# Special Relativity / Cosmology

1. Feb 25, 2010

### paulselhi

2 galaxies are "moving" away from each other due to the expansion of space, if each is moving away at 3/4 the speed of light relative to the other would they not be moving faster than light relative to each other?

Is the expansion of space limited to 1/2 light speed ?
Does the law of non faster than light travel not apply to space itself ?

2. Feb 25, 2010

### CompuChip

When relativistic velocities occur, you cannot add them using the good old Newtonian formula (V = u + v), but you have to use the special relativistic equivalent,
$$V = \frac{u + v}{1 + u v / c^2}.$$

3. Feb 25, 2010

### paulselhi

When does this have to be done? when there is not a common point of reference ? If 2 cars move away from each other do we use the Newt Formula as we have a common static reference point, the start point?

If that is right then is the SPE needed because in the galaxy example there is no static reference point as the galaxies are not in fact moving but space is?

4. Feb 25, 2010

### CompuChip

Ah, I assumed that they were both moving away in opposite directions at 0.75c relative to some reference point.
If I take your question literally, you are asking: "if they are moving at 0.75c relative to each other, then aren't they moving faster than light relative to each other?". In that case, the answer is obviously NO: "if they are moving at 0.75 relative to each other, they are moving at 0.75c relative to each other, which is not larger than c."

So the idea of the addition formula is actually this: suppose that there is some object which you measure as moving at velocity v. I am moving at velocity u with respect to you (in the same direction as that object). Then I will measure that same object from my reference frame to have velocity V (as given by the formula) relative to me. This is actually what we do all the time, but using the less accurate V = u + v.

5. Feb 25, 2010

### paulselhi

well yes and no, they are both moving away from a reference point at .75c the problem is nailing down the reference point as it is space itself which is expanding!!

Perhaps the answer is that they are moving apart at faster than light speeds since as far as i know SR does not constrain the speed of space itself only objects moving through space

6. Feb 25, 2010

### haushofer

Because of spacetime expansion, two objects can have a relative speed which is higher than the speed of light; look at inflation. There is no law which forbids this; the only thing SRT says is that due to it's own motion, an object cannot accelerate from a v<c to a v>c. But the movement of galaxies is not "own movement", but movement due to spacetime expansion.

In GR you have the technicality that you more or less can't uniquely compare velocities troughout the universe, because these are 4-vectors lying in different tangent spaces. Also, when a galaxy emits a photon from A to B, you would say that the time the photon takes to undertake the journey would be t= |A-B|/c, but at the time the photon has arrived B, the space between A and B has expanded. In that sense you could naively think that "the galaxy moves faster than the speed of light".