Will QG leave GR unchanged or QT?

[Sunil]

TL;DR

I argue that there are good reasons to expect that QG will be indeed a standard quantum theory, the general principles of QT remaining unchanged, instead of a modified, generally covariant modification of quantum theory.

The name given for the not yet existing solution is "quantum gravity", suggesting a quantum theory, but no relation to GR. If there are problems of GR which prevent the use of standard quantum theory with the Schrödinger equation, and they can be solved in a modified interpretation of relativity (say, using the neo-Lorentzian interpretation of SR or the field theory version of GR or a neo-Lorentzian interpretation of it) to discuss it in the Special and General Relativity sounds appropriate.

Not at all. Most physicists who use the term "quantum gravity" mean finding a quantum theory that has classical GR as an approximation in some appropriate limit. Discussion of such proposed theories belongs in the Beyond the Standard Model forum.

I think there is nonetheless a difference, and it is in favor of quantum theory.

Having the GR equations as an approximation in some appropriate limit is, of course, required by the correspondence principle, as well as simply of empirical viability. In this sense, the same is obligatory as for GR, as for QT.

But this is something very different from being a general-relativistic theory, that means, a theory with a four-dimensional spacetime manifold. As in LQG, as in string theory there is no such manifold. I know only about a single approach to quantum gravity following this line - the proposal of Penrose (see references in https://en.wikipedia.org/wiki/Penrose_interpretation ) which has a classical GR solution and quantum theory is replaced by an objective collapse theory where the collapse happens when the parts become distinguishable by gravity.

Instead, all other approaches I know about modify GR but leave the principles of quantum theory unchanged. LQG is standard quantum theory of some lattice, string theory is a standard quantum field theory, Schmelzer's proposal would be a standard quantum condensed matter theory.

In principle, one could not exclude that QG modifies as GR, as QT. But I'm not aware of such an approach.

Moreover, I think that there is also a justification for this asymmetry. Classical GR has singularities, so it is known from the start to be wrong, it has to be replaced by a different theory. Quantum theory in the minimal interpretation has no such singularity problems. Then, GR has problems with local energy conservation laws for the gravitational field. But a Hamilton operator defining energy seems obligatory in a quantum theory.

The only counterargument I know about is that in realistic interpretations of quantum theory QT has infinities too, namely the Bohmian velocity, with is the average velocity in other such interpretations like Nelsonian stochastics, becomes singular near the zeros of the wave function. Thus, one has to modify QT as well to get rid of those singularities. But in interpretations of QT which do not give that velocity any physical meaning (given that it is unobservable and its equation violates Einstein locality) this argument would fail. Moreover, it seems not very plausible that such a modification, even if necessary, would give anything for the quantization of GR and the unification of SM and GR into some TOE.

 

[Demystifier]

The only counterargument I know about is that in realistic interpretations of quantum theory QT has infinities too, namely the Bohmian velocity, with is the average velocity in other such interpretations like Nelsonian stochastics, becomes singular near the zeros of the wave function. Thus, one has to modify QT as well to get rid of those singularities. But in interpretations of QT which do not give that velocity any physical meaning (given that it is unobservable and its equation violates Einstein locality) this argument would fail. Moreover, it seems not very plausible that such a modification, even if necessary, would give anything for the quantization of GR and the unification of SM and GR into some TOE.

I liked your post as a whole, but I have some reservations about this paragraph.

First, what exactly is supposed to be a problem if a Bohmian velocity is infinite at one isolated point? I don't see a problem.

Second, if the fundamental theory is not general covariant and Lorentz covariant, there is no problem in the fact that Einstein locality is violated. Just the opposite, it is to be expected.

 

[Sunil]

First, what exactly is supposed to be a problem if a Bohmian velocity is infinite at one isolated point? I don't see a problem.

I think infinities in physical values are always a problem. A problem one can live with, but which tells us that that theory is not fundamental, and becomes a bad approximation near the infinity.

Second, if the fundamental theory is not general covariant and Lorentz covariant, there is no problem in the fact that Einstein locality is violated. Just the opposite, it is to be expected.

I agree that for those who think the fundamental theory will not be a Lorentz covariant theory the violation of Einstein locality is a problem. But this is, yet, a minority position, despite the acceptance that GR is an effective field theory. Not even those who support and develop realist interpretations are immune to this, they often try to develop in one way or another Lorentz-covariant versions. Even Bell has tried, with some flash ontology or so which I have not understood.

 

[Demystifier]

Not even those who support and develop realist interpretations are immune to this, they often try to develop in one way or another Lorentz-covariant versions. Even Bell has tried, with some flash ontology or so which I have not understood.

Yes, I've been trying Lorentz covariant Bohmian mechanics too, and published a few papers, but eventually gave up of that approach.

 

[Demystifier]

I think infinities in physical values are always a problem.

Yes, but the question is what is physical? For instance, is the third derivative of $x(t)$ physical? Would there be a problem if $d^3x(t)/dt^3$ were infinite for some $t$?

You also mentioned Nelson stochastic mechanics. For stochastic trajectories, acceleration $d^2x(t)/dt^2$ is infinite at every $t$. Is that a problem?

 

[bayakiv]

Summary:: I argue that there are good reasons to expect that QG will be indeed a standard quantum theory, the general principles of QT remaining unchanged, instead of a modified, generally covariant modification of quantum theory.

In principle, one could not exclude that QG modifies as GR, as QT. But I'm not aware of such an approach.

There is such an approach when they go beyond space-time, by expanding the space in which matter moves, to a seven-dimensional sphere, and the principle of least action with this approach expands to the principle of the minimum flow. Quantum theory and theory of gravity with this approach are obtained in a completely natural way. Search for "Mathematical Notes on the Nature of Things"

 

[Sunil]

Yes, but the question is what is physical? For instance, is the third derivative of $x(t)$ physical? Would there be a problem if $d^3x(t)/dt^3$ were infinite for some $t$?

You also mentioned Nelson stochastic mechanics. For stochastic trajectories, acceleration $d^2x(t)/dt^2$ is infinite at every $t$. Is that a problem?

Good question. I have to admit that I have not considered this question from this point of view.

But let's try. The standard example for stochastic trajectories is Brownian motion. In this case, we know about its replacement below the atomic distances we can replace them by smooth Bohmian trajectories. The infinite acceleration is simple the artefact of the mathematics created by the short but large acceleration gained by a particular hit by an atom. So with this the approach "infinities are bad" would be fine too. But should higher order derivatives be continuous? Not sure. Neither what the answer is, nor what could be used to justify this.

Hm, one could restrict the requirement to the initial values, or, more general, the state. Than, in classical theory first derivatives would matter, second derivatives not.

 

[Demystifier]

Hm, one could restrict the requirement to the initial values, or, more general, the state.
Than, in classical theory first derivatives would matter, second derivatives not.

Why not? In classical theory infinite second derivative (acceleration) implies infinite force. Are you saying that infinite force is OK?

If your answer is that infinite acceleration is OK in classical mechanics, then this implies that the infinite velocity is OK in Bohmian mechanics. Namely, in Bohmian mechanics you only need to specify the initial position, not the initial velocity. In a sense, Bohmian mechanics is more like Aristotelian mechanics than like Newtonian mechanics, because the cause of particle motion in Bohmian mechanics determines the particle velocity, not the particle acceleration. The cause of motion in Bohmian mechanics is the pilot wave, not the force. If the pilot wave is zero everywhere, the particle stays at rest.

 

[martinbn]

Summary:: I argue that there are good reasons to expect that QG will be indeed a standard quantum theory, the general principles of QT remaining unchanged, instead of a modified, generally covariant modification of quantum theory.
...
Instead, all other approaches I know about modify GR but leave the principles of quantum theory unchanged.
...

And, as of now, none of them is successful!

 

[Sunil]

And, as of now, none of them is successful!

Depends on how you define success.

Using the field theoretic variant of GR, in harmonic gauge, you can do quantum effective field theory and compute all the quantum gravity effects down to the Planck scale. Say, Donoghue, J.F. (1996). The Quantum Theory of General Relativity at Low Energies, Helv.Phys.Acta 69, 269-275, arXiv:gr-qc/9607039. This includes everything we can test. So, if you deny the success, then it is certainly not a failure of the empirical predictions. Thus, you disagree with the metaphysics. Not?

 

[martinbn]

Depends on how you define success.

Using the field theoretic variant of GR, in harmonic gauge, you can do quantum effective field theory and compute all the quantum gravity effects down to the Planck scale. Say, Donoghue, J.F. (1996). The Quantum Theory of General Relativity at Low Energies, Helv.Phys.Acta 69, 269-275, arXiv:gr-qc/9607039. This includes everything we can test. So, if you deny the success, then it is certainly not a failure of the empirical predictions. Thus, you disagree with the metaphysics. Not?

How does this modify GR?

 

[PeterDonis]

This includes everything we can test.

"Everything we can test" does not include any effects that are not also predicted by classical GR. So we currently have no experimental data that distinguishes this effective quantum field theory from classical GR. Nor do we have any prospect of getting any in the near future.

If you want to call that "success", nobody can stop you, but nobody else has to agree with you, either. Generally in science, you don't claim "success" until your theory has had some prediction experimentally confirmed that is different from the predictions of existing theories. That has not happened yet with any theory of quantum gravity.

 

[PeterDonis]

How does this modify GR?

The paper gives the example of a predicted quantum correction to the long-range gravitational interaction between two massive objects. However, the predicted correction is much too small to be observed experimentally.

 

[atyy]

"Everything we can test" does not include any effects that are not also predicted by classical GR. So we currently have no experimental data that distinguishes this effective quantum field theory from classical GR. Nor do we have any prospect of getting any in the near future.

If you want to call that "success", nobody can stop you, but nobody else has to agree with you, either. Generally in science, you don't claim "success" until your theory has had some prediction experimentally confirmed that is different from the predictions of existing theories. That has not happened yet with any theory of quantum gravity.

There is an argument that classical GR fails in theory because it creates split brains.

https://link.springer.com/article/10.12942/lrr-2004-5
"The perceived crisis is the absence of an over-arching theoretical framework within which both successes can be accommodated. Our brains are effectively split into two incommunicative hemispheres, with quantum physics living in one and classical general relativity in the other.

The absence of such a framework would indeed be a crisis for theoretical physics, since real theoretical predictions are necessarily approximate. Controllable results always require some understanding of the size of the contributions being neglected in any given calculation. If quantum effects in general relativity cannot be quantified, this must undermine our satisfaction with the experimental success of its classical predictions."

 

[PeterDonis]

If quantum effects in general relativity cannot be quantified

So far, the approximation of using expectation values for any quantum quantities where quantifying their classical contribution is necessary works just fine in classical GR, as far as I know. The difficulties with combining GR and QM are purely theoretical, based on an assumption that one or the other theory must be fundamental rather than an approximation to some different, deeper theory. If we consider both current theories to be approximations to something deeper, there is no conflict.

 

[atyy]

So far, the approximation of using expectation values for any quantum quantities where quantifying their classical contribution is necessary works just fine in classical GR, as far as I know. The difficulties with combining GR and QM are purely theoretical, based on an assumption that one or the other theory must be fundamental rather than an approximation to some different, deeper theory. If we consider both current theories to be approximations to something deeper, there is no conflict.

But can one put quantum fields into classical GR? It seems that classical GR interfaces with classical fields, not quantum fields.

 

[PeterDonis]

can one put quantum fields into classical GR?

No, and that's not what I described. Taking expectation values removes quantum fields and all other "quantum stuff" from the math. All that's left are values that can be treated as classical variables obeying classical equations. That's the basic content of Ehrenfest's theorem.

 

[atyy]

No, and that's not what I described. Taking expectation values removes quantum fields and all other "quantum stuff" from the math. All that's left are values that can be treated as classical variables obeying classical equations. That's the basic content of Ehrenfest's theorem.

Doesn't that run into the problems described in https://arxiv.org/abs/0803.3456?

 

[PeterDonis]

Doesn't that run into the problems described in https://arxiv.org/abs/0803.3456?

If you try to push it, as an approximation, beyond its workable range, yes. But its workable range includes all observations we have made to date. The issues Carlip discusses are theoretical; they are not issues with predictions of the semiclassical approximation not matching experiments. Our experiments are simply not capable (yet) of probing regimes where the semiclassical approximation, as far as gravity is concerned, breaks down.

 

[Sunil]

How does this modify GR?

The field theoretic variant is defined only on a flat spacetime, and it makes an explicit choice of preferred coordinates.

"Everything we can test" does not include any effects that are not also predicted by classical GR. So we currently have no experimental data that distinguishes this effective quantum field theory from classical GR. Nor do we have any prospect of getting any in the near future.

If you want to call that "success", nobody can stop you, but nobody else has to agree with you, either. Generally in science, you don't claim "success" until your theory has had some prediction experimentally confirmed that is different from the predictions of existing theories. That has not happened yet with any theory of quantum gravity.

Given that nobody expects that any QG predictions can be tested, your argument seems to be that the whole QG research should be excluded from physics, not?

By the way, your claim is wrong, the theory (combined in the straightforward way with the SM) predicts quantum effects, classical GR not. Semiclassical GR is inconsistent as a theory, thus, does not count. Thus, GR quantized as an effective field theory in harmonic coordinates on $\mathbb{R}^4$ predicts things not predicted by classical GR or any other non-quantum theory of gravity.

You could object here that as an effective field theory, GR is not a self-consistent theory too - it fails for very small distances. But this is not problematic because it is easy to construct regularizations, for example, a lattice regularization, which defines already a consistent theory.

In general, one claims success if one has solved some scientific problem. That there was no theory able to predict as what GR predicts as well as the quantum effects was a scientific problem, not? But we have now a theory which solves this problem. So, success.

And this success also means failure for the alternatives which have failed to construct a QG in agreement with its preferred choice of principles. In particular, for the approach which considers relativistic symmetry as fundamental.

 

[PeterDonis]

Given that nobody expects that any QG predictions can be tested, your argument seems to be that the whole QG research should be excluded from physics, not?

Not at all. I am just saying that QG research is still just research--it hasn't (yet) produced any theory that can be tested experimentally. That is a common situation in physics.

your claim is wrong

No, it isn't. See below.

the theory (combined in the straightforward way with the SM) predicts quantum effects,

Which have not been observed, because they are not within our current capabilities to observe. Which is what I claimed. I never claimed QG does not make any different predictions from classical GR. I just claimed, correctly, that no such different predictions can be tested experimentally with our current capabilities.

That there was no theory able to predict as what GR predicts as well as the quantum effects was a scientific problem, not?

No. The scientific problem is that we have no experimentally tested theory of quantum gravity. Until we have a way of experimentally testing quantum gravity effects, it is impossible to claim that any QG theory is "successful", because "success" in science requires experimental confirmation.

And this success also means failure for the alternatives which have failed to construct a QG in agreement with its preferred choice of principles.

Any "preferred choice of principles" is an opinion and cannot be used as the basis for a claim of scientific success.

 

[martinbn]

The field theoretic variant is defined only on a flat spacetime, and it makes an explicit choice of preferred coordinates.

I admit I only glanced at the paper, but if the spacetime is flat, then there is no gravity. My guess is that the spacetime isn't flat, but there is an auxiliary flat metric involved. Also working with a choice of convinient coordinates doesn't make them preffered. Anyway I am not sure this is a modification of GR (apart from the quantization). If it is, how does it differ from GR? Also I am not convinced that this is a success. I might be wrong of course, but what problems can be solved with it?

 

[atyy]

If you try to push it, as an approximation, beyond its workable range, yes. But its workable range includes all observations we have made to date. The issues Carlip discusses are theoretical; they are not issues with predictions of the semiclassical approximation not matching experiments. Our experiments are simply not capable (yet) of probing regimes where the semiclassical approximation, as far as gravity is concerned, breaks down.

Yes, but as I understand, that means that although it is standard to say that current data can be treated using "classical GR + quantum field theory for matter", what we really mean by that is "GR as an effective quantum field theory + quantum field theory for matter", since it is the latter that resolves the problems of "classical GR + quantum field theory for matter" taken literally.

 

[Demystifier]

Generally in science, you don't claim "success" until your theory has had some prediction experimentally confirmed that is different from the predictions of existing theories.

Sorry for nitpicking, but by that criterion the results of Lagrange, Hamilton, Jacobi and others after Newton in classical nonrelativistic mechanics would not be counted as success.

In my view, finding a new way to get old quantitative results can be a success too, especially when the new way gives a new qualitative insight.

 

[martinbn]

Sorry for nitpicking, but by that criterion the results of Lagrange, Hamilton, Jacobi and others after Newton in classical nonrelativistic mechanics would not be counted as success.

But is it success in science? It certainly is a success in maths.

 

[Demystifier]

But is it success in science? It certainly is a success in maths.

Since it's a part of science textbooks (and not in the mathematical appendix part of them), yes, I would call it a success in science.

 

[atyy]

The field theoretic variant is defined only on a flat spacetime, and it makes an explicit choice of preferred coordinates.

It can be defined on a curved background spacetime, it's just that the curvature of the background spacetime is not affected by matter.

https://arxiv.org/abs/2007.01847
Causality in Curved Spacetimes: The Speed of Light & Gravity
Claudia de Rham, Andrew J. Tolley

 

[Sunil]

I admit I only glanced at the paper, but if the spacetime is flat, then there is no gravity.

The field-theoretic approach following Feynman starts like a standard field theory in Minkowski space adding a spin 2 field. It appears one can construct an effective metric out of the Minkowski background and this field, and in the final result nothing from the Minkowski space remains visible. But it is nontheless there, because the whole construction started with it and there was no point of throwing it away.

The effective metric is not flat.

If it is, how does it differ from GR? Also I am not convinced that this is a success. I might be wrong of course, but what problems can be solved with it?

Once you have chosen a gauge, you can identify positions of different solutions. Say, you measure a superposition of gravitational fields with a test particle. If they differ enough, and the test particle comes close enough, the test particle ends in different places, and the superposition is destroyed. If not, the particles place will not change, it will be the same for both gravitational fields. But now stop and think how is this "the test particles position is the same for different gravitational fields" defined in GR. It is not. The problem with this is the hole argument.

If a superposition is destroyed by a measurement or not is an experimental question, you can test this. Of course not in quantum gravity (but who knows, superpositions of things as heavy as possible people try to create). But a theory of QG should give an answer. The answer is straightforward and trivial for reasonable choices of coordinates, but I see no way to compute it without fixing coordinates. I would bet one can sweep this under the carpet, but one cannot get rid of it.

The problem solved is the non-existence of a consistent theory making viable predictions as in the domain of classical GR as in quantum field theory. At least I think the theoretical arguments against semiclassical GR are too serious to ignore them. Instead, to define a finite theory for an effective field theory there are simple possibilities named "regularization".

 

[PeterDonis]

although it is standard to say that current data can be treated using "classical GR + quantum field theory for matter", what we really mean by that is "GR as an effective quantum field theory + quantum field theory for matter"

No, that's not what I am saying. I am saying that "classical GR + quantum field theory for matter", in practice, really means "classical GR + a classical approximation to quantum field theory for matter based on expectation values".

 

[PeterDonis]

finding a new way to get old quantitative results can be a success too, especially when the new way gives a new qualitative insight

Finding new mathematical formulations of existing theories that can be shown to be equivalent to old ones (and therefore make the same predictions) but which offer some advantage in calculating predictions, could be termed a success, yes. But it's a different kind of success from discovering a new theory that makes different predictions from existing theories, and having the new theory's predictions confirmed.