Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

Abstract

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.

Final proceedings version. 6 pages. Presented at the 3rd QTRF conference at Vaxjo, Sweden, June6-11 2005

References in corpus (5)

• Toy Model for a Relational Formulation of Quantum Theory
• Assumptions that imply quantum dynamics is linear
• Informal Resource Letter - Nonlinear quantum mechanics on arXiv up to August 2004
• Lorentz Violation and Gravity
• Quantum Mechanics without spacetime V - Why a quantum theory of gravity should be non-linear-

Cited by in corpus (4)

• Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation
• Exact Solutions of a Non-Polynomially Nonlinear Schrodinger Equation
• Quantum mechanics without spacetime: a case for noncommutative geometry
• The Vertical Logic of Hamiltonian Methods (Part 1)