Deterministic Physical Theories from Geometric Viewpoint

J. Anandan

Alejandro Corichi, Michael P. Ryan

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin- system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed non-standard quantum theories.

Michail A. Zak

There has been proven that mathematical origins of randomness in quantum and Newtonian physics are coming from the same source that is dynamical instability. However in Newtonian physics this instability is measured by positive finite Liapunov exponents averaged over infinite time period, while in quantum physics the instability is accompanied by a loss of the Lipchitz condition and represented by an infinite divergence of trajectories in a singular point. Although from a mathematical viewpoint such a difference is significant, from physical viewpoint it does not justify division of randomness into deterministic (chaos) and true (quantum physics). The common origin of randomness in Newtonian and quantum physics presents a support of the correspondence principle that is being searched by quantum chaos theory.

J. Anandan

J. Anandan

Michail A. Zak

There has been proven that mathematical origins of randomness in quantum and Newtonian physics are coming from the same source that is dynamical instability. However in Newtonian physics this instability is measured by positive finite Liapunov exponents averaged over infinite time period, while in quantum physics the instability is accompanied by a loss of the Lipchitz condition and represented by an infinite divergence of trajectories in a singular point. Although from a mathematical viewpoint such a difference is significant, from physical viewpoint it does not justify division of randomness into “deterministic “(chaos) and “true” (quantum physics). The common origin of randomness in Newtonian and quantum physics presents a support of the correspondence principle that is being searched by quantum chaos theory.