Exploring Alternatives to QFT: A Critique of Non-Interacting Quantum Fields

[waterfall]

Wait. You mean in the Wheeler Gravitation book the writers were referring to low energies only? I thought it includes high energies which if true means the strings were moving in flat background and these graviton modes giving all the curvature. Hence. The flat picture is the real "territory" and the GR picture a mere "map". Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

 

[atyy]

Wait. You mean in the Wheeler Gravitation book the writers were referring to low energies only? I thought it includes high energies which if true means the strings were moving in flat background and these graviton modes giving all the curvature. Hence. The flat picture is the real "territory" and the GR picture a mere "map". Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

Wheeler was referring to classical gravity. In classical gravity there are two pictures. The first is gravity as spacetime curvature, the second is as spin-2 on flat spacetime. The second picture is equivalent to the first picture if spacetime can be covered by harmonic coordinates.

Now what about the quantum versions? The first classical picture has no known quantization. The second classical picture has a quantum version, but the quantum version only works below the Planck scale.

String theory tries to complete the quantum version of the second picture above the Planck scale by introducing new objects called strings. Loops tries to complete the quantum version of the second picture by quantizing the first classical picture.

 

[waterfall]

This sounds right to me. The basic idea of "perturbative" is to make an approximation by fixing a flat or other simple background and studying small "perturbations". It provides excellent means of calculation.

But it has recognized limitations as a way to think about reality. The "flat space+small curvature perturbations" picture is not taken as fundamental.

In non-string QG there was a bunch of papers about gravitons, doing calculations. In Loop the graviton papers started coming in around 2007, certain things had to be checked so people did that.

I think my mistake was thinking it was fundamental when I learned it 5 years ago from sci.physics from Hobba. This was because Brian Greene and other laymen book didn't talk about it. So when Hobba was referring to the following for example.. he was talking only of low energies (which I thought include high energies):

"Gravitons interact with all matter-energy. They interact in such a way as to make rulers and clocks behave as if space-time had curvature. It is a semantic issue of zero scientific value if space-time is thus curved or just appears curved. At this stage their is no way to experimentally distinguish between the two views."

Good to understood now it is only low energies. Thanks.
(Bhobba, who is a participant here, please comment if you don't agree).

 

[marcus]

Maybe Hobba just misunderstood this from Carlip and the Wheeler Gravitation.

Yes, I think that's a good guess. Wheeler's book is a huge thick tome about non-perturbative GR which has a section or two about the perturbative treatment. I've met Carlip when he was here giving a talk about several kinds of non-perturbative QG. He works mainly with that (not with "gravitons"). He has his PhD students working on things like CDT, Loop, Shape Dynamics. A Carlip grad student just finished his PhD on Loop last year, I forget the guy's name.

As far as I know CDT and Shape do not have any graviton papers as yet. It is not the main concern, at some point you want to see if you can handle the low energy nearly flat case and reproduce certain results. Loop has done this now to some extent, but those others not.

I don't know if Hobba misunderstood or whether he knew better but was just goofing off.
Attention-getting? I can't say, because I've only a cursory glimpse. The whole thing with Hobba struck me as having a kind of geriatric flavor. Harking back to papers from the 1970s. Weinberg's *Gravitation and Cosmology* book from 1972 etc. Or something Carlip said at some point in the past.
There was a temporary suspicion among particle theorists back then that you actually did not have to take GR seriously and maybe you could do everything with a fixed flat space.

But you might want to look at Weinberg's NEW book (2008). You can browse the ToC and Index on Amazon. It is called *Cosmology*. You will not find much if anything about the perturbative representation of GR. Very little if any mention of "gravitons".

https://www.amazon.com/dp/0198526822/?tag=pfamazon01-20
The Physics Today review said it would be a great help to "particle physicists tooling up for cosmology"
All based on dynamic changing curved geometry. HEP theorists taking GR more seriously now than, say, in 1972.

Think about a massive star collapsing to form a black hole. Are you going to model that whole process from beginning to end using a fixed unchanging flat space with ripples running around on it? Perturbative methods of calculation very good for some things. Not a full picture of reality. The full picture has to be able to handle extremes, highly dynamic changing geometry, extreme density, extreme moments of expansion. "Graviton" picture is inconvenient not to say unworkable. So (as Atyy indicates) the fashion among researchers has swung towards nonperturbative models. (which is where the relativists have been all along.)

 

[Haelfix]

Think about a massive star collapsing to form a black hole. Are you going to model that whole process from beginning to end using a fixed unchanging flat space with ripples running around on it?

Amusingly, you picked a really bad example. The state of the art in the physics of stellar collapse requires the heavy usage of weak field limits. The only analytic solution in the whole business is known as the Oppenheimer-Snyder solution, which is unphysical for a number of reasons.

 

[marcus]

Amusingly, you picked a really bad example. The state of the art in the physics of stellar collapse requires the heavy usage of weak field limits. The only analytic solution in the whole business is known as the Oppenheimer-Snyder solution, which is unphysical for a number of reasons.

That's interesting. I'm guessing you are talking about numerical modeling of stellar collapse using a computer and I would like to see more! Do you have an arxiv reference to share?

I know that lots of numerical work (black hole merger etc) USES weak field approximation. Almost by definition when you simulate something in a computer you are going to make judicious use of a fixed background geometry---but realizing its limitations and not asking it to do too much. Adjusting it by hand if and when it forms a singularity, and so on.

I don't have any illusion that what you are talking about represents reality, but I would like to see a write-up of a state of the art numerical calculation of stellar collapse.

 

[atyy]

Also, I think harmonic coordinates (the condition for a curved spacetime being exactly realizable as spin-2 on flat spacetime) can penetrate the event horizon. I think it's only close to the singularity that harmonic coordinates fail, where we don't trust GR anyway. I'm not sure, but that's what I think http://relativity.livingreviews.org/Articles/lrr-2000-5/ (discussion around Eq 103,104) says.

 

[marcus]

Let's wait and see what Haelfix comes up with. Atyy what you cite is a static solution in a paper from around 2001. It is not modeling the collapse of a star to form a bh, but a bh that is just sitting there not changing.

It doesn't really matter but I'm curious to see what "state of art" numerical model of bh collapse Haelfix is talking about.

Whatever attitudes and poses people strike, we all know that there is a huge drive in physics theory to get a nonperturbative quantum field theory if possible containing a quantum geometry of the universe.

The intense interest among string people in AdS/CFT for the past 10 years illustrates this trend. You have been pointing this out---AdS/CFT even though the real world does not appear to be AdS offers the hope of a nonperturbative version of string. M-theory though not yet formulated is another hope in the same nonperturbative direction.

Asym Safe gravity is another example---it is precisely a bid for nonperturbative renormalizability.

Triangulations (CDT) gravity is another---it explicitly advertises itself as a nonperturbative QG, like in the first paragraph of the main papers on the subject.

One can go down the list. Loop, of course, is basically nonperturbative (although developing approximation methods).

It's not something I have to talk about, or anyone needs to explain, you just open your eyes and look around. Perturbative computational techniques are techniques. As such they are marvelously well-developed and absolutely indispensable And their limitations are recognized.

 

[waterfall]

I agree. A perturbative approach is useful (even essential) for calculation at low energy. Loop, for instance "has gravitons" when one is explicitly studying low density, nearly flat, geometries. Low energy=low curvature, so that kind of approximation works.

I don't take issue with that. It's not a good way to picture reality when you are thinking about big bang cosmology. I take issue with someone calling the flat picture the real "territory" and the GR picture a mere "map".

There seems to be some vagueness in the use of the terms low and high energy and the source of my confusion as well as most laymen. I know it comes from the fact that the de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle, so you need high energy to probe small spaces. So when you mention high energy, do you only mean small scale only or actually injecting energy? Also I saw the definition of High Energy Physics "It is called "high energy" because experimentally one needs very high energy probes to try to take these "elementary particles" apart.". But in quantum gravity, what are you taking apart? Maybe in quantum gravity. High energy just means small scale? Or do you actually have to inject energy in the Planck scale as in what happens in singularity in black hole or Big Bang? But here's the point. A string is always there in Planck scale. Even if you don't introduce Planck scale energy, a string still exist. So when you mentioned low energy to mean large scale. Note large scale is composed of many small scales. Large scale is still made up of strings in the small scales. Hence when you say these flat spacetime plus spin 2 gravitons giving curved spacetime is only a low energy large scale expression. but note the fact large scale is still composed of low scale so what are those gravitons doing in the small scale during the large scale approximation. Also I don't understand this perturbation thing as applied to quantum gravity. I know what it is in QFT. But in gravitons, I don't understand the connection. Anyway. When you mention low energy large scale, you mean you just pretend the gravitons don't exist and general relativity apply and just give this statement "flat spacetime plus gravitons equal to curve spacetime" without actually admitting the gravitons are really doing that? This is such a serious semantic mismatch issue. Can you give another example in physics where such statements are used because I'd like to understand the subtle semantic context. Thanks.
(atyy, pls. also comment on this message as this is the core of misunderstanding for many because of the many PUN and double entendre meanings used that even differs to standard high energy physics like QCD)

 

[atyy]

There seems to be some vagueness in the use of the terms low and high energy and the source of my confusion as well as most laymen. I know it comes from the fact that the de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle, so you need high energy to probe small spaces. So when you mention high energy, do you only mean small scale only or actually injecting energy? Also I saw the definition of High Energy Physics "It is called "high energy" because experimentally one needs very high energy probes to try to take these "elementary particles" apart.". But in quantum gravity, what are you taking apart? Maybe in quantum gravity. High energy just means small scale? Or do you actually have to inject energy in the Planck scale as in what happens in singularity in black hole or Big Bang? But here's the point. A string is always there in Planck scale. Even if you don't introduce Planck scale energy, a string still exist. So when you mentioned low energy to mean large scale. Note large scale is composed of many small scales. Large scale is still made up of strings in the small scales. Hence when you say these flat spacetime plus spin 2 gravitons giving curved spacetime is only a low energy large scale expression. but note the fact large scale is still composed of low scale so what are those gravitons doing in the small scale during the large scale approximation. Also I don't understand this perturbation thing as applied to quantum gravity. I know what it is in QFT. But in gravitons, I don't understand the connection. Anyway. When you mention low energy large scale, you mean you just pretend the gravitons don't exist and general relativity apply and just give this statement "flat spacetime plus gravitons equal to curve spacetime" without actually admitting the gravitons are really doing that? This is such a serious semantic mismatch issue. Can you give another example in physics where such statements are used because I'd like to understand the subtle semantic context. Thanks.
(atyy, pls. also comment on this message as this is the core of misunderstanding for many because of the many PUN and double entendre meanings used that even differs to standard high energy physics like QCD)

Yes, in the string picture the strings are always there, but at low energy or large length scale it's a pretty good approximation to replace the string with a particle. Low energy or large length scale means we don't look so carefully, since we aren't looking at fine scales, so we could mistake a string for a particle such as a graviton or electron. In this sense particles "emerge" at low energies or large length scales as excellent approximation to strings.

 

[waterfall]

Yes, in the string picture the strings are always there, but at low energy or large length scale it's a pretty good approximation to replace the string with a particle. Low energy or large length scale means we don't look so carefully, since we aren't looking at fine scales, so we could mistake a string for a particle such as a graviton or electron. In this sense particles "emerge" at low energies or large length scales as excellent approximation to strings.

Also this whole argument "flat spacetime + spin-2 gravitons = curved spacetime" is just for illustration or calculation purposes and not to be taken literally. I think what you guys do is to assume flat spacetime, then do perturbations to make it arrive at curved spacetime. But all this just a trick, or even figurative. This is because strings could be having 11 dimensional background or unknown background and it producing our gravity or curved spacetime directly from the 11D without any flat spacetime. Do you agree?

 

[waterfall]

Yes, I think that's a good guess. Wheeler's book is a huge thick tome about non-perturbative GR which has a section or two about the perturbative treatment. I've met Carlip when he was here giving a talk about several kinds of non-perturbative QG. He works mainly with that (not with "gravitons"). He has his PhD students working on things like CDT, Loop, Shape Dynamics. A Carlip grad student just finished his PhD on Loop last year, I forget the guy's name.

As far as I know CDT and Shape do not have any graviton papers as yet. It is not the main concern, at some point you want to see if you can handle the low energy nearly flat case and reproduce certain results. Loop has done this now to some extent, but those others not.

I don't know if Hobba misunderstood or whether he knew better but was just goofing off.
Attention-getting? I can't say, because I've only a cursory glimpse. The whole thing with Hobba struck me as having a kind of geriatric flavor. Harking back to papers from the 1970s. Weinberg's *Gravitation and Cosmology* book from 1972 etc. Or something Carlip said at some point in the past.
There was a temporary suspicion among particle theorists back then that you actually did not have to take GR seriously and maybe you could do everything with a fixed flat space.

But you might want to look at Weinberg's NEW book (2008). You can browse the ToC and Index on Amazon. It is called *Cosmology*. You will not find much if anything about the perturbative representation of GR. Very little if any mention of "gravitons".

https://www.amazon.com/dp/0198526822/?tag=pfamazon01-20
The Physics Today review said it would be a great help to "particle physicists tooling up for cosmology"
All based on dynamic changing curved geometry. HEP theorists taking GR more seriously now than, say, in 1972.

Think about a massive star collapsing to form a black hole. Are you going to model that whole process from beginning to end using a fixed unchanging flat space with ripples running around on it? Perturbative methods of calculation very good for some things. Not a full picture of reality. The full picture has to be able to handle extremes, highly dynamic changing geometry, extreme density, extreme moments of expansion. "Graviton" picture is inconvenient not to say unworkable. So (as Atyy indicates) the fashion among researchers has swung towards nonperturbative models. (which is where the relativists have been all along.)

Marcus, are you saying that if we would use nonperturbative models, "gravitons" are no longer needed or don't have to exist? For example. If reality is ultimately not defined by strings or LQG but by some actual AsD/CFT scenerio where the actual things are in some distant surface or holographic. Then there is no gravitons although we can still use the analysis of flat spacetime + gravitons = curved spacetime maybe as exercise in a physics class for large scale limit or as dual?

 

[atyy]

Also this whole argument "flat spacetime + spin-2 gravitons = curved spacetime" is just for illustration or calculation purposes and not to be taken literally. I think what you guys do is to assume flat spacetime, then do perturbations to make it arrive at curved spacetime. But all this just a trick, or even figurative. This is because strings could be having 11 dimensional background or unknown background and it producing our gravity or curved spacetime directly from the 11D without any flat spacetime. Do you agree?

I don't know - I'm just a guy like you who read Smolin's book. Hopefully others can answer your question.

 

[waterfall]

I don't know - I'm just a guy like you who read Smolin's book. Hopefully others can answer your question.

I'm not asking if strings background is 11 or 25 dimensions. What I'm asking is whether gravitons are kinda like an effective field theory. Meaning if we would say use nonperturbative models, "gravitons" are no longer needed or don't have to exist? For example. If reality is ultimately not defined by strings or LQG but by some actual AsD/CFT scenerio where the actual things are in some distant surface or holographic. Then there is no gravitons although we can still use the analysis of flat spacetime + gravitons = curved spacetime maybe as exercise in a physics class for large scale limit or as dual?

 

[marcus]

... If reality is ultimately not defined by strings or LQG but by some actual AsD/CFT scenerio where the actual things are in some distant surface or holographic...

WF you are conversing very well with Atyy and may get more from your Q&A with him. I watch various lines of QG research and get especially interested when one seems to be making strides. I don't have beliefs about what "reality ultimately is".

I do not suspect "there is some actual AdS/CFT scenario with things on a distant surface". Maybe Atyy has thought more about that and can discuss it with you.

There is a saying "It's not what Nature IS, it's how it responds to measurements." Most of the time that is what I have in mind when I think of physical models. The experimenter defines a state by measuring/establishing initial conditions, then he predicts future measurements, probabilities, expectations consequent on that, and checks. What we experience is a network of related events. That goes for geometric relations as well as other quantum fields that live on or in the geometry.

 

[waterfall]

WF you are conversing very well with Atyy and may get more from your Q&A with him. I watch various lines of QG research and get especially interested when one seems to be making strides. I don't have beliefs about what "reality ultimately is".

I do not suspect "there is some actual AdS/CFT scenario with things on a distant surface". Maybe Atyy has thought more about that and can discuss it with you.

There is a saying "It's not what Nature IS, it's how it responds to measurements." Most of the time that is what I have in mind when I think of physical models. The experimenter defines a state by measuring/establishing initial conditions, then he predicts future measurements, probabilities, expectations consequent on that, and checks. What we experience is a network of related events. That goes for geometric relations as well as other quantum fields that live on or in the geometry.

So Craig Hogan Holometer idea is not supported by mainstream. Wonder how he got the million dollar funding for it. Anyway.

Beckenstein has this interesting article about the holographic principle:

http://www.phys.huji.ac.il/~bekenste/Holographic_Univ.pdf

"CAN WE APPLY the holographic principle to the universe at large? The real universe is a 4-D system: it has volume and extends in time. If the physics of our universe is holographic, there would be an alternative set of physical laws, operating on a 3-D boundary of spacetime somewhere, that would be equivalent to our known 4-D physics. We do not yet know of any such 3-D theory that works in that way. Indeed, what surface should we use as the boundary of the universe? One step toward realizing these ideas is to study models that are simpler than our real universe."

So he is not entirely discounting that there is an actual AsD/CFT counterpart in our universe. Hope Hogan has the results soon so we can discount it or confirm it (if anyone has the results, then update us anytime in the future).

When you build a house. Would you build one with volume or just a wall if they both serve the same purpose. A wall would be fine and one can live in the wall. Lol...

 

[marcus]

So Craig Hogan Holometer idea is not supported by mainstream. Wonder how he got the million dollar funding for it. Anyway.
...

Is there something wrong with the experiment? I don't understand your comment.

I do not suspect that low energy SUSY is right, but I certainly do not begrudge the money and time to test for it at the LHC!
A lot of people are skeptics about SUSY (and extra spatial dimensions) but I don't remember hearing them complaining about resources devoted to testing.

You probably know more about the Hogan experiment than I do, haven't followed that lately. so if there is something you think is wrong why not explain?

If you can't maybe someone else?

 

[waterfall]

Is there something wrong with the experiment? I don't understand your comment.

I do not suspect that low energy SUSY is right, but I certainly do not begrudge the money and time to test for it at the LHC!
A lot of people are skeptics about SUSY (and extra spatial dimensions) but I don't remember hearing them complaining about resources devoted to testing.

You probably know more about the Hogan experiment than I do, haven't followed that lately. so if there is something you think is wrong why not explain?

If you can't maybe someone else?

Isn't it we were discussing it in this thread the other day

https://www.physicsforums.com/showthread.php?t=441577

I became aware of Hogan Holo-meter because it is the cover in this month Scientific American:

http://www.scientificamerican.com/article.cfm?id=is-space-digital

I interpret it as saying he is building the holo-meter to actually test if our universe is some kind of hologram something akin to AsD/CFT! If Sci-Am just exaggerate it to get audience. Pls. let us know the true purpose of the holo-meter.

 

[marcus]

...
I interpret it as saying he is building the holo-meter to actually test if our universe is some kind of hologram something akin to AsD/CFT!...

I can't read the article. I heard about this in 2008, and posted in that thread in 2010. I have no fresh information.

As I say I do not suspect that the universe is a noisy hologram, or any kind of hologram. But I don't know any reason to object to the experiment. Do you? I can't say much because I don't know the details about the actual experiment.

 

[waterfall]

I can't read the article. I heard about this in 2008, and posted in that thread in 2010. I have no fresh information.

As I say I do not suspect that the universe is a noisy hologram, or any kind of hologram. But I don't know any reason to object to the experiment. Do you? I can't say much because I don't know the details about the actual experiment.

The experiment is just an long extended MMX like apparatus. See:

http://www.symmetrymagazine.org/bre...s-to-test-hypothesis-of-holographic-universe/

There are many videos about superstrings but none about LQG. Why don't they make one?
About Superstrings. I wonder if you agree with the following site being labelled the official string theory web site.

http://superstringtheory.com/blackh/blackh4.html

Some interesting bits:

"Is spacetime fundamental?
Note that there is a complication in the relationship between strings and spacetime. String theory does not predict that the Einstein equations are obeyed exactly. String theory adds an infinite series of corrections to the theory of gravity. Under normal circumstances, if we only look at distance scales much larger than a string, then these corrections are not measurable. But as the distance scale gets smaller, these corrections become larger until the Einstein equation no longer adequately describes the result.
In fact, when these correction terms become large, there is no spacetime geometry that is guaranteed to describe the result. The equations for determining the spacetime geometry become impossible to solve except under very strict symmetry conditions, such as unbroken supersymmetry, where the large correction terms can be made to vanish or cancel each other out.
This is a hint that perhaps spacetime geometry is not something fundamental in string theory, but something that emerges in the theory at large distance scales or weak coupling. This is an idea with enormous philosophical implications. "

I wonder if you or Atyy has paper related to it. Aren't there other string theorists or enthusiasts here?

 

[Mike H]

It's strange that billions of dollars have been invested in String theory and many graduates spent all 5 years of their post-graduate time in it when it is fundamentally not background independent (so don't even support GR at its core)... What gave the initial go ahead for billion dollars funding for something that doesn't have promise?

I have to ask - do you have numbers backing up the claim of "billions of dollars have been invested in String theory", or are you pulling that out of thin air? Given that the National Science Foundation only has about $6 to 7 billion per year to work with for everything as of late, I'm not sure I can buy that estimate. While certainly there are other funding sources, it doesn't pass my order-of-magnitude sniff test.

Going back to lurking...

 

[marcus]

I have to ask - do you have numbers backing up the claim of "billions of dollars have been invested in String theory", or are you pulling that out of thin air? Given that the National Science Foundation only has about $6 to 7 billion per year to work with for everything as of late, I'm not sure I can buy that estimate. While certainly there are other funding sources, it doesn't pass my order-of-magnitude sniff test.

Going back to lurking...

Good point Mike H. Welcome and hope you post more. Theorists are not costly to support. Experimental physics is much more costly. I'm glad that string theorists have been handsomely supported for the past several decades so long as they don't abuse the privilege. It is unfortunate only in cases where they dismiss, discredit, and try to shut out other rival programs. Or hype their wares in such a way that it raises unrealistic expectations.

"Billions" sounds ridiculous to me, as I guess it does to you as well. I actually hadn't thought about it and don't feel confident I could make a useful estimate. Would you say that in the USA investment in string research has been perhaps 100 times the investment in LQG? (which is certainly not much!) or 200? or is it more like 500? Hard to say. Investment in string researchers seems to be declining though, judging by the declining rate of first-time faculty hires. Things may eventually come into balance.

 

[Demystifier]

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.

 

[bhobba]

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.

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.

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

 

[waterfall]

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 https://www.physicsforums.com/showthread.php?p=3777052#post3777052

 

[waterfall]

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.

 

[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.

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.

 

[suprised]

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.

 

[marcus]

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 doesn't 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 don't 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.

 

[waterfall]

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
https://www.physicsforums.com/showthread.php?t=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.

 

[bhobba]

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

 

[bhobba]

"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
be made.

Thanks
Bill

 

[waterfall]

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 learned string theory at sci.physics and in the following you wrote in 2007 when someone asked:

http://groups.google.com/group/sci....k=gst&q=bill+hobba+spacetime+unknown+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.

 

[bhobba]

I learned string theory at sci.physics and in the following you wrote in 2007 when someone asked:

http://groups.google.com/group/sci....k=gst&q=bill+hobba+spacetime+unknown+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

 

[waterfall]

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?