Lookback time vs. true distance (Hubble Law)

If we use the redshift of light from a far galaxy to calculate its
radial velocity away from us then use the Hubble Law to find a
distance, what is this distance really? Is it A: distance from
position of galaxy when it emitted its light to position of us AT THAT
TIME or B: distance from position of galaxy when it emitted its light
to position of us RIGHT NOW? Or does it give the distance between
the galaxies right now?

"Lax" wrote in message
...
If we use the redshift of light from a far galaxy to calculate its
radial velocity away from us then use the Hubble Law to find a
distance, what is this distance really? Is it A: distance from
position of galaxy when it emitted its light to position of us AT THAT
TIME or B: distance from position of galaxy when it emitted its light
to position of us RIGHT NOW? Or does it give the distance between
the galaxies right now?

I was hoping that somebody would post a good answer; its a slippery
question.

Firstly, the Universe is expanding, and the distance is actually increasing
as the light travels here. So the distance the light travels is intermediate
in a sense between these two. This is very complicated, and I don't
understand it well myself.

Even if we drop that problem, its still slippery.

You use the term "RIGHT NOW", but due to Special Relativity what is right
now depends on the reference frame you use for measurement, and if the
recession velocity is a significant fraction of c then this matters.
Calculations as to distances and times between events (the light being
emitted by the galaxy and seen in a telescope on earth) will depend on
whether these are measured in our Galaxy's frame of reference or that of the
distant galaxy. Neither can claim to be the centre of the Universe.

Ignoring this complication, by decreeing that the Milky Way is stationary
and all the other Galaxies are moving away from us , then the light emitted
by a galaxy 1 billion light years away shows where it was 1 billion years
ago, and it will have moved since then.

On 4/19/10 11:33 PM, Lax wrote:
If we use the redshift of light from a far galaxy to calculate its
radial velocity away from us then use the Hubble Law to find a
distance, what is this distance really? Is it A: distance from
position of galaxy when it emitted its light to position of us AT THAT
TIME or B: distance from position of galaxy when it emitted its light
to position of us RIGHT NOW? Or does it give the distance between
the galaxies right now?

One need to know absolute brightness. Type Ia supernovae make
reasonable "standard candles".

Lax wrote:

If we use the redshift of light from a far galaxy to calculate its
radial velocity away from us then use the Hubble Law to find a
distance, what is this distance really? Is it A: distance from
position of galaxy when it emitted its light to position of us AT THAT
TIME or B: distance from position of galaxy when it emitted its light
to position of us RIGHT NOW? Or does it give the distance between
the galaxies right now?

A relativistic universe has four distinct distances: luminosity
(inverse square), angular diameter, parallax, and proper motion. No
two of them need agree to maintain consistency. Clocks can only be
synchronized by being local.

Which distance would you like?

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm