Historical research guide · 0556 · 2022
Stochastic Interpretation of Quantum Mechanics Assuming That Vacuum Fields Are Real
Emilio Santos
In one minute
Emilio Santos asks what quantum mechanics looks like if the vacuum fields are taken to be real — an actual random electromagnetic background filling space, not a bookkeeping device. He starts from an old puzzle: a classical atom should radiate its electron into the nucleus. No atom is isolated, he answers; if every atom radiates then space is full of radiation, and each atom settles into a balance between what it emits and what it absorbs. Demand that this background look the same to every observer and its spectrum is fixed — energy rising as the cube of the frequency, which works out to half a Planck quantum per mode. From there he recovers the size and binding energy of hydrogen, the Bohr energy ladder and the Casimir force, then argues that the particle-like behaviour of light — absorption in discrete lumps, needle-like emission, no coincidences after a beam splitter — comes from interference between a signal and the vacuum. He closes with a local model of an entangled-photon experiment that still violates a Bell inequality.
Connection
Chapter 2 holds that the vacuum is a real, structured medium; this is a working physicist carrying that single assumption all the way through quantum mechanics rather than into a few effects only. The hydrogen section is the same balance-with-the-field argument chapter 3 rests on, and the Casimir section makes the site’s own point precisely: what a plate feels is the difference between the radiation arriving on its two faces.
From the source
Atoms are stable because they sit in dynamical equilibrium with a real background radiation: an isolated classical atom would radiate itself into the nucleus, but no atom is isolated — if all atoms radiate, space is filled with radiation and each atom absorbs as much as it emits.Sect. 3.1, The stability of atoms rests on vacuum radiation
Requiring the background to be homogeneous, isotropic and Lorentz invariant forces its spectrum to be proportional to the cube of the frequency, and dividing by the number of modes gives exactly half a Planck quantum of energy per normal mode; the single free constant that fixes the scale is then identified with the Planck constant.Sect. 3.2, Eqs. (1)–(3)
Balancing the electron’s motion against the vacuum modes at its own frequency reproduces the binding energy and the size of the hydrogen atom, and applying the same balance to transitions between neighbouring orbits reproduces the Bohr energy ladder and the quantisation of angular momentum.Sect. 3.3, Eqs. (4)–(5); Sect. 3.4, Eqs. (9)–(13)
The Casimir attraction follows from the same background: the plates exclude the modes with wavelengths comparable to or longer than their separation, and the stochastic-electrodynamics calculation, which is the quantum calculation with stochastic averages substituted for vacuum expectations, reproduces the measured force law — what matters is the difference between the radiation arriving on the two faces of a plate, not the total on one side.Sect. 3.5, Eq. (15)
The particle behaviour of light can be modelled without postulating photons: discrete absorption of about one Planck quantum follows from a signal interfering constructively with the vacuum modes nearest it, needle-like emission follows from emission stimulated along an arriving vacuum wave, and the absence of coincidences after a beam splitter follows from the real vacuum field entering the splitter’s second port.Sect. 5.2, Eqs. (26)–(27); Sect. 5.3, Eq. (28); Sect. 5.5, Eqs. (30)–(32)
Because the vacuum fields carry correlated fluctuations, a local model built from them reproduces the standard coincidence prediction for parametric down conversion and violates a Bell inequality, from which the author concludes that Bell inequalities are not necessary conditions for local realism.Sect. 7.5; Sect. 7.6, Eqs. (82)–(94)
The way in
https://doi.org/10.3390/foundations2020028How to cite it
Emilio Santos (2022) Stochastic Interpretation of Quantum Mechanics Assuming That Vacuum Fields Are Real doi:10.3390/foundations2020028