# Relativity train question

Youre on a train going the speed of light and you look into a mirror and can see your reflection. Which means that light is reflecting off your face and to the mirror. But to do this the light bouncing off your face would have to be going twice the speed of light to an outside observer. Which is impossible for uhhh reasons? So Einstein theorized that the train would need to be compressed and time would need to be slower on it relative to the outside observer. So my question is why is time slowed and the train compressed to make it equal? Im sorry if this is incoherent and that it is probably so far below other topics on this forum that its laughable but any help would be appreciated. Ive never take a physics class and have almost zero physics knowledge. Im just interested.

Related Special and General Relativity News on Phys.org
PeterDonis
Mentor
2019 Award
Hi, DaCouchPutater, and welcome to PF!

Youre on a train going the speed of light
This is not possible; you and the train can't travel at the speed of light. You can travel very close to the speed of light (relative to some other observer), but not at it. In what follows, I'll assume that you actually meant "very close to the speed of light" instead of exactly at the speed of light.

to do this the light bouncing off your face would have to be going twice the speed of light to an outside observer
No, it wouldn't. Light always travels at the speed of light, relative to all observers.

Einstein theorized that the train would need to be compressed and time would need to be slower on it relative to the outside observer.
Yes. But it isn't just theory; thousands of experiments have confirmed that reality actually works this way.

why is time slowed and the train compressed to make it equal?
If you mean, why do we set up the theory of relativity this way, it's because that's the theory that matches experiments; see above.

If you mean, why does reality work this way, that's not really a question about physics, it's a question about philosophy or metaphysics, which are off topic here.

Hi, DaCouchPutater, and welcome to PF!

This is not possible; you and the train can't travel at the speed of light. You can travel very close to the speed of light (relative to some other observer), but not at it. In what follows, I'll assume that you actually meant "very close to the speed of light" instead of exactly at the speed of light.
I hope im replying correctly but here goes. Yeah thats what i meant.

No, it wouldn't. Light always travels at the speed of light, relative to all observers.
Yes i meant that thats what the problem is.

Yes. But it isn't just theory; thousands of experiments have confirmed that reality actually works this way.

I dont know if Einstein actually thought of this when coming up with special relativity but i meant if he did then in that moment it was a theory.

If you mean, why do we set up the theory of relativity this way, it's because that's the theory that matches experiments; see above.

I guess because this is so over my head its hard to explain my question.
But i got this question from a Veritasium video on youtube called can you go the speed of light? where the guy says because the speed of light to the person outside the train cannot be twice the speed of light because light has a constant speed (like you said) So for the person outside the train to measure the correct speed of light the time on the train must slow and the train must contract. My question is why does this make the two speeds of light equal?

If you mean, why does reality work this way, that's not really a question about physics, it's a question about philosophy or metaphysics, which are off topic here.

"I dont know if Einstein actually thought of this when coming up with special relativity but i meant if he did then in that moment it was a theory."

It still is a theory. Probably you don't understand that term properly...

ghwellsjr
Gold Member
"I dont know if Einstein actually thought of this when coming up with special relativity but i meant if he did then in that moment it was a theory."

It still is a theory. Probably you don't understand that term properly...
Yes, Einstein used the word "theory" when he published his 1905 paper which you can read here:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

In the second paragraph, he said, "These two postulates suffice for the attainment of a simple and consistent theory..."

And, yes, it is still called a theory. It's very difficult to come up with a simple theory that is also consistent with all the facts. Very difficult. I don't think anyone is going to disagree with you on that issue.

However, I don't think too many people are going to fit your last sentence. Probably you're alone in that category.

ghwellsjr
Gold Member
Youre on a train going the speed of light and you look into a mirror and can see your reflection. Which means that light is reflecting off your face and to the mirror. But to do this the light bouncing off your face would have to be going twice the speed of light to an outside observer. Which is impossible for uhhh reasons? So Einstein theorized that the train would need to be compressed and time would need to be slower on it relative to the outside observer. So my question is why is time slowed and the train compressed to make it equal? Im sorry if this is incoherent and that it is probably so far below other topics on this forum that its laughable but any help would be appreciated. Ive never take a physics class and have almost zero physics knowledge. Im just interested.
I think spacetime diagrams are very helpful in explaining and understanding Einstein's theory of Special Relativity. The first one shows an observer depicted by the thick blue line looking at his reflection in a mirror that is six feet away from him. He and the mirror are stationary in this diagram. The dots mark off 1-nanosecond increments of time. The thin blue line depicts some light that travels from his face to the mirror and the thin red line depicts the reflected light coming back. Note that the speed of light is 1 foot per nsec and always appears as a 45-degree diagonal line:

I hope this makes perfect sense to you.

Now I'm going to show what this same scenario looks like when the train is going faster and faster. The first speed is 38.4615 percent of the speed of light. I use the Lorentz Transformation process to do this:

As you can see, the distance to the mirror is now about 5.5 feet, compressed, as you say, from 6 feet. And the observer's clock is going slower. It takes 13 nsec of Coordinate Time for it to tick off 12 nsec. But most importantly to your issue is the fact that the light is still traveling at 1 foot per nsec along the 45-degree diagonals but instead of taking 6 nsecs to get to the mirror and another 6 nsecs to get back, it takes 9 nsecs to get to the mirror and 4 nsecs to get back. But it gets back just at the moment the observer's clock ticked 12 so as far as he can tell, everything is the same as when he was stationary.

Next we'll go to 60% of the speed of light:

Now the distance to the mirror is a little less than 5 feet and it takes 12 nsecs for the light to get to the mirror and 3 nsecs to get back but it gets back just at the moment the observer's clock ticks 12 nsecs.

One more transformation for a train speed of 80% of the speed of light:

The numbers are getting more extreme.The distance to the mirror is about 3.5 feet and it takes 18 nsecs for the light to get to the mirror but only 2 nsecs to get back just in time for the observer's clock to tick 12 nsecs.

I think it is clear that the closer the train gets to the speed of light, the longer the light takes to get to the mirror but shorter it takes to get back but never does the light have to propagate at any speed other than 1 foot per nsec.I hope these diagrams make it perfectly clear what is going on but if not, just ask.

Last edited:
thank you this was very helpful.