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Is there such a thing as real phenomena that's classical “all the way down”, as you have put it? If yes, which such phenomena is easiest to understand? I was u

Is there such a thing as real phenomena that's classical “all the way down”, as you have put it? If yes, which such phenomena is easiest to understand? I was under the impression that all of classical physics was special cases of quantum and relativistic physics, just like the relativistic equations of motion "degrade" into classical equations of motion when we postulate that all velocities involved are much lower than the speed of light.

jfengel 7y ago
In this sense "classical" means "not quantum". General relativity is "classic" in the sense that position and momentum are variables rather than operators. They have real values rather than functions. So it's distinct from "classical" meaning "Newtonian" (or, perhaps "Newtonian + Maxwellian"), which is the sense in which "all of classical physics was special cases of quantum and relativistic physics".
- raattgift 7y ago
  Yes, all true, but we have the Hamiltonian formulation (e.g. https://arxiv.org/abs/1505.01403 https://arxiv.org/abs/1505.01403 which is a nice book chapter) which “… is also the starting point for the canonical quantization program, which constitutes one main approach to the as yet unsolved problems of Quantum Gravity. In this approach one tries to make essential use of the Hamiltonian structure of the classical theory in formulating the corresponding quantum theory.” From there you could jump to https://en.wikipedia.org/wiki/Canonical_quantum_gravity https://en.wikipedia.org/wiki/Canonical_quantum_gravity which has references.
raattgift 7y ago
> “all the way down” Nobody knows. Gravitation might be classical “all the way down”. Dark Matter might not be quantum-mechanical. Few people really expect this though: either would be a surprise because as you say, for known macroscopic behaviours of matter they’re almost certainly > special cases of [relativistic] quantum and quantum mechanical objects even when doing funny quantum mechanical things will generate stress-energy and thus the stress-energy tensor (and thus the Einstein gravitational tensor) must reflect that. Unfortunately the obvious easy ways to do this (averaging the stress-energy tensor, quantum corrections to the metric using perturbation theory, second-quantizing the Hamiltonian formulation of General Relativity (cf. objections in near the start of [1]) …) have run into difficult problems. Mostly, however, the problems arise only when curvature is strong, and such strong curvature is hidden from us. These approaches work well for practically all the physics of uncollapsed stars, and a considerable amount of physics even in neutron stars. Thus we tend to say that we have various ways to turn classical General Relativity into an effective field theory [2]. We know — and can and do prove within our solar system — how errors arise in equations of motion that do not take relativistic speeds or non-flat spacetime backgrounds into account. In fact, we have some mathematical theorems about that, and reflect them in post-Newtonian formalisms and expansions, and have ample observational and experimental evidence supporting them. As a result, we can talk about the Newtonian limit and the flat-space limit of General Relativity, and we can derive the theories associated with those limits from the more fundamental theory of General Relativity (recovering Newtonian gravitation requires some extra tricks, and it’s those that help show why Newtonian gravitation is wrong; one is that the propagation of Newtonian gravitation is superluminal (technically infinitely fast) and this is contradicted by experiment (e.g. precession of Mercury’s orbit, MESSENGER, Hulse-Taylor, LIGO)). Unfortunately we’re not as sure about the “errors” in classical matter theories as we fail to take quantum properties into account. It is a principle, rather than something stronger. In https://en.wikipedia.org/wiki/Correspondence_principle https://en.wikipedia.org/wiki/Correspondence_principle one finds: “This concept is somewhat different from the requirement of a formal limit”. We do not know how to derive numerous classical theories from quantum mechanics, correspondence principle notwithstanding, and so while one can claim that e.g. Navier-Stokes (“NS”) can be derived from the Standard Model, nobody has actually shown how to do this mathematically. Indeed, quantum theories of dissipative physics of all sorts are at best exceedingly rare [1], so in NS’s case viscosity has no derivation from quantum principles. - — [1] https://en.wikipedia.org/wiki/Quantum_dissipation https://en.wikipedia.org/wiki/Quantum_dissipation [2] http://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/ http://www.preposterousuniverse.com/blog/2013/06/20/how-quan...

jfengel 7y ago

In this sense "classical" means "not quantum". General relativity is "classic" in the sense that position and momentum are variables rather than operators. They have real values rather than functions. So it's distinct from "classical" meaning "Newtonian" (or, perhaps "Newtonian + Maxwellian"), which is the sense in which "all of classical physics was special cases of quantum and relativistic physics".

raattgift 7y ago
Yes, all true, but we have the Hamiltonian formulation (e.g. https://arxiv.org/abs/1505.01403 https://arxiv.org/abs/1505.01403 which is a nice book chapter) which “… is also the starting point for the canonical quantization program, which constitutes one main approach to the as yet unsolved problems of Quantum Gravity. In this approach one tries to make essential use of the Hamiltonian structure of the classical theory in formulating the corresponding quantum theory.” From there you could jump to https://en.wikipedia.org/wiki/Canonical_quantum_gravity https://en.wikipedia.org/wiki/Canonical_quantum_gravity which has references.

raattgift 7y ago

> “all the way down” Nobody knows. Gravitation might be classical “all the way down”. Dark Matter might not be quantum-mechanical. Few people really expect this though: either would be a surprise because as you say, for known macroscopic behaviours of matter they’re almost certainly > special cases of [relativistic] quantum and quantum mechanical objects even when doing funny quantum mechanical things will generate stress-energy and thus the stress-energy tensor (and thus the Einstein gravitational tensor) must reflect that. Unfortunately the obvious easy ways to do this (averaging the stress-energy tensor, quantum corrections to the metric using perturbation theory, second-quantizing the Hamiltonian formulation of General Relativity (cf. objections in near the start of [1]) …) have run into difficult problems. Mostly, however, the problems arise only when curvature is strong, and such strong curvature is hidden from us. These approaches work well for practically all the physics of uncollapsed stars, and a considerable amount of physics even in neutron stars. Thus we tend to say that we have various ways to turn classical General Relativity into an effective field theory [2]. We know — and can and do prove within our solar system — how errors arise in equations of motion that do not take relativistic speeds or non-flat spacetime backgrounds into account. In fact, we have some mathematical theorems about that, and reflect them in post-Newtonian formalisms and expansions, and have ample observational and experimental evidence supporting them. As a result, we can talk about the Newtonian limit and the flat-space limit of General Relativity, and we can derive the theories associated with those limits from the more fundamental theory of General Relativity (recovering Newtonian gravitation requires some extra tricks, and it’s those that help show why Newtonian gravitation is wrong; one is that the propagation of Newtonian gravitation is superluminal (technically infinitely fast) and this is contradicted by experiment (e.g. precession of Mercury’s orbit, MESSENGER, Hulse-Taylor, LIGO)). Unfortunately we’re not as sure about the “errors” in classical matter theories as we fail to take quantum properties into account. It is a principle, rather than something stronger. In https://en.wikipedia.org/wiki/Correspondence_principle https://en.wikipedia.org/wiki/Correspondence_principle one finds: “This concept is somewhat different from the requirement of a formal limit”. We do not know how to derive numerous classical theories from quantum mechanics, correspondence principle notwithstanding, and so while one can claim that e.g. Navier-Stokes (“NS”) can be derived from the Standard Model, nobody has actually shown how to do this mathematically. Indeed, quantum theories of dissipative physics of all sorts are at best exceedingly rare [1], so in NS’s case viscosity has no derivation from quantum principles. - — [1] https://en.wikipedia.org/wiki/Quantum_dissipation https://en.wikipedia.org/wiki/Quantum_dissipation [2] http://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/ http://www.preposterousuniverse.com/blog/2013/06/20/how-quan...