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David Bohm and Quantum Potential Energy

David Bohm, one of the founders of quantum theory, regarded both waves and particles as real. In order to comply with law of conservation of energy during the wave function of a particle, he introduced quantum potential energy. The energy of the particle transforms between kinetic energy, potential energy and quantum potential energy while obeying conservation law. The quantum potential energy, derived from wave function, carries information and influences the possible paths the particle can take. It may be helpful to think of the analogy of a ship being guided by its radar.

wave particle-1

There have been some questions about his approach. While every classical force has a source, no source has been introduced for this new energy. In addition, classically, as we get further from the energy source, its strength drops (inverse square law). However, quantum potential energy does not suffer a decline in strength over distance. Its effect is felt equally everywhere. Besides, according to Newton’s third law of motion, the exertion of any force by a source receives an equal and opposite force in response. If no source has been introduced for quantum potential energy, how can there be an opposite force in action?

The above model proposes that the all-invasive, information- and energy-rich singularity is the source for the quantum potential energy. This way, quantum potential energy does not have to be local, the inverse square law does not apply to it, and the necessary information and energy can be illustrated everywhere. In this model, the bouncing ball analogy of wave-particle and its interaction with the singularity stands for Newton’s third law action and reaction.

Here the fact that the intrinsic angular momentum has to be added to the total orbital momentum points to similarity between classical and intrinsic angular momentum of electron.

Max Born Postulate

In 1926, Max Born suggested, “An electron wave must be interpreted from stand point of probability. Places where the magnitude of the wave is large are places where the electron most likely to be found. Places where the magnitude is small, are places where the electron less likely to be found. [10]Born’s probability wave favors the presence of the electron near the peak of the translation wave.

About the observed seemingly continuous path of electron in a cloud chamber Heisenberg states “perhaps we merely see a series of discrete and ill-defined spots through which the electron has passed.”[11] He meant that in larger scale discreteness of the path disappears and we see a continuous line.

Here we can offer an explanation for Born’s suggestion. In this model, the speed of the electron is reduced around the peak of the translation wave; this is what makes it more probable to be detected in space-time. On the other hand, we can assume that as the actual velocity increases to reach to the light speed (299,792,458 m/s) the probability to pinpoint it is reduced. At the speed of light, the electron as a mass disappears from space-time. Therefore, we cannot follow its trajectory. Down the slope probability is minimal or non-existent. 

Brian Greene, the Fabric of Cosmos. Vintage Books, New York, 2004 
Jonathan Allday, Quantum Reality, CRC Press, Boca Raton. Fl, 2009 
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