An answer to the Wallstrom objection against Nelsonian stochastics

Abstract

A serious objection made by Wallstrom against quantum interpretations based flow variables, in particular Nelsonian stochastics, is their empirical inequivalence with quantum theory: They are unable to obtain a quantization condition for flows around zeros which is automatically fulfilled by the wave function. It is found that the quantization condition follows from a simple additional postulate: The Laplace operator of the density has to be finite and positive at zeros of the density. This postulate is a quite natural consequence of subquantum theories, as far as they conform to a simple principle of minimal distortion of the quantum solutions.

Considerations about the relevance and rejection of Smolin's attempt added

References in corpus (7)

• Inflationary Cosmology as a Probe of Primordial Quantum Mechanics
• Quantum Theory from Quantum Gravity
• Could quantum mechanics be an approximation to another theory?
• Nelsonian Mechanics Revisited
• Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference
• Matrix models as non-local hidden variables theories
• Generalizations of Quantum Mechanics

Cited by in corpus (7)

• Stochastic Emergent Quantum Gravity
• Splitting the source term for the Einstein equation to classical and quantum parts
• The paleoclassical interpretation of quantum theory
• Stochastic Mechanics Without Ad Hoc Quantization: Theory And Applications To Semiclassical Gravity
• Quantum mechanics as the dynamical geometry of trajectories
• Gravitation and cosmology with York time
• A Thermodynamical derivation of the quantum potential and the temperature of the wave function