Alternatives to QFT

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

bhobba

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

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.

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

waterfall

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?

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

waterfall

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?

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

suprised

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.

waterfall

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.

waterfall

Try reading this which I am right now:

http://www.scribd.com/doc/54251898/T...on-Gravitation

"The Feynman Lectures on Gravitation"

"The claim that the only sensible theory of an interacting massless spin-2 field is essentially general relativity (or is well approximated by general relativity in the limit of low energy) is still often invoked today. (For example, one argues that since superstring theory contains an interacting massless spin-2 particle, it must be a theory of gravity.) In fact, Feynman was not the very first to make such a claim.

The field equation for a free massless spin-2 field was written down by Fierz and Pauli in 1939[FiPa 39]. Thereafter, the idea of treating Einstein gravity as a theory of a spin-2 field in flat space surfaced occasionally in the literature."

juanrga

The idea that GR is just a spin-2 field theory over flat spacetime is completely incorrect. Already Wald, in his General Relativity textbook, warn readers that the term "spin-2" is not well-defined beyond linearized GR. Wald also devotes a chapter of his book to explain different approaches to QG where remarks that the string theory approach (spin-2 approach) misses basic aspects of GR as causality.

Feynman textbook is misguided and usually avoided for serious GR courses. Carlip claims, cited before, do not stand up on close inspection.

The myth that GR is a spin-2 field is very common in the string theory literature, but has always been rejected by general relativists (who started their canonical approach to QG).

Some of typical textbooks mistakes are corrected in From Gravitons to Gravity: Myths and Reality

It is fair to remark that string theorists already abandoned string theory and are now seeking for a background-independent alternative. Since they have no idea of what this alternative has to be, they named it M-theory (M from Mistery). As they agree nobody really know that M-theory is or even if it exists (it is only conjectured that exists).

atyy

Wald's writes about terminology, not that gravity is not massless spin 2.

suprised

This is plain nonsense. If, then they look for an extension of string theory, like an "unbroken topological phase". One interesting recent work in this direction is eg, http://www-spires.dur.ac.uk/cgi-bin/...rXiv:1112.5210

And no, GR ist not just the theory of a spin 2 graviton; string theorists know this probably better than anyone. How often needs it to be repeated that gravitons corresponds to "small ripples on a water surface" and not to the whole ocean including vortices etc.

The amount of misconceptions, desinformation and plain nonsense propagated here is really staggering!

bhobba

I have Wald, it is my favorite GR Textbook, and I can't recall anything in there about spin 2 particles. If anyone knows it give me that page and I would love to read it.

Regarding Feynman's book it may have problems - after all it pretty ancient now, but I have been through it and cant recall anything that looked dubious.

Thanks
Bill

juanrga

Nope. He emphasizes that the both mass and spin of a field require a flat background to be unambiguously defined. Outside linearized GR the background is lost and you cannot unambiguously define basic properties of the field doing that the common claim «full GR is a (massless) spin-2 field theory» is not different from «full GR is a xkgncmcfs», where «xkgncmcfs» is not defined .

waterfall

Here are the relevant passages in Wald's (anyone can read this at scribd which I did):

page 74 in the subject "Linearized Gravity: The Newtonian Limit and Gravitational Radiation

"The aim of this section is to treat the approximation in which gravity is "weak." In the context of general relativity this means that the spacetime metric is nearly flat. In practice, this is an excellent approximation in nature except for phenomena dealing with gravitational collapse and black holes and phenomena dealing with the large scale structure of the universe.

page 76:

"In vacuum (Tab=0) equations (4.4.11) and (4.4.12) are precisely the equations written down by Fierz and Pauli (1939) to describe a massless spin-2 field propagating in flat spacetime (see chapter 13). Thus, in the linear approximation, general relativity reduces to the theory of a massless spin-2 field. The full theory of general relativity thus may be viewed as that of a massless spin-2 field which undergoes a nonlinear self-interaction. It should be noted, however, that the notion of the mass and spin of a field require the presence of a flat background metric n(ab) which one has in the linear approximation but not in the full theory, so the statement that, in general relativity, gravity is treated as a massless spin-2 field is not one that can be given precise meaning outside the context of the linear approximation."

------------

I think linearized approximation means it only works in weak gravity and not near singularity. This may be what atyy means by harmonic coordinates. So Bill. It seems we can't truly model curved space as spin-2 field in flat spacetime. This doesn't work fully therefore do you agree now that gravity is geometry only and can't be modeled by this spin-2 field over flat spacetime thing? If you don't, please elaborate. Thanks.