1. A finite, unbounded universe with positive spacetime curvature.
2. An infinite, unbounded, flat universe (zero curvature).
3. An infinite, unbounded universe with negative spacetime curvature.
In all these cases, the universe expands from a singularity at the big bang.
I can visualise the first case (sort of!), but I have a difficulty with the
second and third. At the singularity, the universe is compressed into an
infinitely small volume. In the next instant, the universe has infinite
volume. I have difficulty in seeing how it can change from infinitely small
to infinitely large in one instant. I appreciate that when a theory of
quantum gravity is perfected, ideas about the singularity may change, but,
in terms of the current mathematical model, can anyone explain to me how
this transition is possible? (Analogy with 2dimensional surfaces is always
good). Perhaps I misinterpret the nature of a singularity?
thanks.
David Scarth.
> In the cosmological model, there are three possible outcomes after the big
> bang:
> 1. A finite, unbounded universe with positive spacetime curvature.
> 2. An infinite, unbounded, flat universe (zero curvature).
> 3. An infinite, unbounded universe with negative spacetime curvature.
Well, those are the three simplest cases.
> I can visualise the first case (sort of!), but I have a difficulty with the
> second and third. At the singularity, the universe is compressed into an
> infinitely small volume. In the next instant, the universe has infinite
> volume.
You should read the Cosmology FAQ.
Damn near anything is possible the instant after the sintularity.
That's why it's a simgularity.
John Anderson
That's because the open/infinite models are nonphysical: They apply the
spherical condition, rhom*R^3 = const, relating the observable surface mass
density rhom to the expansion coordinate R, to a geometry where it could hold
only if mass points were glued to space. There can be no such glue.
However, soap bubbles need not be spherical; they can also spread between an
expanding ring, or a pair of rings being pulled apart. That's what the
Robertson solutions are trying to get at  and at the same time, include the
Hubble effect, by hook or by crook. Stan
That doesn't answer the original question.
Also, the expansion of the universe is observed via
the recession of distant galaxies. This can be observed
without reference to a point of view outside the universe.
John Anderson
But if we are to get at Nature as She is, and not as we think She ought to
be, we have to take off the blinders. An insight from an entirely unexpected
direction may lead to a better fit with experiment, as well as a better
understanding of how things came to be what they are. Stan
 In the cosmological model, there are three possible outcomes after the big
 bang:

 1. A finite, unbounded universe with positive spacetime curvature.
 2. An infinite, unbounded, flat universe (zero curvature).
 3. An infinite, unbounded universe with negative spacetime curvature.

 In all these cases, the universe expands from a singularity at the big bang.
 I can visualise the first case (sort of!), but I have a difficulty with the
 second and third. At the singularity, the universe is compressed into an
 infinitely small volume. In the next instant, the universe has infinite
 volume. I have difficulty in seeing how it can change from infinitely small
 to infinitely large in one instant. I appreciate that when a theory of
 quantum gravity is perfected, ideas about the singularity may change, but,
 in terms of the current mathematical model, can anyone explain to me how
 this transition is possible? (Analogy with 2dimensional surfaces is always
 good). Perhaps I misinterpret the nature of a singularity?
A singularity always involves a discontinuous transition similar
to the transition from zero to one.
Expansion of the universe is equivalent to shrinking of all matter
systems such as particles and galaxies (as long as we assume that
there is nothing outside the universe). So nothing prevents us from
assuming that the volume of the universe has always had the same
size as today.
Under this assumption however, we can recognize that the bigbang
outcome of a finite universe is not so different from the outcome
of an infinte universe as it seems at first sight.
By the way, can black holes explode? If not, this would strongly
suggest that BIG BANG is impossible.
Cheers
Wolfgang Gottfried G.
Liechtenstein
Simple black hole paradox refuting General Relativity:
http://members.lol.li/twostone/E/paradoxGR.html
Interesting, as the Big Bang model was well established before Hawking
proposed the possibility of black hole evaporation. I suggest your
understanding of the Big Bang is in error.
>
> Simple black hole paradox refuting General Relativity:
> http://members.lol.li/twostone/E/paradoxGR.html
I read it. Seems incorrect on the read. If the Sun were to become a black
hole, it would be detected as such both from Earth and outside the galaxy, or
anywhere else one could make observations for.

J. Scott Miller, Program Coordinator Scott....@louisville.edu
Gheens Science Center and Rauch Planetarium
http://www.louisville.edu/planetarium
University of Louisville
My own feeling is that only 1 is possible. I do not expect the physics
to follow the mathematics of singularity.
>A singularity always involves a discontinuous transition similar
>to the transition from zero to one.
>
>Expansion of the universe is equivalent to shrinking of all matter
>systems such as particles and galaxies (as long as we assume that
>there is nothing outside the universe). So nothing prevents us from
>assuming that the volume of the universe has always had the same
>size as today.
>
>Under this assumption however, we can recognize that the bigbang
>outcome of a finite universe is not so different from the outcome
>of an infinte universe as it seems at first sight.
>
>By the way, can black holes explode? If not, this would strongly
>suggest that BIG BANG is impossible.
>
>
>Cheers
>Wolfgang Gottfried G.
>Liechtenstein
>
>
>Simple black hole paradox refuting General Relativity:
>http://members.lol.li/twostone/E/paradoxGR.html
>
>

Charles Francis
cha...@clef.demon.co.uk
Speak to each in accordance with his understanding
If it helps the volume in the second two is still finite. The first expands
to a finite volume and collapses. The second approaches a finite volume but
does not collapse. The third expands forever but still has a finite volume
at any given time.
I try not to imagine what the whole universe looks like from outside and
instead think about what the visible universe would look like from inside as
it develops.
Ed
The simplest way to imagine what happens is to use other words for
explanation what is happening. Let's use coordinates where everything
remains on its place. Such coordinates are not only possible, these
are the coordinates the people really use for computations.
In these coordinates, what happens is that our rulers shrink in time.
That means, the distance we measure becomes smaller. Not necessarily
"space itself". In this picture, it is also easier to understand why
there is no need for a center of expansion of the universe.
Note that the singularity itself is not part of the solution. We have
a solution only for t>0. Not for t=0. Thus, every talk about the
singularity itself is in some sense nonsense. But, if you want to
imagine this singularity nonetheless, imagine it as an infinite
"singular universe" at t=0 where distance measurement fails and
"measures" always "distance=0", simply because it has collapsed.
> By the way, can black holes explode? If not, this would strongly
> suggest that BIG BANG is impossible.
"Exploding" black holes are named white holes, and there is some
similarity between the inner part of an exploding "white hole" and the
observable part of the universe.
Ilja

I. Schmelzer, D10178 Berlin, Keibelstr. 38, <il...@cyberpass.net>
http://www.cyberpass.net/~ilja
Not necessarily. In the usual meaning in GR, a singularity is a locus
deleted from the manifold for which limit points are not well defined.
Equivalently, some curvature scalar diverges as one approaches this
locus. I don;t see ho w a "transition" applies (as you claim).
> Expansion of the universe is equivalent to shrinking of all matter
> systems such as particles and galaxies (as long as we assume that
> there is nothing outside the universe).
This is not true. In particular, the Lagrangians for the dynamics of
all bound systems remain invariant, so one can distinguish between a
global expansion (as in cosmological models) and the "shrinking" of
"all matter systems" (which are bound dynamically).
> By the way, can black holes explode?
Not classically (i.e. in GR). But Hawking radiation does provide a
mechanism for a black hole to become less massive over time, and at
the end of its lifetime it does indeed explode in a burst of radiation.
Note that the lifetime for a solarmass black hole is vastly longer
than the current age of the universe. Note also that virtually any
acretion at all will exceed the mass lost due to Hawking radiation.
> If not, this would strongly
> suggest that BIG BANG is impossible.
I have no idea why you think this. Black holes are vastly different
from the universe.
Tom Roberts tjro...@lucent.com
I have always wondered if after a certain amount of mass
other forces come into play. (Speculating) Here's a poor
analogy. Create a ball of plutonium. Less advanced science would
suggest that adding more plutonium will just increase the size
and mass of the ball. But at a certain mass, this isn't true.
Chain reaction and BOOM!!!!
What if a black hole behaves as is predicted and increases in mass
to a level equal to the current mass in the universe? Couldn't
there be some force that is unknown to us which with a universe
sized mass in a point could cause it to become unstable and
BOOM!! ?
I know about the light speed escape velocity but hasn't it been
said that the laws of physics breakdown at the singularity?
Tony
> That's because the open/infinite models are nonphysical: They apply the
> spherical condition, rhom*R^3 = const, relating the observable surface mass
> density rhom to the expansion coordinate R, to a geometry where it could hold
> only if mass points were glued to space.
"Mass points glued to space" is more of your nonsense. GR requires no
such thing, and the open/infinite universe models are perfectly valid
solutions in GR.
How would you give all of the mass of the universe to a black hole?
More to the point, there is a good discussion of Big Bang not being a black
hole at http://math.ucr.edu/home/baez/physics/universe.html
I don't think this is correct. If the second and third cases are,
respectively, flat and negatively curved, then if they are finite, they
would have to be bounded. I think the correct interpretation is that only
the first case (positive curvature) is finite and bounded. The second and
third cases are infinite.
I think the only plausible answers to my original question are:
1. The equations are not defined at t=0, and therefore one cannot ask what
the singularity is 'like', as suggested by Ilja Schmelzer.
or,
2. The singularity is itself infinite, any finite portion of the universe
(such as the visible universe) being collapsed into a point, as again
suggested by Ilja Schmelzer and in the link provided by Nathan Urban:
http://www.astro.ucla.edu/~wright/infpoint.html
By the way, thanks to all the contributors to this discussion.
David Scarth.
Maybe I'm misunderstanding the question. But if there is enough
mass in the universe isn't the final result supposed to be a collapse
into a singularity?
Tony
This idealized model collapses into a point singularity
with nothing else. When the whole universe collapses
there isn't anywhere else outside to observe it from.
A Schwarschild black hole is a point singularity surrounded by a region
of spacetime in which normal nonsingular things can happen. The
singularity isn't really the thing that is important for distant
observers of the black hole. The event horizon is. Events
inside the event horizon can emit no radiation to events outside.
Anything falling inside the event horizon can never get out.
These are not the same phenomena.
John Anderson
No. In an open universe, it goes on and on and on and on.... Current
observations support such a universe.
As to whether the big bang itself is a black hole, please read
To clarify (since the `No' above is misleading): as Tony correctly
says, if the universe were dense enough, it would collapse again under
its own gravity to a singularity. As Scott correctly says,
observations don't support the idea that it is dense enough to do
this.
Martin

Martin Hardcastle Department of Physics, University of Bristol
Be not solitary, be not idle
Please replace the xxx.xxx.xxx in the header with bristol.ac.uk to mail me
> To clarify (since the `No' above is misleading): as Tony correctly
> says, if the universe were dense enough, it would collapse again under
> its own gravity to a singularity.
I guess the *observable* universe would theoretically collaps to a
singularity. Not the much bigger unobservable universe that is out
there if inflation is correct.

My conscience is clean. I never use it.
88
Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.
1) If the universe were infinite gravitational forces would balance and there
would be no collapse regardless of density. Matter might still temporarily
collect into local dense islands which could exhibit interesting
hightemperature nuclear or chemical reactions.
2) If the universe were finite but bounded (e.g. the surface of a balloon)
gravitational forces also balance, except insofar as they may affect the size
of the balloon.
3) If the universe were already in a state of maximum entropy, collapse would
be very improbable.
4) If our universe were already a singularity we wouldn't necessarily know if
it was collapsing.
5) Gravitation could have a finite range or a longrange repulsive component.
6) The spontaneous appearance of new matter or energy could keep the universe
from ever collapsing.
7) Current interpretations of the galactic redshift could be wrong. The red
shift may be the basis for 6)
8) Dark matter could be hidden from electromagnetic observation.
9) A hitherto undiscovered longrange force might exist.
'Nuff said?
Fair enough, if the distinction is important to you: I was using
`support' to mean more or less `be consistent with'. (How else would
an observation support an idea?)
>1) If the universe were infinite gravitational forces would balance and there
>would be no collapse regardless of density.
Not true. Gravitational forces don't balance regardless of whether the
universe is infinite or not. It's easy to see that this is so in the
Newtonian case: just consider Gauss's law in an infinite homogeneous
medium. Any observer predicts that all other masses will accelerate
towards him, though the acceleration tends to zero as distance tends
to infinity; in other words, a static spatially infinite homogeneous
Newtonian universe collapses to a (spatially infinite) singularity. An
analogous thing is true in GR.
>2) If the universe were finite but bounded (e.g. the surface of a balloon)
>gravitational forces also balance, except insofar as they may affect the size
>of the balloon.
I think you mean `finite but unbounded'. (The surface of a balloon is
unbounded in the sense that you can traverse it for infinite time
without ever finding an edge.) If so, not true, for the same reason as
above. The standard GR closed universe, with a density higher than the
critical density so that it will recollapse into a singularity, is
in fact finite but unbounded.
With a suitable choice of spacetime geometry it's certainly possible
to cause the universe to be static. That was Einstein's original idea
with the cosmological constant. However, observations are not
consistent with the idea that the universe is static, which is why
Einstein abandoned his original model.
>3) If the universe were already in a state of maximum entropy, collapse would
>be very improbable.
Observation shows that it is not. I look out of my window and see
temperature differences (well, actually, `I look out of my window' is
a sufficient disproof of this one).
>4) If our universe were already a singularity we wouldn't necessarily know if
>it was collapsing.
Observation shows that it is not. (Specifically, we're using
`singularity' here to mean `region of very high/infinite density where
the known laws of physics break down': we do not inhabit such a
region, by definition.)
>5) Gravitation could have a finite range or a longrange repulsive component.
True, but so far little (to be fair, not no) evidence supports this
addition to the standard model.
>6) The spontaneous appearance of new matter or energy could keep the universe
>from ever collapsing.
Appearance of new matter only makes things worse in the standard
picture; it's purely the gravitational force from existing matter that
causes it to collapse.
>7) Current interpretations of the galactic redshift could be wrong.
True, but no evidence supports this.
>8) Dark matter could be hidden from electromagnetic observation.
True: that's why it's called `dark matter'.
>9) A hitherto undiscovered longrange force might exist.
True, but no evidence supports this.
Inflation more or less predicts that the universe won't recollapse, at
least not for a very, very long time, because the standard inflation
picture causes the universe's density to be very very close to the
critical density after the inflationary epoch. (To be exact, we expect
 Omega  1  < 10^5, where the number on the right comes from the
COBE observations of CMB anisotropy.)
But apart from that: no. If the whole universe is the same density at a
given cosmic time outside the observable region as in it, and that
density is greater than the critical density, then the whole universe,
not just the observable bit, will recollapse.
If it happens that for some reason we're in a giant overdense bubble
embedded in a lowerdensity region, then a) the cosmological principle
is broken, but b) it's quite possible that we would eventually see
that bubble collapse while the external universe carried on. (In fact,
it's not stretching this too far to say that this has already
happened. Overdense regions have already collapsed out of the
expansion of the universe, though at the moment they haven't yet
become singularities. We call these regions `clusters of
galaxies'. The difference is that their inhabitants, like the
inhabitants of superclusters that are collapsing out at the present
day, can look out of their local region and tell that they're living
in an overdense area.)
Of course, there's no evidence that conditions are the
same in regions of the universe outside our observable region. How
could there be? It just makes more sense to assume they are.
> But apart from that: no. If the whole universe is the same density at
> a given cosmic time outside the observable region as in it, and that
> density is greater than the critical density, then the whole
> universe, not just the observable bit, will recollapse.
What I wondered is this: With inflation, most of the regions of
spacetime in the universe are unconnected (spacelike intervals).
In a big crunch scenario, is it correct to say that, shortly before
recollapsing into a singularity, there might still be huge regions
that are unconnected and will stay unconnected no matter how close
we get the singularity?

When ideas fail, words come in very handy.
In the sense that an observation of someone stealing supports the logical
conclusion that he/she is a thief!
>
> >1) If the universe were infinite gravitational forces would balance and there
> >would be no collapse regardless of density.
>
> Not true. Gravitational forces don't balance regardless of whether the
> universe is infinite or not. It's easy to see that this is so in the
> Newtonian case: just consider Gauss's law in an infinite homogeneous
> medium. Any observer predicts that all other masses will accelerate
> towards him, though the acceleration tends to zero as distance tends
> to infinity; in other words, a static spatially infinite homogeneous
> Newtonian universe collapses to a (spatially infinite) singularity. An
> analogous thing is true in GR.
Well, OK, but it would take an infinite amount of time.
>
> >2) If the universe were finite but bounded (e.g. the surface of a balloon)
> >gravitational forces also balance, except insofar as they may affect the size
> >of the balloon.
>
> I think you mean `finite but unbounded'. (The surface of a balloon is
> unbounded in the sense that you can traverse it for infinite time
> without ever finding an edge.) If so, not true, for the same reason as
> above. The standard GR closed universe, with a density higher than the
> critical density so that it will recollapse into a singularity, is
> in fact finite but unbounded.
I used bounded in the sense that gravity could operate in both directions of a
great sphere. Then points on either end of a diameter would be in a position
of symmetry and zero net force. This is perhaps not the standard GR closed universe.
>
> With a suitable choice of spacetime geometry it's certainly possible
> to cause the universe to be static. That was Einstein's original idea
> with the cosmological constant. However, observations are not
> consistent with the idea that the universe is static, which is why
> Einstein abandoned his original model.
As I understand it, he was not happy with the free parameter being used by
others to hypothesize open or closed universes. He tried but failed to find
some deeper reason why it had to be zero.
>
> >3) If the universe were already in a state of maximum entropy, collapse would
> >be very improbable.
>
> Observation shows that it is not. I look out of my window and see
> temperature differences (well, actually, `I look out of my window' is
> a sufficient disproof of this one).
Maximum entropy is consistent with local structure, in fact equipartition
implies all possible ordered structures with decreasing probability. Enjoy
your window while it still exists!
>
> >4) If our universe were already a singularity we wouldn't necessarily know if
> >it was collapsing.
>
> Observation shows that it is not. (Specifically, we're using
> `singularity' here to mean `region of very high/infinite density where
> the known laws of physics break down': we do not inhabit such a
> region, by definition.)
Well, that's one meaning of singularity. Another might be the sense that the
laws of physics are particularly simple because we're trapped in a single
dense causality mediated by the electromagnetic force. This is not just my own
completely harebrained idea, it is similar to Eddigton's "wandering moon"
interpretation of GR (the moon goes wherever it pleases, space accomodates
itself to maintain the orbital illusion)
>
> >5) Gravitation could have a finite range or a longrange repulsive component.
>
> True, but so far little (to be fair, not no) evidence supports this
> addition to the standard model.
LennardJones, VanDerWaals, Familiaritybreedscontempt. Sign changes often
occur in the force between bodies, as the separation changes. Indirect
evidence, but inductive arguments have a more logical basis than deductive
ones.
>
> >6) The spontaneous appearance of new matter or energy could keep the universe
> >from ever collapsing.
>
> Appearance of new matter only makes things worse in the standard
> picture; it's purely the gravitational force from existing matter that
> causes it to collapse.
New energy could introduce radiation pressure. It's not clear what the effect
of new matter would be on the size or temporal properties of the universe. If,
for example, new positrons were produced in Dirac's sea, the universe could
expand as a result.
>
> >7) Current interpretations of the galactic redshift could be wrong.
>
> True, but no evidence supports this.
>
It doesn't appear to hold true within our own galaxy. Again, an inductive argument.
> >8) Dark matter could be hidden from electromagnetic observation.
>
> True: that's why it's called `dark matter'.
>
> >9) A hitherto undiscovered longrange force might exist.
>
> True, but no evidence supports this.
Thanks for a most enjoyable discussion!
> In article <7raipg$pjs$1...@scorpius.star.bris.ac.uk>,
> Martin Hardcastle <M.Hard...@xxx.xxx.xxx> wrote:
>
> > To clarify (since the `No' above is misleading): as Tony correctly
> > says, if the universe were dense enough, it would collapse again under
> > its own gravity to a singularity.
>
> I guess the *observable* universe would theoretically collaps to a
> singularity. Not the much bigger unobservable universe that is out
> there if inflation is correct.
Hmmm... interesting. I'm not a scientist but I have a problem with that.
Uh... part of the universe that is OUR observable universe should also be
part of the observable universe for others outside our observable universe,
no? Somebody 20 billion light years away would be able to see part way into
our observable universe. There is nothing special about the "edge" of our
observable universe so why would only "it" collapse into a singularity if
the mass is sufficient? Why wouldn't some of it that is very far away from
us collapse in the other direction? Where would the "edges" of such a
collapse be? It's a very different situation from collapsing dust/molecular
clouds in a galaxy that actually have a defined edge.
If inflation is correct and the total mass is sufficient, why won't the
entire inflated universe collapse into the same singularity? If it all came
out of a single singularity, why can't it go back?
Joe Zorzin
> A bit restrictive, don't you think? Observations don't support ideas. Better
> to say they appear consistent or inconsistent with certain ideas.
The usual sense of support in physics is that observations
support a theory if the theory is consistent with the observations.
If it isn't, then the theory is wrong.
> Other ideas
> which these observations may be consistent with are:
>
That's not relevant. The remarks that you're replying to
were made in the context of a particular theory and a
particular model constructed within that theory.
There was no attempt to comment on other alternatives.
John Anderson
I guess so. The contraction doesn't undo the effects of the inflation.
I think it's fair to say that it's also consistent with that conclusion.
(Actually even in this situation you beg the question by saying `an
observation of someone stealing'; someone stealing is necessarily a
thief, but no single observation unambiguously proves that someone is
stealing. But enough of semantics...)
>Well, OK, but it would take an infinite amount of time.
Not convinced; density is increasing in this picture, remember, so
this isn't all that different from the old Jeans' mass situation,
where the increase in density is exponential (until halted by thermal
pressure).
>Maximum entropy is consistent with local structure, in fact equipartition
>implies all possible ordered structures with decreasing probability. Enjoy
>your window while it still exists!
You aren't seriously arguing this, are you? Maximum entropy (to me)
implies that there is no way in which entropy can increase further;
which means no temperature differences exist anywhere in the universe;
which I think we can safely say is not the case.
>Well, that's one meaning of singularity.
It is the usual one...
> Another might be the sense that the
>laws of physics are particularly simple because we're trapped in a single
>dense causality mediated by the electromagnetic force.
Huh? What does `causality' mean in the sense that we can be trapped in
a dense one?
>LennardJones, VanDerWaals, Familiaritybreedscontempt. Sign changes often
>occur in the force between bodies, as the separation changes.
I'm sure you know that van der Waals forces arise because there is
positive and negative electrical charge; there's no evidence at all
for analogous gravitational charge.
Not that that proves there _can't_ be something about longrange
gravity that we don't understand. Modified Newtonian gravitation
explains the rotation curves of galaxies without the need for dark
matter. But the analogy is false.
> Indirect
>evidence, but inductive arguments have a more logical basis than deductive
>ones.
Er, no they don't; see Hume. Induction has no logical basis at all,
deduction is strictly logical (so long as your premises are right).
I cannot induce with certainty that the sun will always rise from
the observations that it always has before.
>New energy could introduce radiation pressure.
Alas, energy density in radiation is also a source of _attraction_ in GR.
>It doesn't appear to hold true within our own galaxy. Again, an
> inductive argument.
But the redshiftdistance relation is not _expected_ to hold true
within our own galaxy, which is a gravitationally bound system; so
your induction fails. (Actually this isn't an induction, just a
deduction on false premises, because there's no element of reasoning
from the specific to the general involved; you are just reasoning from
one specific case to another with a false premise that says that the
two are alike.)