Thursday,
20 April 2006
Technical Tutorial
Functional Relativity:
How to Extend the Principle
of Relativity to Quantum Mechanics
Alexey Kryukov, U. Wisconsin Colleges, Mathematics
2:30 – 4 pm, 817R
Cathedral of Learning
Abstract:
In general terms, the mathematics of quantum mechanics is
the theory of linear operators in Hilbert spaces, while the theory
of gravity is a theory of (pseudo) Riemannian manifolds. The
former is essentially linear and infinitedimensional, while the
latter is nonlinear and finite dimensional.
The aim of the talk is to introduce a new geometric formalism
that naturally relates the apparatuses of both quantum mechanics
and general relativity. The formalism allows one to move a step
forward towards answering the following fundamental questions of
modern physics: How
to define space and time quantum mechanically? How to extend the
principle of relativity to quantum theory?What is the origin of
physical dimensions of observables?Is there a geometric interpretation
of Planck's constant?
