On the relation between measurement outcomes and physical properties

Abstract

One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable quantities, which cannot simply be identified with each other. Our analysis shows that the Hilbert space formalism itself describes a fundamental separation between quantitative properties and qualitative outcomes that needs to be taken into account in an objective description of quantum measurements. We derive fundamental relations between the statistics of measurement outcomes and the values of physical quantities that explain how the objective properties of a quantum system appear in the context of different measurement interactions. Our results indicate that non-classical correlations can be understood in terms of the actual role of physical properties as quantifiable causes of the external effects observed in a quantum measurement.

Control of particle propagation beyond the uncertainty limit by interference between position and momentum

“…The violation of the particle propagation inequality discussed above thus establishes a connection between the rather abstract logic of of quantum paradoxes in few level systems and the more intuitive concept of motion in continuous spaces. This connection would seem to support the idea that quantum mechanics is essentially about a modification of the deterministic relations between physical properties, as suggested in [34]. Specifically, the discussion above shows how quantum interferences modify the physical meaning of the operator relation given in Eq.(1).…”

Nonlocal single particle steering generated through single particle entanglement

“…If a screen is placed for measuring the possible positions (nowadays an alternative is a device which measure the position by sensing the cloud of electrons that is released when the particle hit it, see Arévalo Aguilar, On the Stern-Gerlach experiment, to be published) in the z axe, as it was done in the original experiment, two different spots are got. We recall that there exist a connection between physical properties and measurements formulated in the form of a self-adjoint operator 53 ; this connection is realized in the combination of the eigenstate of the operator with a corresponding eigenvalue 53 . Hence, taking into account that the z position is being measured, then the wavefunction given by Eq.…”

Understanding quantum mechanics: a review and synthesis in precise language

“…3.3 multi-field specifies properties, smoothly across spacetime, by reference to multiple points in spacetime [230,231]; see Sect. 3.4 object that which is being studied, discussed or examined objective relating to an independent reality [49]; what is objective should not depend on the particular perspective used for the description [63, § 3.1] observables operators associated with properties relating to the studied system [193,300] observe to use physics concepts to account for what is done or thought about a measurement; to describe a measurement by associating data [562,563] ontic state a complete specification of the properties of a system (in an ontological model) [212]; see Sect. 3.4 ontology/ontological structures postulated in a physical theory as primary, underlying, explanatory entities [78,564] to account for the existence of events [500]; can be seen as forming the basis for kinematics (all possible values and arrangements of the physical ontology) and dynamics (specific constraints on how the ontology evolves in time) [430]; alternatively can be based on the dynamics [494, § 2]; often expressed in terms of the nature and behaviour of systems as they are [564], independent of any empirical access [233] operator map associating every vector in a Hilbert space with another such vector [25, p. 37] outcome apparatus reading for a single run of a measurement; collectively form the result of a measurement particle entity associated with a group of spatially localized properties, some of which are unchanging [25, § 4.2]; possibly has self-identity [17,388,565] phenomenon observation linked to specified circumstances, including (where appropriate) the experimental set-up [404, p. 64] [405, § 3.3] prepare/preparation (of a system): selection of some of the single runs of a measurement [193] pre-quantum mechanical developed prior to the experimental exploration of subatomic phenomena prequantum relating to a level of independent reality which is assumed to underlie the phenomena dealt with by quantum mechanics; see Sect.…”