🚀 go-pugleaf

In article <25203@dog.ee.lbl.gov> sichase@csa3.lbl.gov writes:
>In article <92216.155158DOCTORJ@SLACVM.SLAC.STANFORD.EDU>, DOCTORJ@SLACVM.SLAC.STANFORD.EDU (Jon J Thaler) writes...
>>This needs some clarification.  Even in the absence of deceleration,
>>the Hubble constant changes with time.  It is empirically
>>observed that the recession speed of galaxies (as measured by red shift)
>>proportional to the distance.  

(Stuff deleted...)

>>Even if
>>there is no deceleration the Hubble constant decreases as time passes.
>>This is simply because the universe is getting older.  More prosaically,
>>receding galaxies get farther away.
>
>Now *I'm* confused.  Take a galaxy G at a distance D from us.  It
>will be receeding at a speed of Ho*D up to some small peculiar velocity.
>Say that in a few billion years (by which time I might even have tenure!) 
>G is now twice as far from us.  Won't its recession speed be 2*Ho*D?
>There is twice as much space expanding between us, so it should be receeding
>at twice the speed.  
>
>Your argument seems to suggest that recession speeds are fixed so that 
>in a few billion years G will be twice as far from us, but still have 
>the same recession speed, causing us to conclude that Ho has shrunk
>to half its current value.

The final paragraph here is closer to the truth than the previous one.  Galaxies
do not speed up as the universe expands; in fact, they gradually slow down.
Think of things in purely Newtonian terms.  (That's not the right way to think
of them, but it gives the right qualitative behavior.)  If there's no force on
a galaxy, it'll just move along at constant speed.  The only forces of any appreciable
magnitude on a galaxy are gravitational, and gravity is an attractive force,
so the net effect of the gravitational forces is to retard the rate at which
things are flying apart.  So galaxies slow down with time.

Now, let's suppose the total mass density in the Universe is very low, so that
we can neglect gravitational forces.  Then the speed of a given galaxy is
constant.  But as time passes, its distance from us increases.  So the
ratio H_0=speed/distance gets smaller.  Therefore H_0 decreases with time.
If you include the effect of gravitational deceleration, then H_0 decreases
even faster.

As other people have pointed out, Hubble's constant is "constant" only in the 
sense that it applies to all cosmological objects at the present time.  It
is not "constant" in the usual sense of "not varying with the passage of time."
For this reason, lots of cosmologists have taken to calling the number
H_0 "the Hubble paramter" rather than the "Hubble constant."  Actually, most
cosmologists just avoid the issue entirely by calling it "H_0" (pronounced
"aitch-nought.")

-Ted
(ted@physics.berkeley.edu)