Originally posted by AndersHermansson
What's the difference between moving special relativistically and moving due to the expansion of space?
Hello Anders, I just now saw your post. (forgot to check this thread for a while). Hurkyl proposed looking at an object in a part of space receding 0.5 c from us, where the object also has its own individual speed (relative to the CMB) of 0.7c.
The important thing to realize is that the 4D coordinates of SR do not fit space at large scale. So the object as no "special relativity" speed relative to us. It simply is not defined. SR type speeds are defined only for objects at the same point or in the same local coordinate chart.
The metric used in cosmology (socalled RW metric) is defined with reference to observers stationary with respect to the CMB or, as cosmologists say, w/rt the Hubble flow (the expansion of the universe). The RW, or RobertsonWalker, metric can handle the speed Hurkyl mentioned. The combined recession speed, the rate of change in RW distance, is meaningful and equal to 1.2 c.
The RW distance, measured at the present moment, is also called the "comoving distance" or the Hubble-law distance because it is the gauge of distance that works in the well-known Hubble law:
v = H
0 D.
The v in the Hubble law is the present rate of change of the RW distance, which is D.
The H
0 parameter is, by definition, the present value of
a
t/a
where a(t) is a numerical valued function of time used to define the RW distance----a distance scale measured from the standpoint of observers at rest with respect to the expansion of space---ie. w/rt the CMB.
a(t) is defined because, in cosmology, all stationary observers everywhere in the universe can have the same time axis---they can have synchronized clocks---essentially one clock for everybody. So there is one scale-function a(t) evolving with time, for everybody.
This is radically different from the picture you get in SR. It is very much a General Relativity picture, by contrast to the local SR picture.
The basic trouble with SR, why it can't be used except locally around a point where there is not much curvature, is that
SR does not allow for space to expand.
The Minkowski 4D coordinates of Special Relativity are rigid and do not let space expand, so these coordinates "fit" the world only in small local patches or local "charts".
this is why the speed of recession of distant objects is not defined in SR coordinates and all that "nothing can exceed the speed of light" business simply does not apply.
Hope this adequately covers the question. the distinction between local SR distance and the real physical distance with the metric is important to make. Please ask further if not clear. I can get you some links to, for instance, Eric Linder's Cosmology Overview (which covers the RW metric) and New Wright's tutorial, which discusses the RW distance and three alternative ideas of distance (angular size, luminosity, light-travel-time). Also other people may want to take a shot at this and you will get several viewpoints.