Quantum & Classical Potential?

[quantumcarl]

Here is part of an article that discusses what Bohm called "Quantum Potential"

Essentially, Bohm and his school re-interpreted the mathematics of Quantum Mechanics and extracted a part of the equation which they called the quantum potential. The quantum potential is non-local, and is responsible for all the non-local effects predicted by the theory.

The quantum potential guides, say, the path of an electron in a way similar to the way a radio beacon can guide an airplane coming in for a landing at the airport. It is the jets, ailerons, rudder, etc. on the plane that mechanically determines where the plane is going, but the beacon guides the way.

In Bohm's ontology electrons really are particles. For the case of, for example, the double slit experiment for electrons, each electron goes through either the upper slit or the lower slit; it has a definite path independent of its observation. However, the quantum potential is different depending on whether the other slit is open or closed; since this potential is non-local it can instantaneously change if the other slit is opened or closed. Thus the electron paths are different depending on whether or not the other slit is open.

From:http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BellsTheorem/BellsTheorem.html

Here is a summary of Issac Newton's definition of "Potential Energy" which I suppose can be classified as Classical Potential... although there are a billion physicists writing papers about "classical potential" that have nothing to do with Issac's definition of potential.

Potential Energy:

Potential energy exists whenever an object which has mass has a position within a force field. The most everyday example of this is the position of objects in the Earth's gravitational field.
The potential energy of an object in this case is given by the relation:

PE = mgh

where

PE = Energy (in Joules)
m = mass (in kilograms)
g = gravitational acceleration of the Earth (9.8 m/sec2)
h = height above Earth's surface (in meters)

From: http://jersey.uoregon.edu/vlab/PotentialEnergy/

Does the word "potential" describe the same condition regardless of it being used in a Quantum context or a Classical context?

Thank you for considering my question here.

 

[selfAdjoint]

I wouldn't depend on Newton's definitions for my understanding of concepts like potential. These ideas remained at a pretty primitive level until the nineteenth century, when people like Poussin, Green, Jacobi, and Dirichlet made a major improvement in understandiing.

The traditional way to acieve a quantum theory is to quantize a classical theory. In that process the variables in the classical theory become operators in the quantum theory. Energy becomes a Hamiltonian operator.

 

[quantumcarl]

I wouldn't depend on Newton's definitions for my understanding of concepts like potential. These ideas remained at a pretty primitive level until the nineteenth century, when people like Poussin, Green, Jacobi, and Dirichlet made a major improvement in understandiing.

The traditional way to acieve a quantum theory is to quantize a classical theory. In that process the variables in the classical theory become operators in the quantum theory. Energy becomes a Hamiltonian operator.

Can potential can be quantizised by assigning a value to a constant unit of potential? I'm not sure what a constant unit of potential could be... perhaps a calorie or Joule of energy,say?!

Potential is defined in layman's terms as the ability and flexibility for an entity to produce a wide variety of results or outcomes.
ie: The potential of fire can be any number of things ranging from the complete destruction of an object to the creation of fine ceramics.
Does this definition change when applied to quantum physics?

It wouldn't surprise me to see the definition of one word change from application to application.
ie:, the term "slip" describes an action often associated with a bannana peel and a pedestrian.

However, in ceramics, "slip" describes clay with a lot of water in it and is often used as a glaze but also lubricates the "throwing" of a cylindrical ceramic object. Langauge is so fickle

Thank you for you input!

 

[quantumcarl]

I suppose as primitive as Newton's attempt was at quantizising potential it was in the spirit of quantizisation and an attempt to objectify the idea of potential.

After considering the pedestrian and the scientific uses of the word, potential, I concluded, (with some help from Zapper z's comments in the thread "Yet Another Cat Question"/Quantum Physics section) that the word Potential is a descriptor or adjective that is applied to an object or situation.

The pedestrian (after Zz) use of the word potential describes the statistical probablilities that are available in any given situation or object. The probablities inherent in a situation or object are arrived at by making note of the elements that compose one or the other. These elements and combinations of elements can then be used to calculate various results/outcomes that are dependent upon various but specific combinations of the elements. This determines the potential(s) that exist in any given set of events.

In physics, as Zz pointed out, potential is measured such as in what he used as an example, electrostatic potential. Here, the number of probabilities are constant and the elements of the situation or object (electrostatic charge) are minimal in number. The potential charge of an electrostatic event is predicted by using a tried and true formula. And I suppose one can apply similar formuli to various other simplistic events like electrostatic charge.