# Alternatives to QFT

by waterfall
Tags: alternatives
 Sci Advisor P: 4,375 Here is my (very very rough) estimate. Assume that there are 1000 scientists in the world working on string theory. If each costs 100.000 $per year, this gives 100 millions$ per year. Applying this number to the last 20 years gives 2 billions $. If half of that money is payed by USA, then it is 1 billion$ in last 20 years payed by USA.
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 Quote by waterfall To people familiar with QFT. You know quantum fields are non-interacting and they use perturbations methods. Is there other studies or programme that would replace conventional QFT with full fledged interacting quantum fields?
Some progress has been made in doing QFT non perturbatively and even in developing a completely mathematically rigorous version similar to what Von Neumann did for QM - but the mathematical difficulty is very formidable. In such a formulation it may be possible to solve stuff non perturbatively. That is not to say QFT is wrong - its just that mathematicians and physicists have different standard of rigour.

 Quote by waterfall Also about Second Quantization where they treat the Klein-Gorden and Dirac equations acting like classical equations like Maxwell Equations and quantize them to create field quantas such as matter or fermionic fields. Is there any studies or programme about alternative to this? Or are you certain 100% that Second Quantization is fully correct?
In normal quantum mechanics time and space are treated differently - time is a parameter - spaces is an observable. In a relativistic theory you really need to treat them on equal footing. QFT makes position a parameter so you deal with fields - the other approach of making time an observable evidently was tried - and failed - even though a textbook I have says it worked - people on this forum who know more than I do said it in fact failed.

 Quote by waterfall And if QFT being not yet perfect due to the non-interacting fields for example. Why are physicists convinced they an arrive at the Theory Of Everything when the foundations are faulty... or maybe they are just contended for now to arrive at Quantum Gravity? And can one even reach it with a possibily faulty QFT foundations? Maybe there is no theory of quantum gravity precisely because QFT is faulty? How possible is this?
To the best of my knowledge QFT is not faulty.

Thanks
Bill
P: 381
 Quote by bhobba Some progress has been made in doing QFT non perturbatively and even in developing a completely mathematically rigorous version similar to what Von Neumann did for QM - but the mathematical difficulty is very formidable. In such a formulation it may be possible to solve stuff non perturbatively. That is not to say QFT is wrong - its just that mathematicians and physicists have different standard of rigour. In normal quantum mechanics time and space are treated differently - time is a parameter - spaces is an observable. In a relativistic theory you really need to treat them on equal footing. QFT makes position a parameter so you deal with fields - the other approach of making time an observable evidently was tried - and failed - even though a textbook I have says it worked - people on this forum who know more than I do said it in fact failed. To the best of my knowledge QFT is not faulty. Thanks Bill
Your post reminds me of this unanswered distinction between time as parameter in non-relativistic QM vs coordinate thing in relativistic QFT and others treating parameter and coordinate as having same meanign so I wrote a thread in the relativity forum for this unresolved question http://www.physicsforums.com/showthr...52#post3777052
P: 381
 Quote by atyy The big problem is gravity which is perturbatively not UV renormalizable. The Wilson-Kadanoff picture of renormalization as a way of seeing how a theory looks like at low energies points to two different approaches. The first is that the theory is incomplete, and new degrees of freedom enter - this is the approach of string theory. The second is that the theory could be UV complete if the renormalization flow is non-perturbatively reversed to high energies - this approach is called Asymptotic Safety.
I'm trying to find the connection between Renormalization Group and the Final Theory that can explain the RG being based on effective field theory. The above doesn't mention about Loop Quantum Gravity, just string theory and Asymptotic Safety. If Loop Quantum Gravity were proven to approximate classical GR. Won't it explain or complete why the Renormalization Group is only an effective field theory.. I wonder why you didn't include LQG above.
 Sci Advisor P: 1,637 I realize that certain people on this forum have a tendency to get ahead of themselves, but I really don't think its ok to throw technical words together willy nilly if you don't understand what they mean. The renormalization group is not an 'effective field theory'. It's not really a group at all! Its a set of partial differential equations (technically 'flow' equations) that explains the scaling behaviour of certain quantities in quantum field theory. More to the point.. Before you can understand advanced topics like string theory, quantum gravity, and so forth, it really behooves posters to first learn some modicum of basic physics first! I assure you, none of the advanced material can possibly make sense unless you get the logic, ideas and preferably the mathematics of the introductory material first.
P: 407
 Quote by Haelfix Before you can understand advanced topics like string theory, quantum gravity, and so forth, it really behooves posters to first learn some modicum of basic physics first!
Absolutely so, I was about saying this too. And I mean real textbooks, written by actual scientists, not books like Not Even Wrong. I see from the kind of questions being asked here, that some minds some completely corrupted by this kind of books, probably confused beyond repair! Sorry to say that.
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Quote by waterfall
 Quote by atyy The big problem is gravity which is perturbatively not UV renormalizable. The Wilson-Kadanoff picture of renormalization as a way of seeing how a theory looks like at low energies points to two different approaches. The first is that the theory is incomplete, and new degrees of freedom enter - this is the approach of string theory. The second is that the theory could be UV complete if the renormalization flow is non-perturbatively reversed to high energies - this approach is called Asymptotic Safety.
I'm trying to find the connection between Renormalization Group and the Final Theory that can explain the RG being based on effective field theory. The above doesn't mention about Loop Quantum Gravity, just string theory and Asymptotic Safety. If Loop Quantum Gravity were proven to approximate classical GR. Won't it explain or complete why the Renormalization Group is only an effective field theory.. I wonder why you didn't include LQG above.
Waterfall, I'm glad to see your friend Bill Hobba has joined us. He seems experienced careful and well-informed. Belated welcome, Bill!

I think I see what you are driving at (the unaccustomed use of some technical terms doesn't bother me in this case as long as the intuition comes thru.) I think there is a kernel of insight.

The RG-based approach (Asym. Safety) might be limited in its ability to resolve certain classical singularities and nevertheless it might be nearly right---effectively right within certain limits.

Let's imagine, just for the sake of illustration, that AS works as long as the underlying manifold which it requires is not going to develop singularities or defects---a topological condition. AS requires you to set out some prior metric on the smooth manifold you plan to be working with, for starters, so that scale can be defined in the first place. then it has some key numbers change with scale and run to a happy conclusion. But in its present form AS seems to be having trouble resolving the big bang singularity.

We can't use the word "effective" because that word is owned by people who do conventional perturbation theory--a type of math where you have a long series of numbers describing a blip on a flat background, and stuff like that. Each number is calculated according to its own elaborate formula and a theory is "effective" if you can just consider the low energy terms and it works OK.

We don't want to offend these gentlemen, so we need a new word like, say, "quasi-excellent" to describe what Asymptotic Safety might achieve. It might be effectively successful as a basis for quantizing gravity EXCEPT for not resolving the big bang singularity.

Because of the breakdown of conventional topology itself or some damn reason like that, so what's a poor theory supposed to do? if it's defined on a smooth manifold model continuum. It is effectively right except it doesnt quite make it where the basic topological or else smoothness assumption breaks down. So we call it "quasi-excellent"

I'm only half serious here, trying to imagine what you are driving at, by attempting a speculative illustration of what might be.

So then you say (to generalize a bit) suppose SOME quantum theory of geometry, Loop or some other, turns out to reproduce Gen Rel.

Then (I hear you reasoning) since Gen Rel is asymptotically safe, then that QG theory, Loop say, must be asymptotically safe. So it would be not only quasi-excellent, it would also resolve the singularity, so it would be fully excellent. It would complete the picture, geometry-wise.

And then you'd have to see if you could build satisfactory matter-fields on it.

It could be very convenient if Loop or some such QG turned out to underly and complete AS, then one could use AS, which is continuum-based and has a conventional manifold, all the way back in time to very near start of expansion and then seamlessly shift theoretical gears and continue on. But that's just speculation. People are only just getting started implementing RG-type stuff in Loop. Maybe some other related QG (like Oriti GFT or Livine's approach) is farther along. I dont have a complete picture, by far.

One extremely nice thing is the recent Cai Easson paper indicating that AS could give inflation "for free" just by the running of the couplings and without a made-up "inflaton" field having to be added on and finetuned. This is the nicest thing I've seen this year. Maybe someone will tell me why it doesn't work.
To me this makes it seem almost imperative that Loop should embrace and encompass AS, to acquire that yummy feature.

Anyway waterfall, I see sense in your post, rebounding off of the Atyy post you copied. IMO there's a valuable kernel of insight.
P: 381
 Quote by Haelfix I realize that certain people on this forum have a tendency to get ahead of themselves, but I really don't think its ok to throw technical words together willy nilly if you don't understand what they mean. The renormalization group is not an 'effective field theory'. It's not really a group at all! Its a set of partial differential equations (technically 'flow' equations) that explains the scaling behaviour of certain quantities in quantum field theory.
Lol.. of course I know that. My post is in the context of the thread we were discussing in
http://www.physicsforums.com/showthr...=579379&page=2 where science advisor atyy (in message #20) replied:

"Renormalization has nothing to do with infinities. QED is renormalizable and it has a cut-off - it is not a true theory valide at all energies, it is only an effective theory like gravity, valid below the Planck scale. Once you have a cut-off, there are no infinities. Sometimes you are lucky and you get a theory where you can remove the cut-off, like QCD. But in QED, as far as we know, the cut-off probably cannot be removed."

 More to the point.. Before you can understand advanced topics like string theory, quantum gravity, and so forth, it really behooves posters to first learn some modicum of basic physics first! I assure you, none of the advanced material can possibly make sense unless you get the logic, ideas and preferably the mathematics of the introductory material first.
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 Quote by marcus Waterfall, I'm glad to see your friend Bill Hobba has joined us. He seems experienced careful and well-informed. Belated welcome, Bill!
Ah shucks. Thanks of course. But do rememberer I am not a physicist - my background is applied math - my interest is in Mathematical Physics and understanding what the equations are telling us rather than in solving actual problems.

Anyway I did join this thread later because I only just saw the message asking me to contribute so I want to get a bit of a feel for those issues people are concerned about before saying anything else.

Thanks
Bill
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 Quote by waterfall "Renormalization has nothing to do with infinities. QED is renormalizable and it has a cut-off - it is not a true theory valide at all energies, it is only an effective theory like gravity, valid below the Planck scale. Once you have a cut-off, there are no infinities. Sometimes you are lucky and you get a theory where you can remove the cut-off, like QCD. But in QED, as far as we know, the cut-off probably cannot be removed."
That is true - with one caveat - I do not agree that re-normalisation has nothing to do with infinities - the purpose it was invented was how to handle the infinities that appeared in equations. I do agree however the effective field theory approach is the correct one, it removed the infinities and a theory based on that is perfectly OK. That is the purpose of the Re-normalisation Group - it tells how the troublesome parameters such as the coupling constant vary with scale and points to areas where new physics is likely to occur - taking a theory beyond that is a very unwise thing to do IMHO.

Also I am very glad to see gravity is mentioned as a quantum theory. Too many people believe gravity has problems with Quantum Theory - that is false - if you impose a cut-off about the plank scale it is a perfectly valid quantum theory - its no different than QED.

http://arxiv.org/pdf/gr-qc/9512024v1.pdf
The conventional wisdom is that general relativity and quantum mechanics
are presently incompatible. Of the “four fundamental forces” gravity is said
to be diﬀerent because a quantum version of the theory does not exist. We feel
less satisﬁed with the theory of gravity and exclude it from being recognized
as a full member of the Standard Model. Part of the trouble is that we
have tried to unnaturally force gravity into the mold of renormalizable ﬁeld
theories. In the old way of thinking, only the class of renormalizable ﬁeld
theories were considered workable quantum theories. For this reason, general
relativity was considered a failure as a quantum ﬁeld theory. However we
now think diﬀerently about renormalizability. So-called non-renormalizable
theories can be renormalized if treated in a general enough framework, and
they are not inconsistent with quantum mechanics[1]. In the framework of
eﬀective ﬁeld theories[2], the eﬀects of quantum physics can be analyzed
and reliable predictions can be made. We will see that in this regard the
conventional wisdom about gravity is not correct; quantum predictions can

Thanks
Bill
P: 381
 Quote by bhobba Ah shucks. Thanks of course. But do rememberer I am not a physicist - my background is applied math - my interest is in Mathematical Physics and understanding what the equations are telling us rather than in solving actual problems. Anyway I did join this thread later because I only just saw the message asking me to contribute so I want to get a bit of a feel for those issues people are concerned about before saying anything else. Thanks Bill
I learnt string theory at sci.physics and in the following you wrote in 2007 when someone asked:

> But in string theory, spacetime still has curvature.

You (Bill) replied: "No it doesn't. It emerges as a limit - but the underlying geometry of space-time - if it has one - is not known."

This statement has perplexed me for 5 years already. I didn't have the chance to ask you there because you no longer participate there. But what do you mean by that. I know that the spin-2 field + flat spacetime can be equal to curved spacetime in what atyy mentioned as described by harmonic coordinates. But in convensional string theory, they assume spacetime has curvature and the gravitons just quantized modes of it. So you are assuming the spin-2 field + flat spacetime as being more primary? or just alternative way of thinking it. If alternative, then you can't say spacetime has no curvature.

Second, you said the underlying geometry of space-time - if it has one, is not known. I assume you were talking about spacetime inside the planck scale. But isn't it that the spacetime inside the planck scale are those 6 dimensional compactified dimensions? So what do you mean it is unknown? Hope to get these things clear up after 5 long years of thinking it. Thanks.
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 Quote by waterfall I learnt string theory at sci.physics and in the following you wrote in 2007 when someone asked: http://groups.google.com/group/sci.p...known+strings# > But in string theory, spacetime still has curvature. You (Bill) replied: "No it doesn't. It emerges as a limit - but the underlying geometry of space-time - if it has one - is not known." This statement has perplexed me for 5 years already. I didn't have the chance to ask you there because you no longer participate there. But what do you mean by that. I know that the spin-2 field + flat spacetime can be equal to curved spacetime in what atyy mentioned as described by harmonic coordinates. But in convensional string theory, they assume spacetime has curvature and the gravitons just quantized modes of it. So you are assuming the spin-2 field + flat spacetime as being more primary? or just alternative way of thinking it. If alternative, then you can't say spacetime has no curvature. Second, you said the underlying geometry of space-time - if it has one, is not known. I assume you were talking about spacetime inside the planck scale. But isn't it that the spacetime inside the planck scale are those 6 dimensional compactified dimensions? So what do you mean it is unknown? Hope to get these things clear up after 5 long years of thinking it. Thanks.
I mostly participated in sci.physics.relativity when guys like Steve Carlip posted there but after a while the cranks took over so I departed. I occasionally go back there but it just seems to get worse and worse.

In string theory its about many more dimensions than we currently perceive - some are suspected to be curled up and the latest thinking seems to be the precise nature of that curling up determines the physics we see ie the standard model. What I probably was referring to is the emergence form that curling up.

Yes I was referring to the geometry and physics below the Plank scale is not known - it may not even be based on what we generally think of as geometry.

Thanks
Bill
P: 381
 Quote by bhobba I mostly participated in sci.physics.relativity when guys like Steve Carlip posted there but after a while the cranks took over so I departed. I occasionally go back there but it just seems to get worse and worse. In string theory its about many more dimensions than we currently perceive - some are suspected to be curled up and the latest thinking seems to be the precise nature of that curling up determines the physics we see ie the standard model. What I probably was referring to is the emergence form that curling up. Yes I was referring to the geometry and physics below the Plank scale is not known - it may not even be based on what we generally think of as geometry. Thanks Bill
But Calabi-Yau manifold inside planck scale is still geometry.

Also I think it's better to think string theory has spacetime curvature outside the planck scale. The alternative about using spin-2 field over flat spacetime is just an alternative. It doesn't have to be a priori.. unless you have reason to think it can be more primary than spacetime curvature?

At sci.physics.relativity, you were one of the few authorities, the others are crank up to now which is much worse so PF is the last and only sensible physics site. The following conversation may make you remember. From time to time, I read it again and again to get some perspective and didn't really understand it well. So please clear it up once and for all.

In the conversation when someone asked:

> You said that GR, with its geometrical interpretation, emerges as a
> limit. This means GR with spacetime curvature, emerges as a limit.
> But then you replied that "No it doesn't" to the statement "But in
> string theory, spacetime still has curvature.". So make up your mind.

You replied:

"I suggest you think a bit clearer. A membrane as a continuum and treated by the methods of continuum mechanics emerges as a limit from the atomic structure of an actual membrane - yet does not imply it is a continuum at the level of individual atoms. The same with GR. Gravity as space-time curvature emerges from spin two gravitons when the underlying geometrical background is not known, but usually assumed to be Minkowskian flat, so the methods on QFT theory can be applied."

Aren't you mixing two concepts above, one below and above the planck scale? This spin two gravitons thing causing spacetime curvature is outside the planck scale. Or are you saying the gravitons exist inside the planck scale and somehow it can cause spacetime curvature outside? This is also a question to others. Do gravitons exist inside or outside the planck scale?
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 Quote by waterfall Aren't you mixing two concepts above, one below and above the planck scale? This spin two gravitons thing causing spacetime curvature is outside the planck scale. Or are you saying the gravitons exist inside the planck scale and somehow it can cause spacetime curvature outside? This is also a question to others. Do gravitons exist inside or outside the planck scale?
Whats going on there is that the properties of spin 2 particles in the background of flat space-time all by themselves leads to GR with its space-time curvature. It causes flat space-time to behave like it has an infinitesimal curvature. It was Steve Carlip that pointed out correctly there is no difference between a theory that causes objects to behave like space-time was curved and it actually being curved. This is the type of thing I mean by emerge. You will find a discussion on this sort of stuff if Feynmans Lectures On Gravitation where the often made claim about spin two particles that it leads to space-time curvature is detailed. I am saying we know so little about the Plank scale don't assume anything - but certainly our usual 4d space can and probably does emerge from whatever it is

Thanks
Bill
P: 381
 Quote by bhobba Whats going on there is that the properties of spin 2 particles in the background of flat space-time all by themselves leads to GR with its space-time curvature. It causes flat space-time to behave like it has an infinitesimal curvature. It was Steve Carlip that pointed out correctly there is no difference between a theory that causes objects to behave like space-time was curved and it actually being curved. This is the type of thing I mean by emerge. You will find a discussion on this sort of stuff if Feynmans Lectures On Gravitation where the often made claim about spin two particles that it leads to space-time curvature is detailed. I am saying we know so little about the Plank scale don't assume anything - but certainly our usual 4d space can and probably does emerge from whatever it is Thanks Bill
I see. So you are not referring actually to string theory which has Calabi-Yau manifold inside the planck scale while that in LQG, the spin network is the size of the planck so there is nothing inside. Since these two are not proven. What is inside planck scale is unknown. It may even be all solid. But our spacetime as a continuum may not be the primary. I guess it's like water molecules. The water is our spacetime, the molecules are the planck scale and there is no water inside the molecules. This may be what you mean GR emerge as a limit of this completely unknown planck scale physics. About the flat spacetime thing. I have questions about it.

1. Are you saying that spin 2 gravitons can produce GR even if the background is not flat? Because Carlip and even Feynman were simply referring to existing flat spacetime with spin 2 gravitons producing spacetime curvature. But you added the planck scale thing or issue.

2. Are you saying unknown physics inside planck scale first produce flat spacetime, then later it goes into spin 2 mode and produce curvature from that flat spacetime to produce gravity?

3. How did the flat spacetime arise from the planck scale? Is this a valid question?
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 Quote by waterfall 1. Are you saying that spin 2 gravitons can produce GR even if the background is not flat? Because Carlip and even Feynman were simply referring to existing flat spacetime with spin 2 gravitons producing spacetime curvature. But you added the planck scale thing or issue. 2. Are you saying unknown physics inside planck scale first produce flat spacetime, then later it goes into spin 2 mode and produce curvature from that flat spacetime to produce gravity? 3. How did the flat spacetime arise from the planck scale? Is this a valid question?
I am saying in a similar, but as yet unknown way, that curved space time emerges from flat via spin 2 particles then flat can emerge from something else eg LQG - but don't ask me because I haven't studied it - might get around to it one day - along with the tons of other stuff I want to study - right now studying Category Theory.

As I said before once you feel comfortable with single variable Calculus - get Boas. If you study a bit each day you will be surprised what you learn over time - an understanding those who just read popular accounts like Hawking can never appreciate.

Thanks
Bill
 P: 407 Why don't you study an easier example, namely classical electromagnetic fields, before trying to understand gravity? Perhaps there it is easier to understand the difference between a classical field configuration, and small oscillations around them, which are called photons when quantized. Then you see that it is a misguided question to ask how a non-perturbative field configuration is made out of "spin 1 photons". At best, it can be viewed as coherent superposition of an infinite number of field quanta, but that viewpoint is not really helpful here. It is by definition not possible that by adding single photons one after the other you can build up a non-perturbative field configuration (with non-trivial, macroscopic curvature = field strength). A photon is a single particle, perturbative concept and this can capture only physics that is close to a given macroscopic background. Sometimes it is possible to resum infinitely many contributions, eg one can show how the classical potential between two charges can be obtained by summing virtual photons. But that won't work for non-perturbative configurations like instantons. This applies analogously to gravity and gravitons.
P: 381
 Quote by bhobba I am saying in a similar, but as yet unknown way, that curved space time emerges from flat via spin 2 particles then flat can emerge from something else eg LQG - but don't ask me because I haven't studied it - might get around to it one day - along with the tons of other stuff I want to study - right now studying Category Theory. As I said before once you feel comfortable with single variable Calculus - get Boas. If you study a bit each day you will be surprised what you learn over time - an understanding those who just read popular accounts like Hawking can never appreciate. Thanks Bill
Ok. Thanks. So our flat spacetime is another Effective Field Theory. Good to know.

Speaking of calculus. Reminds me of the virtual particles. You know what. Perturbation theory is not something permanent like the Diract Equation, it's only because we don't know the interacting theory. Therefore remembering that virtual particles corresponds to each term of the power series of the Perturbation Theory and PT is only a temporarity math rule. Then virtual particles don't exist. We don't even need Neumaier arguments that everything is field.
So what if there is effects in the casimir plates, etc. They can be explained by others because simply of the fact that virtual particles being a symptoms of perturbation theory being a symptoms of non-interacting theory is just a math artifact. I think you agree with this.

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