Observation in quantum mechanics

Mikio Namiki

Hans-Thomas Elze

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM–CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

Jose A. Pereira Frugone

In this work we will answer the following question: What remains of Quantum Mechanics when we transform the background space-time into a space modularized by observation or measurement regions ? This new moduli space is constructed by identifying regions of space-time where quantum phase comparison (observation, measurement) is implied. We call it Observation Modular space (OM-space). In addition we replace in QM statements the Plank constant (h) by the quantity $ζ_0 4 π^2$ (where $ζ_0$ is the Plank Length) or otherwise, replacing $P_0$ (the Planck Momentum) by $4 π^2$. This maps Quantum Mechanics into a very rich dual Number Theory which we call Observation Modular Quantum Mechanics (OM-QM). We find the OM-dual to the Dirac Equation, the quantum Wave Function and a free particle's mass. The OM-QM counterparts of the Energy turns out to be a simple function of the zeroes of the Riemann zeta function. We also find the OM-QM correspondents to the electron spin, the electron charge, the Electric Field and the Fine Structure Constant. We also find the OM-QM correspondents of the Heisemberg uncertainty relation and Einstein's General Relativity Field equation emerging as certain limits of a unique OM-QM equation. We also get the OM-QM correspondents of the Gravitational Constant and the Cosmological Constant. We find the analog of holography in the OM-QM side and we get an interpretation of spin as a high dimensional curvature. An interpretation of the OM-QM correspondence is proposed as giving the part of QM information which is not measurement or observation dependent. Some potential future applications of this correspondence are discussed.

Pierre Jasselette, Jacques Voisin

G. Feild

Shabnam Siddiqui

This chapter discusses the mathematical formalism of the theory of quantum mechanics and present the differences between the theory of classical mechanics and quantum mechanics. The mathematics that is used to account for the indeterminacy of quantum mechanics renders the mathematical approach of quantum mechanics distinct from that of classical mechanics. In quantum mechanics, any dynamical variable that is an observable that can be measured experimentally is described as a linear Hermitian operator. In quantum mechanics, it is not only necessary to define an observable, but it is also necessary to define the states associated with it. When a system is in a linear superposition of states of an observable, the number of different values of an observable observed in an experiment is equal to the number of states that a quantum mechanical system can jump into upon measurement of an observable.