If there ever will be a theory of Quantum Gravity which is testable...

[billtodd]

shouldn't it be a sort of partially GR and partially QM?

I mean in a sort of superposition of both theories such that in the specific limit becomes GR and another limit QM, and in the between both regions it's something entirely else, not QM and not GR.

Is this possible?
I haven't yet done the job of writing such a theory.
It's like in the song of stallion not dead and not alive...


You could write it pictorially as: $a|GR>+b|QM>$ where $a+b=1$.

 

[renormalize]

I mean in a sort of superposition of both theories such that in the specific limit becomes GR and another limit QM, and in the between both regions it's something entirely else, not QM and not GR.

You would have to motivate this distinction between gravity and all the other fields of the standard model. For example, applying your logic to the Maxwell field, I could write by analogy:

"I mean a sort of superposition of both theories such that in the specific limit becomes classical electromagnetism (EM) and another limit quantum electrodynamics (QED), and in between both regions it's something entirely else, not QED and not EM."

But of course this is not true: QED is the exact theory (as far as we know) and contains classical EM as an approximation. There is no "in between" where it's "not QED and not EM". Why should the gravitational field be different?

 

[ohwilleke]

shouldn't it be a sort of partially GR and partially QM?

One expects that quantum gravity would be GR in the classical limit, including in all circumstances where GR matches observation, but different from GR in circumstances where a quantum theory would not be like GR, e.g. it would not be a deterministic theory, gravitational waves of a well defined frequency would correspond to gravitons of a specific energy, etc.

I mean in a sort of superposition of both theories such that in the specific limit becomes GR and another limit QM, and in the between both regions it's something entirely else, not QM and not GR.

Is this possible?
I haven't yet done the job of writing such a theory.

No one has successfully written any theory of quantum gravity that has GR as its classical limit.

On one hand, that means that there is no shame in the fact that you haven't done it either.

On the other, it means that we don't know if it is possible or not. There are no "no go" theories that have been proven that definitively show that you can't have any kind of theory of quantum gravity (although some kinds of quantum gravity theories are ruled out). But there are also no theories that definitively prove that it is possible.

 

[kodama]

No one has successfully written any theory of quantum gravity that has GR as its classical limit.

On one hand, that means that there is no shame in the fact that you haven't done it either.

what about string theory in 11D?

 

[timmdeeg]

No one has successfully written any theory of quantum gravity that has GR as its classical limit.

On the other, it means that we don't know if it is possible or not. There are no "no go" theories that have been proven that definitively show that you can't have any kind of theory of quantum gravity (although some kinds of quantum gravity theories are ruled out). But there are also no theories that definitively prove that it is possible.

Not sure if I understand that correctly.

The "break down" of GR at r=0 requires an extension of the theory such that these infinities are avoided.

If you say we "don't know if it is possible or not" do you say we don't know if such an extension exisits or we will never be able to write it down? I think if it exists then it's mathematical description exists, whether or not we will ever be able to write it down.

The real problem seems if we ever can trust an extension of the theory having no more than mathematical consistency, but no experimental prove.

 

[ohwilleke]

The "break down" of GR at r=0 requires an extension of the theory such that these infinities are avoided.

Maybe. Or, maybe the universe just has infinities even though that is mathematically ugly.

If you say we "don't know if it is possible or not" do you say we don't know if such an extension exists or we will never be able to write it down?

We don't know for sure that gravity even is quantum in nature at all. There are lots of good reasons to think that it is, but there are definitely academic journal articles exploring the possibility that gravity, unlike the other fundamental forces, is fundamentally classical in character (even if it may need a slight tweak or two to fit with the Standard Model and address mathematical pathologies). Every effort to date to find observational evidence of quantum gravity (e.g. by looking at a generalized uncertainty principle/decoherence or other conjectured properties of quantum gravity so far) has come up empty.

I think if it exists then it's mathematical description exists, whether or not we will ever be able to write it down.

The real problem seems if we ever can trust an extension of the theory having no more than mathematical consistency, but no experimental prove.

Well, we aren't able to write down any quantum gravity theory that works with a broad domain of applicability so far, and until someone can come up with a mathematically consistent theory, there is nothing to prove experimentally.

 

[ohwilleke]

what about string theory in 11D?

String theory in 11D has its own problems. We can't even get the Standard Model from it.