The Interpretation of Quantum Mechanics

Wigner’s “Unreasonable Effectiveness of Mathematics”, Revisited

“…Another theorem by Egorov shows that, again with suitable restrictions, the Schrödinger equation preserves this relation between operators and classical propositions [26]. In a nutshell, this implies a derivation of classical dynamics from quantum dynamics, with explicit and usually extremely small errors [27].…”

Decoherence and Wave Function Collapse

“…1, a methodological relation between quantum measurements and the basic principles must start from the case of an isolated system A + m. The relevance of wave functions is less obvious, because the state of this macroscopic system is certainly not defined by a unique wave function. The right approach is rather to define the notion of state from the principles, as done by Von Neumann [12,23]: After associating the physical properties of the system with projection operators in its Hilbert space, the state is defined as a datum attributing a probability to every property. Considering logically compatible properties as associated with commuting projection operators, some basic axioms of logic imply that the state is necessarily associated with a density matrix ρ A+m [25].…”

“…Decoherence was also confirmed by experiment [11]. The emergence of classical dynamics at a macroscopic scale was derived mathematically from quantum dynamics [12], and also less formally from decoherence [13] Consistent histories clarified the language and logic of quantum mechanics [14][15][16][17], and removed many paradoxes [18].…”

A simple Newtonian model for the fractal accelerating Universe

“…On a more abstract level, the so-called decoherence effect is invoked when interpreting the macroscopic properties of a quantum system as due to coupling with the macroscopic environment (see, e.g. Omnes, 1994).…”

“…The principal problem with all newly proposed mechanisms that are supposed to drive the observed acceleration is how to make the hypothetical fields pass from a passive to a driving agent, more precisely, from an attractive at not very large distances to the accelerating, repulsive motive force at large (see, e.g. Parker and Raval, 1999a,b, 2000. For the case of quintessence the way out has been sought by referring to the quantum nature of the proposed field.…”