Based on the hypothesis that the position-representation of a physical state <x|
α> is the Fourier transform of its momentum-representation <P|
α> and that the time-representation <t|
α> is the inverse Fourier transform of its energy-representation <E|
α>, we are able to find the Planck relation E = hv, the de Broglie relation P =
λh. Afterward, utilizing the Dirac delta function
δ(x) and the property FTxf(x) = -i
ℏ∂, pFTxf(x) = -i
ℏ∂, pF(p) we obtain the links between operators in ordinary and Hilbert spaces leading to the Dirac fundamental commutation relation [
p^,x^] = -i
ℏI^, the Schrödinger equations, the Heisenberg uncertainty principle in quantum mechanics, the annihilation & creation of a photon from excitation & de-excitation of an atom according to Bohr.
Planck introduced the constant ℎas the elementary quantum of action, yet its repeatedappearance throughout quantum physics remains one of the deepest structural features ofmodern science. The same constant governs photon energy, matter waves, Schrödingerevolution, angular momentum quantization, and Heisenberg uncertainty. This paperproposes a Space-Phase (SP3) interpretation in which Planck's constant is not primarily aproperty of matter or radiation but an intrinsic action scale of an underlying conditionablemedium.The medium is modeled conceptually as a flexible, interconnected Planck-scale meshcapable of storing, releasing, and transporting energy through localized reorganizationevents. Stable particles correspond to persistent conditioned basins within this mesh,while propagating radiation represents traveling reorganizations of the same medium. Agroove-based analogy is introduced in which observable physical change requires themedium to reorganize by at least one elementary unit of action. The uncertainty relationsare interpreted as minimum reorganization criteria rather than solely mathematical limitsarising from wavefunctions. Planck's relation, de Broglie's relation, Schrödinger's equation,and Heisenberg's uncertainty principle are mapped to this common organizing principle.The paper presents a qualitative framework intended to motivate future mathematicaldevelopment of an SP3 description of quantum action.
Planck introduced the constant ℎ as the elementary quantum of action, yet its repeatedappearance throughout quantum physics remains one of the deepest structural features ofmodern science. The same constant governs photon energy, matter waves, Schrödingerevolution, angular momentum quantization, and Heisenberg uncertainty. This paperproposes a Space-Phase (SP3) interpretation in which Planck's constant is not primarily aproperty of matter or radiation but an intrinsic action scale of an underlying conditionablemedium.The medium is modeled conceptually as a flexible, interconnected Planck-scale meshcapable of storing, releasing, and transporting energy through localized reorganizationevents. Stable particles correspond to persistent conditioned basins within this mesh,while propagating radiation represents traveling reorganizations of the same medium. Agroove-based analogy is introduced in which observable physical change requires themedium to reorganize by at least one elementary unit of action. The uncertainty relationsare interpreted as minimum reorganization criteria rather than solely mathematical limitsarising from wavefunctions. Planck's relation, de Broglie's relation, Schrödinger's equation,and Heisenberg's uncertainty principle are mapped to this common organizing principle.The paper presents a qualitative framework intended to motivate future mathematicaldevelopment of an SP3 description of quantum action
The Interest in the interaction of electromagnetic radiation with matter was the first impulse to structure a series of formulas, postulates and theories that would become the foundation for quantum physics.Under the shadow of statistical determinism, in the XIX and XX centuries, started the studies on the blackbody radiation, a consequent reformulation of various theories of classical physics and the introduction of the concepts of energy quantization, radiation and particles.This article will deal, briefly and chronologically, with the evolution of the old quantum theory.