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From: Han de Bruijn on 15 Mar 2010 10:11
On 15 mrt, 08:34, MicroTech <henry.ko.nor...(a)gmail.com> wrote:

> In physics (and cosmology) I quite often see references to
> "singularities" (as inside "black holes" and as the origin of the so
> called "big bang") as being "points with no size, of infinite mass,
> infinite density, infinite temperature, and infinite pressure" (or
> something to this effect).
>
> As I understand an "infinite quantity", it will stay infinite even if
> one adds n, or subtracts n, or multiplies by n, or divides it by n <>
> 0...
>
> I am told by science that "the universe is estimated to contain 10^80
> particles." This is a big number, for sure, but a far cry from an
> infinite number of particles. It seems to me that if we subtract 10^80
> from an infinity of particles, the remaining number of particles would
> still be infinite... So, if the "original singularity" indeed had
> infinite mass, what in the "big bang" made it finite, suddenly? And
> does not the same question equally apply to density, temperature, and
> pressure?
>
> A related question is, if something has infinite density, how can
> there be room for its constituent particles to freely move around (as
> in temperature)? How can something with infinite density be infinitely
> hot?
>
> Another related question is: if a "singularity" shows up in an
> equation (as is claimed to happen in some of Einstein's equations), is
> this not a sure sign that something in the equation is wrong? Like
> dividing by zero, somewhere?
>
> As I am neither a mathematician nor a physicist, it may well be that
> I've got the concept of "infinity" wrong. I would really appreciate it
> if someone in this forum can point out to me where my understanding is
> wrong (and provide correct interpretations of the term)!
>
> References to published papers (accessible on line), especially papers
> showing what the "Einstein Singularities" are, would be very much
> appreciated!
>
> Henry Norman

From:

http://www.phy.ilstu.edu/~rfm/107F07/EPMjokes.html

Also at:

http://en.wikipedia.org/wiki/Mathematical_joke

An astronomer, a physicist and a mathematician (it is said) were
holidaying in Scotland. Glancing from a train window, they observed
a black sheep in the middle of a field. "How interesting," observed
the astronomer, "all scottish sheep are black!" To which the physicist
responded, "No, no! Some Scottish sheep are black!" The mathematician
gazed heavenward in supplication, and then intoned, "In Scotland there
exists at least one field, containing at least one sheep, at least one
side of which is black."

Too much honour for the physicist. Replace "physicist" by "engineer"
(and "astronomer" by "physicist", eventually) for a more accurate
description of modern times.

Han de Bruijn
From: Pubkeybreaker on 15 Mar 2010 10:38
On Mar 15, 3:34 am, MicroTech <henry.ko.nor...(a)gmail.com> wrote:

> As I understand an "infinite quantity", it will stay infinite even if
> one adds n, or subtracts n, or multiplies by n, or divides it by n <>
> 0...

Infinity is not a real number. One can not do arithmetic with it
in the sense you are using it. Arithmetic with "infinity" is
inconsistent.
oo - oo can be 0,1,2,3,.....oo depending on context.

0*oo can be anything.
From: Uncle Al on 15 Mar 2010 10:52
MicroTech wrote:
>
> In physics (and cosmology) I quite often see references to
> "singularities" (as inside "black holes" and as the origin of the so
> called "big bang") as being "points with no size, of infinite mass,
> infinite density, infinite temperature, and infinite pressure" (or
> something to this effect).

Finite and observable mass, also charge and angular momentum. Don't
try to embed the wildly non-Euclidean geometry of black holes in
peripheral spacetime - that is why we have event horizons.

The outside diameter of an event horizon is trivially quantifiable.
The inside diameter is infinite (re a tardis) with no path through the
event horizon to escape. An easy example (interior view) of this
geometry is our universe. Every contained point is exactly at its
center. All 4(pi)steradians exactly point to an equidistant Big
Bang. There is no path out.

> As I understand an "infinite quantity", it will stay infinite even if
> one adds n, or subtracts n, or multiplies by n, or divides it by n <>
> 0...

Which infinity? The countable infinity of the number of integers, the
infinitely larger than that infinity of the number of points on a
line, the infinitely larger than that infinity of the number of
functions passing through a given point... read Cantor.

> I am told by science that "the universe is estimated to contain 10^80
> particles." This is a big number, for sure, but a far cry from an
> infinite number of particles. It seems to me that if we subtract 10^80
> from an infinity of particles, the remaining number of particles would
> still be infinite... So, if the "original singularity" indeed had
> infinite mass, what in the "big bang" made it finite, suddenly? And
> does not the same question equally apply to density, temperature, and
> pressure?

What makes you think you can see the whole Big Bang? Not after cosmic
inflation! An infinity given an infinitesimal fraction can have a
finite residue. Renormalization in quantum theory cancels an infinite
number of infinities every day six times before breakfast. The
residual is accurate to 14 significant figures, calculation vs.
observation.

> A related question is, if something has infinite density, how can
> there be room for its constituent particles to freely move around (as
> in temperature)? How can something with infinite density be infinitely
> hot?

Infinte mass in infinite volume can be a finite *external* density.
Nobody gets to look under an event horizon and tell about it.

> Another related question is: if a "singularity" shows up in an
> equation (as is claimed to happen in some of Einstein's equations), is
> this not a sure sign that something in the equation is wrong? Like
> dividing by zero, somewhere?

Do you have a problem with y = sin(1/x)? It is perfectly well behaved
except for *one* point in the big infinity of the number of points on
a line.

Do you have a problem with y = tan(x)? Try it for x= 90 degrees. It
is perfectly well behaved except for *two* points in the big infinity
of the number of points on a circle.

> As I am neither a mathematician nor a physicist, it may well be that
> I've got the concept of "infinity" wrong. I would really appreciate it
> if someone in this forum can point out to me where my understanding is
> wrong (and provide correct interpretations of the term)!

Which infinity? Aleph_zero, Aleph_1, Aleph_2... Your answer cannot
be any better than your question. Questions are important. Asnwers
merely require grinding, observation, and imagination (but we have
management to end that).

> References to published papers (accessible on line), especially papers
> showing what the "Einstein Singularities" are, would be very much
> appreciated!

Google

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
From: Robert Israel on 15 Mar 2010 12:50

> On Mon, 15 Mar 2010 00:34:15 -0700 (PDT), MicroTech
> <henry.ko.norman(a)gmail.com> wrote:
>
> >In physics (and cosmology) I quite often see references to
> >"singularities" (as inside "black holes" and as the origin of the so
> >called "big bang") as being "points with no size, of infinite mass,
> >infinite density, infinite temperature, and infinite pressure" (or
> >something to this effect).
>
> Are you sure you've seen a description that includes infinite _mass_?
> I tend to doubt it.
>
> >As I understand an "infinite quantity", it will stay infinite even if
> >one adds n, or subtracts n, or multiplies by n, or divides it by n <>
> >0...
> >
> >I am told by science that "the universe is estimated to contain 10^80
> >particles." This is a big number, for sure, but a far cry from an
> >infinite number of particles. It seems to me that if we subtract 10^80
> >from an infinity of particles, the remaining number of particles would
> >still be infinite... So, if the "original singularity" indeed had
> >infinite mass, what in the "big bang" made it finite, suddenly?
>
> I don't believe that the big bang is supposed to involve infinite
> mass, in the standard story.

If the universe is infinite (and homogeneous on a large scale), the total mass
would indeed be infinite. The 10^80 particles might refer to the finite
part of the universe that we can observe, not the whole thing. Or it might
refer to a "closed" model where the universe is finite.

> >A related question is, if something has infinite density, how can
> >there be room for its constituent particles to freely move around (as
> >in temperature)? How can something with infinite density be infinitely
> >hot?

The infinite density, temperature and pressure occur in the limit as you
approach the singularity. There is no "moving around" at the singularity
itself, which is just a single point.


> >Another related question is: if a "singularity" shows up in an
> >equation (as is claimed to happen in some of Einstein's equations), is
> >this not a sure sign that something in the equation is wrong? Like
> >dividing by zero, somewhere?

It could be. In a typical "real-world" application involving ordinary matter,
you never actually get to a singularity because something breaks
(and thus the assumptions underlying the model become invalid) as you approach
it. For a space-time singularity, we don't really know for sure
what happens as you approach it. For sure, quantum effects will become
important, but we don't have a satisfactory theory of quantum
gravity.

> >As I am neither a mathematician nor a physicist, it may well be that
> >I've got the concept of "infinity" wrong. I would really appreciate it
> >if someone in this forum can point out to me where my understanding is
> >wrong (and provide correct interpretations of the term)!
> >
> >References to published papers (accessible on line), especially papers
> >showing what the "Einstein Singularities" are, would be very much
> >appreciated!
> >
> >Henry Norman
>
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
From: PD on 15 Mar 2010 13:05
On Mar 15, 2:34 am, MicroTech <henry.ko.nor...(a)gmail.com> wrote:
> In physics (and cosmology) I quite often see references to
> "singularities" (as inside "black holes" and as the origin of the so
> called "big bang") as being "points with no size, of infinite mass,
> infinite density, infinite temperature, and infinite pressure" (or
> something to this effect).
>
> As I understand an "infinite quantity", it will stay infinite even if
> one adds n, or subtracts n, or multiplies by n, or divides it by n <>
> 0...
>
> I am told by science that "the universe is estimated to contain 10^80
> particles." This is a big number, for sure, but a far cry from an
> infinite number of particles. It seems to me that if we subtract 10^80
> from an infinity of particles, the remaining number of particles would
> still be infinite... So, if the "original singularity" indeed had
> infinite mass, what in the "big bang" made it finite, suddenly? And
> does not the same question equally apply to density, temperature, and
> pressure?
>
> A related question is, if something has infinite density, how can
> there be room for its constituent particles to freely move around (as
> in temperature)? How can something with infinite density be infinitely
> hot?

One needs to be careful about thinking about it as a hot gas all the
way down. It's not, and there are phase transitions (which in an
ordinary substance would be vaguely like iron gas turning to iron
liquid turning to iron solid) as the density increases.

>
> Another related question is: if a "singularity" shows up in an
> equation (as is claimed to happen in some of Einstein's equations), is
> this not a sure sign that something in the equation is wrong? Like
> dividing by zero, somewhere?

Maybe, maybe not. The evolution to a singularity is officially an
extrapolation beyond where we have any claim of knowledge. What we can
say is "We don't know of anything that would prevent the collapse to a
singularity." But we also know that the theory that projects that
collapse has to break down before the collapse. So officially we don't
know what happens past a certain point.

>
> As I am neither a mathematician nor a physicist, it may well be that
> I've got the concept of "infinity" wrong. I would really appreciate it
> if someone in this forum can point out to me where my understanding is
> wrong (and provide correct interpretations of the term)!
>
> References to published papers (accessible on line), especially papers
> showing what the "Einstein Singularities" are, would be very much
> appreciated!
>
> Henry Norman

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