Historical research guide · 0453 · 2012
An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations
G. Grössing · S. Fussy · J. Mesa Pascasio · H. Schwabl
In one minute
Gerhard Grössing and his colleagues at the Austrian Institute for Nonlinear Studies take the double slit — the experiment usually offered as proof that nothing classical could ever account for quantum behaviour — and account for it classically, provided the vacuum is real. Their picture: a particle is a ‘bouncer’, an oscillator locked in step with the zero-point field it also stirs, much like the walking droplets Yves Couder’s group keep bouncing on a vibrating oil bath. The bouncer follows an ordinary trajectory, but the field it swims in carries waves from everything else in the apparatus, both slits included. Add that field’s diffusion to the classical motion and out come the exact quantum intensity pattern, the exact probability current, and the trajectories Bohmian mechanics predicts — with no quantum potential invoked. Their paths never cross the centre line, and the reason offered here is physical rather than formal: heat accumulates in the compressed vacuum along that line and pushes the two bundles of trajectories apart.
Connection
Chapter 2 holds that the vacuum is a real, structured medium, and this paper takes that literally enough to compute with — the textbook interference pattern comes out of the medium’s thermodynamics rather than out of a postulate. Chapter 5’s programme, reading quantum behaviour off the dynamics of a fluid, has few cleaner worked examples, and it connects straight to Couder’s bouncing-droplet bench experiments. Chapter 13 gets a candidate for one picture in which the zero-point field, quantum statistics and thermodynamics are a single subject. The same group’s book-length development of the idea is on this site at /library/stm-0e3175348a.
From the source
A particle is modelled as an oscillator, a ‘bouncer’, whose oscillation is phase-locked with the zero-point field around it, held in a nonequilibrium steady state by a permanent throughput of energy: its average total energy is the oscillator’s own energy, Planck’s constant times its frequency, plus a kinetic term from the momentum it exchanges with that environment, absorbed and released in equal measure over intervals of about one over the frequency.Section 2, Path excitation field and diffraction at a Gaussian slit; Equations (2.1) to (2.5)
Free quantum motion is exactly equivalent to anomalous, ballistic diffusion — a diffusion whose coefficient grows with time, which makes the process crucially dependent on its initial conditions and, unlike ordinary diffusion, time-reversible. The boundary conditions of the whole apparatus enter through what the authors call a path excitation field, spanned by the average velocity field and the diffusive velocity field together.Section 1, closing paragraphs; Section 2; Section 4, Geometric meaning of the path excitation field
Combining classical wave mechanics with sub-quantum diffusion reproduces the double-slit result exactly: the intensity on the screen is the sum of the two single-slit distributions plus twice the square root of their product times the cosine of a phase difference, where that phase difference is computed from the relative velocity of the two spreading Gaussians including wave-packet dispersion.Section 3; Equations (3.2), (3.4) and (3.5)
The computed trajectories obey the no-crossing rule — paths from the left slit stay left of the centre line and paths from the right stay right — and in this model the cause is kinetic rather than a quantum potential: the heat of the compressed vacuum accumulates along the symmetry line as a reservoir of outward-oriented kinetic energy and repels the trajectories, which the authors present as detailed momentum conservation at the microscopic level. The resulting paths agree with the average photon trajectories Kocsis and colleagues measured in a two-slit interferometer in 2011.Section 4; Figures 1 and 3; the discussion following Equation (4.7)
Rewriting the model’s total average current through the Madelung transformation returns the standard quantum-mechanical probability current and its conservation law exactly, obtained, in the authors’ words, without any quantum mechanics but as a reformulation of their own classical expression.Section 5, The Schrödinger equation revisited; Equations (5.1) to (5.3); Appendix A
The authors name the next target: because one and the same diffusive velocity field spans the whole apparatus, a pair of anti-correlated particles emitted in opposite directions shares that field, which the authors expect to yield nonlocal correlations and an identity with entangled states in quantum mechanics — to be demonstrated in a following paper.Section 6, Conclusions and outlook
The way in
https://doi.org/10.1016/j.aop.2011.11.010How to cite it
G. Grössing, S. Fussy, J. Mesa Pascasio, H. Schwabl (2012) An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations doi:10.1016/j.aop.2011.11.010