Planck Constant
The Planck constant, h, is the constant of proportionality between the energy of a quantum of radiation and its frequency, E = hν. It is the quantity that fixes the scale at which the discreteness of physical action becomes noticeable, and its appearance in an equation is the usual signal that the phenomenon being described is a quantum one.
The standard account
Max Planck introduced the constant in December 1900, in the course of fitting the observed spectrum of black-body radiation. Classical thermodynamics gave the Rayleigh–Jeans law, which diverges at short wavelengths; Planck obtained the correct curve by assuming that the energy exchanged between radiation and the walls of a cavity came in finite portions proportional to the frequency. He regarded the step as a formal device rather than a statement about nature. Einstein took it literally in 1905 in his account of the photoelectric effect, and Bohr's 1913 atomic model made the constant structural: angular momentum in the hydrogen atom comes in multiples of ħ = h/2π, the reduced Planck constant, sometimes called the Dirac constant.
Since the SI redefinition that took effect on 20 May 2019, h is no longer measured but defined: it is exactly 6.62607015 × 10−34 joule seconds, and the kilogram is derived from it by way of the Kibble balance. Before that, the constant was determined experimentally — by Kibble (watt) balances and by X-ray crystal density measurements of silicon spheres — and it was the agreement and residual disagreement between those two routes that governed the timing of the redefinition.
The constant has the dimensions of action, energy multiplied by time, or equivalently angular momentum. Combined with G and c it gives the Planck units — Planck length, time and mass — which are widely taken to mark the scale at which a quantum theory of gravity would be needed. Whether they mark anything physical, as opposed to being a dimensional combination, is not settled.
On this wiki
Researchers catalogued here divide roughly between those who want to explain where h comes from and those who dispute what it has been taken to mean.
William C Daywitt argues that Planck's constant, the fine-structure constant and the gravitational constant all originate in the same underlying polarizable vacuum state. His The Planck Vacuum (Galilean Electrodynamics, 2010) sets out that vacuum as the source of the free particles, the gravitational field and the spacetime of general relativity; Origin of the Compton and de Broglie Relations (2008) derives the two relations most closely bound up with h as a balance of van der Waals and Coulomb forces in that vacuum, rather than as brute quantum postulates.
Milos Abadzic revisits the determination of the constant itself in A New Aspect of Planck's Constant (2008), arguing that its establishment was as much an empirical fitting exercise as the determination of the speed of light and that some of the terms bound up with it deserve re-examination. Thomas N Lockyer's Fundamental Physical Constants Derived From Particle Geometric Structures (2008) attempts to derive h along with the other fundamental constants from the geometry of particle structure, which is the general strategy of the structural modelling tradition on this wiki — see also Toroidal Ring and Common Sense Science.
Tuomo Suntola approaches the constant from the radiation side. In Photon - The Minimum Dose of Electromagnetic Radiation (2005) he treats the quantum of radiation as a single oscillation cycle of a unit charge, an engineer's picture in which h emerges from the emission process rather than being imposed on it — a classical reading of the Photon that recurs throughout Category:Light.
The sharpest challenge comes from Edward Kapuscik, whose Physics Without Physical Constants (1994) observes that neither Newton's mechanics nor Maxwell's electrodynamics contains a physical constant in its basic equations, constants entering only at the point of application, and argues that the universality of those theories is bound up with that fact. Paul Wesley takes the quantum itself to be classical: his Classical Quantum Theory (1996) constructs quantization from classical wave theory, with quantized constants of the motion arising from standing waves rather than from an independent quantum postulate.
Don Briddell's Multiple Certainties (2012) and Rati Ram Sharma's Unified Theory's New Principle of Null Action Replaces Uncertainty & Hamilton Principles (2009) both concern the role h plays in the Uncertainty Principle, where the constant sets the size of the irreducible product of uncertainties.