# Why quantize gravity?

1. Dec 14, 2005

### marcus

Why do we need a quantum theory of gravity?

Lots of people have asked. It is a good question to ask because it evokes interesting answers. I will tell you my current answer---we can all have different reasons, and they can change from year to year---there is no single correct answer for all time, to this question.

Most recently, the Amsterdam physicist Theo Nieuwenhuizen ("theon")
http://staff.science.uva.nl/~nieuwenh/
asked this question in a conversation between several physicists at Peter Woit blog Not Even Wrong
http://www.math.columbia.edu/~woit/wordpress/?p=308
there are currently 39 comments and "Theon" comment is number 35
so to find it you can go to the end and scroll back a few. He said:
"Did anybody question whether we really have to quantize gravity?"

The answer is obviously yes, I have seen this questioned several times, and discussed. So people HAVE questioned whether. But probably Theo knows this, and only asked to encourage people to think.

Maybe we at PF can actually use Theo's question better than the people at N.E.W. because, for one thing, the multithread format of PF board is better than the blog format. In blogs like Peter's, a conversations get covered over and lost very quickly. New comments on a thread do not bring the thread back into sight. (Cosmic Variance has a rudimentary sidebar menu of active threads, but most blogs do not.)

2. Dec 14, 2005

### marcus

I had to go to another thread. I didnt yet say why quantize gravity.
My current reason to do this, that I see, is contained in Freidel's latest paper.

He gets Feynman diagrams out of spinfoam. He gets an effective QFT as the "semiclassical limit" (the zero gravity limit as G -> 0) of a spinfoam model of gravity.

This is done rigorously in 3D. Now that stage is finished and was successful---so they are starting to try the same thing in 4D. There is a Freidel/Baratin paper in preparation. Freidel gave the overview at Loops'05 and talked a little about extending to the 4D case, and then Baratin gave a talk at Loops'05 where he presented stuff from the paper they have in preparation.

the paper in prep is called Hidden quantum gravity in Feynman diagrams. The idea is (what is already shown in 3D) that there is a SPECIFIC spinfoam model which you must have if you want it to have feynman diagrams in its flat, zerogravity, limit.
So a particular QG model is HIDDEN already in the flat, or effective, QFT.

We know that current QFT cannot be fundamental because it is built on a flat non-dynamic spacetime----so QFT is only an effective theory which is an approximation (when gravity is negligible) of the real QFT of matter. OK, Freidel says that he can go beyond the effective theory of matter to a more fundamental theory simply by constructing the unique Quantum Gravity model which the flat gravityless QFT insists on---the spinfoam QG which is "hidden" in the Feynman diagrams.

this is a way of saying why it should be useful to quantize gravity. because it will lead to a more fundamental version of the Standard Model

Last edited: Dec 14, 2005
3. Dec 14, 2005

Staff Emeritus
Well, suppose this was true:
• GR is correct, as interpreted with equivalence classes of diffeomorphisms, but otherwise classical "all the way down". No gravitons, no quantized spacetime; gravity is curved geometry.
• Some extension of the Standard model turns out to work in curved geometry
• And some classical interpretation of quantum measurement turns out to be workable.

4. Dec 14, 2005

### Stingray

Even if spacetime remains completely classical, what determines it? Einstein's equation uses the classical stress-energy tensor as a source. This loses its meaning if matter is described quantum mechanically (as it apparently must be). Simply replacing the right-hand side of Einstein's equation with the expectation value of the stress-energy tensor leads to inconsistencies. So GR must change as far as I can see.

5. Dec 14, 2005

### marcus

and when there is an extension of Std Mdl that works on curved geometry, then what curved geometry do you choose for it to work on?

I actually dont think we have to discuss whether we can MAKE DO with a schizophrenic mix of classical Gen Rel and extensions of the Std Mdl.

this question of "needing" QG is not a practical question. Squirrels live happily without physics and humans can be happy too. We dont need QG for survival but as Fabien Besnard said "for the honor of the human mind"

So this question of Theo in Amsterdam is like a divergent series. Divergent series are good to consider because they give us ideas. hardy said "this series diverges, therefore we can use it to derive numbers!"
THERE IS NO ONE CORRECT ANSWER to why we must find QG.

today, my answer is to point at the work of Laurent Freidel. He has found a spinfoam QG, with matter, which CONTAINS feynman diagrams and reproduces vertex amplitudes. So QG offers a way to a more basic theory of matter (as a zerogravity limit of a theory of spacetime-and-matter)

the latest Freidel is great---I should get a link in case anyone hasnt seen it.

here are some PF posts talking about the Freidel work and giving links

Last edited: Dec 14, 2005
6. Dec 14, 2005

### garrett

Stingray's simple explanation of why gravity needs to be quantized is correct.

7. Dec 14, 2005

### Locrian

Hmm.

The only reason to quantize gravity is to match experimental observations that can't be produced with theory, or invalidate current theory.

Which ones do that?

8. Dec 14, 2005

Staff Emeritus

Well, I sort of addressed that in my third bullet point. See Paul Merriam's paper at http://www.arxiv.org/abs/quant-ph?0506228. Maybe a relative approach gets us a "classical" system.

9. Dec 14, 2005

### turbo

What if:
• GR is incomplete and curved geometry is only an approximation for gravitation. The correcting extension of GR will entail a local mechanism for gravitation and inertia that can be explained by matter's interaction with a single field.
• The standard model requires at least one modification (i.e. no Higgs boson) but it otherwise correct.
• The single field in option 1 is the quantum vacuum field. (Sakharov's conjecture)

Such a scenario would retain the standard model with its many successes and incorporation of the field of the quantum vacuum into GR as the source of gravitation and inertia may entirely remove the need for DM and DE.

10. Dec 15, 2005

### Chronos

Isn't any model necessarily 'flat' within it's own reference frame? If you push any mathematical model through enough integrations, does it not ultimately flatten out?

Conversely, is there really any point in mathematically modeling things beyond observational reality? Do those models necessarily have meaning? I think not. There are many mathematical constructs that have no observational consequences. They might be beautiful, but, still irrelevant IMO.

So, in other words, I agree with Stingray.

11. Dec 15, 2005

### vanesch

Staff Emeritus
I think the main problem is with your 3rd point, IF Bell situations are real. There's no way in which you can have a classical interpretation of quantum measurement that can respect locality (if we accept the Bell type experiments) ; and if you cannot respect locality, GR falls on its flat face. That's why people who cherish GR have some aversion for Bell situations (like our friend Careful).

So or there is some (non-local) collapse of the wavefunction (which will never be able to be formulated in a generally covariant way), or there is NO such collapse, in which case you can have gravitationally significantly different quantum states in superposition, and then the question is: how do you determine a stress-energy tensor from such a superposition ?

Now I have been "dreaming" about a possibility, in which we have a global wavefunction consisting of a "matter" part and a "geometry" part, and you could think of writing:

|psi> = |matter1>|geometry1> + |matter2>|geometry2> + ...

in which you have of course to write the "matter" states in a localized basis (based upon the conjugated geometry state), and which DO have a well-defined energy-momentum tensor. As such, this introduces of course a preferred basis (which looks very classically).

Now, my wet dream would be that in the Schroedinger equation, the "time derivative" becomes a state-dependent operator:

instead of having d |psi> / dt, you would have a DT operator, which reduces to a time derivative wrt to a foliation of each geometry:

DT|psi> = [d/dt1 |matter1>] |geometry1> + [d/dt2 |matter2>] |geometry2> + ...

where d/dt1 only makes sense wrt "geometry1" of course, and d/dt2 only makes sense wrt "geometry2"... and we'd have individual Schroedinger equations for each individual term.

geometry1 could be totally classical (respecting GR), while "matter1" would evolve according to the curved spacetime of geometry 1... UNTIL it becomes gravitationally "superposed" in which case we'd have to split the term into two different terms "matter1a" and "matter1b" with "geometry1a" and "geometry1b".

The difficulty will be to recombine these different terms into one single wavefunction. One might even hope that we get out a non-unitary combination that way (although the individual matter terms do evolve strictly unitary, the recombination into one wavefunction might be non-unitary).

Now, I should send myself warning points for over-speculative stuff :-)

It is rather my question: I'm pretty sure that such a semi-classical approach has already been considered and it must have a lot of problems.

12. Dec 15, 2005

Staff Emeritus
Patrick, do have a look at the paper I linked to in post #8, building on Rovelli's relational approach, Merriam imagines a law that requires different interacting systems to see the same value of h (a la c with relativity) which requires a relative adjustment of their mass scales.

Now imagine in the spirit of DSR that the laws of nature require all systems to see the same values of c, G, and h (and thus in particular the same values of the Planck dimensions), Work out the transformations that do this and then build it into the tangent spaces of, umm, Relative General Relativity (RGR).

13. Dec 16, 2005

### Chronos

A naive question: Is it necessary to break this down to a wave function?

14. Dec 19, 2005

### hossi

Another reason why gravity should be quantized: singularity avoidance. The appearance of singularities seems to tell me that we are doing something wrong. However, though this seems a good motivation for me, it is not so completely strict. I.e. modifications on a classical level (meaning non-quantized but beyond standard) might do that.

I totally agree with Stingrays argument, just ask: what is the gravitational field of a quark? However, also that does not necessarily mean that gravity itself has to be quantized, just that we don't really understand QFT in curved space or its observables. BTW, intersting paper about that

Observables in effective gravity
Authors: Steven B. Giddings, Donald Marolf, James B. Hartle

What I mean is: if we understand how the source-term arises from a quantum theory (right hand side) that does not imply that we have to quantize gravity (left hand side).

However, what is clear is that gravity at the Planck scale is a key point for our understanding of a unified theory. And therefore pretty addictive - at least for me.

What if instead of quantizing gavity, gravity is the CAUSE for quantization?

15. Dec 19, 2005

### marcus

simply want to echo that question

16. Dec 20, 2005

### Careful

Hi,

Let me first say that this is a good question and that many physicists actually see no need at all for this quest. Most take the pragmatic attitude that it is sufficient to have generation C of the standard model + Einstein gravity (with the *correct* cosmological model) to calculate whatever you desire. For me, QG is about the clash between different mutually exclusive religions, so clearly at least one has to be sacrified (it is fashionable to sacrifice the superior *theory* - which is GR). Therefore, QG is the name given to the Platonic desire to know how two contradictory visions can emerge in opposite limits of one and the same theory. At least this is the merchandising pep talk. In this quest, people see the need to go to Planck energies wich is entirely ridiculous IMO since neither theory says something about this kind of exotism (it seems to me that one should better start looking for unification at distance scales which are at least a factor of 10^{14} higher). To keep this short, I will comment on some remarks made by das schones madchen´´ to join the discussion.

**
Another reason why gravity should be quantized: singularity avoidance. The appearance of singularities seems to tell me that we are doing something wrong. However, though this seems a good motivation for me, it is not so completely strict.**

Well it is good that you at least mention that this is not a strict reason at all. Actually, it is far from clear that a theory of QG (whatever this is) is going to avoid singularities. In the same spirit, it is by far not said that nature imposes a dynamical UV cutoff.

** I.e. modifications on a classical level (meaning non-quantized but beyond standard) might do that. **

Well, I know a method which brakes the equivalence principle and does this (you know of any other?). The point I want to make is that one should not worry at all yet about -say- black hole singularities: the energy scales involved are way too high to get any experimental indication about this for the moment. IMO, it is much better to start from an effective unifying theory which is *clearly* open to fasification, that is the only way we can learn something and going down to the Planck scale right away postpones such criterion for at least another century.

**I totally agree with Stingrays argument, just ask: what is the gravitational field of a quark? **

I did not read this argument, but it is for sure not the main question to ask. A better one would be : how much is gravity going to change the EM field of the quark and on what distance scales ? (the compton scale)

** However, also that does not necessarily mean that gravity itself has to be quantized, just that we don't really understand QFT in curved space or its observables. BTW, intersting paper about that**

We do not even have a realistic, rigorous QFT in FLAT space time which is known to satisfy the Wightman axioms AFAIR. In curved spacetime the situation is even far worse...

**
However, what is clear is that gravity at the Planck scale is a key point for our understanding of a unified theory **

No, I disagree ... very interesting gravitationally induced effects already show up at the Compton scale of elementary particles. The Planck scale is not needed at all.

**And therefore pretty addictive - at least for me.
What if instead of quantizing gavity, gravity is the CAUSE for quantization?**

Exactly (but you might want to include EM) ! And if you want to understand that, you better start out from *classical* gravitation and EM and *concrete* test models (as some crazy person half a century ago, I am for example not convinced that we *need* the strong nuclear forces at all as a fundamental building block). Of course, this is not done because you draw then the local realist card (as I do) and that is bad, bad, bad ... There are many who support such ideas but very few who actually *do* it.

By the way, you have a really cute nose

Cheers,

Careful

17. Dec 20, 2005

Staff Emeritus
Careful, what I take from this post is that YOU have a theory, effective at the Compton scale, which "brakes (sp? breaks?) the Equivalence Principle" and in some way unifies EM and GR. I know a couple of theories that claim to do things like that, for example Schifflet's development of Einstein Schroedinger Unified Theory. Without breaking our guidelines could you indicate the basic approach of your theory? If you don't want to air it here, you could PM me.

18. Dec 20, 2005

### Careful

As always you are too enthousiastic If I would have such theory already, you could for sure find it on the arxiv. I did not know about Schifflet but the equivalence breaking mechanism which avoids singularities (this is not a theorem but there is some evidence) can be found in the work of Shojai (not that I put my hand in the fire for this, far from) which is a de Broglie type approach to QG. That ordinary gravitation can drastically modify EM (through the Einstein - Maxwell equations) at the Compton scale of elementary spinning particles (such as the electron) was already mentioned by myself before (actually, this was already known at the end of the sixties...). I remind you that this was simply a reaction against the usual statement that new effects (in comparison to the flat spacetime approximation) are to be found at the Planck scale - which is rubbish.

Cheers,

Careful

19. Dec 20, 2005

### hossi

Hi Careful,

Sounds like a good definition... can we make that 'seemingly' contradictory?

That's why one should think about it.

Right. But it seems to me that singularity avoidence will lead towards the question of renormalization. At least we know that physcical quantities of objects around us are not usually infinite, so nature knows how to deal with divergences.

I think you are right about the importance of effective theories but it is not the only way and it should not be the only way considered.

At least it works.

Depends on what you mean with unified theory: you mean the 'effective unifying theory' you mentioned above? Anyway, I admit: I use Planck scale as a synonym for 'the scale at which effects of quantum gravity become important', so you might have a point here.

EM does not so really excite me, but yeah, concrete test models, phenomenology, let nature decide, blabla, exactly

On the other hand it would be good to see how such effective models can follow from some fundamental theory.

Concerning my nose: it is pretty red, seems as if I brough a cold from Canada :yuck:

Take Care,

Sabine

20. Dec 21, 2005

### Careful

Hi Hossi,

**Hi Careful,
Sounds like a good definition... can we make that 'seemingly' contradictory? **

No, they are strictly speaking contradictory.

**That's why one should think about it. **

I disagree, it is not the right time to think about this. There is no experimental evidence for physics at those scales at all, and people tend to forget that IF there were something like a *lattice - like* Planck scale cutoff, then a simple electron would involve something like 10^{56} interacting degrees of freedom. That is way beyond anything we are capable off

**Right. But it seems to me that singularity avoidence will lead towards the question of renormalization. **

I think that *physically* renormalization is not even the right kind of question to ask in a satisfying theory with a realistic *particle* notion (singularities or no singularities).

** At least we know that physcical quantities of objects around us are not usually infinite, so nature knows how to deal with divergences. **

Perturbatively in general (so that does not say anything strictly speaking) : example, the weak interactions.

** I think you are right about the importance of effective theories but it is not the only way and it should not be the only way considered. **

I disagree again (I was once also of Planck scale signature); it is actually the only way we can LEARN something.

**
Depends on what you mean with unified theory: you mean the 'effective unifying theory' you mentioned above? Anyway, I admit: I use Planck scale as a synonym for 'the scale at which effects of quantum gravity become important', so you might have a point here. **

This effective theory is the best we can reasonably do; and it should be a priority to first find at least ONE (that is how physics used to work )

** EM does not so really excite me, but yeah, concrete test models, phenomenology, let nature decide, blabla, exactly **

That might be a big mistake, all the interesting effects which are known are of course electromagnetic in origin (since the mass/charge ratio of elementary particles is so damn small in geometric units). However, the gravitational potential/unit mass = EM potential/unit charge at the Compton scale of elementary spinning particles - say -. That is why gravitation CAN influence the EM force (and quite drastically - equal charges strongly attract on these scales ). So, if you want to: gravitation works indirectly through EM. You cannot just focus on one field in physics, you need to take all forces into account (that is one of the mistakes of LQG and all these pure gravitation oriented approaches).

**
On the other hand it would be good to see how such effective models can follow from some fundamental theory. **

But such effective theory IS the fundamental one by lack of any further experimental input !

**
Concerning my nose: it is pretty red, seems as if I brough a cold from Canada :yuck: **

Ah, cure it well