Question about Relativity

[Cornfed]

This is a question I wanted to ask my physics 101 lecturer a long time ago but never got the chance. It is a central postulate of relativity that nothing with mass can travel faster than the speed of light. Since all motion is said to be relative, it logically follows that no atom in the Universe can be travelling faster than the speed of light relative to any other atom in the Universe.

Suppose I have two spaceships at some starting point. I accelerate Spaceship A in one direction so that it is travelling at 60% of the speed of light relative to the starting point (perfectly theoretically possible within the theory). I then accelerate Spaceship B in the opposite direction until it is also travelling at 60% of the speed of light relative to the starting point. If we take Spaceship A as being stationary (perfectly acceptable within the theory, since all motion is relative), then wouldn’t Spaceship B be moving at 120% of the speed of light? What am I missing?

[Rock]

This is a question I wanted to ask my physics 101 lecturer a long time ago but never got the chance. It is a central postulate of relativity that nothing with mass can travel faster than the speed of light. Since all motion is said to be relative, it logically follows that no atom in the Universe can be travelling faster than the speed of light relative to any other atom in the Universe.

Suppose I have two spaceships at some starting point. I accelerate Spaceship A in one direction so that it is travelling at 60% of the speed of light relative to the starting point (perfectly theoretically possible within the theory). I then accelerate Spaceship B in the opposite direction until it is also travelling at 60% of the speed of light relative to the starting point. If we take Spaceship A as being stationary (perfectly acceptable within the theory, since all motion is relative), then wouldn’t Spaceship B be moving at 120% of the speed of light? What am I missing?

Or, if light waves from 2 stars are emanating in different (opposite) directions, wouldn't they pass each other at say twice the speed of light?

[fschmidt]

I believe this has to do with the time distortion effect of relativity. So if objects X and Y are moving at 60% speed of light relative to each other, then time will appear to slow down when looking at the other object. So if Y launches Z at some speed, say 60% speed of light away from X, then because of the time distortion, Z will appear to move more slowly as viewed by X. The faster the relative speeds, the more the time distortion so the less any new incremental speed will appear, with the speed of light being the limit of the total.

[Cornfed]

Or, if light waves from 2 stars are emanating in different (opposite) directions, wouldn't they pass each other at say twice the speed of light?

Apparently not according to the theory. In any case photons/quanta are said to have no rest mass (although they do have momentum somehow) so they are not such a good example, hence my spaceship example.

[Wolfeye]

I believe relativity was disproven. The idea that nothing CAN go faster than the speed of light doesn't even make sense- is there supposed to be some existential action that keeps things from going this way? Besides, I read about scientists accelerating something past the speed of light (I think it was a different form of light, but still- something going faster than that speed).

The idea that motion is relative to each other doesn't really make sense, since if one thing moves it doesn't matter if something else is moving at all. Something could be moving equally fast as something else, that doesn't make the something else's motion nullified.

[droid]

it logically follows that no atom in the Universe can be travelling faster than the speed of light relative to any other atom in the Universe.

The way I see it, relativity applies only with respect to an Observer, so I would rephrase the above as follows

"no atom in the Universe can be travelling faster than the speed of light relative to any observer in the Universe"

So as far as the example you give, lets say the spaceships are A and B, and they are traveling towards C (cornfed) in this fashion:

A>>>>>> C <<<<<<<B

I think you can actually claim in Newtonian terms that, from C's view, they are travelling at 120% SoL with "respect to each other", but that would be kind of useless information, what matters in relativity terms for C is that A is going towards him at 60% SoL, and B is going toward him at60% SoL, nothing more.

It's not the same when you describe things from the point of view of observer A. In this case A will have a different time frame (as fschmidt stated) so that he sees B approach at tops 100% SoL (from the fundamental constrain), and he sees C approach at 50% SoL, so that he reaches both simultaneously, as expected from the diagram.

From this I would claim that if C sees everyone come together in 1 minute for example, A would see this take (1/0.6)=1.66 minutes in his watch.
In other words they would indeed have different time frames.

Where I'm screwing up here is that A would be older than C when they meet, which is the opposite of what the 'twin brothers' parable claims.

I hope someone adds more insight here.