A Generic Model for Quantum Measurements

Abstract

In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" required to define these modalities.In the present article we provide a unified picture of quantum measurements within our approach, and justify further the role of the system-context dichotomy, and of quantum interferences. We also discuss links with stochastic quantum thermodynamics, and with algebraic quantum theory.

Deriving Born’s Rule from an Inference to the Best Explanation

“…Therefore the randomness is not only from C u to C v , but also back from C v to C u [12]. This makes clear that probabilities do follow from the fixed value of N , i.e.…”

Stable Facts, Relative Facts

“…The interaction with the context determines the fact that a certain variable has a value in that context. 1 Stable facts are a strict subset of the relative facts: there are many relative facts that are not stable facts. Quantum theory provides probabilities relating relative facts, but these satisfy (1) only if b and the a i are facts relative to the same system.…”

“…(2) P b (F) 1 We use 'variable' to denote any quantity that in the classical theory is a function on phase pace. We prefer to avoid the expression 'observable' because it is loaded with irrelevant extra baggage: the ideas of observation and a complex observer.…”

Quantum Randomness is Chimeric

“…One could still maintain that, through nesting [ 25 , 47 ] and the effects of the translational environment the number of degrees of freedom during the measurement cannot be bounded from above and approaches infinity, resulting in nonseparable hyper-Hilbert spaces [ 81 ], a situation which might yield a sort of irreducible randomness based on the diverging complexity of the environment [ 82 ]. Note that even classically the hypothetical invocation of infinity “in the limit produces” provable random sequences, such as Chaitin’s halting probability Omega [ 83 ].…”