What are the lessons of quantum foundations for quantum gravity?

Problem of localization in a quantum field theory. Schroedinger’s equation evolves wave- functions in a non-local way, so there seems to be a problem with superluminal propagation.

Klein’s paradox. Problem of localization of a quantum state in a gravitational theory. Gravity-induced decoherence.

Pointed out that there might be problems with quantum field theory itself, which will propagate to a gravitational theory too.

The AMPS paradox certainly fits into the realm of this question. It points to a deep problem within quantum gravity. Which of the standards assumptions should we drop? Unitarity or low- energy effective field theory. Dropping unitarity would have deep consequences all around the field.

Do these problems have some implications for quantum key distribution? Not at the level that we can see in a lab. In fact, there are quite precise tests of unitarity in the lab, in particular the Born’s rule, which is intimately tied to unitarity.
Maybe, through some new insights on causality that will change our understanding about quantum mechanics

Through giving us insights on how to modify quantum mechanics.

Through identifying the principles which quantum mechanics is based on.

Maybe lessons we are learning from

Quantum gravity means many things depending on who your speaking to. It is the UV completion of general relativity, an attempt to make GR predictive at high energies. But since GR is the geometry of spacetime, there are subtlteties in quantizing it. It's not straightforward.

It is interesting to start from a quantum theory that doesn't make any reference about spacetime, and attempt to make a statement about quantum mechanics in this environment. However, not much progress has been made.

Quantum mechanics has one thing, time, which is absolute. But general relativity tells us that space and time are both dynamical so there is a big contradiction there. So the question is, can quantum gravity be formulated in a context where quantum mechanics still has absolute time? Or does time have to give. The answer, yes or no, is interesting. If the answer is no, then perhaps some experiment can probe whether or not time is absolute?

“I very much doubt that quantum mechanics will stay valid up to the Planck scale... but so far there's no experimental signal that challenges quantum mechanics.”

“The problem is that neither theory, general relativity or quantum mechanics, has hit an experimental obstacle yet.”

Giving up absolute time is equivalent to sacrificing unitarity. So people asked if there's anything that tells us unitarity should be violated. Some at the table argued that it's “too beautiful to be true, too protected.”  Others pointed out that the three sacred principles: unitarity, Lorentz symmetry, and locality, seem to be incompatible and that one has to give. And they felt that unitarity was the weakest link.
A more preliminary question is what do we even mean by quantum gravity? What do we mean by gravity? General Relativity? Some other theory that will replace it?

It could be that all current approaches to quantum gravity are wrong headed and end up having very little to do with what a true quantum theory of gravity looks like.

The quantum mechanics and general relativity revolutions were data driven. There was some experimental phenomena that was unexplained by current theories. What about now? With a lack of data how do we know if a given approach is even headed in the correct direction.

We talk about quantum foundations, but what about some foundational issues in gravity? Why do we only have a classical understanding of gravity when we have valid quantum field theories for everything else.

Does GR even need to be qunatized?

Understanding the measurement problem could help in our understanding of quantum gravity.

    - More troubling, could the measurement problem be related to a breakdown in the scientific method; we only have one universe so whatever happened can’t be replicated.

Non-locality signals a change in how we should think about spacetime structure – indicates a breakdown of effective field theory.

What exactly are we trying to accomplish when formulating quantum gravity?  We want to find a deeper mathematical theory which, in various limits, may be approximated by either traditional quantum theory or classical general relativity.  To do this, one approach is to search for the most salient conceptual principles underlying quantum theory and general relativity.  We then hope that some of these principles will also serve as the foundation for quantum gravity.   Salient features of quantum theory are the presence of irreducible probabilities and a lack of local realism as described by Bell. These features are “radical,” compared to the traditional way that  conventional quantum theory treats time and space.  Meanwhile, general relativity uses traditional notions of probabilities and local realism, but it is radical in its treatment of causal structure, which becomes dynamical.  Most likely a theory of quantum gravity will need to be radical in both of these ways, possessing both irreducible indeterminism and dynamical causal structure.  But if a causal structure evolves and evolution is indeterminate, we arrive at indefinite causal structure.
The coupling and string tension parameters in string theory form a two-dimensional parameter space, different regions of which yield different types of theories: geometric and non-geometric, quantum and non-quantum.  How does this parameter space correspond to our conceptual map of different regimes in quantum gravity?

When searching for quantum gravity, we assume we are trying to recreate QFT and GR.  But all we need to reconstruct is the experimental observations from which we built those theories.  We must keep this in mind so as not to limit the scope of our search for a theory of quantum gravity. 

Given the above, our task is to reconstruct a large list of experimental results using some new theory (as well as predict new results).  But it is difficult to specify or list all of the desired experimental results (of gravitional physics, say) without simply specifying the underlying theory (classical general relativity, for instance).  In fact, one may imagine physical theories as tools that take lists of experimental results and compress them in some elegant way.  Which compressed version of our experimental results should we keep in mind when attempting to reconstruct a theory?  For instance, are the correlation functions of quantum field theory the relevant data that we should attempt to reconstruct with any more advanced, underlying theory?  Or should we first try to build an underlying theory that adheres to general foundational principles, without worrying about the reproduction of specific data n-point correlation functions?
If you do experiments with results that deviate from what's expected, will you notice? Think of BICEP and cosmology, for instance.  Even we if obtain data that would indicate new physics if viewed in retrospective one millenium from now, we might not recognize the new physics today.  Perhaps we must better understand the physics we already know in order to recognize when something new appears.  For instance, we were able to recognize QM when it “appeared” in the early 20th century precisely because we knew enough classical physics to recognize something new.  Meanwhile, new formalisms often use elements of older formalisms.  (Is this just the result of a lack of human creativity, though?)  Totally new theories don't spring into existence; instead, they arise form well-understood prior theories: nineteenth century physics prepared Schrodinger for QM, for example.


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