QFT with respect to general relativity

  • #51
tom.stoer said:
Good point.

But of course we know that there are vacuum solutions in GR with non-trivial dynamics (dS spacetime, black holes, brill waves, ...), so it's not totally unreasonable.

That's why I'm thinking that this is where virtual particles come in. At least there are virtual particles in the vacuum to establish relative distances with respect to them. But if geometric quantities are justifiably quantized irrespective of particle quantization, then there is nothing to specify when to quantize and when not to quantize any geometric quantities simply because it is there. If you take away the context of QFT of particles away from the quantization of geometry, then it seems arbitrary to quantize geometry. So I think we need to formulate the problem of quantum gravity by finding geometric quantities as dynamic variables in a more diffeomorphic generalization of the usual QFT.
 
Physics news on Phys.org
  • #52
I don't think that virtual particles are of any relevance as they are purely perturbative artefacts; OK, perhaps matter will play a key role, but not via virtual particles
 
  • #53
suprised said:
Well I am not talking about cosmological pictures, but just a transplanckian scattering experiment, if you wish with asymptotic oberservers. So what is the S-Matrix for this scattering? It should have a concrete answer, and better be unitary.

If you dispute the valitidy of QM and the S-Matrix - well QM has been proven to be extremely robust against deformations and so far no one, AFIAK, was able to replace it by something else. It is very common (because cheap) to say "according to my opinion QM needs somehow be modified", but very difficult to actually do it ...

Sorry for the slow response, haven't had much time lately :( a short comment.

First of all, I agree it's cheap to say you need something better, without actually showing what this better thing is. But it's still of importance to be able to distinguish problem if there is one. To cure it is hard, but it gets even harder if you don't see it first.

My objection to your transplanckian scattering picture is this: I agree with you that given a FIXED given observer, the scattering must be unitary due to consistency. The problem is that I think it's still ambigous, becaseu there is not unique "asymptotic observer", there is rather a sort of landscape of them. (I'm not talking just about string landscape, I'm talking generally).

And I do not think there exists a conventional "renormalization" picture where you can define observer invariants here.

Cheap as it may be, I think one needs to consider the backreaction on the observing context, and then referring to the "asymptotic limiting observer" sort of misses the point.

I sure don't have anything better at the moment, but I see problems with current approach, that for myself I'm not letting pass.

/Fredrik
 
  • #54
@Dickfore

1. lhs means left hand side, rhs means right hand side. The reference in this case is to the conventional formulation of general relativity which on the left hand side has a tensor that represents the geometrical manifestation of gravity, and on the right hand side has a tensor called the stress energy tensor.

2. A tensor is another name for a matrix, usually in the context of a tensor that is used in the physical sciences to represent quantities analogous to vectors but that contain more data points. In the matrix that is the stress-energy tensor there is an element for each possible source of matter or energy in a given matter-energy field (e.g. rest mass, kinetic energy in three directions, pressure in three directions, electromagnetic flux in three directions, etc.) in each direction. The magnitude of each element of mass and energy in each direction contributes individually to the distortion in space-time geometry that we call gravity, so in general relativity, rather than merely the total amount of mass in Newtonian gravity mattering we care about its character and dynamics (and of course, since it is geometric, even massless stuff like photons are affected by it until Newtonian gravity) - hence we get gravitomagnetic effects (those arising from the motion of matter), etc.

3. A good quick introduction to the equations of general relativity and what each part stands for can be found in the relevant wikipedia articles, but it is all a little opaque if you don't have a good grasp of tensor mathematics (usually taught at the upper division undergraduate level to math and physics and engineering majors) and both the notion that general relativity is based on a continuous matter-energy field rather than a point sources that emit forces like Maxwell's equations, Newtonian gravity and to Standard Model interactions do and the notion that it is geometric while observing special relativity makes it all rather mind numbing and hard to process.

4. When we talk about quantitizing general relativity, several concepts are implicated: (a) general relativity is formulated with regard to continuous matter-energy fields while a quantum gravity theory would operate at the level of individual particles of matter, energy; (b) general relativity envisions space-time as continuous, while quantum gravity could have a discrete space-time; (c) most theories of quantum gravity would suggest a mechanism such as force carrying by a graviton which is a spin-2 boson, rather than a mere equation that says that two continuous quantities are related in a particular way which would give gravity particle-like as well as wave-like properties; amd (d) a quantum gravity theory would probably have a mechanism that propogates these bosons via a probabilistic rather than deterministic set of rules.

5. A quantum gravity theory could have little elaboration of general relativity at all, but provide a way to incorporate gravitational effects into quantum field theory, for example, in strong gravitational fields at the boundaries of black holes and in the Big Bang. In weak gravitational fields, the corrections would be on orders of magnitude so trivial relative to Standard Model forces that we don't care. In hyperprecise applications for fairly strong fields, we do care. Point-like particles are inherently inconsistent with general relativity, in ways that don't matter in Standard Model equations, but create general relativity singularties. The QFT on curved space-time approach you mention is basically an ad hoc, non-rigorous way of pushing classical GR and Standard Model physics as far as they will go and estimating on that basis with a fair bit of artfulness what their mutual natural extensions would suggest.

6. There are two practical reasons to do this, aside from the joy of having a fully rigorous and consistent set of equations of everything. One is that there are some extreme situations where no amount of artful extensions of each is enough to resolve how GR and the Standard Model forces interact because there are multiple, mutually inconsistent ways of going about doing it and we don't have enough guidance to say. The other one is that lots of people think that while a quantum gravity theory that is true must reduce to GR in ordinary consideration that there may be new physics predicted in very weak gravitational fields in deep space (the IR limit) and in very strong fields like those of the Big Bang and black holes (the UV limit). Many people also think that by putting them together in a way that explains how matter and energy took the forms that it did after the Big Bang (baryogenesis, leptogenesis, dark matter formation, inflation, cosmic background radiation, etc.) that we might be able to discern UV behavior of not only gravity but all Standard Model forces in a way that would make clear how to unify them into a fundamental theory of everything at high energies that naturally segments into the distinct low energy four forces and x many particles we observe governed by the equations we use in a low energy limit.
 
  • #55
tom.stoer said:
I don't think that virtual particles are of any relevance as they are purely perturbative artefacts; OK, perhaps matter will play a key role, but not via virtual particles

Well let's see, what about the graviton? Even the trajectories of gravitons are at least particles which can be used to establish relative distances, ... as opposed to quantizing geometry for the sake of geometry just to see what happens.

Here's a question: Suppose we have a complete diffeomorphic invariant generalization of QFT. Could that formulation be separated into a purely geometric component coupled to a particle component? Then it would make sense to try to quantize the geometric component first and add matter latter. Is this decoupling of geometry from particles the thing that we are assuming? Do we have a diffeomorphic invariant generalization of QFT?
 
  • #56
friend said:
Is this decoupling of geometry from particles the thing that we are assuming?

No, at least not in string theory. There the particles arise from geometry, and are unified with gravity in one coherent framework in higher dimensions. Quantum consistency actually requires extra matter fields, so if string theory is any right, pure gravity cannot be consistently quantized.
 
  • #57
suprised said:
friend said:
Is this decoupling of geometry from particles the thing that we are assuming?
No, at least not in string theory. There the particles arise from geometry, and are unified with gravity in one coherent framework in higher dimensions. Quantum consistency actually requires extra matter fields, so if string theory is any right, pure gravity cannot be consistently quantized.
Yes, at least in LQG, AS, ... ;-) these guys assume that a stepwise approach is fine and that unification of matter and geometry is not required for a consistent quantization of gravity. So 'stepwise' means that one can indeed quantize gravity but postpone unification.

LQG as of today is by no means complete, i.e. the quantization itself is still not fully understood (especially not in the celebrated spin foam models which I would describe as preliminary). But the technical problems in LQG are - as far as I can see - not related to the missing matter degrees of freedom. Another approach without relation between quantum gravity and unification is the asymptotic safety program which again points towards a consistent theory of quantum gravity to which matter degrees of fredom can be added later. So it seems that there are promising proposals for consistent theories of quantum gravity w/o unification. Whether they are physically right is a different question!

Nevertheless my feeling is that matter d.o.f. have a geometric origin and that a consistent and correct theory of quantum gravity along the lines of LQG or AS may not be the final word. Perhaps there is some potential in q-deformed / framed spin networks and 'braided matter", but this is more an idea than a theory. Another very interesting approach (with a very small community) seems to be the "exotic smoothness program".
 
  • #58
tom.stoer said:
But the technical problems in LQG are - as far as I can see - not related to the missing matter degrees of freedom...

Indeed so, they have problems already at a much more basic level. The issues I mean have to do eg with consistent graviton scattering at higher order (where, as seen from string theory, matter is needed to render the amplitudes finite and unitary). LQG is still far away to even see and address this question.
 
  • #59
The question in LQG is if you need something like perturbative gravitons, if it's the right question to be asked. If it changes the fundamental structure of spacetime its fundamental d.o.f. will not be gravitons at all.

(In lattice gauge theory there is neither the possibility nor the need to ask for perturbative quark-gluon scattering; in full QCD this is a valid question, but only b/c there is the regime of asymptotic freedom; so you need something but lattice gauge theory, too; it may very well be that there is no regime in gravity where gravitons and graviton scattering are required)

So the problem is NOT that LQG is not able to provide tools for calculating graviton scattering, the problem is that LQG is not able to tell you if this is a reasonable question. It all boils down to the incomplete quantization regarding dynamics, constraints, hamiltonian, PI measure, anomalies etc.

As soon as these issues are solved you are able address all these physical questions.
 
  • #60
suprised said:
No, at least not in string theory. There the particles arise from geometry, and are unified with gravity in one coherent framework in higher dimensions. Quantum consistency actually requires extra matter fields, so if string theory is any right, pure gravity cannot be consistently quantized.

tom.stoer said:
Yes, at least in LQG, AS, ... ;-) these guys assume that a stepwise approach is fine and that unification of matter and geometry is not required for a consistent quantization of gravity. So 'stepwise' means that one can indeed quantize gravity but postpone unification.

What does it tell us about this decoupling between geometry and matter to know that kinetic energy associated with travel through spacetime is converted to particles and visa versa? What does it tell us that event horizons associated with accerated frames radiate particles? Here it seems spacetime features equate to particles and so cannot be decoupled.
 
  • #61
"it may very well be that there is no regime in gravity where gravitons and graviton scattering are required"

I don't think so.

There is always a regime where the latter is important, and is basically a consequence of various non-decoupling theorems and renormalization group arguments. One can show that b/c the gravitational coupling constant is small (and in fact it always stays small relative to the other forces at any scale), there will always be an effective semiclassical description that must exist at some scale.

As a consequence you can't ignore the divergences that occur there, which is why all quantum gravity theories implicitly require the existence of either a nontrivial fixed point set or alternatively a UV completion.

The former of course hits a big problem (amongst many), which is that even if such a thing existed for pure gravity, b/c gravity couples to everything one must understand the dynamics of all the other forces to perfect precision and hope that they do not alter the UV critical surface. Which is of course rather silly, since the other forces are manifestly more important to gravitational dynamics than gravity is to itself at those energies.

So I mean its perfectly valid to look for novel top down approaches, but you do eventually have to answer the above foundational questions.
 
Last edited:
  • #62
Haelfix said:
"it may very well be that there is no regime in gravity where gravitons and graviton scattering are required"

I don't think so.

There is always a regime where the latter is important, and is basically a consequence of various non-decoupling theorems and renormalization group arguments. One can show that b/c the gravitational coupling constant is small (and in fact it always stays small relative to the other forces at any scale), there will always be an effective semiclassical description that must exist at some scale.

As a consequence you can't ignore the divergences that occur there, which is why all quantum gravity theories implicitly require the existence of either a nontrivial fixed point set or alternatively a UV completion.

The former of course hits a big problem (amongst many), which is that even if such a thing existed for pure gravity, b/c gravity couples to everything one must understand the dynamics of all the other forces to perfect precision and hope that they do not alter the UV critical surface. Which is of course rather silly, since the other forces are manifestly more important to gravitational dynamics than gravity is to itself at those energies.

So I mean its perfectly valid to look for novel top down approaches, but you do eventually have to answer the above foundational questions.

I do agree that there is a regime where gravitons are valid but...

The gravitational coupling increases with energy where as yang-mills couplings decrease with energy. So at high energies we would expect that gravity becomes stronger than the other forces. Of coarse we could only know for sure by preforming the calculation. But your claim that "one can show" that the other forces remain stronger than gravity at all scales is certainly not the case.

You're right that one must couple matter gravity to check that the UV surface remains finite dimensional. In the end if someone can do the calculation and show that there is some asymptotically safe theory that reproduces GR coupled to the SM at low energies then that is that.
 
  • #63
friend said:
I just had a thought, perhaps this is the best place for it.

Considering the nature of spacetime and QFT, as I understand it, virtual particles pop into existence, travel about, and then come back together such that the uncertainty principle is not violated. But how much space do the virtual particles travel through before coming back together? And how can you define space without events in the form of particle trajectories that establish the concept of relative distances? It may be that we cannot define one without the other. And the ultimate equations will have to account for both in a single equation.

Other questions would be what mechanism causes the virtual particles to come back together. They were created, go out in opposite directions, and then somehow curl around and come back together. Is this because spacetime is curved at that level to cause the particles to come back together? That suggests that the uncertainty principle is somehow connected to the curvature of spacetime. Any thoughts?
 
  • #64
friend said:
Other questions would be what mechanism causes the virtual particles to come back together. They were created, go out in opposite directions, and then somehow curl around and come back together. Is this because spacetime is curved at that level to cause the particles to come back together? That suggests that the uncertainty principle is somehow connected to the curvature of spacetime. Any thoughts?
Yes, some thoughts:

This is over-interpreting virtual particles; they do not have position, direction, they do not got here or there, they don't come back and neither do they follow spacetime curvature.

It's is hard to describe or explain what particles are in QFT; it's even harder to describe virtual particles. They are just mathematical entities - Forget about them!
 
  • #65
tom.stoer said:
Yes, some thoughts:

This is over-interpreting virtual particles; they do not have position, direction, they do not got here or there, they don't come back and neither do they follow spacetime curvature.

It's is hard to describe or explain what particles are in QFT; it's even harder to describe virtual particles. They are just mathematical entities - Forget about them!

What about the Casimir effect. That seems to prove the zero point energy made up of virtual particles, right? What about black hole radiation, where the negative energy virtual particles fall into the black hole near the horizon, but the positive energy virtual particles get stripped away from their partners and float off from the horizon as radiation. That seems to prove the existence of virtual particles too, right? And like the Casimir effect, aren't these virtual particles of the zero point energy the very thing causing the accelerated expansion pressure of the cosmological constant?
 
Last edited:
  • #66
"So at high energies we would expect that gravity becomes stronger than the other forces."

Gravity does increase in strength and become strongly coupled at the Planck scale. And exactly there, all other couplings are of order unity in the effective lagrangian. So there is no regime where gravity ever becomes stronger (indeed the first major divergences occur in the matter couplings), and so for N particle species one quickly see's that they end up dominating the dynamics. In other words, there is no regime where you can ever safely integrate out the other forces. I don't have time to track down references, but this is essentially a non-decoupling theorem.

You can make this relatively tight for beyond the standard model physics by analyzing bounds on black hole states and so forth and it goes by the name of the 'Weak gravity conjecture'. Arkani Hamed and collaboraters have done a lot of work on this.
 
Last edited:
  • #67
friend said:
What about the Casimir effect. That seems to prove the zero point energy made up of virtual particles, right? What about black hole radiation, where the negative energy virtual particles fall into the black hole near the horizon, but the positive energy virtual particles get stripped away from their partners and float off from the horizon as radiation. That seems to prove the existence of virtual particles too, right? And like the Casimir effect, aren't these virtual particles of the zero point energy the very thing causing the accelerated expansion pressure of the cosmological constant?
Sometimes interpreting virtual particles is nice, sometimes it's nonsense.

Even Hawking radiation explained in terms of virtual particles is over-interpretation; it's funny, Hawking provides such an explanation, but in his original calculation there are no virtual particles at all ;-) For the Casimir effect there are two different calcutions, one using 'vacuum fluctuations' and another one using 1st order 'virtual particles'.
 
Last edited:
  • #68
Haelfix said:
"So at high energies we would expect that gravity becomes stronger than the other forces."

Gravity does increase in strength and become strongly coupled at the Planck scale. And exactly there, all other couplings are of order unity in the effective lagrangian. However there is no regime where gravity ever becomes stronger (indeed the first major divergences occur in the matter couplings). In other words, there is no regime where you can ever safely integrate out the other forces. I don't have time to track down references, but this is essentially a non-decoupling theorem.

You can make this relatively tight for beyond the standard model physics and it goes by the name of the 'Weak gravity conjecture'. Arkani Hamed and collaboraters have done a lot of work on this.

You make some claims but I see nothing to back these up. If we take the ratio of some gauge coupling with the gravity coupling. Are there calculations that show that the gauge coupling diverges with respect to gravity?? You seem to be claiming that when gravity couples to other forces that it spoils asymptotic freedom? Please do provide me with the references to support your claims.
 
  • #69
Finbar said:
You make some claims but I see nothing to back these up. If we take the ratio of some gauge coupling with the gravity coupling. Are there calculations that show that the gauge coupling diverges with respect to gravity?? You seem to be claiming that when gravity couples to other forces that it spoils asymptotic freedom? Please do provide me with the references to support your claims.

No I am saying that the ratio of the gravitational coupling constant with other gauge coupling constant never exceeds one..

Please read the introduction of Birrel and Davies or alternatively section 3 of this introductory paper
arXiv:1011.0543

and the following gives the details of the energy expansion in slightly more detail, including a test case calculation of the change to the effective gravitational coupling constant where you see the effects arising from quantum corrections.

http://arxiv.org/abs/gr-qc/9712070v1

Alternatively the papers on asymptotic safety also seem show the same general pattern (Geff goes to zero)

Slightly more universal and highbrow statements can be found in this brilliant paper

http://arxiv.org/abs/hep-th/0601001

where they argue that the existence of incredibly small coupling constants arising from new Yang Mills like physics cannot occur in nature.
 
  • #70
We don't actually know that there is a consistent approach to quantizing General Relativity. What we do know is the following:

(1) in 2+1 dimensions, one can consistently formulate a quantum theory of "gravity". The reason for the scare-quotes is that no quantum theory in less than 4 dimensions can lead to the quantization of independent gravitational degrees of freedom -- because there are none. More precisely: the Weyl tensor (which contains the gravitational degrees of freedom) is 0 in less than 4 dimensions. Or, to put it another way: all quantum theories of gravity in 3 or fewer dimensions have c-number Weyl tensors (since the 0 tensor is a c-number).

(2) In 3+1 dimensions, the only known approach that has led to a quantization of Einstein's law of gravity was that devised by Carmelli in the 1980's. The most important feature of the formalism is that it is not cast in Riemannian geometry, but Riemann-Cartan geometry. The distinction is crucial because in it, the metric remains classical, while the connection is quantized as the connection of a gauge field (namely, an SL(2,C) gauge field).

The reason this has not been heralded as the Final Definitive Solution to the Problem is that it only works for purely gravitational fields. That is, if all you're interested in is the exterior solutions in a matter-free vacuum, Carmelli does the job. Unfortunately, Carmelli never found a way to even couple the classical theory with matter, much less the quantum theory.

The most notable feature of the theory is that the Weyl tensor is a c-number.

(3) The approach "Quantum Field Theory in Curved Spacetime" succeeds in formulating quantum theory in a general relativistic context. However, there are two main features that are both regarded as drawbacks (whether regarded rightly so as drawbacks, on the other hand, is itself a question for contention). First, there is no reaction of matter on geometry. Rather, the curved background serves to condition the propagation (the Greens functions) and the wave equation. Second, one needs to make restrictive assumptions that, themselves, cannot be framed in operator form in any theory that has the metric as a quantized dynamic variable -- namely, that the underlying spacetime be globally hyperbolic.

The global hyperbolicity assumption is not expressible in operator form. So in a prospective quantized theory of gravity, one could literally have a superposition of a globally hyperbolic state with one that is not. Unfortunately, since nobody's ever found a consistent way to do quantum theory in a globally non-hyperbolic setting (this is much of what the 1990's papers about time travel and closed time loops was about) then the situation could be likened with the worst form of a Schroedinger Cat: a superposition of a (globally hyperbolic) universe in which quantum theory can be defined, with a (globally non-hyperbolic) universe where it can't be.

The more basic problem is that even metric signature is not something that can be expressed in operator form. So, one could even have a superposition of a state that is a 3+1 spacetime with a state that corresponds to a 4 dimensional timeless space. Given how central the notion of time is to quantum theory, this seems to entail some serious consistency problems.

(4) Loop Quantum Gravity takes place in the setting of Riemann-Cartan geometry. It tries to adopt a "background free" approach, placing the diffeomorphism group at the center. Unfortunately, not all things relevant to physics are acted on by the diffeomorphism group, so that the very notion of background freeness itself can't be consistently defined. More precisely: the kinds of objects acted on by the diffeomorphism group are what mathematicians call "natural objects", and the corresponding operations are called "natural", while the underlying geometries are referred to as "natural bundles". The kind of geometry required for a theory of gravity that satisfies the equivalence principle is a subset of the tangent bundle known as an "orthonormal frame subbundle". I don't believe the orthonormal frame bundles are natural. This is closely tied to the problems raised at the end of (3). In addition, fermions require spinors. These reside on spinor bundles and I don't believe these are natural bundles either.

One way to approach this may be to relax (or redefine) the requirement so as to only require "gauge naturalness". In place of the diffeomorphism group Diff(M) on a spacetime manifold M, this broadens to the gauge group Gau(P) and automorphism group Aut(P) on a principal bundle P that has M as a base space. Gauge natural objects over P need not be reduce to natural objects on M. In addition, I don't believe gauge natural objects on P are natural on P (i.e. that they are not acted on by the diffeomorphism group Diff(P)). So, one has background structure by virtue of the confinement of focus to Aut(P) and Gau(P).

(5) Sardanashvily, Mangiarotti, et. al work off of a long-lasting strand that originated with Heisenberg and Ivanenko. They (rightly) point out that the reduction of the manifold M's tangent bundle TM to the orthonormal frame bundle F_g(M) associated with a metric g is a form of symmetry breaking. All this, of necessity, takes place in the broader setting of Riemann-Cartan geometries. This puts the spotlight on either the metric g or the frame fields as being the corresponding Goldstone-Higgs fields. In general, when you have symmetry breaking, the Goldstone-Higgs fields are essentially classical. Each different configuration corresponds to a different vacuum state and different coherent subspace; and between any two coherent subspaces no quantum superpositions can occur.

They highlight the issue of the fermions, noting that the very process of quantizing it, itself, critically depending on which subbundle F_g(M) of TM you choose; so that two quantizations corresponding to inequivalent g's must lead to different quantum state spaces; i.e. no quantum superpositions of the usual kind between different states can exist if the states disagree on whose motions are free fall/inertial.

Among other things, when symmetry breaking is present, the vacuum is no longer a unique state. So the premise of a unique state |0><0| underlying an equation such as <0|T|0> = kG (which the approach in (3) may use) is false, because the equation can't even be written down.

(6) String theory. I don't know enough to say anything about it.

(7) Arguments against classical/quantum hybrids, such as the famous Feynman argument tend to be premised on Riemannian geometry. When the arguments pass into folklore this tends to muddy the issue and lead to fallacious claims. In fact, the Feynman argument employs fermions, which require a Riemann-Cartan geometry. In a Riemann-Cartan geometry one necessarily make a distinction between a metrical extreme curve and a geodesic curve. The former is a "geodesic" for the Levi-Civita connection, while the latter (the *actual* geodesics) are geodesic for the connection native to the Riemann-Cartan geometry.

The Riemann-Cartan geodesics for two electrons in different spin states CAN diverge from one another, in the way that the Feynman argument visualizes.

Another issue, whose premise on Riemannian geometry is often forgotten, is the question of what equation would govern the determination of geometry from quantized matter. Here, the problem is that (in a Riemannian geometry) if the metric is classical, then so is the Levi-Civita connection. Therefore, the field equation would have a (classical) Einstein tensor G on one side and a (quantized) stress tensor T on the other. So, one tends to use a proxy, like <0| T |0> = kG, where |0><0| is the (assumed unique) vacuum state.

Given the issues previously raised about vacuum degeneracy, the premise of the equation is questionable.

If, on the other hand, the vacuum is degenerate with (say) one state |g><g| for each orthonormal frame bundle F_g(M) then it is quite feasible to write down an equation such as <g|T|g> = k G(g), where the right hand side is the Einstein tensor G for a given metric configuration g. The same question regarding how the matter is to be coupled to gravity still arises, but is partially negated in a Riemann-Cartan geometry since in such a geometry the connection is an independent object. So one could quantize the connection, while keeping the metric classical.

(8) Closely linked to this is the idea of gravity NOT being a fundamental force at all, but effective. This is advanced by Padmanabhan, Verlinde, et al.; and should also be linked to Sardanashvily, Mangiarotti et al. as well as to Jacobson's Gravity-as-Thermodynamics idea, which Verlinde descends from.

This is the approach I think is the right one. It can be deepened if one is able to derive an equation such as the one I posed <g|T|g>/h-bar = 8 pi A G(g) (A = Planck area) as something arising from an anomaly associated with a breakdown of classical symmetry. In particular, this could be something that comes about as a result of diffeomorphism symmetry being spoiled upon quantization.

(8) Classical/quantum hybrids.
All successful approaches I've described entail the same thing: the Weyl tensor is a c-number and the metric is classical -- even if the connection is quantized. This is not consistent in a Riemannian geometry, but is perfectly well feasible in a Riemann-Cartan geomtetry. The main observation is that the equations governing matter (particularly fermions) only see gravity through the connection, and only see it as just another gauge field. So, as long as the connection can be quantized, this part of the consistency problem is resolved.

The main issue with approaches to quantum field theory that adopt microcausality as a postulate is this. Since the axiom is posed at the operator level, as a defining condition on the field algebra itself, this has the effect of building in the light cone structure of WHATEVER geometry emerges from the algebra. But that sets into motion a chain of consequences:
(a) once you have the light cones, you have the conformal geometry
(b) once you have the conformal geometry, you have the Weyl tensor -- a unique tensor for each field algebra; i.e. a c-number tensor.
(c) once you have a c-number Weyl tensor, you have no quantized gravitational modes, since it's the Weyl tensor that defines the gravitational degrees of freedom.

So, eventually the correct approach to the problem will lead to an IMPOSSIBILITY THEOREM for Quantum Gravity (when "Quantum Gravity" is meant in the sense of "quantized metric" or "quantized Weyl tensor"), and the establishment of a quantum theory in which gravity emerges as an effective force, rather than as a fundamental force.

In such an approach, the item (3) "quantum theory in a curved background" IS all you have and all you need. The back-reaction of matter on geometry is embodied in an effective dynamics, such as the one I posed: <g|T|g> = kG(g).

Last, but not least, bearing on this question are the works of Penrose, Diosi et al., who have been seeking ways to hybridize classico-quantum forms of gravity.
 
  • #71
Haelfix said:
No I am saying that the ratio of the gravitational coupling constant with other gauge coupling constant never exceeds one..

Please read the introduction of Birrel and Davies or alternatively section 3 of this introductory paper
arXiv:1011.0543

and the following gives the details of the energy expansion in slightly more detail, including a test case calculation of the change to the effective gravitational coupling constant where you see the effects arising from quantum corrections.

http://arxiv.org/abs/gr-qc/9712070v1

Alternatively the papers on asymptotic safety also seem show the same general pattern (Geff goes to zero)

Slightly more universal and highbrow statements can be found in this brilliant paper

http://arxiv.org/abs/hep-th/0601001

where they argue that the existence of incredibly small coupling constants arising from new Yang Mills like physics cannot occur in nature.

There is no solid evidence to support your claim that the ratio never exceeds one here. Only


http://arxiv.org/abs/hep-th/0601001

sugests that the mass/charge ratio never exceeds one and only for U(1).

If we take a yang-mills coupling it will go to zero as it is asymptotically free at high energies. The dimensionless gravitational coupling grows with energy and even in AS will reach a non-zero fixed point (note: you can't take the ratio of the dimensionful gravity coupling with the gauge one since this will carry dimensions and there would be no meaning to it being one). Now gravity might spoil asymptotic freedom but the current evidence suggests it might not. If we still have asymptotic freedom for YM theories then the ratio of the gravity to gauge coupling will exceed one.


Now I am in complete agreement that we can't neglect the running of any of the couplings once gravity is involved. But we have to do the calculation to see what the ratio of different couplings will do. I think you make a good point that pure gravity it is not a good enough model to tell us about QG and we need to include matter too.
 
  • #72
Finbar said:
If we take a yang-mills coupling it will go to zero as it is asymptotically free at high energies.
Yes.

Finbar said:
The dimensionless gravitational coupling grows with energy and even in AS will reach a non-zero fixed point (note: you can't take the ratio of the dimensionful gravity coupling with the gauge one since this will carry dimensions and there would be no meaning to it being one).

Yes. I didn't want to get into this, b/c it gets away from the point and becomes technical, but what we actually compare are the couplings in the energy expansion (the Cn's in the derivative expansion of the effective lagrangian of gravity coupled to whatever matter survives up to the Planck scale) not the uncoupled SM gauge couplings by themselves (which probably are altered by strongly coupled GUT dynamics anyway). The former by construction has the same units, however, there are ambiguities in what one means by this, arising from renormalization scheme differences ... Again its not difficult, but its a bit of a chore to identify b/c there is a tremendous amount of mixing and field redefinitions taking place when you take the counter lagrangian etc.. Especially when you have a large amount of matter species. Suffice it to say, you can show that my statement will hold in some sense.

Anyway let's go over this again from the top. I'm sure you have seen the famous RG log graphs where you have the 3 SM couplings that unify as lines, and the gravitational constant that also unifies about 2 orders of magnitude later from underneath. We both agree that up until the Planck scale, gravity is certainly the weakest force (at least with just the SM + gravity). Good!

What happens when quantum mechanics becomes involved and the expansion becomes strongly coupled?

Well, the previous behaviour of the couplings alters, and a precise description would require calculating the new beta functions of the full Planckian theory (requiring knowledge of whatever physics and matter exists there). Of course a UV completion would completely alter the physics entirely, and it wouldn't make sense to talk about 'gravity' perse anymore. --So I will assume from here on out that we are not doing that and are not introducing new degrees of freedom--

So can we make some guesses as to the behavior? You bet! The first guess is to examine what happens to the effective gravitational coupling constant with the first quantum corrections arises at one loop in the case of pure gravity in the context of graviton graviton scattering. If you read page 13-14 of the Donoghue paper, you will see that he refers to a calculation that gives a correction that is *negative*. The first analytic albeit perturbative evidence that the behaviour actually turns around and becomes weaker again.

Second piece of evidence. In asymptotic safety papers, they find the same exact phenomenon.. EG the weakening of Newtons constant! This is slightly more powerful than the previous result, b/c they are probing some amount of strongly coupled behavior through the method of the exact renormalization group equations.

See Percacci's FAQ and the references he links too

http://www.percacci.it/roberto/physics/as/faq.html

Now the final piece of evidence comes from Nima's paper that I linked earlier.

There the conjecture is claimed to be universal for all BYSM physics that you might include before the Planck scale -its motivated in part with a U(1) but can be generalized to any Nonabelian group that can be higgsed down to the U(1)- They further motivate it with several no go arguments. The point is that if you include new YM forces with absurdly tiny couplings (in such a way that it would actually be weaker than gravity), you are secretely introducing a new intermediate scale in physics, and are conspiring for there to be an infinite tower of very light stable charged particles that are not protected by any symmetry. The nonobservation thereof and theoretical implausibility of such objects is then claimed to be evidence for the conjecture.

So I would say the case is very strong, that gravity always stays the weakest force in our world, or indeed any consistent world with physics like our own.
 
Back
Top