Consequences of Quantum Gravity

[sanman]

http://en.wikipedia.org/wiki/Quantum_gravity

Is Quantum Gravity considered to be beyond the Standard Model? Why or why not?

What are the implications of Quantum Gravity, and the possibility of a dynamic aether?

What are the practical means for investigating Quantum Gravity? Is Atom Interferometry the only known method so far?

http://www-conf.slac.stanford.edu/orion/PAPERS/D02.PDF

 

[marcus]

Sanman you refer to a paper by Robert Bingham. Here is a spires search for that author's papers:
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+eA+BINGHAM%2C+ROBERT+AND+DATE+%3E+2004&FORMAT=www&SEQUENCE=

Bingham is not well known and is not much cited by the main QG research papers. I don't even think QG is his primary specialty.

I don't think Wikipedia on QG is a good place to start. Their QG articles were far from balanced or complete for several years and they haven't really recovered: you can see that the article has an SOS diagnostic at the top saying "expert attention needed".

If you want to learn about Quantum Gravity testing, the best thing to do is to start with a search for the recent quantum cosmology literature. Certain QG approaches lead to predictions about the big bang, which involve features of the cosmic microwave background (CMB) that current instruments can look for.

So most of the testing literature of the past 3 years or so (dozens of papers by now, I guess) has focused on Quantum Cosmology.

Some author names, if you want to search directly by author: Aurelien Barrau, Julien Grain. Just do a search for papers by Barrau or by Grain that appeared since 2006.
You don't need the first names. They will be about testing models of QC which are based on the Loop approach to QG. And you can find references to other authors' work in their papers and branch out from there.

Just for general education, quantum cosmology has become a hot field lately because it extends what we can model in time back before the big bang. You should get familiar with the QC literature overall picture. Here is a Spires search. You can see who is active in the field and whose papers are getting cited. I have ranked the recent papers by citation count.

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=dk+quantum+cosmology+and+date+%3E2007&FORMAT=WWW&SEQUENCE=citecount%28d%29

This uses keyword "quantum cosmology" and restricts to date more recent than 2007.

Maybe I should explain. When we look at the microwave sky we see an enormously expanded picture of the early universe. This in a certain sense provides us with a "microscope" to see QG effects (which would otherwise be very small.) For instance if inflation occurred, according to one of the various possible inflation scenarios, this also would have involved an enormous expansion. So that would contribute to making QG effects visible.
If, for example, QG affected the spectrum of primordial gravitation waves in the early U, then these primordial waves should be visible, greatly magnified, as ripples frozen in the map of the CMB microwave sky. We just need to look more carefully at the CMB map, with more accurate instruments (one of which was launched last year and has begun taking data.)
So the time is now, for QG theories to make predictions about features of the CMB which will, or will not, be seen over the next 2 or 3 years.

That is the current testing picture, and basically why the field has become hot. This is why Barrau, Grain, and others have been writing about it and doing calculations. Another one is Mielczarek, and he has some collaborators whose names I cannot recall.

I would not worry about Robert Bingham right now, because the other stuff is more active. Eventually of course what you have read about by Bingham might become relevant, but it is more remote and speculative IMHO.

 

[Naty1]

"Is Quantum Gravity considered to be beyond the Standard Model? Why or why not?"

There is no gravity in the standard model of particle physics...strong,weak, electromagnetic forces and all particles are included. Nobdoy knows how to reconcile gravity with Quantum Field theory that is a basis for the standard model.



A good introductory book, no math, is Lee Smolin's THREE ROADS TO QUANTUM GRAVITY (2001) in which he discusses loop quantum gravity, string theory and independent approaches from people like Roger Penrose, Alain Connes and Chris Isham. Inexpensive used copies are available from sources like Amazon.com.

 

[tom.stoer]

Is Quantum Gravity considered to be beyond the Standard Model?

Yes. The is no gravity inside the SM. The quantization of the SM model relies on flat space. Quantization of gravity based on methods used in the SM is not working; new insights are required.

What are the implications of Quantum Gravity

"fundamental length = discretized" spacetime structure (which we should not consider as spacetime any more)
entropy of geometry
resolution of black hole information paradox
resolution of black hole and big bang singularities

What are the practical means for investigating Quantum Gravity?

I know of no direct method as the Planck length is much below any experimentally reachable length scale.

However there are highly speculative ideas regarding large extra dimensions resulting in larger Planck length and experimental signatures like micro black holes at the TeV scale (e.g. at the LHC). In addition there are ideas regarding QG theories resulting in "broken" or "deformed" Lorentz invariance which leads to frequency-dependent speed of light in vacuum and time-of-flight signatures e.g. for gamma-ray bursts. These ideas seem to be speculative as well. The idea to derive such effects within the LQG framework failed as these effects seemed to be artefacts of approximations methods only.

 

[ensabah6]

Yes. The is no gravity inside the SM. The quantization of the SM model relies on flat space. Quantization of gravity based on methods used in the SM is not working; new insights are required. y.

Do you consider SM on curved spacetime to be a counterexample?

 

[tom.stoer]

Do you consider SM on curved spacetime to be a counterexample?

No, I consider it to be still an incomplete theory. Afaik there are still special requirements for spacetime geometry. Are there proofs (!) that all quantization methods known from the SM are available for arbitrary curved spacetime?

 

[ensabah6]

No, I consider it to be still an incomplete theory. Afaik there are still special requirements for spacetime geometry. Are there proofs (!) that all quantization methods known from the SM are available for arbitrary curved spacetime?

I've heard conflicting claims about whether string theory as a theory of QG is "consistent" i.e borel summable, perturbatively finite to all orders, converging, etc.

 

[tom.stoer]

I am not talking about string theory. I see the same problems as you are mentioning plus some others ...

I only talk about "standard QFT" on curved manifolds. I don't think that you can define QFT on arbitrary spacetimes, but that you have to insist on special geometries (stationary, Killing vectors, ...). But I am not an expert!

 

[friend]

I am not talking about string theory. I see the same problems as you are mentioning plus some others ...

I only talk about "standard QFT" on curved manifolds. I don't think that you can define QFT on arbitrary spacetimes, but that you have to insist on special geometries (stationary, Killing vectors, ...). But I am not an expert!

Isn't the background locally flat in any arbitrarily curved spacetime? And can't we do QFT on flat spacetimes? I would think that it would be straightforward to do QFT on a flat background, change the background to a incrementally different flat background with slightly different properties, and then see show changes in geometry affect the particles of QFT, and visa versa.

 

[tom.stoer]

Isn't the background locally flat in any arbitrarily curved spacetime? And can't we do QFT on flat spacetimes? I would think that it would be straightforward to do QFT on a flat background, change the background to a incrementally different flat background with slightly different properties, and then see show changes in geometry affect the particles of QFT, and visa versa.

Unfortunately this is not the case. Usually you cannot define a vacuum in non-trivial backgrounds. This is due to the fact that you cannot define positive and negative frequencies, you cannot distinguish between particles and anti-particles, etc.

Two famous effects are the Hawking radiation and the Unruh effect. I think they both rely on special assumptions regarding geometry. I do not know if its possible to define QFT on arbitrarily curved backgrounds. I don't think that locally flat backgrounds are sufficient as they do not allow you to study perturbation theory which is based on asymptotically free particles (but what is "asymptoticylla free" if your theory is only locally valid?). But you need perturbation theory in order to define the quantization of the SM, in order to define the renormalization etc. I simply haven't seen any review articles summarizing QFT on curved backgrounds providing the same proofs as for flat spacetime. Perhaps it exists, but I am not aware of it.

 

[bapowell]

Isn't the background locally flat in any arbitrarily curved spacetime? And can't we do QFT on flat spacetimes? I would think that it would be straightforward to do QFT on a flat background, change the background to a incrementally different flat background with slightly different properties, and then see show changes in geometry affect the particles of QFT, and visa versa.

Good question. Locally, spacetime is indeed flat. However, in QFT, one needs to address the behavior of particles of all wavelengths. Low momentum modes with wavelengths larger than the radius of curvature of the manifold cannot be treated as living in the locally flat tangent space. As Tom mentions, the Unruh and Hawking effects are two manifestations of this issue, and the horizons that arise in both situations can be associated with the curvature scale.

 

[tom.stoer]

Two references:

http://arxiv.org/abs/gr-qc/9707062
Title: Quantum Field Theory in Curved Spacetime
L.H. Ford
(Submitted on 30 Jul 1997)
Abstract: These lectures deal with selected aspects of quantum field theory in curved spacetime including the following topics: (1) Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an expanding universe; moving mirror radiation. (2) The Hawking effect - particle creation by black holes. (3) Ultraviolet and infrared divergences, renormalization of the expectation value of the stress tensor; global symmetry breaking in curved spacetime. (4) Negative energy in quantum field theory, its gravitational effects, and inequalities which limit negative energy densities and fluxes. (5) The semiclassical theory of gravity and its limitations, breakdown of this theory due to metric fluctuations, lightcone fluctuations.

http://arxiv.org/abs/gr-qc/0308048
Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect
Ted Jacobson
(Submitted on 14 Aug 2003 (v1), last revised 9 Apr 2004 (this version, v3))
Abstract: These notes introduce the subject of quantum field theory in curved spacetime and some of its applications and the questions they raise. Topics include particle creation in time-dependent metrics, quantum origin of primordial perturbations, Hawking effect, the trans-Planckian question, and Hawking radiation on a lattice.

=> seems to be much better understood than expected :-)

 

[friend]

Good question. Locally, spacetime is indeed flat. However, in QFT, one needs to address the behavior of particles of all wavelengths. Low momentum modes with wavelengths larger than the radius of curvature of the manifold cannot be treated as living in the locally flat tangent space. As Tom mentions, the Unruh and Hawking effects are two manifestations of this issue, and the horizons that arise in both situations can be associated with the curvature scale.

So are you saying that lower frequency particle waves don't propagate, or do their frequencies change as they propagate. Such a thing would show exactly how the gravitational field interacts with particles, right?

 

[bapowell]

Basically one finds that the 0-particle state (vacuum) gets populated with these low frequency modes. The vacuum becomes momentum-dependent, and the gravitational field is said to induce particle production. The mode frequencies can also be time dependent, for example, in time dependent backgrounds. During inflation, the wavelength of quantum modes increases with the expansion. When these wavelengths become of order the Hubble radius (the event horizon during inflation), the quantum fluctuations become real, classical perturbations -- ie the quantum vacuum gets populated with low momentum modes (here termed perturbations).

Even though it's a tricky subject, much is known about formulating fully consistent QFTs in curved spacetime. Check out Tom's references, or the books by Birrell&Davies, Fulling, and/or Wald. These consistent QFTs do show exactly how a (classical) gravitational field interacts with quantum fields.

 

[George Jones]

Even though it's a tricky subject, much is known about formulating fully consistent QFTs in curved spacetime. Check out Tom's references, or the books by Birrell&Davies, Fulling, and/or Wald. These consistent QFTs do show exactly how a (classical) gravitational field interacts with quantum fields.

Or the new book by Parker and Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity,

https://www.amazon.com/dp/0521877873/?tag=pfamazon01-20.

 

[Haelfix]

Unfortunately this is not the case. Usually you cannot define a vacuum in non-trivial backgrounds. This is due to the fact that you cannot define positive and negative frequencies, you cannot distinguish between particles and anti-particles, etc.

To be precise, its not that you can't define a vacuum, its that you can define altogether too many and there is no obvious canonical choice.

Heurestically, the technical problems of qft in curved spacetime are ok so long as you restrict attention to either situations where you have simple and well behaved metrics and perturbations thereof (Schwarschild, FRW, DeSitter, etc) and/or where you are suitably far away from the places where you know the theory breaks down (Planck scale and/or places of violent curvature changes). Outside of those regimes, and only outside of those regimes, you can trust the calculation.

Of course that's not entirely satisfying, but for now that's the state of the art and is a notoriously difficult mathematical problem.

It should be emphasized that adding symmetries and dynamical consistency constraints (like supersymmetry, conformal symmetry and or stringy constraints) ameliorates the situation a lot (but not entirely).

Either way its likely the full solution will occur decades after the heurestic physics is ironed out. Much like the theory of distributions occurred many years after the Dirac Delta function was pulled out of a hat.

 

[tom.stoer]

Heurestically, the technical problems of qft in curved spacetime are ok so long as you restrict attention to either situations where you have simple and well behaved metrics and perturbations thereof (Schwarschild, FRW, DeSitter, etc) and/or where you are suitably far away from the places where you know the theory breaks down (Planck scale and/or places of violent curvature changes). Outside of those regimes, and only outside of those regimes, you can trust the calculation.

Of course that's not entirely satisfying, but for now that's the state of the art and is a notoriously difficult mathematical problem.

That is certainly satisfiying for QFT on curved classical spacetime. One cannot expect to solve the problems of QG via QFT + classical GR.

Last question: what about renormalizibility to all orders in perturbation theory?

 

[timetravel_0]

What exactly is the problem with Gravity? I know its probably something quite complex, but why can't gravity be included in the SM?

 

[tom.stoer]

What exactly is the problem with Gravity? I know its probably something quite complex, but why can't gravity be included in the SM?

This is a rather lengthy story. I don't know what you know about quantum field theory, so here's a simple explanation: Einstein's equation formally read

G[g] = T[g, SM]

Here G is the Einstein tensor constructed purely from spacetime g, whereas T is the energy-momentum density of all fields of the standard model. In order to harmonize gravity and the SM one has to quantize both sides of this equation

G_quant = T_quant

Quantizing only the right side and using its expectation value like

G_class = <T_quant>

is a first step but not fully consistent.

But quantizing the left side = quantizing gravity

G_class => G_quant

is still under debate. There are a lot of different approaches or research programs (string theory, loop quantum gravity, asymptotic safety, non-commutative geometry, ... to name a few) but there is no fully complete and consistent and commonly accepted theory of quantum gravity.

What we know for sure is that due to several reasons the straightforward quantization of gravity along the lines of the SM (on top of a classical spacetime background) fails! New methods are required. The basic reason is that the construction of QFTs for the SM relies on a fixed background spacetime whereas in GQ spacetime becomes a dynamical entity. That means that a lot of methods (some have been discussed here in this post) do no longer work in QG.

 

[timetravel_0]

Could you quantitatively messure gravity by messuring time dilation between two different proximities to a gravitational field? Stupid suggestion... :)

I guess the problem is fitting the physics of gravity to the man made instrument... shouldn't it be the other way around?

Are bosons really particles, or is it just a method of messuring? Has it been proven that a Photon is really a particle? Sorry for all the stupid questions - but I'm trying to understand. Thanks.

 

[Haelfix]

Last question: what about renormalizibility to all orders in perturbation theory?

Badly divergent by naive power counting methods. Semiclassical gravity typically truncates the series after an order or two.

As for how you renormalize that first counterterm. Well, its much more technically sophisticated and difficult than in flat space. DeWitt and a few others devised a few different ways on how to proceed. The regularization is often done by point splitting or adiabatic regularization, and you will have to renormalize the stress energy tensor, the coupling constants and the effective action.

Actually it depends a little bit on what you are trying to solve. For instance when you are studying inflation, sometimes you can cut some steps by judicious guessing.

 

[tom.stoer]

Badly divergent by naive power counting methods. Semiclassical gravity typically truncates the series after an order or two.

I do not understand.

I know that quantum gravity is non-renormalizable (powercounting, dimension of Newtons constant). But I do not understand how this relates to QFT on curved (but classical!) spacetime. Powercounting is not affected by curvature, is it?

 

[Haelfix]

"But I do not understand how this relates to QFT on curved (but classical!) spacetime"

Ahh ok this is a common source of confusion (somewhat due to the fact that the word semiclassical is mangled). Consider the case of QCD. Imagine that you were to treat the gluon field classically (call it the color field), and try to write down a quantum theory of quarks that propagate in this classical field. The problem is that whenever you write down that theory, you immediatly notice that any time an important quantum effect of quarks take place, you have to allow for an analogous effect for gluons. These gluons will of course change the classical field that you have posited in the first place. This happens everywhere, and the theory is manifestly inconsistent when done this way.

So b/c of the nonlinearity involved (unlike the QED case where you can do such a thing), there is no way to ignore the quantum theory of gluons and instead you have to do everything at once.

Similarly when you are doing QFT in curved space, precisely b/c gravity is now turned on and is nonlinear (eg the equivalence principle), there is no way to simultaneously treat quantum matter effects while ignoring quantum gravity, at any length scale. Nevertheless, you can get away with an approximation, where you treat the quantum gravity part as being a small perturbation, similar to a weak field approximation in general relativity and then move that over to the right hand side of the field equations as part of the source term.

So when people do QFT in curved spacetime, there is always, by necessity a notion of 'gravitons'.