Quantum Potential in Bohmian Mechanics?

In summary, the de broglie-bohm theory has two different formalisms: one explaining it with quantum potential, and the other with the guiding equation. Both formalisms say the same thing and can be used together in the same formulation. However, the notion of quantum potential is not necessary and can be seen as an unnecessary element in the theory. Some references, like Bohm, use it a lot and describe it as active information, but particles can also be seen as moving by the guiding equation.
  • #1
cryptist
121
1
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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  • #2
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.
 
  • #3
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.""
 
  • #4
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).
 
  • #5
Thank you very much for the answers.
 

1. What is the concept of quantum potential in Bohmian Mechanics?

The quantum potential is a theoretical concept in Bohmian Mechanics that describes the effects of quantum phenomena on the movement of particles. It is a non-local potential that influences the trajectory of particles, taking into account the wave-like behavior of particles in quantum mechanics.

2. How is the quantum potential calculated in Bohmian Mechanics?

The quantum potential is calculated using the wave function of a system, which is derived from the Schrödinger equation. The quantum potential is then added to the classical potential in the Bohmian Mechanics equations of motion to determine the trajectory of particles.

3. What is the significance of the quantum potential in Bohmian Mechanics?

The quantum potential plays a crucial role in Bohmian Mechanics as it explains the non-local behavior of particles in quantum systems. It also provides a deterministic explanation for the probabilistic outcomes of quantum measurements, which is a fundamental aspect of understanding quantum mechanics.

4. Can the quantum potential be measured or observed in experiments?

No, the quantum potential is a theoretical concept and cannot be directly measured or observed in experiments. However, its effects can be observed indirectly through the movement of particles in a quantum system, which can be compared to the predictions of Bohmian Mechanics.

5. Are there any controversies or criticisms surrounding the concept of quantum potential in Bohmian Mechanics?

Yes, there have been debates and criticisms surrounding the concept of quantum potential in Bohmian Mechanics. Some argue that it is a non-local, unobservable quantity that goes against the principles of relativity. Others argue that it is a necessary component in understanding the underlying determinism of quantum mechanics. Further research and experiments are needed to fully understand the implications of the quantum potential in Bohmian Mechanics.

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