“Energy” in Quantum Mechanics

Reference: Fundamentals of Physics

Energy is a classical concept that applies to Newtonian mechanics as “the capacity for doing work.” But this same word “energy” has gone through a fundamental shift in its meaning in Quantum Mechanics.

The word QUANTUM means, “quantity or amount”. It refers to the smallest quantity of radiant energy, equal to Planck’s constant times the frequency of the associated radiation (E = hf). “Quantity of radiant energy” means that radiant energy is a substance that can be collected and measured. This is a revolutionary thought. 

Quantum refers to “the smallest quantity of substance,” where substance means “something substantial enough to be sensed.” 

The basis of substance is impact, which comes from a change in momentum. This is the classical definition of force. Light has momentum. Light can have impact and force. Therefore, light is substance. It was for establishing the reality of quantum as quantity of substance, which he demonstrated through the phenomenon of photoelectricity, that Einstein got a Nobel Prize.

The classical sense of energy is derived from force as the product “force x distance.” Thus, energy is a mathematical concept, much like the “lagrangian” and “hamiltonian” functions. But force is a real concept that can be experienced. The concept of “energy” in Quantum Mechanics is closer to the sense of force and substance.

Quantum is closer to the basic sense of FORCE as in the “impact of substance” than to ENERGY as in the “capacity for doing work.”

It was Faraday who first articulated that the concept of force is more basic than energy in his thesis: On the Conservation of Force. Maxwell, who applied mathematics to Faraday’s ideas, disagreed with Faraday on his notion of force (see Faraday & Maxwell). But Einstein, who kept a picture of Faraday on his wall, did understand the notion of force as Faraday intended.

Thanks to Faraday and Einstein, that we can visualize a broad spectrum of substance today (see The Spectrum of Substance). The concept of substance translates into having an atom-less consistency and not just atomic mass. The concept of inertia is not just limited to mass, but it applies to consistency as well.

Mass is, essentially, “frozen inertia” as in the case of the nucleus of atom. It is more like “liquid inertia” as in the case of electrons; and it is “vaporized inertia” as in the case of radiant energy. The property of inertia is the core of substance as it generates sensation.

Underlying substance, mass, consistency and inertia is the concept of FORCE.

This force is proportional to frequency.



Energy is a mathematical concept derived from force. It is a mathematical function, much like the “lagrangian” and “hamiltonian” functions. 


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