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AKPhil: Arbeitskreis Philosophie der Physik

AKPhil 7: Interpretations of Quantum Theory 2

AKPhil 7.3: Vortrag

Donnerstag, 8. März 2007, 17:45–18:15, KIP SR 3.401

Can Quantum Mechanics be Shown to be Incomplete in Principle? — •Carsten Held — Universität Erfurt, Wissenschaftsphilosophie, Postfach 900221, 99105 Erfurt, Germany

Given four plausible principles, quantum mechanics (QM) can be shown to contradict the standard expression of completeness, the eigenstate-eigenvalue link (EE). Consider:
(P0) If, for a proposition A (describing a possible event), a theory T yields another proposition p (A) > 0, then it is not the case that T, A⊢⊥.
(P1) A QM probability, being of the form p ([A] = a_i) = Tr (W (t) P(a_i)), is to be interpreted as p ([A] = a_i (t)) (“the probability that S has a_i of A at t").
(P2) There is a parameter t within QM such that the expression [A] = a_i is read as [A] = a_i (t)(“S has a_i of A at t").
(P3) Function P : S(H) → [0, 1] (collecting the QM probabilities for some suitable Hilbert space H) can be defined as a generalised probability function.
It is easy to show, for a non-eigenstate of some observable A and QM probabilities interpreted as prescribed by (P1), that (EE) transforms QM into a theory contradicting (P0). But (P0) is eminently plausible, so the defender of (EE) will naturally reject (P1). It can now be shown that retaining (P0) entails the rejection of all of (P1)-(P3).