singularities and infinite universes

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David Scarth

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Sep 4, 1999, 3:00:00 AM9/4/99
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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 2-dimensional surfaces is always
good). Perhaps I misinterpret the nature of a singularity?

thanks.
David Scarth.


Nathan Urban

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Sep 4, 1999, 3:00:00 AM9/4/99
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In article <7qrvbl$8hr$1...@nclient15-gui.server.virgin.net>, "David Scarth" <d.sc...@virgin.net> wrote:

> 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.

http://www.astro.ucla.edu/~wright/infpoint.html

and...@ibm.net

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Sep 4, 1999, 3:00:00 AM9/4/99
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David Scarth wrote:
>
> 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 2-dimensional surfaces is always
> good). Perhaps I misinterpret the nature of a singularity?
>

Damn near anything is possible the instant after the sintularity.
That's why it's a simgularity.

John Anderson

StanAZ

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Sep 6, 1999, 3:00:00 AM9/6/99
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David Scarth: "...At the singularity, the universe is compressed into an
infinitely small volume. In the next instant, the universe [in the open models]

has infinite volume. I have difficulty in seeing how it can change from
infinitely small
to infinitely large in one instant."

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

Ed Keane III

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Sep 6, 1999, 3:00:00 AM9/6/99
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Perhaps if the Universe is a closed system that encompasses everything it is
not reasonable when considering it in its entirety to define a changing size
for it.

and...@ibm.net

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Sep 6, 1999, 3:00:00 AM9/6/99
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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

StanAZ

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Sep 7, 1999, 3:00:00 AM9/7/99
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Dictionary definitions represent common usage, and/or pop prejudices, Ed.
Physics often reflects such views.

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

z@z

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Sep 7, 1999, 3:00:00 AM9/7/99
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David Scarth wrote:

| 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 2-dimensional 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 big-bang
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

J. Scott Miller

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Sep 7, 1999, 3:00:00 AM9/7/99
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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

Charles Francis

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Sep 7, 1999, 3:00:00 AM9/7/99
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In article <7r3ent$v4$1...@pollux.ip-plus.net>, z@z <z...@z.lol.li> writes

>David Scarth wrote:
>
>| 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 2-dimensional surfaces is always
>| good). Perhaps I misinterpret the nature of a singularity?
>

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 big-bang
>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

Ed Keane III

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Sep 8, 1999, 3:00:00 AM9/8/99
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David Scarth <d.sc...@virgin.net> wrote in message
news:7qrvbl$8hr$1...@nclient15-gui.server.virgin.net...

> 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 2-dimensional surfaces is
always
> good). Perhaps I misinterpret the nature of a singularity?
>
> thanks.
> David Scarth.
>

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

Ilja Schmelzer

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Sep 8, 1999, 3:00:00 AM9/8/99
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"z@z" <z...@z.lol.li> writes:
> | 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.

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, D-10178 Berlin, Keibelstr. 38, <il...@cyberpass.net>
http://www.cyberpass.net/~ilja

Tom Roberts

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Sep 8, 1999, 3:00:00 AM9/8/99
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"z@z" wrote:
> A singularity always involves a discontinuous transition similar
> to the transition from zero to one.

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 solar-mass 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

Tony Suessine

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Sep 8, 1999, 3:00:00 AM9/8/99
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>>By the way, can black holes explode? If not, this would strongly

>>suggest that BIG BANG is impossible.


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

Nathan Urban

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Sep 9, 1999, 3:00:00 AM9/9/99
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In article <19990906023920...@ng-fq1.aol.com>, sta...@aol.com (StanAZ) wrote:

> 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.

J. Scott Miller

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Sep 9, 1999, 3:00:00 AM9/9/99
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Tony Suessine wrote:
>
> >>By the way, can black holes explode? If not, this would strongly
> >>suggest that BIG BANG is impossible.
>
> 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!! ?

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

David Scarth

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Sep 9, 1999, 3:00:00 AM9/9/99
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Ed Keane III <ke...@northweb.com> wrote in message
news:7r4e3h$n8m$0...@207.127.211.58...

>
> David Scarth <d.sc...@virgin.net> wrote in message
> news:7qrvbl$8hr$1...@nclient15-gui.server.virgin.net...
> > 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 2-dimensional surfaces is
> always
> > good). Perhaps I misinterpret the nature of a singularity?
> >
> > thanks.
> > David Scarth.
> >
>
> 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
>


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.


Tony Suessine

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Sep 9, 1999, 3:00:00 AM9/9/99
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J. Scott Miller wrote in message <37D7C4A6...@louisville.edu>...

>How would you give all of the mass of the universe to a black hole?


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

and...@ibm.net

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Sep 9, 1999, 3:00:00 AM9/9/99
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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 non-singular 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

J. Scott Miller

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Sep 9, 1999, 3:00:00 AM9/9/99
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Tony Suessine wrote:
>
> J. Scott Miller wrote in message <37D7C4A6...@louisville.edu>...
> >How would you give all of the mass of the universe to a black hole?
>
> 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

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

Martin Hardcastle

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Sep 10, 1999, 3:00:00 AM9/10/99
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In article <37D86784...@louisville.edu>,
J. Scott Miller <Scott....@louisville.edu> wrote:

>Tony Suessine wrote:
>> if there is enough
>> mass in the universe isn't the final result supposed to be a collapse
>> into a singularity?
>
>No. In an open universe, it goes on and on and on and on.... Current
>observations support such a universe.

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

octo...@hotmail.com

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Sep 10, 1999, 3:00:00 AM9/10/99
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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.

--
My conscience is clean. I never use it.
8-8


Sent via Deja.com http://www.deja.com/
Share what you know. Learn what you don't.

D.A.Kopf

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Sep 10, 1999, 3:00:00 AM9/10/99
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Martin Hardcastle wrote:
>
> In article <37D86784...@louisville.edu>,
> J. Scott Miller <Scott....@louisville.edu> wrote:
> >Tony Suessine wrote:
> >> if there is enough
> >> mass in the universe isn't the final result supposed to be a collapse
> >> into a singularity?
> >
> >No. In an open universe, it goes on and on and on and on.... Current
> >observations support such a universe.
>
> 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.
>
A bit restrictive, don't you think? Observations don't support ideas. Better
to say they appear consistent or inconsistent with certain ideas. Other ideas
which these observations may be consistent with are:

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
high-temperature 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 long-range repulsive component.

6) The spontaneous appearance of new matter or energy could keep the universe
from ever collapsing.

7) Current interpretations of the galactic red-shift 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 long-range force might exist.

'Nuff said?


Martin Hardcastle

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Sep 10, 1999, 3:00:00 AM9/10/99
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In article <37D91541...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
>A bit restrictive, don't you think? Observations don't support ideas. Better
>to say they appear consistent or inconsistent with certain ideas. Other ideas
>which these observations may be consistent with are:

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 space-time 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 long-range 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 red-shift 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 long-range force might exist.

True, but no evidence supports this.

Martin Hardcastle

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Sep 10, 1999, 3:00:00 AM9/10/99
to
In article <7rb6fn$ebr$1...@nnrp1.deja.com>, <octo...@hotmail.com> wrote:
>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.

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 lower-density 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.

octo...@hotmail.com

unread,
Sep 10, 1999, 3:00:00 AM9/10/99
to
In article <7rbb5h$son$1...@scorpius.star.bris.ac.uk>,
Martin Hardcastle <M.Hard...@xxx.xxx.xxx> wrote:

> 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.

D.A.Kopf

unread,
Sep 10, 1999, 3:00:00 AM9/10/99
to
Martin Hardcastle wrote:
>
> In article <37D91541...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
> >A bit restrictive, don't you think? Observations don't support ideas. Better
> >to say they appear consistent or inconsistent with certain ideas. Other ideas
> >which these observations may be consistent with are:
>
> 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?)

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 space-time 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 hare-brained 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 long-range repulsive component.
>
> True, but so far little (to be fair, not no) evidence supports this
> addition to the standard model.

Lennard-Jones, Van-Der-Waals, Familiarity-breeds-contempt. 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 red-shift 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 long-range force might exist.
>
> True, but no evidence supports this.

Thanks for a most enjoyable discussion!


Joseph Zorzin

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Sep 11, 1999, 3:00:00 AM9/11/99
to
octo...@hotmail.com wrote:

> 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


and...@ibm.net

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Sep 11, 1999, 3:00:00 AM9/11/99
to
D.A.Kopf wrote:
>

> 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

Martin Hardcastle

unread,
Sep 13, 1999, 3:00:00 AM9/13/99
to
In article <7rbpbu$tcc$1...@nnrp1.deja.com>, <octo...@hotmail.com> wrote:
>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?

I guess so. The contraction doesn't undo the effects of the inflation.

Martin Hardcastle

unread,
Sep 13, 1999, 3:00:00 AM9/13/99
to
In article <37D973F6...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
>In the sense that an observation of someone stealing supports the logical
>conclusion that he/she is a thief!

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?

>Lennard-Jones, Van-Der-Waals, Familiarity-breeds-contempt. 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 long-range
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 redshift-distance 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.)

J. Scott Miller

unread,
Sep 13, 1999, 3:00:00 AM9/13/99
to
Martin Hardcastle wrote:
>
> In article <7rbpbu$tcc$1...@nnrp1.deja.com>, <octo...@hotmail.com> wrote:
> >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?
>
> I guess so. The contraction doesn't undo the effects of the inflation.
>
> Martin

Now I'm curious. If contraction of the universe occurs because of sufficient
gravity to stop the expansion, it seem, whether in the inflation scenario or
not, that the universe as a whole will collapse. Different part may be
disconnected in terms of light travel time, but not necessarily disconnected
gravitationally. Or am I missing a subtle point about inflation?

D.A.Kopf

unread,
Sep 13, 1999, 3:00:00 AM9/13/99
to
Martin Hardcastle wrote:
<snip>

>In article <37D973F6...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
> >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.
>
Yes, actually it makes sense to me (as it did to Eddington) although it
doesn't imply a particularly attractive destiny for homo sapiens. The
probability of Earth and all the rest of it in a terminal universe is still
nonzero. Winning a big lottery is also improbable - except for the winner.

> >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?

I refer to the peculiar nature of photon exchange, which could be interpreted
not only as sampling the entire universe for every interaction, but also as
(mostly) defining the causal metric. This is certainly a degeneracy and
arguably a singularity. Thus the infinity of possible Euclidean or lumpy
metrics which could be chosen to describe how the universe "really" is. [If
you have a physical feel for the imaginary t axis, please share it with the
rest of us].

>
> >Lennard-Jones, Van-Der-Waals, Familiarity-breeds-contempt. 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 long-range
> 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.

Yes but in deduction the premises postulate the conclusion, however obscure
the connection may be at the outset (Aristotle). With induction one looks
directly for the governing laws. In neither case, of course, can predictions
be made with absolute certainty.

>
> >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 redshift-distance 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.)

I don't know...the specific case is our 1 solar system volume, the successor
case is the n+1 solar system volume. When do the the red shifts begin? And are
you applying Occam's razor judiciously?

Alun WIlliams

unread,
Sep 14, 1999, 3:00:00 AM9/14/99
to
If Black holes exist, and I bhelieve that they do, and at the centre of the
black hole there is a singularity, is not true that our universe is already
collapsing into a singularity. It may be that there is in facty only one
singularity that can manifest itself in different spatial locations
throughout the universe. If the singularity represents absolute chaos (I
believe it does) then it also represents maximum disorder and thus maximum
entropy, which all things will tend toward. If this is the case then the
universe is already collapsing into a singularity even though it is still
expanding spatially.

What do you think?

Alun

J. Scott Miller

unread,
Sep 14, 1999, 3:00:00 AM9/14/99
to

Alun WIlliams wrote:
>
> If Black holes exist, and I bhelieve that they do, and at the centre of the
> black hole there is a singularity, is not true that our universe is already
> collapsing into a singularity.

Since observational evidence indicates that we are in an expanding universe
and that there is insufficient mass to stop that expansion, then, based on
observation, the answer is no. Also, there is a difference between black hole
solutions in GR and expanding universe (big bang models) solutions in GR. You
might visit: http://math.ucr.edu/home/baez/physics/universe.html which gives a
discussion of big bang versus black holes.

Alun WIlliams

unread,
Sep 14, 1999, 3:00:00 AM9/14/99
to
Thanks for the web site address. I had a look through the discussion. There
was a great deal of conjecture with the final comment "WHO KNOWS". It was
interesting though. From what I gather there is a possibility that the big
bang was a white hole rather than a black hole. I still believe though that
given enough time black holes will eventually mop up all the space time and
matter in the universe.

Cheers

Alun


J. Scott Miller <Scott....@louisville.edu> wrote in message
news:37DEABAB...@louisville.edu...

J. Scott Miller

unread,
Sep 14, 1999, 3:00:00 AM9/14/99
to
Alun WIlliams wrote:
>
> Thanks for the web site address. I had a look through the discussion.
> There was a great deal of conjecture with the final comment "WHO KNOWS".
> It was interesting though. From what I gather there is a possibility that
> the big bang was a white hole rather than a black hole.

I don't think that this claim could really be substantiated, as a white hole
is an object that fills space with matter/energy and there was no space to
fill in the big bang event, as it was the creation of space-time.

> I still believe though that given enough time black holes will eventually
> mop up all the space time and matter in the universe.

Black holes are too small compared to galaxies, let alone the space between
galaxies to do any such thing. If our galaxy was suddenly to become a black
hole, its Schwarzschild radius would be some 3 trillion kilometers. The
galaxy itself spans 9.46 x 10^17 kilometers. Based on how gravity works, a
star at half that distance from that central black hole would experience a
gravitational field no different than it does from the galaxy in its current
state. And a galaxy like Andromeda would experience no difference in the
gravitational field it experiences from the presence of the Milky Way whether
as itself or its black hole equivalent. And, if there is no difference at
those great distances just within the Local group, whether extended galaxy or
supermassive black hole of the equivalent mass of that galaxy, then there is
no way "black holes will eventually mop up all the space time and matter in
the universe", whether the universe is open or closed. And this is assuming
that all of the matter in our galaxy could even get together to form such a
massive black hole to begin with. At best, if the universe is open and
expands forever, these galaxy-massed black holes will evaporate. But the
evaporation times for that are (shall I say it) astronomical. For an
estimate, evaporation times is gotten from the formula:

t = 10,240 (pi)^2{[G^2*M^3]/[h*c^4]}

Put in a trillion times the Sun's mass and the values of the gravitational
constant, Planck's constant, and the speed of light. You can bet that it is
quite likely a close universe would collapse before this time period and in an
expanding universe, the black holes would be so far apart as to probably be
undetectable from each other even when they did evaporate.

and...@ibm.net

unread,
Sep 14, 1999, 3:00:00 AM9/14/99
to
Alun WIlliams wrote:
>
> If Black holes exist, and I bhelieve that they do, and at the centre of the
> black hole there is a singularity, is not true that our universe is already
> collapsing into a singularity. It may be that there is in facty only one
> singularity that can manifest itself in different spatial locations
> throughout the universe. If the singularity represents absolute chaos (I
> believe it does) then it also represents maximum disorder and thus maximum
> entropy, which all things will tend toward. If this is the case then the
> universe is already collapsing into a singularity even though it is still
> expanding spatially.
>
> What do you think?
>

I think that you're full of shit. What is this "one singularity"
or "absolute chaos" nonsense? Stop trying to appear profound
by term dropping.

Theoretical physics isn't a result of a bunch of people shooting
the breeze.

John Anderson

Martin Hardcastle

unread,
Sep 15, 1999, 3:00:00 AM9/15/99
to
In article <37DD41F3...@louisville.edu>,

J. Scott Miller <Scott....@louisville.edu> wrote:
>Now I'm curious. If contraction of the universe occurs because of sufficient
>gravity to stop the expansion, it seem, whether in the inflation scenario or
>not, that the universe as a whole will collapse. Different part may be
>disconnected in terms of light travel time, but not necessarily disconnected
>gravitationally.

I'm not saying anything very subtle here; I must just be being
unintentionally opaque. So to recap: the point about inflation, as you
know, is that there are regions of the sky which have very similar
appearance despite, in non-inflationary models, never having been in
causal contact. Inflation explains the similarity of these regions by
saying that they _were_ in causal contact back in the very early
universe. If somehow you manage to produce an inflationary model with
omega systematically greater than one, then, as you say, the universe
as a whole will systematically collapse. I'm saying that I don't see
an obvious reason why all pairs of regions should come back into
causal contact (i.e. start seeing light from one another) in the
course of that collapse. But that doesn't mean that they won't all
collapse.

In reality, standard inflation models predict very small differences
between the density of a given region and the critical density; but
these differences are random, and so different bits of an inflationary
universe, after a very long time, may do different things. `our'
universe might have omega ~ 1 + 10^-5, and recollapse, while the
next-door inflationary bubble might have omega ~ 1 - 10^-5 and expand
forever; so it might not be true to say the `whole universe' will
collapse just because our local bit does. Not that that will make a
whole lot of difference to us, even if we stick around for the
required (extremely long) time...

Marrin


--
Martin Hardcastle Department of Physics, University of Bristol

`Innocent light-minded men, who think that astronomy can be learnt by
looking at the stars without knowledge of mathematics, will become birds...'

Martin Hardcastle

unread,
Sep 15, 1999, 3:00:00 AM9/15/99
to
In article <37DD5A0A...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
>Yes, actually it makes sense to me (as it did to Eddington)

I still don't see what you're driving at. We see entropy increasing
throughout the observable universe; therefore the observable universe
is, trivially, not in a state of maximal entropy.

Want to give us a reference for what Eddington thought about this?

>I refer to the peculiar nature of photon exchange, which could be interpreted
>not only as sampling the entire universe for every interaction, but also as
>(mostly) defining the causal metric. This is certainly a degeneracy and
>arguably a singularity. Thus the infinity of possible Euclidean or lumpy
>metrics which could be chosen to describe how the universe "really"
>is.

I understand all the individual words here, but none of the sentences.
In standard physics there is certainly nothing particularly privileged
about photon exchange vs. exchange of some other massless particle. I
don't know what you mean by the `causal metric'; `degeneracy' and
`singularity' (as I've already said in the latter case) have
well-defined meanings which don't appear to correspond to the way
you're using them. I'm not arrogant enough to assume that anything I
don't understand is nonsense, but there is a communication difficulty
here...

>I don't know...the specific case is our 1 solar system volume, the successor
>case is the n+1 solar system volume.

Heh. Induction, in the purely mathematical sense, from the n=1 case to
the n>1 case is a _really_ dodgy thing to do. (Have you seen the proof
that all horses are the same colour? Suppose that all sets of n horses
are the same colour. Lemma: all sets of n+1 horses are the same
colour. Proof: remove one horse. There are now n horses. By
supposition, they are all the same colour. Replace the horse and
remove another. There are still n horses and they are the same
colour. So all n+1 horses must be the same colour; so if this is true
for n horses, it is true for n+1 horses. Consider n=1; all the horses
in this set are the same colour. Therefore, by induction, all horses
are the same colour.)

In the case of the solar system, simple induction might lead us to
expect that there should be 1 sun per solar system volume, for
example, which would certainly make the night sky a more interesting
place if you like stars...

Fortunately we have this thing called `observation' which is a great
substitute for trying to work these matters out a priori.

> When do the the red shifts
>begin?

There is no boundary in standard cosmology where you can say `beyond
this point are the cosmological redshifts.' The only thing you can say
is that the further away you go, the more accurate is the assumption
that the dominant contribution to redshift is cosmological.

The reason for this is that there are gravitationally bound systems in
the universe. Our solar system is one; our galaxy is one; our local
group of galaxies is one; clusters of galaxies are bound
systems. These systems all started out as part of an expanding
universe, but since they were unusually dense, and since the force of
gravity acts against the local expansion, they ended up being
decoupled from the expansion. So you see stars in our galaxy, or
galaxies in clusters, with motions which have everything to do with
standard Newtonian orbits and nothing to do with cosmological
expansion. On the largest scales, local overdensities are not
important, the universe is (probably) not gravitationally bound, and
you continue to see expansion.

This is not an ad hoc refinement of the model, it's a necessary
consequence of it as soon as you allow the density of the universe to
be non-uniform (which it rather clearly is at the present day).

Martin

J. Scott Miller

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Sep 15, 1999, 3:00:00 AM9/15/99
to
Not to beat a dead horse, but this part of the inflation models either never
were driven home or I just daftly missed the point. To whit:

Martin Hardcastle wrote:

[stuff deleted as recap]

>
> In reality, standard inflation models predict very small differences
> between the density of a given region and the critical density; but
> these differences are random, and so different bits of an inflationary
> universe, after a very long time, may do different things. `our'
> universe might have omega ~ 1 + 10^-5, and recollapse, while the
> next-door inflationary bubble might have omega ~ 1 - 10^-5 and expand
> forever; so it might not be true to say the `whole universe' will
> collapse just because our local bit does. Not that that will make a
> whole lot of difference to us, even if we stick around for the
> required (extremely long) time...

Time I have no problem with. I just am not familiar with the aspect that the
inflation models allow for the possibilities of multiverses that could be
disconnected. I guess I pictured inflation accounting for the horizon problem
of how can points at distances greater than light-travel distances look so
similar and the flatness problem of the actual density being so close to
critical density, allowing the universe to expand as a whole from time after
inflation. The possibility that our observable universe might have densities
different from the next observable universe over, and that each could collapse
or not collapse, independent of each other and apparently independent of the
whole is something outside my reading on the topic, I guess.


>
> Marrin


> --
> Martin Hardcastle Department of Physics, University of Bristol
> `Innocent light-minded men, who think that astronomy can be learnt by
> looking at the stars without knowledge of mathematics, will become birds...'
> Please replace the xxx.xxx.xxx in the header with bristol.ac.uk to mail me

--

Alun WIlliams

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Sep 15, 1999, 3:00:00 AM9/15/99
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> I think that you're full of shit. What is this "one singularity"
> or "absolute chaos" nonsense? Stop trying to appear profound
> by term dropping.
>
> Theoretical physics isn't a result of a bunch of people shooting
> the breeze.
>
> John Anderson

I wasn't trying to be profound. They were just simple suggestions!!! I
have had quite a lot of constructive comments to them. Yours wasn't one.

Alun


D.A.Kopf

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Sep 15, 1999, 3:00:00 AM9/15/99
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Martin Hardcastle wrote:
>
> In article <37DD5A0A...@dakx.com>, D.A.Kopf <d...@dakx.com> wrote:
> >Yes, actually it makes sense to me (as it did to Eddington)
>
> I still don't see what you're driving at. We see entropy increasing
> throughout the observable universe; therefore the observable universe
> is, trivially, not in a state of maximal entropy.

The possibility that one starts with certain instinctive or otherwise
ingrained conceptions, then fleshes them out into scientific logic with
various proportions of analysis and rationalization. Under the paradigm
theory, these initial concepts limit the scope of reasoning until the
gradually accumulating body of rationalization becomes apparent to some future
Einstein. Don't you think such a person could start with the conception of a
maximal entropy universe, and (with suitable modifications) derive galaxies on
a local scale and red shifts on a large scale? After all, there is no
temperature difference in a 1 nanometer volume of insterstellar space, but QM
postulates that it contains virtual particles. Temperature is inherently a
statistical property of a large number of degrees of freedom, all of which
have statistical fluctuations.

>
> Want to give us a reference for what Eddington thought about this?
>
> >I refer to the peculiar nature of photon exchange, which could be interpreted
> >not only as sampling the entire universe for every interaction, but also as
> >(mostly) defining the causal metric. This is certainly a degeneracy and
> >arguably a singularity. Thus the infinity of possible Euclidean or lumpy
> >metrics which could be chosen to describe how the universe "really"
> >is.
>
> I understand all the individual words here, but none of the sentences.
> In standard physics there is certainly nothing particularly privileged
> about photon exchange vs. exchange of some other massless particle. I
> don't know what you mean by the `causal metric'; `degeneracy' and
> `singularity' (as I've already said in the latter case) have
> well-defined meanings which don't appear to correspond to the way
> you're using them. I'm not arrogant enough to assume that anything I
> don't understand is nonsense, but there is a communication difficulty
> here...
>

The basic point is that the laws of physics are abstract relations among
entities, these entities themselves possibly being abstract relations among
entities, et cetera. When the relations form a group like SU(3), for the
purposes of study it really doesn't matter what the "real" entities are, but
when the physics can be interpreted as the relation of relations then one
might well wonder whether there are any entities at all. Degeneracy enters
when the same observation results from a mixture of pure quantum states, so I
think it an appropriate word.

In "The Nature of the Physical World", 19?? and "New Pathways in Science"
(1935), Eddington raises points similar to the above, suggesting (if I might
presume to summarize) that GR is a perfect end-theory precisely because it tells
us how the universe will appear regardless of any underlying (and forever
unobservable) physical reality. I once put this point to J. Wheeler at a
seminar, and his tangential answer was that Eddington's thinking wasn't so
well thought of nowadays.


> >I don't know...the specific case is our 1 solar system volume, the successor
> >case is the n+1 solar system volume.

<snip example of an inductive fallacy involving horse color. No time to respond,
other than pointing out there is no such thing as n horses, only n
observations of horse-hood>

>
> > When do the the red shifts
> >begin?
>
> There is no boundary in standard cosmology where you can say `beyond
> this point are the cosmological redshifts.' The only thing you can say
> is that the further away you go, the more accurate is the assumption
> that the dominant contribution to redshift is cosmological.
>
> The reason for this is that there are gravitationally bound systems in
> the universe. Our solar system is one; our galaxy is one; our local
> group of galaxies is one; clusters of galaxies are bound
> systems. These systems all started out as part of an expanding
> universe, but since they were unusually dense, and since the force of
> gravity acts against the local expansion, they ended up being
> decoupled from the expansion. So you see stars in our galaxy, or
> galaxies in clusters, with motions which have everything to do with
> standard Newtonian orbits and nothing to do with cosmological
> expansion. On the largest scales, local overdensities are not
> important, the universe is (probably) not gravitationally bound, and
> you continue to see expansion.
>
> This is not an ad hoc refinement of the model, it's a necessary
> consequence of it as soon as you allow the density of the universe to
> be non-uniform (which it rather clearly is at the present day).

Necessary in the sense of relation among abstract operators, or necessary in
the sense of satisfying "physical laws"?


Frank Wappler

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Sep 15, 1999, 3:00:00 AM9/15/99
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Martin Hardcastle wrote:
> We see entropy increasing throughout the observable universe

How do we measure "entropy" of (the portion of) the universe
that we see/observe;
trial by trial, in order to compare and identify an increase?

> So you see stars in our galaxy, or galaxies in clusters,
> with motions which have everything to do with standard
> Newtonian orbits and nothing to do with cosmological expansion.

> [...] the universe is (probably) not gravitationally bound

How does one measure "motions" of stars; especially before
knowing if and how they might be "gravitationally bound"?

Also (perhaps related): how might we determine "temperature"?,
(or the corresponding four-vector, or tensor?)

Thanks, Frank W ~@) R


p.s.

> Fortunately we have this thing called `observation' which is a great
> substitute for trying to work these matters out a priori.

However (and also fortunately, IMHO) observations are being collected
by distinct unique individuals.
The procedures for deriving measurements from those individual
observations can and must still be worked out a priori.

> Have you seen the proof that all horses are the same colour?
> Suppose that all sets of n horses are the same colour.
> Lemma: all sets of n+1 horses are the same colour.
> Proof: remove one horse. There are now n horses.
> By supposition, they are all the same colour. Replace the horse and
> remove another. There are still n horses and they are the same
> colour. So all n+1 horses must be the same colour;
> so if this is true for n horses, it is true for n+1 horses.

> Consider n=1; all the horses in this set are the same colour.
> Therefore, by induction, all horses are the same colour.

Which nicely illustrates that "the same" (one individual) and
"the same" (as measured and agreed upon between distinct individuals)
are not necessarily the same ...

and...@ibm.net

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Sep 15, 1999, 3:00:00 AM9/15/99
to

It wasn't meant to be for the reasons that I suggested. A
suggestion that contains undefined terms isn't much use
to anyone.

John Anderson

Martin Hardcastle

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Sep 16, 1999, 3:00:00 AM9/16/99
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In article <37DFD611...@louisville.edu>,

J. Scott Miller <Scott....@louisville.edu> wrote:
>Time I have no problem with. I just am not familiar with the aspect that the
>inflation models allow for the possibilities of multiverses that could be
>disconnected.

Bits of our own observable universe have been causally disconnected
since the inflationary epoch! It's easy to imagine that there are
causally disconnected regions further out beyond our present horizon,
therefore.

>The possibility that our observable universe might have densities
>different from the next observable universe over, and that each could collapse
>or not collapse, independent of each other and apparently independent of the
>whole is something outside my reading on the topic, I guess.

This is speculation, but I'm certainly not making it up.

Here's a quote from Rees's book on _Perspectives in Astrophysical
Cosmology_ which illustrates the sort of thing I'm handwaving
about. Rees is a Real Cosmologist...

Many theorists now favour the idea of _chaotic inflation_.[ref] In
this model there is not necessarily [...] an initial simple
singularity, with the inflationary phase being an intermediate
interlode. Linde invisages a more complex situation where the
collapse of some region triggers creation of a new cosmos. If our
universe is almost flat, it extends vastly beyond our present
horizon of 10-20 billion light-years and is destined to expand
much more, with many more galaxies coming into view. It may still
eventually recollapse, but only after expanding by a further factor
10^10^5! But what we call `_our' universe may be just one domain, or
one phase, of an eternally reproducing cycle of different
`universes'. These are not now in causal contact, but can be traced
back to common ancestors. [...]

[ref: Linde, A.D., _Particle Physics and Inflationary Cosmology_,
Harwood, Switzerland.]

Martin

octo...@hotmail.com

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Sep 16, 1999, 3:00:00 AM9/16/99
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In article <7rqclh$33s$1...@scorpius.star.bris.ac.uk>,
Martin Hardcastle <M.Hard...@xxx.xxx.xxx> wrote:

> Here's a quote from Rees's book on _Perspectives in Astrophysical
> Cosmology_ which illustrates the sort of thing I'm handwaving
> about. Rees is a Real Cosmologist...

The relevant paper from Linde might be
http://xxx.lanl.gov/abs/astro-ph/9601004

--
It ain't necessarily so

PDavis

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Sep 17, 1999, 3:00:00 AM9/17/99
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On the subject of black holes: When matter enters the black hole, it "leaves" our
universe, correct? Okay, if that's the case, does that mean that matter entering
the black hole adds to it's mass or not?

If matter entering black holes does increase their mass, then black holes will
eventually keep "slopping" up stuff... Of course, that said, by the time that
happens all the stars will probably be burnt out and we won't be here, so not much
point...

"J. Scott Miller" wrote:

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