Relativity Question

I'm hoping somebody who knows physics can help me out with this question...

If rocket A flys away from the earth at .866 the speed of light and rocket B flys away from the earth from the opposite side in the opposite direction at .866 the speed of light, then how can they still be moving < the speed of light away from each other?

I'm having trouble understanding how it works with these kind of paradoxes, twin paradox is something else I don't get.

Thanks if you can explain it in an intuitive way

yeah, all the math in the world showing calculations is fine, but i just don't get it.

Well, first thing to remember is they shouldn't be seen as travelling relative to the earth! The earth moves. You can technically jump slightly further in one direction. If both of these rockets do the same action, relative to the earth, one will travel faster. We should measure them relative to a hypothetical stillness (which can be worked out by looking at how things are moving, but can be hard to conceive.) If both of the rockets fly away relative to a hypothetical stillness at 0.8 the speed of light, then everything is fine. They aren't travelling faster. Relative to each other, yes they are. If you shone a light from rocket A, it would reach rocket B before rocket B could escape, so we don't have a problem.

Originally posted by doodinthemood
... We should measure them relative to a hypothetical stillness (which can be worked out by looking at how things are moving, but can be hard to conceive.) If both of the rockets fly away relative to a hypothetical stillness at 0.8 the speed of light, ...

There is no 'stillness' in universe, not even a hypothetical one. The universe is simply not built that way.
No points in space are absolute, the space itself is invariant.

Originally posted by Mickey Knox
I'm hoping somebody who knows physics can help me out with this question...

If rocket A flys away from the earth at .866 the speed of light and rocket B flys away from the earth from the opposite side in the opposite direction at .866 the speed of light, then how can they still be moving < the speed of light away from each other?

I'm having trouble ...[text shortened]... in paradox is something else I don't get.

Thanks if you can explain it in an intuitive way

It depends on which relative is flying which rocket. It's all relatives. Pure logic.

Originally posted by Mickey Knox
I'm hoping somebody who knows physics can help me out with this question...

If rocket A flys away from the earth at .866 the speed of light and rocket B flys away from the earth from the opposite side in the opposite direction at .866 the speed of light, then how can they still be moving < the speed of light away from each other?

I'm having trouble ...[text shortened]... in paradox is something else I don't get.

Thanks if you can explain it in an intuitive way

The math doesn't work that simply at relativistic speeds. That's because there is a value called the Lorenz factor which depends on velocity. The Lorenz factor is:

L = 1/(1-(v^2/c^2))

At normal velocities, the Lorenz factor is approximately 1, because the value (v^2/c^2) is approximately 0. However as v (velocity) rises, this fraction becomes larger and larger, which causes the denominator to get smaller, which causes the whole Lorenz factor to get bigger.

When you multiply something by 1, it's as though you didn't do anything, so at normal speeds we can ignore the factor.

This is what happens in mechanics (introductory physics). At +/-100 kph relative to a space station, the rockets are moving at 200 kph from one another. That's because the Lorenz factor is almost exactly 1 and so can be ignored. At the much higher speed you referred to, one can no longer ignore L, and the math changes.

I don't understand the twins paradox either, mostly because I have trouble understanding what exactly is supposed to be happening. How do you decide which twin is the one moving?

Originally posted by FabianFnas
There is no 'stillness' in universe, not even a hypothetical one. The universe is simply not built that way.
No points in space are absolute, the space itself is invariant.

Of course there is. We can calculate how fast our solar system is moving, find a spot that we were 6 billion year ago, imagine we're still there now, and we've stayed still. This doesn't happen, but it's the hypothetical stillness that you should judge speeds against.

Originally posted by doodinthemood
Of course there is. We can calculate how fast our solar system is moving, find a spot that we were 6 billion year ago, imagine we're still there now, and we've stayed still. This doesn't happen, but it's the hypothetical stillness that you should judge speeds against.

Relative to what? To some 'hypothetical stillness' that isn't defined.
There is no point in universe that can be considered an absolute zero point. We can define one, yes, but the point is arbitary chosen. No point is more zero than any other.
Space is invariant.

The point in the middle is still. This is what we judge galaxies movement against.

Originally posted by doodinthemood
The point in the middle is still. This is what we judge galaxies movement against.

There is no middle in the universe. Exactly of the same reason there is no edge.

The point at which the universe is expanding from, the point at which the big bang first occured. This is stillness. But really, there needn't even be that. As I said, we can calculate where our galaxy has moved from over the last billion years. And had it stayed there, we would have been still.

Originally posted by doodinthemood
The point at which the universe is expanding from, the point at which the big bang first occured. This is stillness. But really, there needn't even be that. As I said, we can calculate where our galaxy has moved from over the last billion years. And had it stayed there, we would have been still.

BigBang occurred in every point of the universe at the same time, not just one single.
The universe is expanding in every point to every direction, not just in one.
There is no 'stillness', not even a hypothetical one. Space is invariant.

The big bang was an expansion of the universe into space. It's meaningless to say it happened in every point in the universe. Nevertheless, the entire universe is expanding outwards from a fixed point. For calculations to be correct, this point is still.

Originally posted by doodinthemood
The big bang was an expansion of the universe into space. It's meaningless to say it happened in every point in the universe. Nevertheless, the entire universe is expanding outwards from a fixed point. For calculations to be correct, this point is still.

How could the universe expand into 'space'? There was no space. The singularity was the entire universe and therefore the whole of 'space'.

Originally posted by doodinthemood
The big bang was an expansion of the universe into space. It's meaningless to say it happened in every point in the universe. Nevertheless, the entire universe is expanding outwards from a fixed point. For calculations to be correct, this point is still.

If we think of universe as everything, there is no space around the universe. If it were it would be a part of universe and then universe has to expand into itself, which is contradictory.

There is no center in the niverse - or - every point of universe can be considered being the center. 'Center of universe' has thus no meaning, nor 'the edge of universe'.

Space is invariant.