# Help understanding a relativity train

Hi all,

I've read some references to an example of a person on a train using a flashligt and one outside the train also using a flashlight and as I understand it both flashes would travel at the same speed even if the train was moving?
Also as I understand nothing can travel faster then the speed of light?

But suppose then that you are on a train travelling just 20 km/h below the speed of light and then started running down the isle at 30 km/h wouldn't you go faster then the speed of light then?

...also as more energy is needed to accelerate closer to the speed of light, would you expell more energy(calories) running down a train that was moving fast than running at the same speed down a train that was moving slower since your combined speed would be closer to the speed of light?

Hope im making any sense Just trying to wrap my head around this...

Drakkith
Staff Emeritus
From the runner's point of view (or frame of reference) it isn't they who are moving, but everything else. That means that YOU wouldn't feel any different than you normally did and everything you did would be normal. However, when you look at the outside world at that speed it is VERY different. Everything in your direction of travel is severely distorted and blue shifted, while everything behind you is severely redshifted.

Now from you're perspective on the train, everything in front is approaching you at 20 Km/h under the speed of light. If you ran down the isle at a local speed of 30, then you WOULDN'T see everything coming at you at 10 KM/H over the speed of light. Instead everything would distort slightly more and you would measure it still being under the speed of light, just a bit closer to c than it was, but still under it. If you somehow kept accelerating you would find that no matter how fast you tried to go, nothing would be coming at you at the speed of light. Each increase in you're velocity would net you a smaller and smaller actual increase in speed. Note that this is all from YOUR perspective. It's kind of complicated and i suggest you hit up wikipedia or do a google search and try to learn some basics of relativity.

Fredrik
Staff Emeritus
Gold Member
I've read some references to an example of a person on a train using a flashligt and one outside the train also using a flashlight and as I understand it both flashes would travel at the same speed even if the train was moving?
Also as I understand nothing can travel faster then the speed of light?
Both correct.

But suppose then that you are on a train travelling just 20 km/h below the speed of light and then started running down the isle at 30 km/h wouldn't you go faster then the speed of light then?
No, if the speed of the train relative to the ground is u, and your speed relative to the train is v, special relativity says that your speed relative to the ground isn't u+v, but

$$\frac{u+v}{1+\frac{uv}{c^2}}$$

Try it out with your numbers, and you'll see that it's less than c.

...also as more energy is needed to accelerate closer to the speed of light, would you expell more energy(calories) running down a train that was moving fast than running at the same speed down a train that was moving slower since your combined speed would be closer to the speed of light?
No, the speed of the train is irrelevant for how hard it's going to be for you to run at a given speed relative to the train.

Hope im making any sense
The questions make sense, but they've been asked and answered many, many times before. You might want to look around and see if you find anything interesting in older threads.