Historical research guide · 0694 · 2009
Quantum Mechanics as an Emergent Property of Ergodic Systems Embedded in the Zero-point Radiation Field
L. de la Peña · A. Valdés-Hernández · A. M. Cetto
In one minute
Luis de la Peña, Andrea Valdés-Hernández and Ana María Cetto ask what happens if you take an ordinary classical charged particle — one that obeys Newton’s laws and radiates when it accelerates — and never let it out of contact with the zero-point radiation field, the electromagnetic jitter that fills empty space. Their answer, worked out over thirty-three pages of Foundations of Physics, is that quantum mechanics is what such a system looks like from outside. It is not put in by hand; it emerges. Two ingredients do the work. The field supplies the ceaseless random driving that shows up in the finished theory as quantum indeterminism, and it is where Planck’s constant enters. And an ergodic condition — the demand that a long look at one particle and a snapshot of many give the same statistics — is what converts a description in ordinary space and time into the operator, matrix description Heisenberg wrote down. The same treatment underwrites simulations that reproduce the hydrogen atom’s ground-state distribution.
Connection
Chapter 2 needs the vacuum to be a real, physically active medium rather than an accounting device, and this is the strongest form of that argument: the authors do not merely allow the zero-point field to exist, they make it the thing quantum mechanics is made of. Chapter 5 gets its picture of the vacuum as a medium whose statistics a particle eventually inherits — the same intuition the walking-droplet experiments make visible.
From the source
The central result: non-relativistic quantum mechanics is revealed as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum, the zero-point radiation field. Nothing quantum is postulated at the start. The particle obeys classical mechanics and classical electrodynamics; what is added is a real random electromagnetic background with energy one half h-bar omega per mode, present at every frequency, from which the particle can never be isolated. The quantum description is the end state of that permanent interaction.Abstract; and title
Ergodicity is the hinge, and it is what produces Heisenberg’s formulation specifically. The action of the field on matter is essential to the approach, but it is the ergodic demand that ultimately leads to the matrix formulation of quantum mechanics. The authors state the step plainly in their later review: under conditions of ergodicity, the dynamical variables describing the statistical properties of an ensemble in a given pure state are expressed by the corresponding quantum operators, which is a derivation of quantum mechanics in Heisenberg’s form rather than Schrödinger’s.Abstract, closing sentence; restated in arXiv:2010.06780, footnote 5, citing this paper
Quantum indeterminism is the field’s randomness, not an intrinsic acausality of matter. In the authors’ own summary of this paper, the zero-point field has been shown to play an essential role in producing quantum features such as so-called quantum indeterminism. That reading removes the postulate Heisenberg introduced and never tested — that a particle is inherently indeterministic — and replaces it with a physical cause outside the particle.arXiv:2010.06780, Introduction, citing this paper as reference 17
The paper supplies the theory behind an already-published numerical result: statistical analysis of an atomic electron interacting with the zero-point field furnishes the quantum probability distribution for the ground state of the hydrogen atom. The simulations had produced the right answer; this work says why they should. That is a strong test, because the hydrogen ground state is the case where the classical picture is supposed to fail catastrophically — a radiating orbiting electron should spiral in — and the balance with the field is what holds it.Abstract, second sentence
Planck’s constant and the wave element of quantum mechanics come from the field, not from a quantisation rule. In the same programme the authors identify the zero-point field as what accounts for the appearance of Planck’s constant and the wave element in quantum mechanics, together with Born’s rule that goes with it. The constant is then a measured property of the background, not an axiom.arXiv:2010.06780, Section 1, drawing on this paper and The Emerging Quantum
What to watch: the derivation is stated for non-relativistic quantum mechanics and under defined conditions and approximations, so the open questions are how far it extends. Two measurements would move it. First, numerical experiments of the kind this paper underwrites, pushed past the hydrogen ground state to excited states and to more than one electron, where earlier classical attempts broke down. Second, laboratory analogues: the authors argue that any corpuscle held in permanent contact with an oscillating background should quantise the same way, and point at walking-droplet systems, where orbit quantisation and interference are already observed, as the place to test whether the mechanism is general.Abstract; programme set out in arXiv:2010.06780, Sections 1 and 5
The way in
https://doi.org/10.1007/s10701-009-9348-zHow to cite it
L. de la Peña, A. Valdés-Hernández, A. M. Cetto (2009) Quantum Mechanics as an Emergent Property of Ergodic Systems Embedded in the Zero-point Radiation Field doi:10.1007/s10701-009-9348-z