From: ynecgan@cid.aes.doe.CA (Greg Neill)
Newsgroups: sci.physics
Subject: Re: Expansion
Date: 29 Sep 92 04:04:37 GMT
Organization: Environment Canada (CID), Dorval, QC

I am posting the following e-mail correspondence between myself and Mr.
Ben Zellner in order to invite further comment by the members of this
newsgroup.

In response to article 24011, Mr. Zellner writes:

> I'm just a planetary astronomer, not a cosmologist, but I don't think
> there is a real problem here.  The confusion comes from a too-literal
> interpretation of loose language.  There isn't any "expansion force". 
> Gravity doesn't work like a string and cannot be "broken"; it just obeys
> the inverse-square law. 
> 
> Suppose you had two gravitating masses moving away from each other at an 
> initial distance and relative velocity:
> 
>        <<----- M1            M2 ----->>
>       velocity                  velocity
> 
> Without gravity, they would continue to move apart forever at the initial
> velocity.  In an expanding universe, the initial velocity depends linearly 
> on the initial distance.  (By "initial" I mean pick any convenient point
> in time before large mass concentrations had time to aggregate.)
> 
> With gravity, each mass experiences an acceleration toward the other
> one:
> 
>          M1 ---->>       <<----M2
>             accel          accel
> 
> As the system evolves it swaps kinetic energy for gravitational poten-
> tial energy.  The physics is really no different from standing on the
> surface of the earth and throwing a ball upwards.  When you integrate
> over the subsequent motion, you might find that the two masses will
> continue to move apart forever, or move out to a certain distance and
> then collapse back together, just depending on the initial distance 
> and velocity. 

To which I responded (via e-mail):

Doesn't the above assume that space is not expanding?  It is a simple
"explosion" model, in which the fragments of the Big Bang explosion go
flying off into an already existing space.  In this case, I completely
agree with your analogy.

But the current Big Bang model assumes that space and matter were
initially contained within an infinitly small/dense singularity.  There
was a large "KABLOOEY" and space has been expanding ever since.  The
expansion of space itself is used, for example, to explain the current
temperature of the background radiation (about 3 Kelvins) as the result
of the initial "hot" radiation being redshifted by the expansion too the
currently observed wavelengths.

Now, if space itself is indeed expanding, and if it is happening at all
scales, then we would expect that the gravitational potential energy of
all gravitating systems to be increasing at the expense of the kinetic
energy of the universal expansion as a whole.  Take, for instance, the
often used ballon analogy, where dots on the balloon's surface are meant
to represent individual galaxies.  As air is pumped into the balloon,
"space" expands and the dots move further apart from each other.  Notice,
however, that the dots themselves will become "larger", because the
expansion is occurring at all scales.  If we say that the dots do not
grow larger, that their "gravity" is too strong to allow that, then we
are effectively saying that the overall expansion observed does not work
at small scales, or when the gravitational field is larger than some
particular value.  This leads us to the "piece of string" model for
gravity, which is something we want to avoid.

So the question is, is space really expanding, and if so, does this
expansion take place at all scales?

> 
>   >  Is it possible that, by happy coincidence, the rate of expansion 
>   >  is just exactly enough to compensate for energy loss due to 
>   >  gravitational radiation?  
> 
> No.  Gravitational radiation is exceedingly small for accelerations like
> those in our solar system.  In a real solar system there is also a little 
> bit of friction (gas drag, particle collisions, radiation pressure, etc.) 
> which turns kinetic energy into heat, which is ultimately radiated away.
> A star cluster can lose energy by "evaporation" of the high-velocity
> tail of its stellar velocity distribution.  But there isn't any "expanding
> force". 

Actually, almost immediately after posting I thought of an argument
against my gravitaional radiation hypothesis.  If space is expanding, we
would expect that objects further apart are affected more by the
expansion than objects closer togther.  That is, the further apart, the
greater the rate of increase in separation.  But one would expect the
amount of gravitational radiation to be inversely proportional to
separation (i.e. orbital radius).


And in a followup letter, Mr. Zellner provides the following:

Greg,

 >  Doesn't the above assume that space is not expanding?  It is a simple
 >  "explosion" model, in which the fragments of the Big Bang explosion go
 >  flying off into an already existing space.  In this case, I completely
 >  agree with your analogy.

 >  But the current Big Bang model assumes that space and matter were
 >  initially contained within an infinitly small/dense singularity.  There
 >  was a large "KABLOOEY" and space has been expanding ever since.  

This really ought to be addressed to a relativist/cosmologist.  But my 
understanding is that this "expansion of space" is really just a figure
of speech.  There isn't any difference between saying "Objects A and B
are moving apart" and saying "Space is being created between A and B."
You COULD, in principle, have a tape measure with one end attached to 
object A and reeling out from object B.  You wouldn't expect the foot-
markers on the tape to get further apart, would you?  The "expansion of 
space" doesn't stretch the tape, it just makes it reel out.

 >  The expansion of space itself is used, for example, to explain the 
 >  current temperature of the background radiation (about 3 Kelvins) as 
 >  the result of the initial "hot" radiation being redshifted by the 
 >  expansion to the currently observed wavelengths.

As we look further and further into space, we are seeing light that just
now reached us from material that is now further and further away from us, 
and we are seeing it when it was correspondingly further back in time.  
Because of the general expansion of the universe, the more distant objects
are moving away from us faster and are more red-shifted.  At some point
we will presumably run out optical sources (like galaxies or quasars) to 
see.  Space Telescope was to probe that region, and it may yet after the
optical refurbishment. 

Anyway, there was a light source, thermal in nature, that was earlier than 
the earliest stars or galaxies, namely the hot plasma of the big-bang fireball 
itself.  It was opaque until it cooled enough for hydrogen atoms to form
(around 10000K), after which it became transparent.  The 3K radiation is simply
the radiation from that plasma, at the point where it first became transparent,
extremely red-shifted.  We don't see it CLOSER to us or LESS red-shifted simply
because it was transparent at later times.  Amazingly enough, a red-shifted
black body is still a black body. 

 > Now, if space itself is indeed expanding, and if it is happening at all
 > scales, then we would expect that the gravitational potential energy of
 > all gravitating systems to be increasing at the expense of the kinetic
 > energy of the universal expansion as a whole.  

That is absolutely correct, whether you want to think about "expanding space"
or just gravity versus inertia.

 > Take, for instance, the often used ballon analogy, where dots on the 
 > balloon's surface are meant to represent individual galaxies.  As air 
 > is pumped into the balloon, "space" expands and the dots move further 
 > apart from each other.  Notice, however, that the dots themselves will 
 > become "larger", because the expansion is occurring at all scales.  

Yes, but the point of that analogy is to illustrate a three-dimensional 
expansion by a two-dimensional model.  It illustrates the lack of a "center"
of expansion, and illustrates how the recession velocity increases with
distance.  But careful writers always point out that the "dots" - galaxies -
are not themselves expanding.  For sure you cannot "expand" a solar system;
the orbital periods don't scale linearly with the distances, and you would
at some point find the earth in a resonance with Jupiter, and we wouldn't
be here.

 > If we say that the dots do not grow larger, that their "gravity" is too 
 > strong to allow that, then we are effectively saying that the overall 
 > expansion observed does not work at small scales, or when the gravitational 
 > field is larger than some particular value.  

That is true.  Otherwise as you originally pointed out the expansion would be
pumping energy into something like a solar system.  The only way to avoid
that, or the destructive resonances mentioned above, would be via some exotic 
mechanism like a changing value of the gravitational constant.

 > So the question is, is space really expanding, and if so, does this
 > expansion take place at all scales?

The INERTIA - the original "kick" from the big bang - was originally there at 
all scales, small for small scales and large for large scales.  At sufficiently 
small scales, of course, the "kick" was small and was soon eaten up by 
frictional forces.  At larger scales, a volume containing a fixed amount of
matter would have first expanded, then re-contracted to form a galaxy, for
example, as the gravity overcame the inertia.  At very large scales, the 
relative "kick" was strong and gravity is weak, and the expansion is still 
going on. 

 >  ... the fragments of the Big Bang explosion go flying off into an 
 >  already existing space"

I don't think cosmologists would talk about "already existing space", but
there my Newtonian analysis fails, and my competence along with it.  I think
perhaps with a correct relativistic treatment the distinction between 
"already existing space" and "creation of new space" vanishes, but there 
I am a blind guide.

Cheers, Ben

PS:  If you wish, post this on the net.  Maybe we can get a real cosmologist
to clear things up.

--
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Greg Neill,               |
HNSX Supercomputers   Inc.|"How come there is only one Monopolies Commission?"
ynecgan@cid.aes.doe.ca    |           -- Nigel Rees
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Newsgroups: sci.physics