Quantum Potential in Bohmian Mechanics?

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Discussion Overview

The discussion revolves around the concept of quantum potential in de Broglie-Bohm (dBB) theory, exploring its role as a potential "hidden variable" and its relationship with particle positions. Participants examine whether the quantum potential is essential or merely a formalism, and how it compares to the guiding equation in the theory.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question the necessity of quantum potential in dBB theory, suggesting it may only serve to align the theory with Newtonian mechanics.
  • Others assert that the positions of particles are indeed the "hidden variables" in dBB theory, while the quantum potential is not considered a hidden variable.
  • There is a suggestion that dBB theory has multiple formalisms, similar to classical mechanics, and that both quantum potential and guiding equation can be used interchangeably.
  • One participant argues that while Bohm frequently references quantum potential, its utility is debated, particularly in the context of spin.
  • Concerns are raised about whether particles are influenced by quantum force from quantum potential or by the guiding equation, with a preference expressed for the latter as a simpler explanation.
  • Active information is mentioned as a philosophical aspect of Bohm's approach, though its necessity is questioned.

Areas of Agreement / Disagreement

Participants express differing views on the role and necessity of quantum potential in dBB theory, with no consensus reached on its importance or utility. The discussion remains unresolved regarding the relationship between quantum potential and guiding equations.

Contextual Notes

Some participants highlight the philosophical implications of active information and the varying interpretations of quantum potential, indicating a lack of clarity in definitions and assumptions within the discussion.

cryptist
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What is the meaning of quantum potential in de broglie-bohm theory? Is that the "hidden variable"? Or are the positions of particles "hidden variables"?

As far as I see, some references explains theory with quantum potential (Bohm, Holland) but some references explains it with guiding equation. (Dürr, Goldstein)

Has de broglie-bohm two different formalisms, or what? Are they say same thing? Can we use both of them in same formulation?
 
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cryptist said:
What is the meaning of quantum potential in de broglie-bohm theory?
It is an unnecessary element of dBB theory the only role of which is to write the theory in a form that more closely resembles Newtonian mechanics.

cryptist said:
Is that the "hidden variable"?
No.

cryptist said:
Or are the positions of particles "hidden variables"?
Yes.

cryptist said:
Has de broglie-bohm two different formalisms, or what?
You can put it this way if you like, in analogy with the fact that classical mechanics has different formalisms, like those Newton, Hamilton, Lagrange, Hamilton-Jacobi, etc.

cryptist said:
Are they say same thing? Can we use both of them in same formulation?
Yes and yes.

It should also be pointed out that in dBB theory with spin, the notion of the quantum potential is quite useless.
 
Thank you for your answers. However Bohm uses quantum potential a lot (so is it really useless or unnecessary?) and as far as I understand, he describes it as active information. So are the particles move by the quantum force coming from quantum potential or they move by the guiding equation?
Because on that link: (http://plato.stanford.edu/entries/qm-bohm/#qp) it says "describing particles moving under the influence of forces, among which, however, one must include a force stemming from a "quantum potential.""
 
cryptist said:
Thank you for your answers. However Bohm uses quantum potential a lot (so is it really useless or unnecessary?) and as far as I understand, he describes it as active information. So are the particles move by the quantum force coming from quantum potential or they move by the guiding equation?
Because on that link: (http://plato.stanford.edu/entries/qm-bohm/#qp) it says "describing particles moving under the influence of forces, among which, however, one must include a force stemming from a "quantum potential.""
I wouldn't say that quantum potential is useless, but is definitely not necessary. The notion of active information is certainly not essential, but Bohm liked it for some philosophical reasons. It is definitely simpler to think of particles as moving by the guiding equation (that determines the velocity), rather than by the quantum force (that determines the acceleration).
 
Thank you very much for the answers.
 

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