FTL Expansion of Space: Rapidity & Infinity

[AlexDB9]

If the expansion of space in the macrolevel is faster than the speed of light then it should have "more" than infinite rapidity. How does that work out?

Thanks.

 

[George Jones]

Actually, the recession speeds in cosmology are, in special relativity, analogous to rapidity rather than speed.

 

[AlexDB9]

I understand that, but how faster than light avoids transfinite, or "more" than infinite, rapidity?

 

[George Jones]

As light has infinite rapidity, in this view, there is no faster than light expansion.

 

[AlexDB9]

But I thought it is proven, or at least largely believed, that space expansion is faster than light at the greatest scales. Quote from Wikipedia: "Two reference frames that are globally separated can be moving apart faster than light without violating special relativity". So rapidity ceases to be valid here?

 

[George Jones]

Since speed = distance/time, the definition of "speed" depends on the definitions of "distance" and "time". The definitions used in special relativity do not generalize easily to the curved spacetimes of cosmology. The definitions used in cosmology are, however, easily applied in special relativity. When this done, speed turns out to rapidity!

 

[Khashishi]

Expansion is best represented by a scaling factor and not a speed. It acts as a multiplicative factor on distances. If two "comoving" points are separated by a distance of 2 light years at time t, and the distance becomes 2.1 light years at time (t+1year), then the same rate of expansion will take a distance of 200 light years to 210 light years. That's an increase of 10 light years in 1 year, or "faster than the speed of light". But any rate of expansion will have a "faster than light" increase in distance if you start with a large enough distance between points. Of course, the speed of light limit only applies to the relative speed of two objects at the same point in space, not two distant points.

 

[soothsayer]

As far as I understand it, for two distant points in space, like two far off galaxies, unless there is motion between the two relative to the expansion of space, then there is no relative rapidity or velocity between the two. I.e, you wouldn't have a Lorentz boost between their frames.

 

[PeterDonis]

I thought it is proven, or at least largely believed, that space expansion is faster than light at the greatest scales.

While this phrasing is common, it's misleading. The easiest way to see how it's misleading is to observe that, by this definition of "faster than light", light itself can move faster than light! That is, if we take a galaxy that is further from us than our current Hubble radius, so that it is moving away from us "faster than light", and look at light emitted by this galaxy in the direction away from us, the galaxy will not "outrun" the light; the light will "outrun" the galaxy, i.e., it will move away from us faster than the galaxy itself does. So nothing actually moves faster than light in any invariant sense; no object outruns a light beam in its local vicinity.