Exact uncertainty, quantum mechanics and beyond

Abstract

The fact that quantum mechanics admits exact uncertainty relations is used to motivate an ‘exact uncertainty’ approach to obtaining the Schrödinger equation. In this approach it is assumed that an ensemble of classical particles is subject to momentum fluctuations, with the strength of the fluctuations determined by the classical probability density [1]. The approach may be applied to any classical system for which the Hamiltonian is quadratic with respect to the momentum, including all physical particles and fields [2]. The approach is based on a general formalism that describes physical ensembles via a probability density P on configuration space, together with a canonically conjugate quantity S [3]. Quantum and classical ensembles are particular cases of interest, but one can also ask more general questions within this formalism, such as (i) Can one consistently describe interactions between quantum and classical systems? and (ii) Can one obtain local nonlinear modifications of quantum mechanics? These questions will be briefly discussed, with respect to measurement interactions and spin-1/2 systems respectively. 1. M.J.W. Hall and M. Reginatto, “Schroedinger equation from an exact uncertainty principle”, J. Phys. A 35 (2002) 3289 (http://lanl.arxiv.org/abs/quant-ph/0102069). 2. M.J.W. Hall, “Exact uncertainty approach in quantum mechanics and quantum gravity”, Gen. Relativ. Gravit. 37 (2005) 1505 (http://lanl.arxiv.org/abs/gr-qc/0408098). 3. M.J.W. Hall and M. Reginatto, “Interacting classical and quantum systems”, Phys. Rev. A 72 (2005) 062109 (http://lanl.arxiv.org/abs/quant-ph/0509134).