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"Rich" <[EMAIL PROTECTED]> wrote in message
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Alfred A. Aburto Jr. replied:
"Rich" <[EMAIL PROTECTED]> wrote in message
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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?
This is not an infinity in nature Alfred. Let me translate it for you, if something takes infinite time to happen, it never happens. Rather than showing an infinity, you've shown something that can never happen. Your singularity can never happen.
> never get there ...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
You'll never get 'where'? You still refer to infinity as if it were a number.
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 ...
It's an equation, what you are talking about is a real physical object, which by the very physics that created it can never happen. Don't confuse the map and the territory.
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
Yes, math, which is not the real world. Nothing in the real world is infinite.
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).
There are several alternatives that make sense logically and mathametically, you need to look into hyperbolic and elliptical universes. As to whether the universe is finite or infinite, no one knows, and no one can know as we can see only so far out (for very physical reasons).
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.
And I keep asking you to prove it but you've not yet come up with any of these many infinities you claim are the basis of physics and nature.
It is an integral part of mathematics and mathematics is how we describe our universe.
> I can't wait! It should be mind blowing. Here's the show's web site:
> http://www.pbs.org/wgbh/nova/elegant/ If you have been following recent threads in sci.physics.research you
know how interesting the program could be. String theory is in
crisis. It has infinite solutions both physical and (mostly)
non-physical. It has no unique empirically testable predictions.
Anything this complex and useless is usually called "economics." Galileo traded his personal freedom to insist on experimentation
overruling theory. We have expertly gotten away from that, and are
paying the exhorbitant price of erecting huge empty cathedrals to the
great god of least publishable unit theory (probably Sterculius).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 ...
That you cannot imagine it no more creates an infinity than it creates ET.
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 ...
Very little in the real world is accurate to 10 significant digits. And you again confuse artifacts of the method of solution for infinities IRL.
The integral is related to Gaussian functions and physically it could be the power in Gaussian noise for example.
As I said, it's an artifact of the method of solution, not the real world itself.
There are many many examples like this in math and physics...
http://groups.google.com/groups?q=problem+of+infinities+in+physics&hl=en&lr=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
&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 */
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