The Evolution of States as the Fourth Pillar of Quantum Mechanics

Abstract: I present ideas about how to extend the standard formalism of Quantum Mechanics in such a way that the theory actually makes sense. My tentative extension is called

"ETH-Approach to Quantum Mechanics"

(for "Events, Trees and Histories").

This approach supplies the last of four pillars QM can be constructed upon, which are:
(i) Physical quantities characteristic of a physical system are represented by self-adjoint operators;
(ii) the time evolution of these operators is given by the Heisenberg equation;
(iii) meaningful notions of states and of "potential" and "actual events" have to be introduced; and
(iv) a general law for the time evolution of states (superseding Schroedinger evolution, which is inadequate) must be formulated.

Besides briefly sketching the ETH-Approach in the setting of non-relativistic QM, I present a family of very simple models of a very heavy atom coupled to the radiation field in a limit where the speed of light tends to infinity, An analysis of these models, which illustrate the ETH Approach, is the main subject of the talk.

mathematical physics

Audience: researchers in the discipline

( slides | video )

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