Re: Infinities in Physics: was-> Re: OT: Universe Born in Black Hole Explosion?

>"Rich" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
>
>
> Alfred A. Aburto Jr. replied:
> >>"Rich" <[EMAIL PROTECTED]> wrote in message
> >
> > news:[EMAIL PROTECTED]
> >
> >>Alfred A. Aburto Jr. replied:
> >>
> >>[ grind, hack, delete delete delete, renormalize ]
> >>
> >> > You're right Mike. Infinities, division by zero (the essence of a
Black
> >
> > Hole
> >
> >> > --- 1/r^2 where r goes to 0) are found throughout physics and our
> >> > description of nature ...
> >>
> >>Really? Show me an example.
> >
> >
> > See above. Black holes where the mass of an object is so large that
nothing
> > can stop it from collapsing to a "point" (a "singularity" the 1/r^2 -->
oo
> > as r --> 0). The object basically disappears from our universe and all
we
> > can tell about it is the effects of its gravity (so we know it is there
and
> > can "feel" it or measure its gravity) and the effects of matter falling
into
> > and interacting with matter falling into the black hole. We can't know
> > infinity directly of course --- except in conceptual ways, but it is
real
> > and produces effects and consequences that we can observe ... it could
be
> > that "r" does not really ever get to zero, but we'll never know that
either.
> > Right? I would not voluntarily venture into a black hole to test this
theory
> > :-) ...
>
> Small problem there. Think GR and time dilation.
>
> http://casa.colorado.edu/~ajsh/schwp.html
>
> Gravitational slowing of time
>
> In general relativity, clocks at rest run slower inside a
> gravitational potential than outside.
>
> In the case of the Schwarzschild metric, the proper time, the actual
> time measured by an observer at rest at radius r, during an interval
> dt of universal time is (1 - rs/r)1/2 dt, which is less than the
> universal time interval dt. Thus a distant observer at rest will
> observe the clock of an observer at rest at radius r to run more
> slowly than the distant observer's own clock, by a factor
> ( 1 - rs / r )1/2 . This time dilation factor tends to zero as r
> approaches the Schwarzschild radius rs, which means that someone at
> the Schwarzschild radius will appear to freeze to a stop, as seen
> by anyone outside the Schwarzschild radius.
>
> As the gravitational field strength increases, time slows. It will
literally
> take forever for gravitational collapse to result in a singularity (if in
> fact this is what happens).

Isn't "forever" infinity?

>
> So you may have a black hole, and there are many candidates, but you
cannot
> show that any have yet collapsed into a singularity.

Yes, that is the point of infinities ... you'll never see it ... you'll
never get there ...
even when 1/r = 10^(100000) you are still a long ways from infinity ...
But often in physics when one, conceptually, mathematically, takes something
to the limit (let "n" go to infinity say in a series expansion) then there
is a residue
left that is observable and measurable.

>
> > Well, it could be that there are observational effects that one can
measure
> > that might indicate that "r" does not go to zero exactly, but so far
that
> > hasn't happened as far as I know ...
>
> Read up on GR, it has indeed happened.
>
> > scientists pretty much accept that
> > black holes are real and there are plenty of measurements and
observations
> > to support those ideas as oulined by Einstein's gravitational field
> > equations ...
>
> Which also state that for the collapse to reach r=0 will take an infinite
> amount of time. Ergo, no singularities yet, in fact, no singularities
ever.

1/r^2 as r--> 0 is a sigularity ...

>
> >> > Physicists are always doing things like "in the limit as epsilon goes
> >> > to zero or infinity this is what is left over" kind of thing that
describes
> >> > (attempts anyway) a specific phenomena of nature.
> >>
> >>You visions are interesting, but it is a fact that infinities that occur
are
> >>always the result of the mathametical method employed, and it is also a
fact
> >>that unless the infinities can be eliminated, you have no solution.
Infinity
> >>is an artifact, and a problem.
> >
> > But it is a very useful and necessary concept ...
>
> Odd then that no one has yet been able to show me a use for it. And
necessary
> in what way? Zero is useful and necessary. Infinity ain't either.
Everything we
> do today can be done without the concept of infinity. Everything we do
today
> *is* done without the concept of infinity. Drive over any bridge, you can
rest
> assured that the mechanical engineer calculated no infinite stresses, used
> a finite amount of materials that have finite strength and finite weight
and
> finite cost, and that no matter how well that bridge is designed and
built,
> it will last a finite length of time. No infinities anywhere, none needed
and
> none wanted.

It is only odd to you I think ... infinities are part of mathematics and
mathematics is the tool we use to try to understand and describe the
universe (which we take as infinite, because nothing else seems to
make sense philosophically).

>
> > I don't think I'd call infinity an artifact ...
>
> It is, in every case I know of, an artifact of the method of mathematical
> solution.

Still, despite what you say, it is not an artifact. It is an integral part
of
mathematics  and mathematics is how we describe our universe.

The universe may not be infinitely big or infinity small, but it is so much
beyond anything that I can imagine that it might as well be ... to me
the difference is trivial if there is no measurable or observable
difference between say something like 10^(-99) and zero or
10^(10^80) and infinity.

You're making a vaild point I think, but it is not worth alot of argument
...

>
> > I don't see infinity as necessarily a problem either ...
>
> OK, you've calculated that the new charmed_one quark will have infinite
> mass. Now tell me how you're gonna create one. The real world has no
> infinities in it. Any real world solution to any real world problem *must*
> unconditionally be finite. If you're answer is infinite, it's wrong on
> the face of it. Cantor had fun playing with symbol sets, but it has no
> practical applications.

I think the universe must be infinite in size for example, but, true, I
cannot
prove this ...

Mathematics and infinities are very useful ... here is an example:

integral[ 0 to +infinity] of x^2*exp(-x^2) dx = SQRT(pi) / 4 ...
This is very interestingl result I think, but still in building a space
ship communication device for example I might just use
0.443113462 instead of SQRT(pi)/4 ...

The integral is related to Gaussian functions and physically it could be the
power in Gaussian noise for example.

There are many many examples like this in math and physics...

>
> You claim that infinities "are found throughout physics and our
description
> of nature", you've yet to show even one example. What you do show is an
> incomplete understanding of nature.
>
> Rich
>
>
> >
http://groups.google.com/groups?q=problem+of+infinities+in+physics&hl=en&lr=
> >
&ie=UTF-8&oe=UTF-8&selm=pecora-070794121039%40lou-pecora.nrl.navy.mil&rnum=4
> >
> >>From: Louis M. Pecora ([EMAIL PROTECTED])
> >>Subject: Re: The outstanding problem in mathematical physics
> >>Newsgroups: sci.math.research
> >>Date: 1994-07-07 10:01:23 PST
> >>
> >>In article <[EMAIL PROTECTED]>,
> >><[EMAIL PROTECTED]> wrote:
> >>
> >>
> >>>i think the outstanding problem in mathematical physics is how we deal
> >>>with infinities. so far, we have developed renormalization/
> >>>regularization theory to deal with infinities which arise in field
> >>>theory. unfortunately, we can do this only in the context of
> >>>pertrubation theory , an asymptotic expansion of interacting fields
> >>>and their matrix elements in terms of teh free in/out fields and THEIR
> >>>matrix elements. but outside the region of applicability of pert. th.
> >>>we don't know too well what to do. related to this  attempt to go
> >>>beyond pert. th is an approach i learned about recently, non-standard
> >>>analysis. it seems like it might be a promissing approach and am
> >>>wondering what people know about its applications ot field theory.
> >>>so far i have looked at rather old books by a. robinson on nsa, w.
> >>>luxemburg's lecture notes as well as an article by farrukh on jmp
> >>>1983. is there anything else people know about ?
> >>>take care/shalom
> >>>ovid
> >>
> >>I messed around with nonstandard analysis some years ago (even published
> >>a paper in J.Math.Phys. -- not worth much, IMHO). It is a neat system of
> >>analysis. I found myself liking it because the thinking it requires
> >>seems more natural than delta-epsilon stuff. However, I came away with
> >>the opinion that although it is a good tool, it will *not* automatically
> >>give answers to mathematical problems plagued by infinities. It may
> >>facilitate the solution, but hard work will still be needed. I vaguely
> >>recall some early work on infinity problem in Q.Field Theory, but I
> >>can't recall the exact references. Unfortunately, I haven't kept up with
> >>applications of nonstandard analysis. If you (or anyone) finds anything
> >>in the physics/nonlinear dynamics areas, I would be interested.
> >>
> >>As for the actual problem of perturbations and infinities, I suspect
> >>that the infinities are more a sign of perturbation failure. The
> >>problems are, after all, nonlinear. A bigger challenge is to tackle
> >>those problems without perturbation. That's a tough assignment, but at
> >>the beginning of this thread someone asked for BIG problems in math.
> >>physics. There's one.
> >>
> >>--
> >>Lou Pecora
> >>code 6341
> >>Naval Research Lab
> >>Washington, DC  20375
> >>[EMAIL PROTECTED]
> >>/* My comments are my own and do not represent the views of the Navy */
>
>
>