Could QM Arise From Wilson's Ideas

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In adding some detail to a question about mass, I gave a link to an article by Sean Carrol:
https://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/
'Nowadays we know you can start with just about anything, and at low energies, the effective theory will look renormalizable. This is useful, if you want to calculate processes in low-energy physics; disappointing if you’d like to use low-energy data to learn what is happening at higher energies. Chances are, if you go to energies that are high enough, spacetime itself becomes ill-defined, and you don’t have a quantum field theory at all. But on labs here on Earth, we have no better way to describe how the world works.'

If QFT is the low energy approximation of just about anything, and QM is a limiting case of QFT, it struck me that could possibly be the 'why' of QM?

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Bill
 
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stevendaryl
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In adding some detail to a question about mass, I gave a link to an article by Sean Carrol:
https://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/
'Nowadays we know you can start with just about anything, and at low energies, the effective theory will look renormalizable. This is useful, if you want to calculate processes in low-energy physics; disappointing if you’d like to use low-energy data to learn what is happening at higher energies. Chances are, if you go to energies that are high enough, spacetime itself becomes ill-defined, and you don’t have a quantum field theory at all. But on labs here on Earth, we have no better way to describe how the world works.'

If QFT is the low energy approximation of just about anything, and QM is a limiting case of QFT, it struck me that could possibly be the 'why' of QM?

Thanks
Bill
I don’t understand the claim that “we know you can start with just about anything, and at low energies, the effective theory will look renormalizable”. I thought that the whole reason that quantum gravity is so hard is because the most naive way to quantize GR leads to something that is non-renormalizable.
 
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I don’t understand the claim that “we know you can start with just about anything, and at low energies, the effective theory will look renormalizable”. I thought that the whole reason that quantum gravity is so hard is because the most naive way to quantize GR leads to something that is non-renormalizable.
Quantum Gravity is not renormalisable. But using the Wilsonian view that is not an issue. You know we can find a low energy approximation that calculations can be done with (an effective field theory):
https://blogs.umass.edu/donoghue/research/quantum-gravity-and-effective-field-theory/

We now think that all our QFT theories are effective field theories - even the standard model. It could break down earlier (indeed QED becomes the electroweak theory) but none are generally trusted when we get to the Plank Scale.

The interesting thing and the details are beyond my current knowledge, is you can start with just about anything to get that effective field theory. Lubos, who I normally do not like giving links to, wrote a deeper article about it:
https://motls.blogspot.com/2013/06/kenneth-wilson-rip.html

As I said it is above my level.

Thanks
Bill
 
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PeterDonis
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I don’t understand the claim that “we know you can start with just about anything, and at low energies, the effective theory will look renormalizable”. I thought that the whole reason that quantum gravity is so hard is because the most naive way to quantize GR leads to something that is non-renormalizable.
Yes, but at low enough energies, the quantum aspects of gravity are negligible; you just have a fixed classical spacetime geometry. I think that is the context in which to understand Carroll's remark.
 
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atyy
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If QFT is the low energy approximation of just about anything, and QM is a limiting case of QFT, it struck me that could possibly be the 'why' of QM?
No, the Wilsonian view of renormalization is just about actions. How one uses the actions (eg. as part of a quantum theory) has to be put in by hand.

For example, QFT may arise from string theory, so string theory may provide an explanation for QFT. However, it does not provide an explanation for the "quantum" part of QFT, since string theory is itself a quantum theory.
 
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  • #6
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Yes, but at low enough energies, the quantum aspects of gravity are negligible; you just have a fixed classical spacetime geometry. I think that is the context in which to understand Carroll's remark.

Way back in the day when I posted on sci. Physics. Relativity I asked Steve Carlip the same question. Certainly, we have an EFT theory of gravity thought valid to about the Plank scale. His views are interesting:



The problem is it does not tell us much. It predicts a few interesting things, e.g., Hawking Radiation can be derived from it, but it does not get us terribly much. The link I gave to John Donoghue's work attempts to see exactly what such a theory may tell us.

Thanks
Bill
 
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If QFT is the low energy approximation of just about anything, and QM is a limiting case of QFT, it struck me that could possibly be the 'why' of QM?
As @atyy said, the Wilson effective theory framework requires that the fundamental microscopic theory should be quantum, but apart from that, it can in principle be any quantum theory. In the paper linked in my signature, I propose that the fundamental theory is a nonrelativistic quantum theory, which resolves many conceptual problems in standard and Bohmian quantum theory.
 
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  • #9
atyy
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As @atyy said, the Wilson effective theory framework requires that the fundamental microscopic theory should be quantum, but apart from that, it can in principle be any quantum theory. In the paper linked in my signature, I propose that the fundamental theory is a nonrelativistic quantum theory, which resolves many conceptual problems in standard and Bohmian quantum theory.
In a way we can also link that to Wilson by his pioneering work on lattice gauge theory, which in some philosophies may provide a non-relativistic non-perturbative definition of quantum field theories (of course, we don't yet have a consensus lattice standard model - it'll be interesting to see if the muon g-2 is really helped by the lattice!)

As I have said before, lattice research is secretly Bohmian :oldtongue:
 
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stevendaryl
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Yes, but at low enough energies, the quantum aspects of gravity are negligible; you just have a fixed classical spacetime geometry. I think that is the context in which to understand Carroll's remark.

My problem is not with the claim that we can have a sensible low-energy theory of quantum gravity, but with the claim that at low energies it "looks renormalizable". What does it mean to look renormalizable?
 
  • #14
atyy
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My problem is not with the claim that we can have a sensible low-energy theory of quantum gravity, but with the claim that at low energies it "looks renormalizable". What does it mean to look renormalizable?
Carroll's explanation:
"But we don’t care about high energies! We are trying to construct an effective theory at low energies, so we care about the terms for which N≤4 — those are the ones that dominate at low energies. In fact, we have lingo to encapsulate this importance.
...
And that’s it! Those pieces give you the important low-energy description of any theory of a single scalar field, no matter what new particles and crazy nonsense might be going on at higher energies. Of course we don’t work at strictly zero energy, so the “irrelevant” parts might also be interesting and useful, but Wilsonian effective field theory gives you a systematic way of dealing with them and estimating their importance.
...
The old-school idea that a theory is “renormalizable” maps onto the new-fangled idea that all the operators are either relevant or marginal — every single operator is dimension 4 or less."
 
  • #15
PeterDonis
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My problem is not with the claim that we can have a sensible low-energy theory of quantum gravity
I didn't say we did; I said that at low energies the quantum aspects of gravity are negligible, so the whole idea of a "low-energy theory of quantum gravity" is unnecessary. All we need is the classical theory of gravity we already have.

but with the claim that at low energies it "looks renormalizable".
For gravity, "looks renormalizable" at low energies really means "looks classical". See above.

The old-school idea that a theory is “renormalizable” maps onto the new-fangled idea that all the operators are either relevant or marginal — every single operator is dimension 4 or less."
And for the "naive" quantum theory of gravity, i.e., the massless spin-2 field theory whose field equation turns out to be the Einstein Field Equation, there are no such operators--that's why the theory is said to be non-renormalizable. The coupling constant for this theory has units of mass to the power -2, which makes it "irrelevant" in Wilson's terminology. There aren't any relevant or marginal terms in the Lagrangian at all. So when you look at this theory at low energies, it says there's no quantum stuff going on at all; as I said above, all you have left is a fixed classical spacetime geometry.
 
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stevendaryl
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So when you look at this theory at low energies, it says there's no quantum stuff going on at all; as I said above, all you have left is a fixed classical spacetime geometry.
A theory with a fixed geometry can’t describe the gravitational interaction between two objects.

So the meaning of Wilson’s statement is that at low energies, the only relevant interactions are renormalizable ones. (I’m not using “relevant” in the technical sense, which I don’t understand…) Nonrenormalizable interactions can only come into play as fixed background fields.
 
  • #17
PeterDonis
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A theory with a fixed geometry can’t describe the gravitational interaction between two objects.
Sure it can. The interaction is encoded in the spacetime geometry.

So the meaning of Wilson’s statement is that at low energies, the only relevant interactions are renormalizable ones. (I’m not using “relevant” in the technical sense, which I don’t understand…) Nonrenormalizable interactions can only come into play as fixed background fields.
That seems correct to me, yes.
 
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stevendaryl
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Sure it can. The interaction is encoded in the spacetime geometry.
No, it can’t be. You can’t have a fixed background geometry to represent an electron, for example, if the electron is treated as a quantum particle.

So the particles that are described by QM don’t interact with each other gravitationally.
 
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PeterDonis
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You can’t have a fixed background geometry to represent an electron, for example, if the electron is treated as a quantum particle.

So the particles that are described by QM don’t interact with each other gravitationally.
I don't think this viewpoint is correct.

If it were really true that you can't have a fixed background geometry with a quantum particle, that would apply just as much to flat Minkowski spacetime ("no gravitational interaction") as any other spacetime. So you would be unable to have a model that included both a spacetime geometry and quantum particles at all. All of quantum field theory would go out the window.

What physicists actually do in these types of situations is to use an effective stress-energy tensor for the quantum matter (usually the expectation value of some appropriate operator) as the source in the Einstein Field Equation, and obtain a self-consistent solution in which the gravitational interactions encoded by the spacetime geometry are the "right" ones for the matter that is present. This approach assumes that whatever quantum stuff is going on does not produce any effects that would invalidate the effective stress-energy tensor being used at the classical level. Basically, it means you don't have any superpositions of macroscopically different distributions of matter.
 
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stevendaryl
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I don't think this viewpoint is correct.

If it were really true that you can't have a fixed background geometry with a quantum particle,

It’s not that you can’t have a background geometry, but that geometry cannot take into account quantum particles.

You can have electrons moving in a background geometry but by definition that background doesn’t include the effect of those electrons. The background geometry would (contrary to the spirit of Newton’s third law) act on the electrons but would not be acted on by them.
 
  • #21
atyy
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My problem is not with the claim that we can have a sensible low-energy theory of quantum gravity, but with the claim that at low energies it "looks renormalizable". What does it mean to look renormalizable?
Carroll is probably not claiming that gravity is renormalizable in the sense that he's using, since he qualifies his statement with "just about" ("Nowadays we know you can start with just about anything"). He also has other qualifications in his explanation like "(Strictly speaking, even “irrelevant” operators can be important. In the Fermi theory of the weak interactions, the lowest-order operator you can construct that gives rise to any interaction at all is dimension 6. So you have to keep that interaction to have anything interesting happen — but we say that the resulting theory is “non-renormalizable.”) (And while we’re speaking strictly, this dimensional analysis gives the leading behavior, but not the whole story. In QCD, for example, the coupling is marginal, but it doesn’t remain exactly constant with energy, but rather changes slowly [logarithmically]. If all of your couplings are exactly constant, you have a conformal field theory.)"

So for his "just about" he probably was thinking about the interactions of the standard model (without gravity) which were historically obtained by considerations of "renormalizability". He's saying why although it doesn't really make sense to insist on "renormalizability" ("Pre-Wilson, it was all about finding theories that are renormalizable, which are very few in number"), it was historically a very successful approach.
 
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PeterDonis
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It’s not that you can’t have a background geometry, but that geometry cannot take into account quantum particles.

You can have electrons moving in a background geometry but by definition that background doesn’t include the effect of those electrons. The background geometry would (contrary to the spirit of Newton’s third law) act on the electrons but would not be acted on by them.
I'm sorry, but you are not responding to the part of my post that specifically addressed exactly this issue: yes, the background geometry can take into account the presence of quantum particles, through their effective stress-energy tensor. If you are claiming that it is impossible to have a self-consistent solution in which the source of gravity in a curved spacetime is the effective stress-energy tensor of quantum particles, so that the spacetime geometry includes gravitational interactions between different lumps of stress-energy made of quantum particles, you are simply wrong. There is plenty of literature on this approach; I first learned of it in Wald's 1993 monograph Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics.
 
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stevendaryl
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I'm sorry, but you are not responding to the part of my post that specifically addressed exactly this issue: yes, the background geometry can take into account the presence of quantum particles, through their effective stress-energy tensor.

No, it doesn't address the issue. The approach you're talking about doesn't describe the gravitational effect of one electron on another. You can't calculate the gravitational scattering of one particle by another.
 
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stevendaryl
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No, it doesn't address the issue. The approach you're talking about doesn't describe the gravitational effect of one electron on another. You can't calculate the gravitational scattering of one particle by another.

Let me illustrate with an analogous approach for electrodynamics. Before QED was developed, one could attempt to compute the electromagnetic interaction of two electrons this way:
  1. Start with an ansatz ##J^\mu## for the current due to the two electrons.
  2. Use Maxwell's equations to calculate a corresponding electromagnetic potential ##A^\mu##.
  3. Calculate the wave functions for the two electrons using ##A^\mu## as a background vector potential.
  4. Using the results of step 3, adjust ##J^\mu##.
  5. Repeat 1 through 4 until you have a self-consistent solution.
(Actually, I think that an approach like this may have actually been used to calculate energy levels for many-electron atoms.)

This approach might give good results for some circumstances. But it's not at all clear to me that it is some kind of low-energy limiting case of QED.
 
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PeterDonis
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The approach you're talking about doesn't describe the gravitational effect of one electron on another.
It's not just the gravitational effect that you are talking about, it's the quantum aspect of such a gravitational effect. (The classical gravitational effect is described perfectly well by GR.) And, since we are talking about the low energy regime, any such quantum aspects are negligible, as I have already said. (For electrons, we can't even detect the classical gravitational interaction between them, let alone any quantum aspects of it.)

Furthermore, the quantum aspect of gravitational interaction is not the same as background geometry taking into account the presence of quantum particles, which is what you were saying was not possible; the latter is much broader. The Earth is made of quantum particles, but we can describe its gravitational effects just fine using a background spacetime geometry. I understand how that that is not the case you were trying to focus on, but that wasn't clear to me before.

This approach might give good results for some circumstances. But it's not at all clear to me that it is some kind of low-energy limiting case of QED.
The approach you describe here is not the same as the approach I was describing for quantum fields in curved spacetime. An EM analogy to the approach I was describing would be computing the wave functions for electron orbitals in the hydrogen atom by treating the proton purely as a source of an external potential in the Hamiltonian and ignoring all of its quantum properties. (IIRC, in the Feynman Lectures on Gravitation, Feynman tried to make a similar computation for a hypothetical electrically neutral proton and electron, interacting only through gravity, and came up with a Bohr radius for the lowest orbital of the electron larger than the observable universe and a binding energy for that orbital of something like ##10^{-70}## Rydbergs.)

Again, I understand now that this "semiclassical" approach is not what you want to focus on; but in the low energy regime, there isn't anything else there, as I've already said. An interaction like quantum gravitational scattering of one electron off of another simply doesn't appear at all in the low energy effective theory.
 

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