Some geometrical analogies between the states space and the events space

Abstract:
The space of stochastic states includes microstates of quantum dynamics and macrostates of statistical thermodynamics. A mutuality of their statistical description in the form of the same statistical ensemble version can be a basis for its physical interpretation as a holistic states space. The geometrical structure of this states space is discussed from various points. We can impart the pseudo-Euclidean structure to the microstates space. In this case the Bogoliubov transform group plays the same role as the Lorentz group in relativity. In accordance with that the Planck constant would play the same restrictive role in this space as the inverse light velocity plays in the events space. In the same manner one can introduce the Riemannian structure in the macrostates space. A curvature of this space dependents on the Boltzmann constant. Some geometric analogy allow us to compare it to the gravitational constant in Newton – Cartan geometry. The analysis of the quantum oscillator in the thermostat allows us to make a preposition that there is a total analogy between the states space and the events space.

Joint work with Olga Golubjeva (Russian People Friendship University, Moscow, Russia).