Spoonfed wrote:
Jim Black wrote:

That's why the velocity of galaxies away from us is proportional to
their distance (until relativistic effects kick in, and their relative
velocity compared to us becomes ambiguous).

Relative velocity does not become ambiguous when relativistic effects
kick in. There might be a bit of extra work involved in establishing
precisely when and where the relative velocity happened or how long it
lasted, it is all very definable and not ambiguous at all.

Events can be described in space and time very precisely according to
an agreed upon reference frame, just as we on earth all describe time
on earth according to GMT.

If we want to make a meaningful statement about the relative velocity
between us and very distant galaxies, we must specify the path one
taken in going from one object to the other, and how much time is spent
on each part of the path. Otherwise, the statement is ambiguous, not
because of special relativity, but because of general relativity. The
idea that one gets different answers for different ways of getting from
one object to the other is at the very core of general relativity.

Consider the situation in which we want to compare the velocity of the
center of the earth (A) at a certain time t1 with the velocity of an
object (B) falling towards the earth at some later time t2. Suppose
that if we compare the velocity of A and B at time t1, that we find
that they are at rest with respect to each other. If we then wait at
object B until time t2, we will detect no velocity change, since the
object is freely falling. We would conclude that the relative velocity
between A at time t1 and B at time t2 was zero. If on the other hand,
we begin by waiting at point A until time t2, and then make the
comparison with object B, we will detect a velocity difference.