Historical research guide · 0567 · 2010
Sub-Quantum Thermodynamics as a Basis of Emergent Quantum Mechanics
Gerhard Grössing
In one minute
Gerhard Grössing asks a simple question with a startling answer: what if the Schrödinger equation is not a postulate but a consequence? In this review from the Austrian Institute for Nonlinear Studies he collects a decade of work in which he and his colleagues treat a quantum particle as a small oscillator sitting in the zero-point field — the residual energy that fills empty space even at absolute zero — constantly absorbing energy from that field and giving it back. Treat that exchange with ordinary nonequilibrium thermodynamics, the physics of systems held away from equilibrium by a steady throughput of heat, and the exact Schrödinger equation falls out, with the energy-frequency relation as the only input taken from experiment. Planck’s relation, the Heisenberg uncertainty relations, the superposition principle, Born’s rule and the spreading of a Gaussian wave packet all follow the same way. His picture of a particle is Yves Couder’s bouncing oil droplet: a walking drop that steers by the waves it makes.
Connection
Chapter 2 argues that the vacuum is a real, structured medium, and this is the paper that takes that seriously enough to rebuild quantum mechanics on it: the zero-point field is not background noise here, it is the thing doing the work. Chapter 5 gets its clearest picture — Couder’s walking droplet, a real laboratory object that diffracts, tunnels and obeys an uncertainty relation — and chapter 13 gets the payoff, a route in which quantum behaviour, the vacuum and thermodynamics are one subject rather than three.
From the source
The vacuum unambiguously turned out during the twentieth century to be permeated by what is generally called the zero-point energy — a residual field in any accessible spacetime volume, even as the temperature goes toward zero — and every particle of nature has turned out to be characterised by a fundamental angular frequency in its rest frame, such that its total energy is given by Planck’s relation, energy equals the reduced Planck constant times that frequency.Sect. 1, Introduction
The exact Schrödinger equation can be derived from classical physics by assuming that a particle of energy equal to the reduced Planck constant times its frequency is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy, a heat flow drawn from and returned to the zero-point field. The energy-frequency relation is the only empirical input; the derivation covers both conservative and integrable non-conservative systems, and the author claims it as the only exact derivation of the Schrödinger equation from classical physics in the literature.Abstract and Sect. 3.1, Introduction
A quantum particle is modelled as a dissipative phase-locked steady state: an amount of zero-point energy of the wave-like environment is absorbed by the particle and then, during a characteristic relaxation time equal to the inverse of its frequency, dissipated into the environment again — radially symmetrically in the simplest case, thereby maintaining the zero-point energy’s wave-like structure through the phase locking. Planck’s relation on this reading does not describe an object oscillating at a frequency but a process of fleeting constancy, heat quantities absorbed and given back so that the total particle energy emerges.Sect. 1, and Sect. 2.4, Eqs. (2.4.1) to (2.4.13)
Yves Couder’s bouncing liquid droplets are a completely classical laboratory system in which a whole set of features previously thought exclusively quantum can be shown to occur: single-particle diffraction and interference, the Heisenberg uncertainty principle, indeterministic behaviour of a single particle despite a deterministic ensemble evolution, nonlocal interaction and tunnelling. Couder and Fort show how this wavelike behaviour of particle trajectories can result from the feedback of a remote sensing of the surrounding world by the waves the droplets emit.Sect. 1, Introduction
A vanishing quantum potential is proven to be exactly equivalent to a classical heat, or diffusion, equation whose solutions are radially symmetric thermal diffusion wave fields; a non-vanishing quantum potential is therefore the expression of a particle’s surrounding diffusion wave field when that radial symmetry is broken by something else in the environment, and the gradient of the quantum potential is a completely thermalised fluctuating force field whose origin is exactly identical to the zero-point fluctuation field.Sect. 1, and Sect. 5, Thermodynamic Origin of the Quantum Potential
Free quantum motion is proven to equal sub-quantum anomalous, that is ballistic, diffusion, and averaged Bohmian trajectories can be computed purely from a real-valued classical model using coupled map lattices, in excellent agreement with the analytical expressions of both approaches. Diffusion wave fields carry no travelling waves, no wave fronts and no phase velocity — the entire domain breathes in phase with the oscillating source, leaving only spatially correlated phase lags set by the diffusion length — which is what makes them a candidate for modelling quantum mechanical nonlocality, with a relativistic formulation the next thing needed.Sect. 8, and Sect. 9, Conclusions and Outlook
The way in
https://doi.org/10.3390/e12091975How to cite it
Gerhard Grössing (2010) Sub-Quantum Thermodynamics as a Basis of Emergent Quantum Mechanics doi:10.3390/e12091975