Is renormalization in quantum field theory a valid approach?

[oldunion]

I had a dream this morning about a Stargate type device, and i remembered that a singularity is infinity. And i got to thinking that a black hole is supposed to be a singularity.

So is a black hole a physics representation of infinity? and what does that mean?

 

[marcus]

...
So is a black hole a physics representation of infinity? and what does that mean?

the old model of BH had an infinity, which meant there was a mistake in the theory---it broke down and would not compute, or would compute nonsense like infinite density, curvature etc.

that was fixed last year, the new models of black holes do not have infinities, they still being worked on

here are some names of people who have written research papers about this, mostly this year and last year

Abhay Ashtekar, Viqar Husain, Oliver Winkler, Leonardo Modesto, Martin Bojowald, Roy Maartens, Rituparno Goswami, Parampreet Singh,

It is an active area of research (getting rid of the singularity and figuring out what really might be there instead of the infinities)

Here are some recent research papers about the improved models of BH
that don't break down and make infinities (i.e. compute nonsense)

http://arxiv.org/abs/gr-qc/0504029
http://arxiv.org/abs/gr-qc/0503041
http://arxiv.org/abs/gr-qc/0504043
http://arxiv.org/abs/gr-qc/0411032
http://arxiv.org/abs/gr-qc/0407097
http://arxiv.org/abs/gr-qc/0412039
http://arxiv.org/abs/gr-qc/0410125

 

[oldunion]

if the singularity was an error in the equations of black holes, is it not logical to make the relation that infinity in mathematics is also an error?

 

[SpaceTiger]

if the singularity was an error in the equations of black holes, is it not logical to make the relation that infinity in mathematics is also an error?

Mathematical relationships and definitions are developed independent of physics. There is no need to make one-to-one compatible. Besides, we're not even sure that infinities can't exist in nature, it's just an assumption.

 

[The Bob]

An interesting thought would be that as the idea was fixed a year ago, is Penrose still right on the Big Bang being the opposite of a singularity? If the definition has changed then what he was working on must have changed as well.

The Bob (2004 ©)

 

[turbo]

Mathematical relationships and definitions are developed independent of physics. There is no need to make one-to-one compatible. Besides, we're not even sure that infinities can't exist in nature, it's just an assumption.

True. Infinities abound in mathematics, but may be restricted in the physical universe. We can define an infinite number of values lying between the integers zero and one. The intersection between imaginary and real numbers (as exemplified by fractals such as the Mandelbrot set) is mind-boggling. And these are very limited mathematical domains. There are of course a LOT more ways that infinities can be expressed in mathematics.

It is harder to conceptualize infinities in our physical universe, that does not mean that we can easily discount their existence. Infinities confront quantum physicists every day, which is why renormalization is a popular tool.

 

[marcus]

... If the definition has changed then what he was working on must have changed as well.
...

unless what he was working on was ahead of the current research, and the papers that I gave links to are just catching up with Penrose's thinking.

do you have an online quote from Penrose talking about what you mention?
or do you have any online article by Penrose discussing this?

the papers I gave links to are nuts-and-bolts type that go slowly along equation by equation----more patient calculation
it would be easy for Penrose, using speculation and vision, to get out ahead of rigorous slow progress.

the trouble is I cannot tell what you are referring to that Penrose was talking about! I can only guess and that is not good enough for me to be able to answer.

BTW here is an hour talk by Penrose, given recently at penn state.
the audio and slides are online (also video if you can make it work)

http://www.phys.psu.edu/events/index.html?event_id=1122;event_type_ids=0;span=2004-12-26.2005-05-31

this was a talk given 29 April 2005, just about a week ago

 

[Chronos]

.. Infinities confront quantum physicists every day, which is why renormalization is a popular tool.

Why do you say that? Renormalization is not a bit popular, but it works... in a MOND sort of way. No physicist I know has ever been happy with renormalization.

 

[turbo]

Why do you say that? Renormalization is not a bit popular, but it works... in a MOND sort of way. No physicist I know has ever been happy with renormalization.

Popular as in "widely used and accepted", not as in "beloved".

 

[Chronos]

Agreed. I merely wished to raise the point that renormalization, while effective, is not mathematically sound.

 

[selfAdjoint]

Agreed. I merely wished to raise the point that renormalization, while effective, is not mathematically sound.

IMHO this is an urban myth. Can you supply mathematical argument, and not just people's unsupported opinions, for it?

 

[The Bob]

do you have an online quote from Penrose talking about what you mention?
or do you have any online article by Penrose discussing this?

This is where I may look a fool. I got the information from a TV documentary on Stephen Hawking. It was very, very simplistic as it was for anyone to watch. It showed Hawking running off a train to say 'The big band was a singularity in reverse' (bascially). This is what I am basing it on which as you can see is feable. However, if Penrose did use an infintie singularity and we now use a finite singularity, then there maybe some change in theroy. It is still feable though. I do apologise.

The Bob (2004 ©)

 

[Hurkyl]

IMHO this is an urban myth.

I think it's more historical than mythical: there wasn't a fully rigorous justification when the technique was discovered. (But that has changed!)

 

[turbo]

I think it's more historical than mythical: there wasn't a fully rigorous justification when the technique was discovered. (But that has changed!)

Feynman, who helped invent renormalization, at times called it "dippy", "a scandal", "a shell game", and lots of other disparaging things. He was frustrated with the fact that we have to resort to such tricks to get reasonable results from quantum field theory.

Feynman's outlook was very similar to that of Stevie Wonder - "If you believe in things that you don't understand, you will suffer. Superstition ain't the way." The fact that Richard Feynman was never comfortable with renormalization does not significantly detract from it's usefulness in quantum calculations, but it speaks volumes about his loathing of ad hoc answers that appear without underlying reasons.

 

[Chronos]

IMHO this is an urban myth. Can you supply mathematical argument, and not just people's unsupported opinions, for it?

That is a very fair request. Give me a few days to do the math. I admire your insights.

 

[Spin_Network]

This is where I may look a fool. I got the information from a TV documentary on Stephen Hawking. It was very, very simplistic as it was for anyone to watch. It showed Hawking running off a train to say 'The big band was a singularity in reverse' (bascially). This is what I am basing it on which as you can see is feable. However, if Penrose did use an infintie singularity and we now use a finite singularity, then there maybe some change in theroy. It is still feable though. I do apologise.

The Bob (2004 ©)

I believe you may be 'mixing' a line of thought by Penrose, with one of Hawking?

Penrose was instrumental in guiding Hawking's early theory of Singularities(the platform quote in the documentary).

But it is well known that Penrose had developed "information extraction" for Blackhole Singularities, he had suggested that you could extract more information from a Blackhole (thus a Galactic Singularity), than gets inputed to a Blackhole.

The recent Information Paradox has Hawking stating he was wrong about Singularities( 2004 conference in Eire)..but reallistically, he was really commenting on a Penrose early line of thought, one that Penrose had been contemplating long before Hawking Thesis of the early Seventies?

 

[The Bob]

I believe you may be 'mixing' a line of thought by Penrose, with one of Hawking?

Fair enough. Cheers.

The Bob (2004 ©)

 

[Chronos]

Having revisited renormalization, it appears group theory has put some distance between renormalization and the realm of the purely ad hoc. There is no denying it works. I have some discomfort with the approach and I don't think I'm alone. But it is also safe to say no one has come up with a better approach. The main issue is the apparent arbitrariness in choosing which solutions to ignore. The risk of missing a solution that does turn out to be meaningful appears unavoidable. Of course you can always come back and revisit these solutions if need be, but that seems a rather haphazard way of doing science. The history of this controversy is interesting in itself. Bear with me if some of these references are dated and the questions raised have since been satisfactorily answered.

First, by Popper: Moreover, the situation is unsatisfactory even within electrodynamics, is spite of its predictive successes. For the theory, as it stands, is not a deductive system. It is, rather, something between a deductive system and a collection of calculating procedures of somewhat ad hoc character. I have in mind, especially, the so-called 'method of renormalization': at present, it involves the replacement of an expression of the form 'lim log x - lim log y' by the expression 'lim (log x - log y)'; a replacement for which no better justification is offered than that the former expression turns out to be equal to - and therefore to be indeterminate, while the latter expression leads to excellent results (especially in the calculation of the so-called Lamb-Retherford shift). It should be possible, I think, either to find a theoretical justification for the replacement or else to replace the physical idea of renormalization by another physical idea - one that allows us to avoid these indeterminate expressions. (Karl Popper: Quantum Theory and the Schism in Physics).

By Sachs:The well known trouble with RQFT [Relativistic Quantum Field Theory] is that when its formal expression is examined for its solutions, it is found that it does not have any! This is because of infinities that are automatically generated in this formulation. After this failure of the quantum theory was discovered, renormalization computational techniques were invented that provide a recipe for subtracting away the infinities and thereby generating finite predictions--some which had amazing empirical success. But the trouble is that a) such a scheme is not demonstrably mathematically consistent (implying that, in principle, any number of predictions could come from the same physical situations, though one of them is empirically correct) and b) there still remains the problem that there are no finite solutions for the problem.(http://www.compukol.com/mendel/)

By Penrose:A popular approach to quantum field theory is via 'path integrals', which involve forming quantum linear superpositions not just of different particle states (as with ordinary wave functions), but of entire space-time histories of physical behaviour (see Feynman 1985, for a popular account). However, this approach has additional infinities of its own, and one makes sense of it only via the introduction of various 'mathematical tricks'. Despite the undoubted power and impressive accuracy of quantum field theory (in those few cases where the theory can be fully carried through), one is left with a feeling that deeper understandings are needed before one can be confident of any 'picture of physical reality' that it may seem to lead to.(Roger Penrose: The Emperor's New Mind).

By Davies: ...it may be assumed that the theory will last. Nevertheless, the presence of the infinite quantities which are formally removed by the renormalisation procedure is worrying. (Paul Davies: Superforce: The Search for a Grand Unified Theory of Nature).

By Feyerabend: This procedure [renormalization] consists in crossing out the results of certain calculations and replacing them by a description of what is actually observed. (http://en.wikipedia.org/wiki/Paul_Feyerabend)

And of course the famous one by Feynman: But no matter how clever theword, it is what I call a dippy process! Having to resort to such hocus pocus hasprevented us from proving that the theory of quantum electrodynamics is mathematically self consistent. I suspect that renormalization is not mathematically legitimate.
http://www.quantummatter.com/documents/Einstein-WebPage.pdf.

And one by the somewhat obscure Hanson: When he is absorbed in high-energy problems the scientist must renormalize his equations in order to continue with his physics at all, but the consequences may be more costly than the gain. Before renormalization, he assumed, let us say, that a certain volume of space contained a number of particles, and the physical problem was to discover the probabilities that these particles would have certain positions, velocities or densities. But the mathematical form in which he describes his experiment is altered by renormalization, and altered in such a way that he can no longer assume that there really are any actual particles within the volume he is considering . . . since the equations are applicable either way, particle or not. The physicist's probability determinations then become shadowy references to the 'ghost states of particles', the references themselves are called 'negative probabilities'; and it is difficult to attach any real physical sense to these expressions. (N.R. Hanson: Quanta and Reality).

I do not think group theory puts to rest all of these past criticisms.