I Is the Hamilton-Jacobi Formalism a Classical Analogue to Quantum Wave Functions?

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The discussion centers on the relationship between the Hamilton-Jacobi formalism in classical mechanics and quantum wave functions, emphasizing that while wave functions exist in Hilbert space, they are not literal waves. The Hamilton-Jacobi equation is a classical tool for solving equations of motion and is distinct from quantum theory, despite its application in Bohmian mechanics. The conversation explores how classical mechanics can be expressed in terms of wavefronts and the implications for higher-dimensional mathematical spaces. Additionally, it touches on the connection between the Hamilton-Jacobi equation and quantum mechanics through methods like the WKB approximation and Feynman path integrals. Ultimately, the Hamilton-Jacobi formalism remains a powerful classical approach that can inform quantum mechanics without directly replacing Hilbert space concepts.
  • #61
Demystifier said:
@fanieh you are so fast in making questions. Do you ever try to answer them by yourself?

Ive been thinking of this for months. Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.

Anyway. You sure there is no fatal flaw in the concept that a 5th fundamental force created the position preferred basis in MWI to become BM. Well. I'd lecture this to thousand of students so hope it's not illogical or false.. lol.. thanks..
 
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  • #62
fanieh said:
Oh. I wrote the reply before I saw you asked it.. Again..

Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.

Anyway. You sure there is no fatal flaw in the concept that a 5th fundamental force created the position preferred basis in MWI to become BM. Well. I'd lecture this to thousand of students so hope it's not illogical or false.. lol.. thanks..

The Schlosshauer book didn't mention about the Factorization Problem that's why I was kinda confused about it. Well.. the mere fact our universe has environment and system splitted in the Big Bang means there is already position chosen.. and it doesn't mean there is BM, right? so it appears BM is just alternative way of looking at it or addition to preferred basis chosen in the initial environment-system decomposition isn't it? Schlosshaer nearly talked about this when he mentioned Stapp paper in page 337.. but he stopped short and so readers would not be aware of the problem. That's why I'm confused about this.
 
  • #63
fanieh said:
Ive been thinking of this for months. Schlosshauer only mentioned about the theme about "nothing happens in many worlds" indirectly only in 2 pages.. in page 337 "Everett Branches and the Preferred-Basis Problem". The book doesn't mention at all how the initial environment and system got decomposed in MWI. It didn't mention about the Factorization problem. It is only in PF archives that I can read about it.
You can read https://arxiv.org/abs/1703.08341 Sec. 3.3 Refs. [22,23,24].
 
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