Why is Quantum Gravity theory still not "finished"?

[Tio Barnabe]

Physicists had success in developing a relativistic quantum mechanics, also Quantum Field theory.

I wonder why it's not the same with a quantum gravity theory. I suppose this is mainly because we do not have good emphirical information from a place where Einstein's theory fails: black holes.

Never the less, why can't we just use our theoretical knowledge (as we did with relativistic QM and QFT) to derive equations etc for a quantum gravity theory?

 

[DrChinese]

Physicists had success in developing a relativistic quantum mechanics, also Quantum Field theory.

I wonder why it's not the same with a quantum gravity theory. I suppose this is mainly because we do not have good emphirical information from a place where Einstein's theory fails: black holes.

Never the less, why can't we just use our theoretical knowledge (as we did with relativistic QM and QFT) to derive equations etc for a quantum gravity theory?

For one thing, there is no requirement that gravity should be quantized. And there are many folks who have spent entire careers working on just this. Obviously this is no cup of tea.

 

[Tio Barnabe]

there is no requirement that gravity should be quantized

But would not this quantization come in automatically from the theory? As it is with the electron energy, modes on a vibrating string, etc.

 

[DrChinese]

But would not this quantization come in automatically from the theory? As it is with the electron energy, modes on a vibrating string, etc.

What I mean is that gravity may not be a quantum force. There are sensitive experiments being constructed to determine whether it is or not. There is currently nothing "wrong" with General Relativity as it stands. However, it does not appear to work in extreme conditions (think: the very very early universe), although there is no way to be sure such conditions ever existed.

 

[DrChinese]

The idea around some of the current experiment proposals is something like this: if you could detect collapse due to a gravitational interaction, that would prove gravity is a quantum force.

Experimentally testing decoherence due to gravity, Zeilinger et al.
https://arxiv.org/abs/1703.08036
"... a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. ..."

 

[OCR]

Obviously this is no cup of tea.

Yeah, you are probably right, but still...

[COLOR=#black]...[/COLOR]

...

 

[king vitamin]

I suppose this is mainly because we do not have good emphirical information from a place where Einstein's theory fails: black holes.

Yes, a big issue is that quantum gravity effects are only really strong in black holes and during the big bang. It might not be possible to ever make an experimental test of quantum gravity, depending on what the correct theory for quantum gravity in our universe is. Coming up with new theories while having zero experimental input is tough, and the fact that we've been able to make some predictions (like Hawking radiation or holography for example) is impressive.

For one thing, there is no requirement that gravity should be quantized.

What sort of alternatives are there? There's no obvious way I know of to couple classical gravity to matter (which is demonstrably quantum) without making some sort of alterations to the theory.

 

[bhobba]

I wonder why it's not the same with a quantum gravity theory.

Well atually we do:
https://arxiv.org/abs/1209.3511

The problen is its only valid to about the Plank scale.

But that's exactly the same for the standard model - no one would really push it to the Plank scale either and we have hints it has issues if you do that eg the Landau Pole.

So I would change the question - what's going on below the plank scale. Answer - blankout. That's the number one theoretical question that needs answering.

Thanks
Bill

 

[bhobba]

There's no obvious way I know of to couple classical gravity to matter (which is demonstrably quantum) without making some sort of alterations to the theory.

Sure there is - the usual way - you add the matter Lagrangian to the GR Lagrangian - take the variation and - viola - by definition you get the stress energy tensor.

See for example appendix E of Wald.

It is possible that gravity isn't quantum - I think its very unlikely - but we don't really know because the quantum theory we do have we know isn't correct - its just an effective theory.

Thanks
Bill

 

[Haelfix]

Sure there is - the usual way - you add the mattter lagrangiasn to the GR lagrangian - taks the variation and - viola - by definition yopu get the stress energy tensor.

It is possible that gravity isn't quantum - I think its very unlikely - but we don't really know because the quantum theory we do have we know isn't correct - its just an effective theory.

Thanks
Bill

That doesn't work. The quantum matter lagrangian yields contributions to the stress energy tensor, and therefore the latter must be expressed as an operator. So presumably you will want to promote Tuv to something like its expectation value in Einstein's field equations.. The problem with that, is that this expectation value depends nonlinearly on the state of the matter system, so when you go back to solve for the time evolution of the system by solving for the metric, you find that the Hamiltonian is no longer given by a linear operator. This is a real inconsistency, and the conclusion is that quantum matter is unreconcilable with Einstein's field equations (or alternatively you have to promote the left hand side into operator equations as well in some way).

You can say the same thing another way involving gravitational superpositions, and well i'll leave it to the master himself (Feynman) to describe the setup (from page 4 onwards):
https://arxiv.org/abs/0804.3348

 

[bhobba]

(or alternatively you have to promote the left hand side into operator equations as well in some way).

I was speaking classically because he was speaking of classical gravity - but yes deep issues remain if you go to QFT.

Indeed that's what the EFT approach does. But we are in deep do do below the Plank scale.

For the nittty gritty of such an approach see Ohanian:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

The strange thing about GR is the linearised equations that you would use to quantise in the usual way imply the full EFE's (as carefully explained by Ohanian) - but of course the resultant theory is not renormaliseable and you can only have an effective quantum theory that breaks down at the Plank scale.

BTW nice paper about Feynman whose lectures on gravitation I have and read with great interest many many moons ago - I forget now how he arrived at the Lagrangian from the assumption of spin 2 particles, but it was exhilarating reading how a master went about it.

Thanks
Bill

 

[Dr_Zinj]

Burkhart Heim attempted to create a theory of everything by developing a quantizing space-time. I'm of the understanding that there were some fundamental errors in either his initial propositions, or in his early conversions that invalidated any of his future work. Point being is that I seem to recall that theory required the quantization of gravity. There are a small group of people working on Extended Heim Theory (mainly Walter Dröscher and Jochem Hauser) that corrected those errors and have been building on that work. Is that what you are referring to as an unfinished theory of quantum gravity?

 

[king vitamin]

I was speaking classically because he was speaking of classical gravity - but yes deep issues remain if you go to QFT.

I was speaking of classical gravity (the subject of DrChinese's post) in context of quantum matter, so I was thinking of the exact issues that Haelfix is bringing up: the stress-energy tensor is an operator.

You can have a classical graviton field coupled to a classical stress-energy tensor, or you can put that action inside a path integral (as an effective field theory with a cutoff) to get quantum gravity coupled to quantum matter, but treating the gravitational field as classical and the matter as quantum can't be done in any "obvious" way.

You probably already know this; you cited Wald, and he has a nice discussion of this exact issue.

 

[bhobba]

You probably already know this; you cited Wald, and he has a nice discussion of this exact issue.

Of course.

My bad - I thought you meant classical and classical but I didn't read carefully enough.

And, again of course, Wald gives the detail - like it does on most things GR related - but don't ask me the page - I haven't studied that tome for years - it even took me a while to dig up my copy and see the classical case was in appendix E,

Thanks
Bill

 

[exponent137]

Well atually we do:
https://arxiv.org/abs/1209.3511

The problen is its only valid to about the Plank scale.

But that's exactly the same for the standard model - no one would really push it to the Plank scale either and we have hints it has issues if you do that eg the Landau Pole.

So I would change the question - what's going on below the plank scale. Answer - blankout. That's the number one theoretical question that needs answering.

Thanks
Bill

I read your link, but I did not find, how it is with the gravitational principle of equivalence? Is it still valid at such models?

 

[bhobba]

I read your link, but I did not find, how it is with the gravitational principle of equivalence? Is it still valid at such models?

Of course it's still valid in the classical limit - but the approach is not the usual one based on geometry.

The classical bit is explained in Ohanian:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

Its based on field theory and the most reasonable Lagrangian analogous to the Lagrangian of Maxwell's equations. It turns out to be what's called linearised gravity. That is what is quantisised similar to Maxwell's equations - except it's not renormalisable hence you only have an effective QFT theory. The very strange thing as explained by Ohanian is if you examine the equations even though its in flat space-time particles move as if it has an infinitesimal curvature. Even more amazing is they immediately imply the full Einstein Field Equations. So what's going on - is space-time curved or is it flat? I had a long discussion with a well known quantum gravity expert, Steve Carlip, about it. What it boils down to is there is no way to tell the difference between flat space-time and objects that act as if it was curved and actually being curved.

Thanks
Bill

 

[exponent137]

Of course it's still valid in the classical limit - but the approach is not the usual one based on geometry.

The classical bit is explained in Ohanian:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

Its based on field theory and the most reasonable Lagrangian analogous to the Lagrangian of Maxwell's equations. It turns out to be what's called linearised gravity. That is what is quantisised similar to Maxwell's equations - except it's not renormalisable hence you only have an effective QFT theory. The very strange thing as explained by Ohanian is if you examine the equations even though its in flat space-time particles move as if it has an infinitesimal curvature. Even more amazing is they immediately imply the full Einstein Field Equations. So what's going on - is space-time curved or is it flat? I had a long discussion with a well known quantum gravity expert, Steve Carlip, about it. What it boils down to is there is no way to tell the difference between flat space-time and objects that act as if it was curved and actually being curved.

Thanks
Bill

1. it's still valid in the classical limit Does this mean that equivalence principle (EP) is not valid in quantum regime?

2. As I understand, scattering of two gravitons disagrees with EP in quantum regime, as well as running coupling constant of gravitation?

 

[bhobba]

1. it's still valid in the classical limit Does this mean that equivalence principle (EP) is not valid in quantum regime?

It's a meaningless question since we are dealing with flat space-time.

2. As I understand, scattering of two gravitons disagrees with EP in quantum regime, as well as running coupling constant of gravitation?

Well since we are dealing with flat space-time I don' follow your query.

Really the only way to understand this deeper than what I explained is to read Ohanian - I have explained all I can of the approach in a post like this. He casts strong doubt on the EP, its vacuous because tidal forces are a dead give away - that's his view anyway - I don't agree with it but that is way beyond this thread - you need to go over to the relativity section.

The following are all subject to controversy:

1. The EP
2. The principle of general co-variance (it's basically vacuous)

However everyone I am aware of accepts the principle of general invariance - but again that is for the relativity forum.

The real basis of GR in not 1 and 2 as Einstein thought - its that space-time geometry is described by its own Lagrangian - sometimes colloquially called space-time is dynamical. Now is that because space-time is flat and due to gravitations just seems like that or is it really like that? We do not know and in fact its a pretty meaningless question.

Thanks
Bill

 

[PhysicsExplorer]

Physicists had success in developing a relativistic quantum mechanics, also Quantum Field theory.

I wonder why it's not the same with a quantum gravity theory. I suppose this is mainly because we do not have good emphirical information from a place where Einstein's theory fails: black holes.

Never the less, why can't we just use our theoretical knowledge (as we did with relativistic QM and QFT) to derive equations etc for a quantum gravity theory?

Arguably, there is no quantum theory of gravity, because we do not have a complete picture of gravity in the context of quantum theory. This may be for a number of reasons, one reason may be because we are lacking a complete theory of quantum mechanics, irrespective of a model for gravity. Things like entanglement and non-locality may not be fully understood. In the context of spacetime, this entanglement property becomes important for a gravitational interpretation.

Maybe it's the method of quantization... Perhaps gauge theory leading to spin-2 gauge bosons is not the correct way, even though it looks quite appealing. There may be real reasons why we cannot compile gravity into the other fields of nature - for starters, gravity is treated very differently to the quantum fields. Technically speaking, gravity is a pseudo force - that means, it does not actually require a mediator particle to explain it. This hasn't been for the lack of trying with many physicists though.

Perhaps a re-understanding of gravity needs to be understood in the context of a Hilbert space. If so, what is the correct way to envision gravity at this level? Does it follow unitarity? Does a Planck spacetime exist, and do quantum fluctuations ferociously come into existence at this scale, like Wheeler himself preached? All these questions are important for gravity and I barely scratched the surface.

 

[PhysicsExplorer]

What I mean is that gravity may not be a quantum force. There are sensitive experiments being constructed to determine whether it is or not. There is currently nothing "wrong" with General Relativity as it stands. However, it does not appear to work in extreme conditions (think: the very very early universe), although there is no way to be sure such conditions ever existed.

Relativity would certainly agree, it is not a quantum force. Gravity is by definition, a pseudo force, so technically speaking, it is not the same as a true quantum field.

 

[tom.stoer]

Relativity would certainly agree, it is not a quantum force. Gravity is by definition, a pseudo force, so technically speaking, it is not the same as a true quantum field.

Why should this be the case? All other "forces" are not "forces" in the classical sense when analyzed at the quantum level. That's why we are using the term "interaction".

You can quantize gravity in a couple of different approaches. Assume for a moment at string theory would result in a unique vacuum and would predict the field content, i.e. the standard model. Then there would be no reason go criticize quantizing gravity in this approach, quantum gravity would be well-defined and unified with other interactions (even so classically it would appear slightly different, i.e. as a pseudo-force).

 

[atyy]

Physicists had success in developing a relativistic quantum mechanics, also Quantum Field theory.

I wonder why it's not the same with a quantum gravity theory. I suppose this is mainly because we do not have good emphirical information from a place where Einstein's theory fails: black holes.

Never the less, why can't we just use our theoretical knowledge (as we did with relativistic QM and QFT) to derive equations etc for a quantum gravity theory?

Quantum electrodynamics (QED) is also not "finished". So it is not just quantum gravity.

At the non-rigourous level, only quantum chromodynamics (QCD) is "finished". At the rigourous level, even QCD is not "finished".

 

[musician ilhan]

Quantum electrodynamics (QED) is also not "finished". So it is not just quantum gravity.

At the non-rigourous level, only quantum chromodynamics (QCD) is "finished". At the rigourous level, even QCD is not "finished".

I don't understand why QED is not finished.

 

[tom.stoer]

This is due to the Landau pole of QED, saying that the running coupling constant diverges (when calculated based on perturbative quantization and the renormalization group). QCD is asymptotically free and is immune to these sicknesses.

At the rigorous level no interacting and non-trivial quantum field theories has ever been defined mathematically (afaik).

 

[Zafa Pi]

the quantum theory we do have we know isn't correct - its just an effective theory.

Could you elaborate at the I level?

 

[Zafa Pi]

Obviously this is no cup of tea.

I am familiar with the expression "not my cup of tea", but after a google search the best I can come up with for "no cup of tea" is that one is not consenting to having sex.

Perhaps you mean "no piece of cake".

 

[bhobba]

Could you elaborate at the I level?

We have issues like the Landau pole, and a similar version in the electroweak theory:
https://en.wikipedia.org/wiki/Landau_pole

How is it resolved in QED - well long before that the electroweak theory takes over.

It is suspected all our theories are like that - they break down if pushed too far.

But a few things to consider:
1. This is perturbatve QFT - would a non-pertubative approach resolve it - computer simulations have shown some interesting hints.
2, Our experimental data at that level is lacking.

So the bottom line is we don't really know - further research is required - however the suspicion is some new theory is needed about the Plank scale. Certainly I know of no papers, books, physicists etc that would trust our equations at that energy level.

Thanks
Bill

 

[tom.stoer]

This is related to one (of seven) millemium prize problems:

https://en.wikipedia.org/wiki/Millennium_Prize_Problems
https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap

 

[PhysicsExplorer]

Why should this be the case? All other "forces" are not "forces" in the classical sense when analyzed at the quantum level. That's why we are using the term "interaction".

You can quantize gravity in a couple of different approaches. Assume for a moment at string theory would result in a unique vacuum and would predict the field content, i.e. the standard model. Then there would be no reason go criticize quantizing gravity in this approach, quantum gravity would be well-defined and unified with other interactions (even so classically it would appear slightly different, i.e. as a pseudo-force).

The definition of pseudo force is quite exact. It is not a real force like the other forces, and I don't know what you mean when you say all other forces are not forces, none of that makes sense to me.Quantum fields are very exact in their definition as well - they require a mediator particle. Gravity is not a real force as it does not technically require a mediator particle (graviton).

 

[tom.stoer]

The definition of pseudo force is quite exact. It is not a real force like the other forces, and I don't know what you mean when you say all other forces are not forces, none of that makes sense to me.

Concepts like force and pseudo-force are purely classical reasoning.

Quantum fields are very exact in their definition as well - they require a mediator particle.

That is an interpretation derived from perturbative quantization methods only. It is different e.g. in lattice gauge theories.

Quantum field theory requires a quantum field, but there is no need to interpret this as "mediator particle". In lattice gauge theory no "mediator particle" ever arises from the gluon field. This concept is simply not applicable in the IR regime of QCD, and there are hints that is not applicable in quantum gravity as well (have a look at the asymptotic safety approach).

Gravity can be reformulated as gauge theory with a connection and a canonically conjugate field strength. So gravity looks formally - already at the classical level - very similar to any other non-abelian gauge field theory. You may quantize it w/o ever referring to perturbative methods.

Gravity is not a real force as it does not technically require a mediator particle (graviton).

Neither does any other quantum field theory. As said above: the mediator particle is an artifact of pertubative quantization only.

 

[DrChinese]

I am familiar with the expression "not my cup of tea", but after a google search the best I can come up with for "no cup of tea" is that one is not consenting to having sex.

Perhaps you mean "no piece of cake".

I have the cake after my tea.

 

[atyy]

I don't understand why QED is not finished.

QED does not make sense at very high energies (above the Planck scale). However, QED makes sense at low energies, which is the regime that current experiments test.

See tom.stoer's reply about the Landau pole (#24), and bhobba's reply about effective field theory (#27), which state the same thing.

 

[PhysicsExplorer]

Concepts like force and pseudo-force are purely classical reasoning.

Indeed, but you seem to be missing the point. The point is from first principles, gravity is not a quantum field but relativity treats it specifically like a pseudo force. So nothing implies from first principles quantization even makes sense.

 

[PhysicsExplorer]

Neither does any other quantum field theory. As said above: the mediator particle is an artifact of pertubative quantization only.

But this is counter-intuitive. It's not the kind of physics I am accustomed with: particles do seem to exist and it seems the consensus is that they share mediator particles. To exchange forces, you need the quantization particle of the field, which we already know for each field. Unlike gravity, gravity doesn't need a particle - maybe history will prove me wrong, but I'm willing to bet on it.ps. a good question would be if the quantum fields don't require mediator particles, why have we found the quantization of each field, or are you suggesting we have misinterpreted something?

 

[PeterDonis]

But this is counter-intuitive. It's not the kind of physics I am accustomed with

So what?

particles do seem to exist

Real particles (external lines in Feynman diagrams, on shell) do "seem to exist", certainly--we observe them in experiments. But we're talking about virtual particles here (internal lines in Feynman diagrams, can be off shell). We don't directly observe them, so they don't "seem to exist" the way real particles do.

it seems the consensus is that they share mediator particles

Science doesn't work by consensus. It works by making accurate predictions.