EPR-Bell-Schrödinger Proof of Nonlocality Using Position and Momentum

The Time-Evolution of States in Quantum Mechanics according to the ETH-Approach

“…This argument is based on a quantitative analysis of correlations between the outcomes of measurements of physical quantities (spins) referring to two different sub-systems that have been prepared in an entangled state. The analysis in [14] also illustrates what people call the "non-locality" of Quantum Mechanics; for a recent study, see, e.g., [30]. (For a discussion of the crucial role of locality in relativistic quantum theory, in the sense of Einstein causality, as opposed to the "non-locality" just referred to, the reader may consult [13,23].…”

The Time-Evolution of States in Quantum Mechanics

“…where the union is a disjoint union ranging over all normal states ω on the algebra E, and Z ω (E) is the center of the centralizer of the state ω restricted to the algebra E; see Eq. (27) of Sect. 4.…”

“…This formula is claimed to correctly describe the correlations between measurements of components of the spins of L and of R even if, for example, the direction of e is suddenly changed before the silver atom R has traversed the magnetic field between the Stern-Gerlach magnets, but in such a way that the change of the direction of e cannot causally affect the fate of the electron L. This is what is often called the "non-locality" of Quantum Mechanics (see, e.g., [27]). It is not captured by Schrödinger evolution.…”

“…( 26), of Sect. 4 determine a stochastic branching process on the noncommutative spectrum Z S := ω ω, Z ω (N ) , where N E (0) ≥0 , see (27), and ω ranges over all states given by density matrices Ω on H S . It is quite subtle to describe this process explicitly, because it is "non-Markovian", i.e., it has memory.…”