neophyte question about hubble's law

Thus spake Phillip Helbig---remove CLOTHES to reply
LOTHESvax.de
In article , Oh No
writes:

Thus spake dfarr --at-- comcast --dot-- net
The 'Hubble's law' Wikipedia article states '...that the velocity at
which various galaxies ARE receding from the Earth IS proportional to
their distance from us.' (emphasis added)

Bear in mind that this applies only for small cosmological distances

That depends on how one defines Hubble's Law. See my other post in this
thread and the recent thread in sci.physics.research.

Hubble's law is defined as a linear relationship between redshift and
distance. This relationship only holds for small cosmological distances.
For large cosmological distances such a relationship doesn't even make
sense unless you first define what you mean by distance, and there
certainly isn't a natural definition of distance which would give a
linear relationship. You would only get a linear relationship if you
defined distance from Hubble's law - which is tautology, and certainly
an unhelpful measure of large scale structure.

Perhaps. It's just a pity Harrison's ideas about the expansion of space
time are somewhat inaccurate.

Care to elabourate?

I have only dipped into the book, so cannot comment on much of it, but
the discussion of the Hubble sphere on p281 struck me as particularly
misleading. It is absolutely not meaningful to talk about the recession
velocity of a star in the early universe with respect to ourselves now.
Think of the balloon analogy. Cosmological redshift is the consequence
of cosmological expansion, not recession velocities. It just happens
that, for small cosmological distances, cosmological expansion looks
like recession velocity. You can't take that concept too far.

Regards

--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces an=
d
braces)

http://www.rqgravity.net

In article , Oh No
writes:

Hubble's law is defined as a linear relationship between redshift and
distance.

Some people define it as the linear relationship between velocity and
distance, i.e. between the present derivative, with respect to cosmic
time, of the proper distance and the proper distance of the object.
(Hubble OBSERVED a relation between redshift and luminosity, which can
be taken as a proxy for distance. At small redshifts, none of these
distinctions matters.

Perhaps. It's just a pity Harrison's ideas about the expansion of spac=
e
time are somewhat inaccurate.

Care to elabourate?

I have only dipped into the book, so cannot comment on much of it, but
the discussion of the Hubble sphere on p281 struck me as particularly
misleading. It is absolutely not meaningful to talk about the recession
velocity of a star in the early universe with respect to ourselves now.
Think of the balloon analogy. Cosmological redshift is the consequence
of cosmological expansion, not recession velocities. It just happens
that, for small cosmological distances, cosmological expansion looks
like recession velocity. You can't take that concept too far.

Yes, but it does go this far. Assuming a homogeneous and isotropic
expansion, the recession velocity is proportional to
distance---otherwise the homogeneity and/or isotropy are destroyed. At
large redshifts, though, these aren't observable distances and
observable velocities. (Knowing the cosmological parameters, though,
they can still be calculated.)