## A train going with the speed of light

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HomerJ
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### Re: A train going with the speed of light

pauxlo wrote: To restate the problem:

We have an observer A, and a rocket B which flies relative to A with velocity v. Then we have a rocket C which flies relative to B with velocity u (in same direction, to simplify things). The question is, what velocity of C will A measure?

The formula is s = (v + u) / (1+v*u/c^2) (with c being the speed of light).

If we put 0.6c for v and u, we receive s = (0.6c + 0.6c)/(1+ 0.36c^2/c^2) = 1.2c/1.36 ≈ 0.88c.
Ah... 11th grade physics... good times. Good times.

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Anonymissimus
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### Re: A train going with the speed of light

pauxlo wrote: We have an observer A, and a rocket B which flies relative to A with velocity v. Then we have a rocket C which flies relative to B with velocity u (in same direction, to simplify things). The question is, what velocity of C will A measure?

The formula is s = (v + u) / (1+v*u/c^2) (with c being the speed of light).

If we put 0.6c for v and u, we receive s = (0.6c + 0.6c)/(1+ 0.36c^2/c^2) = 1.2c/1.36 ≈ 0.88c.
Also note that for v and u much smaller than c, v*u/c^2 is about 0 so the formula becomes s = v + u of Newton's mechanics...
Well, I seriously don't think relativity is part of any school physics course.
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HomerJ
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### Re: A train going with the speed of light

Anonymissimus wrote:
pauxlo wrote: We have an observer A, and a rocket B which flies relative to A with velocity v. Then we have a rocket C which flies relative to B with velocity u (in same direction, to simplify things). The question is, what velocity of C will A measure?

The formula is s = (v + u) / (1+v*u/c^2) (with c being the speed of light).

If we put 0.6c for v and u, we receive s = (0.6c + 0.6c)/(1+ 0.36c^2/c^2) = 1.2c/1.36 ≈ 0.88c.
Also note that for v and u much smaller than c, v*u/c^2 is about 0 so the formula becomes s = v + u of Newton's mechanics...
Well, I seriously don't think relativity is part of any school physics course.
We have definitely discussed this equation in school, but it was rather in 12/13 grade. The more I think about it, it might have been in a project week about the history of physics... I recall watching a movie about Einstein for example.

Anyway, the physics in itself is not so much over the top for higher school grades. There's probably not enough room for it though.

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artisticdude
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### Re: A train going with the speed of light

Hmm, what would happen to the people on the train? Traveling at the speed of light... I guess that they would be stuck in semi-darkness until they stopped?

But seriously, what would happen to the lighting in such a circumstance? Would the light remain normal, since the train is traveling at the same speed as the light?
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MCP
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### Re: A train going with the speed of light

Dunno wrote:Can they breathe...? And blood, does it circulate in their bodies...? I'm just new to this kind of physics and it just blows my mind
My guess is, as they approach the speed of light, gravity would mess them up, and it would end very very badly for all aboard. This is ignoring the chance of colliding with matter, which would be devastating for everything in and around it.

Am I wrong about the gravity thing? I was thinking as they slowly accelerate around the earth, the effect of gravity increases as they approach the speed of light. Or am I way off and gravity stays almost the same?

Damn, did we just invent a train bomb? Just get it up to the speed of light and this mad scientist can blow up the earth .
Dunno
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### Re: A train going with the speed of light

Well, as far as I know, gravity doesn't depend on velocity. Besides, this is a purely hypothetical scenario because, as many people mentioned, you can't reach speed of light unless you are pure energy. So we don't discuss about HOW they reach it and HOW people are affected by enormous acceleration. There simply IS a train with v=c and let's see what happens.
Anonymissimus wrote:
pauxlo wrote: We have an observer A, and a rocket B which flies relative to A with velocity v. Then we have a rocket C which flies relative to B with velocity u (in same direction, to simplify things). The question is, what velocity of C will A measure?

The formula is s = (v + u) / (1+v*u/c^2) (with c being the speed of light).

If we put 0.6c for v and u, we receive s = (0.6c + 0.6c)/(1+ 0.36c^2/c^2) = 1.2c/1.36 ≈ 0.88c.
Also note that for v and u much smaller than c, v*u/c^2 is about 0 so the formula becomes s = v + u of Newton's mechanics...
Well, I seriously don't think relativity is part of any school physics course.
That also means that assuming v and u can only be as high as c, the highest value s can be equal to is... c. Awesome!
s=(c+c)/(1+c*c/c^2)=2c/2=c
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Insinuator
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### Re: A train going with the speed of light

MCP wrote:My guess is, as they approach the speed of light, gravity would mess them up, and it would end very very badly for all aboard.
No it would not. Gravity is independent of light, a completely different phenomenon.
Dunno wrote:Besides, this is a purely hypothetical scenario because, as many people mentioned, you can't reach speed of light unless you are pure energy. So we don't discuss about HOW they reach it and HOW people are affected by enormous acceleration. There simply IS a train with v=c and let's see what happens.
A hypothetical scenario, BY DEFINITION, has to be possible. Yours is not. Therefore, you can not just "see what happens". It is a paradox. Most of the silly ideas that people are putting forward are nonsense, stimulated by an impossible scenario.
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### Re: A train going with the speed of light

Insinuator wrote:
MCP wrote:My guess is, as they approach the speed of light, gravity would mess them up, and it would end very very badly for all aboard.
No it would not. Gravity is independent of light, a completely different phenomenon.
Dunno wrote:Besides, this is a purely hypothetical scenario because, as many people mentioned, you can't reach speed of light unless you are pure energy. So we don't discuss about HOW they reach it and HOW people are affected by enormous acceleration. There simply IS a train with v=c and let's see what happens.
A hypothetical scenario, BY DEFINITION, has to be possible. Yours is not. Therefore, you can not just "see what happens". It is a paradox. Most of the silly ideas that people are putting forward are nonsense, stimulated by an impossible scenario.
Well there might be a way to get a train .99c. You have to have amazing tech but you could hit the train with something bigger going light speed while the train is already going .97c. So, is this possible?
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Dunno
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### Re: A train going with the speed of light

of course it is, some people just don't know how to have fun
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Viliam
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### Re: A train going with the speed of light

Dunno wrote:Can they breathe...? And blood, does it circulate in their bodies...?
artisticdude wrote:But seriously, what would happen to the lighting in such a circumstance? Would the light remain normal, since the train is traveling at the same speed as the light?
If the train (after achieving the speed) is moving in uniform linear motion (at whatever speed), everything inside the train seems normal for a person inside the train.
For a person inside the train, strange things happen only ouside the train.

So the light inside the train works normally, also breathing, blood, etc. Only the light coming through windows from outside may seem strange. From the passengers' point of view, the universe is moving extremely slowly around the train, and the "relativistic effects" are happening to the rest of universe, not to the train.

That's the point of relativity. Each system in uniform linear motion seems normal to itself, and the strange effects seem to happen in the other systems (while in their point of view, they are normal, and the strange effects happen to us).

In some situations it seems logically impossible -- for example, how can A's time move slower from the point of view of B, and also B's time move slower from the point of view of A? (If one is slower than the other, then the other should be faster, right?) In a Newtonian physics this does not make sense. However in Einsteinian physics, there is no such thing as an "(absolute) time interval", only "time interval seen by X". Therefore we can say that "A's time (seen by B) moves slower than B's time (seen by B)" and "B's time (seen by A) moves slower than A's time (seen by A)", and these are two different statements that don't contradict each other, because "A's time as seen by A" is something different than "A's time as seen by B". Only when A and B do not move relatively to each other, their observations are the same. Or if they move very slowly... compared to the speed of light... their observations are very similiar. This is what in normal circumstances creates the illusion of absolute time. But if you measure time very precisely (e.g. in satellite GPS), the differences appear.

More precisely, if two systems move relatively to each other, then "time interval" in one system becomes a mix of "time interval" and "space interval" as seen by other system. (Also "space interval" becomes a mix of "space interval" and "time interval".) Simply said, the other object appears shorter and frozen in time, because part of their "time" we see as "space". However, from their point of view, we are shorter and frozen in time, because part of our "time" they see as "space". That's why you hear about "time-space" when talking about relativity.

Now it seems totally unfunny... but you can read Mr Tompkins if you want fun with relativity!
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### Re: A train going with the speed of light

It doesn't matter if the train actually could reach the speed of light, it would still be late.
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### Re: A train going with the speed of light

Sgt. Groovy wrote:It doesn't matter if the train actually could reach the speed of light, it would still be late.
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### Re: A train going with the speed of light

What if two trains were to be accelerated until the point where they'd go with the speed of light, to the opposite directions? You know, like... what would they see when they'd look into the other train that goes just as fast? The normal people, or would they see each other aging faster than normal, or slower...?

EDIT: Sorry about the bump, just thought this is an interesting thread, which I completely missed earlier...
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Dunno
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### Re: A train going with the speed of light

Well we came to the conclusion that you don't really see stuff outside. Just read through the whole thread and you'll see. I'm telling you, it's worth your while
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