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atyy

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There does seem to be another form of nonlocality in string theory related to the Holographic principle. Here is a Scientific American article about the holographic principle in string theory by Juan Maldacena, who first concretely raised the conjecture: https://www.scientificamerican.com/article/the-illusion-of-gravity-2007-04/

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haushofer

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MathematicalPhysicist

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I find it hard to grasp a theory such as string theory called either Classical or Quantum, where an alleged theory of QGR should be neither quantum nor classical; obviously in the appropriate limits we should get back both theories, but in the intermediate we should get something different from both, otherwise it's not a different theory but a patch of differing theories.forstring theory, just as it possible to do it for any other quantum theory.

Now, this is akin the question what are those limits?

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forstring theory, just as it possible to do it for any other quantum theory.

I had the idea that string theory was nonlocal even classically, although the nonlocality is only significant over short distances.

https://arxiv.org/pdf/1310.4957.pdf

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PAllen

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I don't think it is a given that the QG solution is neither quantum nor classical. For example, asymptotic safety would be a pure quantum approach that would (if it worked) fully solve quantum gravity and include a complete theory of matter (unlike e.g. LQG, which in addition to other issues, has not yet accommodated anything like the standard model). That AS (asymptotic safety) does nothing to resolve various other issues in physics (the observations bundled in "the dark matter problem", the cosmological constant problem, etc.) is irrelevant. There is no a priori expectation that a QG solution should resolve these.I find it hard to grasp a theory such as string theory called either Classical or Quantum, where an alleged theory of QGR should be neither quantum nor classical; obviously in the appropriate limits we should get back both theories, but in the intermediate we should get something different from both, otherwise it's not a different theory but a patch of differing theories.

Now, this is akin the question what are those limits?

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Where did you get it from?an alleged theory of QGR should be neither quantum nor classical

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Are you one of the authors of that paper?I had the idea that string theory was nonlocal even classically, although the nonlocality is only significant over short distances.

https://arxiv.org/pdf/1310.4957.pdf

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MathematicalPhysicist

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Just because a theory is not quantum

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MathematicalPhysicist

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Then what makes a theory quantum?Just because a theory is not quantummechanicsdoesn't mean that this theory isn't quantum.

I have seen the trichotomy in Zelevinsky's textbook of Quantum Mechanics, Quantum Physics and another term which I have forgotten.

Shouldn't a new theory transcend beyond the quantum?

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For instance, quantum field theory is not quantum mechanics, but is quantum. Quantum mechanics is a quantum theory of pointlike particles.Then what makes a theory quantum?

I have seen the trichotomy in Zelevinsky's textbook of Quantum Mechanics, Quantum Physics and another term which I have forgotten.

Shouldn't a new theory transcend beyond the quantum?

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MathematicalPhysicist

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OK, so string theory is quantum of strings which aren't fields nor points.For instance, quantum field theory is not quantum mechanics, but is quantum. Quantum mechanics is a quantum theory of pointlike particles.

So the thing that makes something 'quantum' is what exactly?

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MathematicalPhysicist

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Maybe because no technical book that I read discuss this matter.

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If observables are represented by non-commuting operators, then it's quantum. If probabilities are given by something of the form ##|\psi|^2##, then it's quantum.So the thing that makes something 'quantum' is what exactly?

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MathematicalPhysicist

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In QM ##\psi## are wave-functions, in QFT they are wave-functionals.If observables are represented by non-commuting operators, then it's quantum. If probabilities are given by something of the form ##|\psi|^2##, then it's quantum.

So only these two conditions are enough to declare a theory as quantum.

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Superficially speaking, yes. But if you want a deeper insight, see my paper https://arxiv.org/abs/quant-ph/0505143 where classical mechanics is represented by a quantum-like formalism.In QM ##\psi## are wave-functions, in QFT they are wave-functionals.

So only these two conditions are enough to declare a theory as quantum.

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Are you one of the authors of that paper?

No! Did I give that impression, somehow?

I actually was trying to find a John Baez comment from years ago saying that string theory was slightly nonlocal. I say "slightly", because the nonlocality was confined to a region the size of the length of the string. I didn't remember the argument for why.

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OK, so string theory is quantum of strings which aren't fields nor points.

So the thing that makes something 'quantum' is what exactly?

The difference between a classical field theory and a quantum field theory is that whereas a classical field theory is deterministic--the configuration of the field and its sources at one time determines the configuration at later times---a quantum field theory is nondeterministic. The equations of quantum field theory describe not the fields themselves but probability amplitudes for the field.

The relationship between classical field theory and quantum field theory is very similar to the relationship between Newtonian physics and the Heisenberg equations of motion for quantum mechanics. The Newtonian equations of motion (or actually, the Euler-Lagrange equations, which are equivalent) for the harmonic oscillator, say, are:

##\frac{dx}{dt} = \frac{p}{m}##

##\frac{dp}{dt} = -K x##

Those are exactly the same as the Heisenberg equations of motion for a harmonic oscillator, but in the Heisenberg equations, ##x## and ##p## are operators, rather than real-valued functions of time.

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You wrote "I had the idea ..." and then linked the paper.No! Did I give that impression, somehow?

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You wrote "I had the idea ..." and then linked the paper.

Ha, ha. I guess there's an ambiguity in the meaning of "I had the idea that". Or for that matter, "my idea is that...". It might mean that I am the originator of the idea. Or it might mean (which is does in this case) that it's the idea (belief, notion) that is currently in my head. My thoughts are the thoughts that are currently in my brain, whether or not they are original with me.

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I had the idea that string theory was nonlocal even classically, although the nonlocality is only significant over short distances.

Discussion of non-locality of string theory goes back to

- Emil Martinec, "Strings and Causality" (pdf) in L. Baulieu, V. Dotsenko, V. Kazakov, P. Windey (eds.) "Quantum Field Theory and String Theory" , NATO ASI Series B: Physics Vol. 328 (1995)

- Theodore Erler, David Gross, Locality, "Causality, and an Initial Value Formulation for Open String Field Theory" (arXiv:hep-th/0406199)

- M. Maeno, "Canonical quantization of Witten’s string field theory using midpoint light-cone time", Phys. Rev. D43 no. 12 (1991).

See also nLab: causal locality -- In S-matrix theories and string theory, and see the string theory FAQ entry

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