# Hardy's approach to quantum gravity and QM interpretation

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## Main Question or Discussion Point

Work in quantum foundations is partly considered important because of the hope that the way we think about QM may point to a road to quantum gravity. Lucien Hardy, who is well-known in quantum foundations for his reformulation of QM in terms of five "reasonable" axioms, is one of the people who try to make this really tangible.

A couple of weeks ago, he put a new preprint with the title The Construction Interpretation: Conceptual Roads to Quantum Gravity on the arXiv.

This sounds ambitious, and it is. The main theme of the paper is to learn the right lessons from the conceptual development of GR which combined Newtonian gravity with special relativistic field theory and apply them in order to discover QG.

He notes that GR as the solution to the problems with Newtonian gravity (action at a distance) looked nothing like the efforts of Newton and his successors to solve these problems. And he argues that even if they did manage to solve the problem from the inside, they would have only gotten Newton-Cartan theory which isn't of much physical interest. So instead of trying to solve the problem of QG from within the paradigm of either QM or GR, he argues for a more radical starting point. (String theory, for example, operates under the quantum paradigm and attacks the problem by making gravity quantum (please correct me if I'm wrong))

For people who are interested in the interpretation of QM, Hardy has a rather sobering message:

Lucien Hardy (https://arxiv.org/abs/quant-ph/0101012 - p.7) said:
If Quantum Gravity requires a radical departure from existing theories, the most interpretations of Quantum Theory can aspire to is to be the correct limiting version of Quantum Gravity just as the Newton-Cartan formalism is the correct limit of General Relativity. [...] Few physicists wish to dedicate themselves to merely providing amusement to future historians. The point of The Construction Interpretation is to take the noble instincts that lead us to attempt to understand Quantum Theory in conceptual terms and re-purpose them to the problem of constructing a theory of Quantum Gravity.
His suggestion is to chop the process of the discovery of GR into 7+3 distinct conceptual steps and perform analogous steps in order to find QG. His steps involve a quite instrumentalist and unusual way of looking at things which I can't digest easily. But I have only superficial knowledge of QFT and GR, so I can't follow the details anyway.

Thoughts? It looks like a very rough sketch to me. But I can neither judge how sensible this research program is, nor how far it already got. In QM, he does cite quite a bit of research of which I wasn't aware.

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MathematicalPhysicist
Gold Member
I thought to myself that a new theory is in order which is different from both QFT and GR.

But I don't know how to even start building such a theory.
I might give a look at his paper.

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atyy
There is already one good suggestion for quantum gravity - AdS/CFT. In informal remarks, it has been said (not sure who, Arkani-Hamed, Polchinski maybe) that this is because quantum mechanics needs an observer, and AdS provide a space for the observer on the boundary. So perhaps it might be a good idea to see if we can generalize the notion of observer in QM (eg. Brukner, Hardy), or if we can get rid of the observer (measurement problem).

I'm not sure if Witten's remarks about observables in dS space are related: https://arxiv.org/abs/hep-th/0106109.

There is also interesting work in AdS/CFT about how quantum mechanics arises in the bulk: https://arxiv.org/abs/1801.08101.

Personally, I'd like to see someone try to develop Bohmian AdS/CFT.

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Fra
Demystifier
Gold Member
Personally, I'd like to see someone try to develop Bohmian AdS/CFT.
As far as I know, the only person in the world who might be crazy enough* to try to do something like that is - me.
But the problem is that I don't really buy AdS/CFT in the usual form, for the reasons I explained in https://lanl.arxiv.org/abs/1507.00591 . In short, I buy that boundary can be reproduced from the bulk, but I don't buy the converse, that the bulk can be reproduced from the boundary.

*By "crazy enough", I mean in the sense of Bohr's famous "Your theory is crazy but not crazy enough".

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Lindsayforbes
MathematicalPhysicist
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As far as I know, the only person in the world who might be crazy enough* to try to do something like that is - me.
But the problem is that I don't really buy AdS/CFT in the usual form, for the reasons I explained in https://lanl.arxiv.org/abs/1507.00591 . In short, I buy that boundary can be reproduced from the bulk, but I don't buy the converse, that the bulk can be reproduced from the boundary.

*By "crazy enough", I mean in the sense of Bohr's famous "Your theory is crazy but not crazy enough".
What did Bohr mean?

literally or metaphorically?

Demystifier
Gold Member
What did Bohr mean?
literally or metaphorically?
Metaphorically, of course.

MathematicalPhysicist
Gold Member
Metaphorically, of course.
I don't know, QFT is quite a crazy theory...
literally.

Demystifier
Gold Member
I don't know, QFT is quite a crazy theory...
literally.
What do you find the craziest part of QFT?

MathematicalPhysicist
Gold Member
What do you find the craziest part of QFT?
The whole edifice, loads of calculations and nothing is truly rigorously mathematically justified.

At least with GR I can tell that it's really all about Riemannian Geometry.
But in QFT I find it hard to comprehend all the implications, and in Peskin and Schroeder it's hard to find how every equation is entailed from the one before.

If they had written a book that portrays every implication it would be something like 1000-2000 pages of calculations, too much to not find some error in it.

And Peskin and Schroeder is only an introduction!

atyy
As far as I know, the only person in the world who might be crazy enough* to try to do something like that is - me.
But the problem is that I don't really buy AdS/CFT in the usual form, for the reasons I explained in https://lanl.arxiv.org/abs/1507.00591 . In short, I buy that boundary can be reproduced from the bulk, but I don't buy the converse, that the bulk can be reproduced from the boundary.

*By "crazy enough", I mean in the sense of Bohr's famous "Your theory is crazy but not crazy enough".
I need to read your explanation, but before that, I think there are many who would allow that it may not be a true duality, and that the boundary may serve as the definition of the bulk, but not the other way round.

Demystifier
Gold Member
I think there are many who would allow that it may not be a true duality, and that the boundary may serve as the definition of the bulk, but not the other way round.
Do you have some references?

atyy
Do you have some references?
These are all not exactly it, but maybe:

https://arxiv.org/abs/1007.4001
As a consequence of the last property, we consider such QFTs to be definitions of models of quantum gravity, with fixed asymptotic background. The idea that AdS/CFT defines a duality between two independently defined theories, is probably without merit.

https://arxiv.org/abs/1501.00007
While the AdS/CFT duality as such has not been rigorously ‘proved’ (partly because we do not yet have a complete independent definition of the quantum gravity side of the correspondence), ...

https://arxiv.org/abs/1609.00026
These realize the holographic principle directly: the quantum gravitational theories are defined as ordinary non-gravitational quantum theories (typically quantum field theories) on a fixed lower-dimensional spacetime

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Fra
As far as I know, the only person in the world who might be crazy enough* to try to do something like that is - me.
You solipsist hidden variables are IMO an interesting research direction from someone in the bohmian field. I can relate to this idea, which is that "problem" of the hidden variables in ordinary bohmian mechanis is solves simply because they are not inferrable from other perspectives; but while the actual hidden structure EXPLAINS the interactions, but they remain probabilistic. So i do not think one will recover determinism, but the idea itself is interesting and it will unify both the world of uncertainy and realism, except the realism is observer dependent. This may sound like toying with words but i can envision how it actually makes sense.

I would enjoy reading any follow up papers you may have in this direction.

/Fredrik

Personally, I'd like to see someone try to develop Bohmian AdS/CFT.
The immediate problem here is the need for gauge-fixing. I don't know any way to preserve gauge symmetry or general covariance in Bohmian mechanics. You have to just fix a gauge, as in Shtanov's Bohmian gravity. It's not very satisfying, though it would still be of interest to see it done for AdS/CFT. Perhaps one could start with a study of Shtanov supergravity in AdS.

Demystifier and atyy
atyy
The immediate problem here is the need for gauge-fixing. I don't know any way to preserve gauge symmetry or general covariance in Bohmian mechanics. You have to just fix a gauge, as in Shtanov's Bohmian gravity. It's not very satisfying, though it would still be of interest to see it done for AdS/CFT. Perhaps one could start with a study of Shtanov supergravity in AdS.
I was thinking Hamiltonian lattice gauge theory for the CFT side. I'm not sure what the status of lattice supersymmetry is.

martinbn
In short, I buy that boundary can be reproduced from the bulk, but I don't buy the converse, that the bulk can be reproduced from the boundary.
I may be confused by the language, because I don't even know what the statements of AdS/CFT are, but often the solutions to the equations in the whole region are determined by the values on the boundary. So, at least superficially it seems ok as a proposal (whatever the conjecture might be).

Fra
I suspect my ideas are even further from the original ambitions of Hidden variables, but i defend and enjoy the principal idea (although the principal idea may be implemented in various programs)

The immediate problem here is the need for gauge-fixing. I don't know any way to preserve gauge symmetry or general covariance in Bohmian mechanics. You have to just fix a gauge,
As I see it, one way of solving this is to accept that the need for gauge-fixing, and choosing an observer, is more fundamental and prior to desire to preserve gauge invariance and observer equivalence.

H.Nikolic in Solipsistic hidden variables https://arxiv.org/abs/1112.2034 said:
...the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer...
One possible solution then is to view gauge symmetry and observer consistency as emergent and NOT fundamental in the sense that all the different "hidden variables" in all the various obserers in the physical systems, with time, due to their interactions evolve to be in TUNE. Its the initial inconsistencies that constitute the evolutionary "forces" to deform the internal structure of observers. But the actual mechanism can be evolutionary self-organisation, so there are not non-local interactions as the inteactions are in the history.

But to implement this, requires a model for the "microstructure" of the observers, to see how they "negotiate" and interact. And probably requires this to be combined with something more radical. Closes thing that comes to mind from main programs is strings and the 6D manifolds. And maybe the selection of the manifolds in some landscape can be identified with the negotiation process. Then the string itself would be considered as an elementary observer. But the same idea could be tried with other microstructures as well.

/Fredrik

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Demystifier
Gold Member
I may be confused by the language, because I don't even know what the statements of AdS/CFT are, but often the solutions to the equations in the whole region are determined by the values on the boundary. So, at least superficially it seems ok as a proposal (whatever the conjecture might be).
As the simplest example, consider the equation
$$\frac{d^2f(x)}{dx^2}+k^2f(x)=0$$
for ##x\in [0,2\pi]## and ##k## a real number. Let the boundary condition be ##f(0)=f(2\pi)=0##. How that determines ##f(x)## for all ##x##?

martinbn
Is that supposed to convince me that boundary conditions never determine the solution?

Demystifier
Gold Member
Is that supposed to convince me that boundary conditions never determine the solution?
No, it's supposed to convince people who know something about AdS/CFT that the statement that bulk is encoded in the boundary is a very nontrivial statement.

Do you know how this fits into the framework with the 7+3 steps of Hardy's paper?

AdS/CFT is part of string theory and string theory is a quantum theory. So it operates mostly from within one of the two old paradigms which makes me suspect that it doesn't fit well into Hardy's approach. He also doesn't mention AdS/CFT in his last chapter on future developments.

My impression is that Hardy would see AdS/CFT as a coincidence which needs an explanation and that this explanation can't be given from within currently available approaches but only from the yet-to-be-constructed theory of QG which he expects to look very different from string theory.

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martinbn
No, it's supposed to convince people who know something about AdS/CFT that the statement that bulk is encoded in the boundary is a very nontrivial statement.
But you said that you didn't buy it, which suggests more than it being a difficult problem. It suggests that you think it is more likely to be false. Then again in physics almost everything is of that form when it comes to equations, the solution in the bulk is determined by the boundary conditions.

Demystifier
Gold Member
Then again in physics almost everything is of that form when it comes to equations, the solution in the bulk is determined by the boundary conditions.

martinbn
I cannot think of an example that is not like that! In fact it is a crucial part of what science is! Take any initial value problem, which is what predictability is about, the state of affairs at a given moment say ##t=0## determines the state of affairs at later times. But ##t=0## is the boundary (in space-time) and the later times is the bulk.

Fra
If one takes an instrumental approach, the only thing that an observer scientifically can say about the "bulk" has to be based on inferences on something that is communicated through the only available communication channel (the boundary).

Thus it seems logically possible that there are hidden information (hidden variables) that are not inferrable from the boundary?

If realism was hard to save with bell experiments, this makes it even harder, as the communication channel constrains what a scientist one one side can ask of the other side. But maybe from Bohmian view, depending on how you see it, it can also be exploited to argue that there is a difference betwen hidden variables such as simply "unknown" or one that are non-inferrable. Bell experiments presumes that there is a define sampling distribution. This does not even make sense for the latter case.

Black Holes, AdS, and CFTs, Donald Marolf
"...Thus, in what some readers may consider an ironic twist, it may be fair to say that in AdS/CFT the Bekenstein-Hawking entropy counts “not the full set of states describing the black hole interior, but only those states which are distinguishable from the outside,” a point of view which has long been championed within the relativity community...."
-- https://arxiv.org/pdf/0810.4886.pdf

/Fredrik

atyy