Garnet N. Ord

Department of Math, Physics and Computer Science

 
Main

Research Interests

Courses Links  

Quantum Equations and Classical Statistical Mechanics

The aim of my research is to construct microscopic models of the equations of quantum mechanics. 

Although it is generally accepted that microscopic models of the full theory (equations plus measurement postulates) are not possible (or at least unlikely), recent work has shown that neither the Schroedinger, nor the Dirac equation in a restricted domain, are outside the domain of classical statistical mechanics. This means that it is possible to construct statistical mechanical models of the components of wavefunctions using only ensembles of classical point particles moving on continuous trajectories in space-time. As a result, the Schroedinger and Dirac equations have real microscopic models within classical probability theory where the objects being described are ensembles of classical point particles. This places the quantum equations in a very different context than is usual. In this new context, wave functions are observable and correspond to measurable properties of ensembles of particles.

This embedding of the quantum equations in classical physics has the effect of providing many-particle simulations of quantum mechanics using only classical statistical mechanics. The above figure is an example of such an embedding (click on it to make it larger). There, a cellular automaton model was used to count paths in a binary random walk. The density of particle paths has a typical Gaussian shape but the automata, which find the expectation of a classical variable over the ensemble of paths, project out the irreversible diffusive behaviour and produce a discrete approximation to one component of the Feynman propagator for a free particle.

The most recent result is that, not only can you generate the quantum equations using only projections from ensembles of classical particles, you can now replace the ensemble of paths by a single space-time trajectory. This is at least true for a free particle in one dimension. For more complicated systems the result has yet to be established, but ... stay tuned.