Re: Creation (long)

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Jim Green wrote (somewhat abreviated):
> From the point of cosmology *THIS* Universe (there may be many others) was
> "created" ex nihilo ~15billion years ago -- at a *point* of zero volume.
> Since then, this Universe has been expanding BUT it is not expanding into
> some extant space -- it is creating its OWN space ie space is expanding as
> well and the stuff of this Universe is expanding into this expanding space.

The idea of the spatial 'size' of the big bang singularity being a "*point*
of zero volume" is somewhat problematic if the whole universe (not just
the observable part of it) is actually infinite in extent.  If the universe
is *finite* in extent then this concept is imaginable, for in this case the 
spatial shape of the universe is presumably (unless we imagine a more
complicated topology) something like a 3-D 'surface' of a 4-D (hyper)sphere
whose radius in increasing with time as the universe expands.  (Here the
universe is like the 3-D 'surface' of a 4-D rubber balloon which is being
inflated.)  As we extrapolate back in time the radius of this 'sphere'
continually shrinks until the whole spherical "surface" is compressed to a
single point (of zero 3-D volume).  OTOH, if the universe is *infinite* in
extent then its extent is always infinite at all (nonsingular) times in the
past and the future.  At no nonsingular time can the universe
discontinuously jump from being finite to being infinite.  In this case the
universe expands like a 3-D version of an infinite rubber sheet which is
uniformly stretching everywhere at a constant rate.  As we extrapolate back
in time the sheet is more compressed, but it stays infinite; only its scale
factor changes.  At the limit of the Big Bang singularity the sheet
approaches a state of infinite compression.  How big is an infinite object
which has been infinitely compressed?  This is an indeterminant concept
analogous to asking what is the product of [zero]*[infinity].  The
indeterminant result could be *any* size from zero to infinity.

Also it is *not* thought to be the case that "the stuff of this Universe is
expanding into this expanding space".  The stuff of the universe is thought
to completely fill out the whole universe at *all* times.  The stuff just
gets more rarified (the distance between the galaxies grows) as the 'fabric
of space' stretches and this stuff continues to fill an ever larger fabric.
This is somewhat like the mean distance between the gas particles in a
cylinder of gas becoming larger as a piston confining the gas is pulled
outward.  At all times the gas completely fills the cylinder.  Suppose the
temperature of the gas in the cylinder analogy is very cold but kept under
nearly isothermal conditions (by an external heat bath) as the cylinder is
pulled out.  Also imagine the gas to have a high enough viscocity so that
no macroscopic motion such as eddies or turbulence develops as the piston
is withdrawn.  Now consider a small parcel of gas in the middle of the
cylinder.  The neighboring gas particles of a given gas particle are moving
essentially randomly wrt each other (but slowly since the gas is cold). 
This is like the mutual local motions neighboring galaxies and galactic 
clusters.  Both red and blue shifted Doppler motions happen.  As time
goes on however the the gas thins out and the average distance between the
particles increases as the piston is withdrawn.  Now consider a typical gas
particle near the piston surface and another gas particle near the opposite
fixed end of the cylinder.  As the piston is withdrawn each of these gas
particles stays near its respective surface because there is sufficient
viscosity to damp macroscopic motions of the gas (which has a mean free
path length *very* tiny compared to the size of the cylinder and the
particles don't get to diffuse very far past their original neighbors).
Since each of these two gas particles are staying close to their respective
boundary surfaces they are separating at an average rate which is close to
the piston's withdrawal speed.  For any other pair of gas particles
that are not originally quite so far apart they will separate at an average
speed which is slower than the piston's withdrawal speed.  The average
separation rate will be proportional to their initial separation in the
gas.  This is like the cosmological Hubble red shift between the distant
galaxies.

This gas analogy has its share of problems.  First, the Hubble expansion of
the universe is quite isotropic, whereas the piston withdrawal is
unidirectional.  Second, at large cosmologically significant distances the
intergalactic motion is dominated by the background Hubble expansion of
space and not by the local motions (quasi-random thermal-like motions in
the gas analogy) of the galaxies.  This means that the temperature in the
gas analogy has to be so cold that the piston is withdrawn much faster than
the speed of sound in the gas so that the background motion of the piston
at large distances dominates over the thermal motions.  But in this case we
would not realistically be able to prevent macroscopic turbulent motions
in the cylinder and keep the gas density uniform throughout the cylinder as
the piston is removed so quickly.  In real life such a rapidly moving
piston pulled out of the cylinder would leave a vacuum behind it which
would later be filled by the gas as it rushes in to try to equalize the
pressure through out the cylinder.  Third, the cylinder bounds the gas,
whereas in cosmology the space does not have an external boundary (even if it
is spatially finite).

Perhaps a better analogy is a uniformly distributed population of ants
walking on an expanding rubber sheet.  Locally, the neighboring ants are
wandering aimlessly in all directions.  (Maybe there is somewhat of a pattern
as the ants move in response to each other's pheromone secretions.  The local
motions of nearby galaxies is not really random either, since they move
in response to each other's gravitational fields.)  On very large length
scales though the distance between any two widely separated ants increases 
essentially at the rate that the underlying rubber sheet is stretching,
and this rate is proportional to the separation distance (and dominates over
the local ant wandering speeds at large separations).

> ....
> There is a debate as to whether the things (galaxies, etc) of the Universe
> will catch up or not OR if the things of the Universe will collapse in
> several billion years OR if space will collapse back to a point.

Again, there is no need for the "things (galaxies, etc)" to "catch up"
since they *already* fill out all of the space of the universe.  There are
no unoccupied virgin regions of the universe waiting to be filled with
approaching matter.  Even deep in intergalactic space there is a small
residual density of matter.  The reason that such regions are now nearly
empty is not that they never were occupied, but that the gaseous matter
which previously was in them left them as the matter gravitationally
collapsed into the surrounding galaxies and galactic clusters when those
objects were being formed.

> ....
> Is there any hope of talking about "where" this occurred for this Universe
> as opposed to "where" it might of occurred for any other Universe?  Or for
> that matter "when"?

The Big Bang happened everywhere.  This singularity is *not* a point *in*
space.  Rather, it is the confluence of all of space to an infinitely
compressed state at a finite point *in time* in the past.  I would not want
to speculate about the dynamical behavior of the spacetime of 'other
universes', but if they exist, then their spacetime manifolds are
disconnected (by definition of *other* spacetime) from the spacetime of our
universe and the concept of 'where' or 'when' they are makes no sense
within our our own spacetime.

>   ....               Things seem already out of hand, but could one ask how
> a "quantum fluctuation" could occur in a point/place of zero (or near zero)
> volume? -- I guess not.

I sure wouldn't want to speculate about the possible creation of baby
universes via quantum fluctuations.  That's much too advanced for me, and I
expect it is also too advanced for a lay audience.
 
Some of what Dan Schroeder wrote in response to Jim was:
> ...                                         .  Extrapolating backward
> (with large uncertainties due to the uncertainties in current distances
> and the unknown deceleration rate) leads us to believe that everything
> in the observable universe was much closer together, more or less in
> the same place, about 10-15 billion years ago.

Again, it's not so much that everything was "more or less in the same
place", as that all places were much closer together.  The Big Bang
happened *everywhere* some 10-15 billion years ago.

> ...                                                  .  The observable
> universe is limited in size not by the size of our telescopes, but by
> the finite amount of available lookback time:  if the universe as we
> know it is only 10 billion years old, we can't look out farther than
> 10 billion light years.  (The practical limit is very slightly less
> because at high temperatures the universe was opaque to light.)  Hence
> we have no idea what lies beyond our 10-15 billion-light-year horizon.
> It's possible that space goes on forever in all directions, or that it
> curves back on itself to make a finite total volume.  Or something
> much more complicated and bizarre.

Actually, if the universe is 10 billion years old we *can* see farther
than 10 billion light years because of the expansion of the universe.  If
a photon has been travelling for 10 billion years from when it was emitted
until it was absorbed, the proper distance between the emission point and
the absorption point is significantly *greater* than 10 billion light years
at the moment of absorption, and is *much* less than 10 billion light years
at the moment of emission.  The space between the emission point and the
absorption point is stretching while the photon is propagating.  If the
universe is 10 billion years old, and if the universe is the asymptotically
spatially flat borderline case between openness and closedness
(as predicted by inflationary senarios, and if the cosmological constant is
really close to zero) then the current proper distance to the observational
horizon is just under *30* billion light years because for such a spacetime
the proper spatial separation between the emission point and the absorption
point at the moment of absorption (given that the emission time was
immediately after the Big Bang) is *3 times* the light travel distance that
a photon propagating for the same amount of time on a static spacetime
would have.

If the average density of matter in the universe is greater than the
critical closing density so that the universe is spatially finite (the
balloon case that will undergo a Big Crunch in the future) then a photon
emitted at a time close to the BB will be absorbed significantly *less*
than 3 times farther away (from its emission point at the moment of
absorption) than if it travelled on a static spacetime, but it would still
be farther than 1 times farther away.  OTOH, if the average density of
matter in the universe is less that the critical closing density (as seems
to be the case unless a lot more dark matter is found) so that the infinite
universe will expand forever, then a photon emitted at a time close to the
BB will be absorbed significantly *more* than 3 times farther away (from
its emission point at the moment of absorption) than if it travelled on a
static spacetime for the same amount of time.

These above statements assume that the spatial locations of the points of
emission and absorption are fixed in so-called comoving coordinates.  Since
the typical local intergalactic motions are much slower than the overall
Hubble expansion of space on the large length scales (the typical inter-
galactic velocities are only a few hundred km/s w.r.t. the comoving frame
in which the cosmic background radiation is isotropic) it is a good
approximation to consider that the emission and absorption points *are*
fixed in comoving coordinates for photons that were emitted when the
universe was very young and are just now being absorbed.

Jim Green later wrote:
> And if we can say something helpful to lay people about the first
> (relatively long) minute or so, (after all National Geographic did it) how
> do we answer the question of what happened before that minute -- Is it that
> here was NO such thing as time or was it that nobody was around to start
> counting. (:-)

According to the Big Bang cosmological models physical time came into being
with physical space at the BB.  The BB singularity is the 'edge' of time.
If there is/was any 'time' 'before' the BB then it is not our usual
physical time that we measure with clocks and is part of the usual
spacetime 'fabric' (i.e. manifold).  Using any other time concept 'earlier'
than the BB is pure speculation and not very related to known physics.
(The Hawking-Hartle 'no boundary' proposal using imaginary time is still
speculation as far as I'm concerned.)

> >    Your phrase
> > "ex nihilo" seems to imply a time before the beginning when there was
> > nothing, and this bothers me.
>
> Well, it bothers everybody -- or at least ought to -- but then some people
> are willing to talk about other universes -- which presumably *could* have
> been created billions of years before ours -- I confess to really stretching
> things here.

If you wish to speculate about other universes you need to make clear what
you mean by "*could* have been created billions of years before ours" since
each such universe would have its own spacetime manifold which would give
each one its own time.  If you want to compare the 'creation times' of
various universes you will need to define some kind of extra-universal
'time' that is not specifically tied to each universe's own spacetime.
Such a 'time' concept has nothing to do with physics (which only takes
place *within* a given universe).

Some of what Dan later wrote was:

> "Moving apart" and "distance between them is getting bigger" are
> synonymous, though neither is a "reason" in the causal sense.

These concepts do not have to be synonomous.  I think in the context in
which Jim was trying use these concepts is that he meant "moving apart"
to refer to motions that increase the separation between objects as
denominated in comoving coordinates (i.e. an increasing comoving coordinate
spatial separation with time), and he meant "distance between them is
getting bigger" as meaning that the physical proper spacelike geodesic
distance between the objects increases from one spacelike time slice to the
next spacelike time slice.

David Bowman
dbowman@gtc.georgetown.ky.us