light beam will continually cover 50% more distance, right?
According to the frame in which the light source is at rest, yes. However, in your rest frame you are at rest, the light source is moving at 0.5c, and light is moving at c relative to you. Requiring both these descriptions of reality to be consistent leads directly to time dilation, length contraction, and the relativity of simultaneity.
What if I were to then strike a match while going at 50% the speed of light, would that ray of light go 50% faster or 100% faster relative to my position?
All light always travels at the same speed. So you will see the light leaving at c, and so will someone at rest with respect to the lamp at point A.
What I'm getting at is this: does light get affected if its source is already moving?
Its speed is not affected by the source's motion. Its direction and colour will be affected.

#### Nugatory

Mentor
So motion, or lack thereof, is relative. Does that mean if we could ascertain the boundaries of the physical universe then we could (in theory) determine the speed and direction of everything in relation to everything else? I mean if we, for instance, assume the universe as shaped like a box, for example.
There is no such boundary, so the issue never arises.
The speed of light is a constant, right?
In the sense that everyone (everyone moving inertially, a qualifier that usually goes without saying in these discussions) finds that light is moving at the same speed $c$ relative to them, yes.

If I start off, stationary (relative to the fixed speed of light)
You are always “stationary relative to the fixed speed of light” - that’s what it means to say that the speed of light is $c$ for everybody.
beside a light source, at starting point A, and immediately set off at 50% the speed of light, and simultaneously that light producing source emits a beam heading off in the same direction, then that light beam will continually cover 50% more distance, right?
the flash of light will move away at a speed c relative to you. It will also move away from the original light source at speed c. If you properly allow for length contraction, time dilation, and the relativity of simultaneity there will be no contradiction, no paradox, and everything will be consistent.

What if I were to then strike a match while going at 50% the speed of light, would that ray of light go 50% faster or 100% faster relative to my position?
Same answer. It doesn’t matter whether you or the light source in the previous question emitted the flash of light

What I'm getting at is this: does light get affected if its source is already moving?
no.

#### DavidMCR

Thanks for the replies, I'll digest them and give my take on it. Need to digest some food also.

#### DavidMCR

You should get away from the ground analogies. You keep thinking of the train as being the moving object when the reality is that you can't say who is actually moving.

For the spaceship example, they could pass really close such that they appear to 'move' rapidly. The distance illusion has no bearing in the problem.
I know the draw distance illusion has no bearing, it just reminded me of it, as an illusion.

#### Mister T

Gold Member
Why would an observer inside the moving train, relative to the platform, view the flash of light reaching both ends of the traincar at the same time?
Because he can measure that the distance from the center to one end is the same as the distance from the center to the other end.

Does that not suppose the train to be motionless?
No, it assumes the speed of the light headed for one end is the same as the speed of the light headed for the other end. This is the new thing that makes us balk. We would instead expect the speeds of the beams to be different, that the beam headed in the forward direction moves faster than the beam headed in the backward direction.

The famous Michaelson-Morley experiment was an attempt to observe and measure this difference. Despite numerous repetitions and variations of this experiment, no difference was ever found.

It was Einstein's great insight to realize that this implies that simultaneity is not absolute.

The person on the platform notices the light at a different point in time since it takes longer to reach his eyes, but if the light were to be produced halfway between both observers then both would perceive it at the same time.
It's assumed that the distance between the observers is negligible. In other words, the distance between the observers is much much smaller than the length of the train car.

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