Quantum Causality Relations and the Emergence of Reality from Coherent Superpositions

Abstract

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the observable input-output relations. In this paper, I investigate the relation between the classical notion of reality and quantum superpositions by identifying the conditions under which the intermediate states can have real external effects, as expressed by measurement operators inserted into the inner product. It is shown that classical reality emerges at the macroscopic level, where the relevant limit of the measurement resolution is given by the variance of the action around the classical solution. It is thus possible to demonstrate that the classical notion of objective reality emerges only at the macroscopic level, where observations are limited to low resolutions by a lack of sufficiently strong intermediate interactions. This result indicates that causality is more fundamental to physics than the notion of an objective reality, which means that the apparent contradictions between quantum physics and classical physics may be resolved by carefully distinguishing between observable causality and unobservable sequences of hypothetical realities "out there".

What Does the Operator Algebra of Quantum Statistics Tell Us about the Objective Causes of Observable Effects?

“…This is actually very close to the original justification of quantum mechanics associated with Niels Bohr and Copenhagen. However, it should be emphasized that the physics of state preparation and measurement is still not sufficiently understood because there is no convincing method of resolving the entanglement with the environment that is part of any quantum description of such processes [ 35 , 36 , 37 ]. The theory presented here describes only the deterministic causality within the quantum system.…”

“…The formalism of quantum mechanics thus separates the internal causality of a system from the possibility of control from the outside. As the analysis of entanglement suggests, this is achieved through the selection of specific patterns of uncertainty associated with the means of control outside of the system [ 36 , 37 ]. In the end, external observations of the relations between causes a and effects b are always governed by positive expressions of the form given in Equation ( 1 ).…”

What does the operator algebra of quantum statistics tell us about the objective causes of observable effects?

“…The formalism of quantum mechanics thus separates the internal causality of a system from the possibility of control from the outside. As the analysis of entanglement suggests, this is achieved through the selection of specific patterns of uncertainty associated with the means of control outside of the system [36,37]. In the end, external observations of the relations between causes a and effects b are always governed by positive expressions of the form given in Eq.…”