From: Lee Corbin (lcorbin@tsoft.com)
Date: Sun Aug 18 2002 - 22:26:24 MDT
Emlyn writes about our concepts of what, realistically and
ontologically, our universe is like:
> So this whole business about the expanding universe and the cosmological
> constant is about whether everything falls toward everything else quicker or
> slower than space is added between? And consensus now is that it doesn't?
Let me approach from a different direction than the "raisins in a loaf"
imagery. You recall Escher's "Demons and Angels" print? It shows a
disk (the hyperbolic disk of non-Euclidean geometry) where in the
center one sees recognizable angels and demons who define the boundaries
and shapes of each other (sort of like posters on this list).
Suppose then that each angel is to be thought of as a galaxy.
We now have infinitely many galaxies occupying (I think) a
curved space. (It appears to me to be curved because of the
great numbers of galaxies (i.e. angels) to be found at a
certain "distance" from the center, although I may be wrong
if hyperbolic distance is used instead of what is visually
driving my intuitions at this moment.)
Anyway, curved or flat, this picture can be a first step towards
conceptualizing what happened at the big bang. Suppose that the
Escher disk faithfully represents where all the galaxies are now,
where "now" is to be taken as imposed by the local coordinate
system. (I am well-aware that in special relativity, we need be
very careful about attributing simultaneity to separated events,
but to quote Wheeler on p. 100 of "Gravitation and Inertia",
> If the spacetime is static, we can find a coordinate system
> where the metric is time-independent...therefore the coordinate
> time T required for a [photon] to go from coordinate point A
> to coordinate point B is the same as the time to go from B to A.
> Therefore one can consistently define *simultaneity* on the
> manifold using light signals...)
Okay, so if the Escher disk is a picture of now, what did it
look like twice as close to the big bang, say around 7 billion
years ago? Well, the galaxies were all closer to the center by
a factor of two. And twice as close as that, yet still closer
together. (Remember that each galaxy is the center in its own
coordinate system, and that when you look at Escher's diagram
you are to suppose that if you could somehow move and be "right
over" some other angel or devil, the picture would be exactly
the same all the way out to infinity.)
If this process keeps up (our traveling back in time, as it were)
then prior to the formation of the galaxies we can only talk
about the density of matter. The Escher picture still holds,
however. It's just that the density is much higher. So in
our conception, the density just keeps getting higher and
higher all the way back to any point before the big bang.
At any such point, no matter how close to the big bang, the
Escher disk still looks quite full, and still looks to be
depicting events infinitely far away (by some metric).
So perhaps one can think of the big bang as a completely
black Escher disk, where infinite density throughout the
universe is reached.
The above does not address several points, however. First
is the fact of curvature (the above does not attempt to say
anything about General Relativistic concerns), and second
is the still mysterious (to me) stretching of space (since,
like Emlyn, I can still think of questions that I cannot
answer). I hope, however, that perhaps this picture will
enable other descriptions to make more sense.
Lee
> -----Original Message-----
> From: owner-extropians@extropy.org
> [mailto:owner-extropians@extropy.org]On Behalf Of Emlyn O'regan
> Sent: Thursday, August 15, 2002 5:11 PM
>
> The balloon model stinks because the dots expand as well as the space
> between. So from the point of view of a dot, there is no expansion (hmm kind
> of).
>
> What that model implies to me is that there would be no integrity in small
> local systems; all *atoms* would move away from each other, with disastrous
> results.
>
> The dough analogy seems better. We assume infinite dough, yes? :-) So
> expansion is really a statement about density, not overall size?
>
> Am I correct in assuming that the raisins remain raisin sized regardless of
> expansion, which is a metaphor for galaxies, solar systems, small objects
> staying cohesive due to local forces (gravity, nuclear forces)?
>
> So this whole business about the expanding universe and the cosmological
> constant is about whether everything falls toward everything else quicker or
> slower than space is added between? And consensus now is that it doesn't?
> Rather, like a nightmare where you try to run somewhere but seem to get
> further away, gravity is not enough to overcome this constant (or
> accelerating!) influx of space?
>
> Does this mean that all the local forces, ie: the nuclear and
> electromagnetic forces binding the little things, are acting against this
> influx of space too?
>
> Emlyn
>
> > -----Original Message-----
> > From: Eugen Leitl [mailto:eugen@leitl.org]
> > Sent: Thursday, 15 August 2002 22:23
> > To: extropians@extropy.org
> > Subject: Re: Nature Article
> >
> >
> > On Thu, 15 Aug 2002 Spudboy100@aol.com wrote:
> >
> > > The balloon analogy, that astronomers frequently use,
> > really stinks. Why?
> >
> > Not really, because the rubber skin is meant to be a 2d model of the
> > universe. If you want a 3d analogy, think dough with embedded raisins
> > increasing volume due to yeast's carbon dioxide. The average distance
> > between each raisin increases.
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