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arXiv:quant-ph/9810029

Many Time Interpretation Of the Quantum Measurement Process

M. Dugić

Published Oct 10, 1998• 1 citation
arXivHTMLPDF

Abstract

Many Time Interpretation (MTI) proposes that each stochastic "quantum jump" ("reduction") concerning each single object (of an ensemble) represents a consequence of a (stochastic) choice (change) of Time. Therefore, each single object experiences its own (local), stochastically chosen Time, which is as real for it, as the macroscopic Time is real in classical physics. Therefore, instead of the "indeterminism" with regard to the macroscopic Time, MTI proposes "determinism", but with regard to the set(s) of (stochastically chosen) local Times. Within an axiomatization, which includes the composite system "single object+apparatus+environment, MTI leads to : (i) Recognizing the amplification process as the fundamental "part" of the measurement process, (ii) Nonvalidity of the Schrodinger equation concerning the "whole", O+A+E, which makes the "state reduction process" unnecessary and unphysical, (iii) Natural deducibility of the macroscopic irreversibility, and (iv) Nonequivalence of MTI with any existing measurement theory, or interpretation. Thus, within MTI, the measurement problem reduces basically onto the search for quantum effect, which would allow forthe local, stochastic change of Time.

DOI
10.48550/arxiv.quant-ph/9810029

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Many Time Interpretation (MTI) proposes that each stochastic "quantum jump" ("reduction") concerning each single object (of an ensemble) represents a consequence of a (stochastic) choice (change) of Time. Therefore, each single object experiences its own (local), stochastically chosen Time, which is as real for it, as the macroscopic Time is real in classical physics. Therefore, instead of the "indeterminism" with regard to the macroscopic Time, MTI proposes "determinism", but with regard to the set(s) of (stochastically chosen) local Times. Within an axiomatization, which includes the composite system "single object+apparatus+environment, MTI leads to : (i) Recognizing the amplification process as the fundamental "part" of the measurement process, (ii) Nonvalidity of the Schrodinger equation concerning the "whole", O+A+E, which makes the "state reduction process" unnecessary and unphysical, (iii) Natural deducibility of the macroscopic irreversibility, and (iv) Nonequivalence of MTI with any existing measurement theory, or interpretation. Thus, within MTI, the measurement problem reduces basically onto the search for quantum effect, which would allow forthe local, stochastic change of Time.
The main theme of this book is the idea that quantum mechanics is valid not only for microscopic objects but also for the macroscopic apparatus used for quantum mechanical measurements. The author demonstrates the intimate relations that exist between quantum mechanics and its interpretation which are induced by the quantum mechanical measurement process. Consequently, the book is concerned both with the philosophical, metatheoretical problems of interpretations and with the more formal problems of quantum object theory. The consequences of this approach turn out to be partly very promising and partly rather disappointing. On the one hand, it is possible to give a rigorous justification of some important parts of interpretation, such as probability, by means of object theory. On the other hand, the problem of the objectification of measurement results leads to inconsistencies which cannot be resolved in an obvious way. This open problem has far-reaching consequences for the possibility of recognising an objective reality in physics.
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the quantum measurement process. The modified Schroedinger formalism involving multivalued effective dynamical functions reveals the dynamic origin of quantum measurement indeterminacy as the intrinsic instability in the compound system of 'measured object' and (dissipative) 'instrument' with respect to splitting into spatially localised 'realisations'. As a result, the originally wide measured wave catastrophically (and really!) "shrinks" around a random accessible point thus losing all its 'nonlocal properties' with respect to other points/realisations. The dissipativity of one of the interacting objects (serving as 'instrument') is reduced to its (arbitrarily small) openness towards other systems (levels of complexity) and determines the difference between quantum measurement and quantum chaos, the latter corresponding to an effectively isolated system of interacting (micro-) objects. We do not use any assumptions on particular "classical", "macroscopic", "stochastic", etc. nature of the instrument or environment: physical reduction and indeterminacy dynamically appear already in interaction between two microscopic (quantum) deterministic systems, the object and the instrument, possessing just a few degrees of freedom a part of which, belonging to the instrument, should correspond to locally starting, arbitrarily weak excitation. This dynamically indeterminate wave reduction occurs in agreement with the postulates of the conventional quantum mechanics, including the rule of probabilities, which transforms them into consequences of the dynamic uncertainty.
Abstract Nearly a century has passed, since the birth of quantum mechanics, and yet the measurement problem has not been solved. We investigate the measurement problem from two aspects. First we scrutinize the basic postulates adopted by existing theories and identify the postulate of classicality of apparatus (PCA) to be the origin of the trouble. Second, we analyze the simplest possible experimental setup, a single photon particle as an observed system S and a detector as an apparatus A, and we find that a quantum jump occurs as a microscopic interaction between S and a single particle in A. We call this a microscopic quantum jump (MIJ). The MIJ selects system eigenvalues (SEVs) such as a two-dimensional position and arrival time for an incident photon. The MIJ outputs a microscopic particle (MIP), which carries the information of the SEVs potentially. In the apparatus A, the MIP triggers amplification cascade of secondary particles, which we call the intermediate particles (IMPs). The IMPs are initially a few, but become plenty after the amplification. The output of the amplification is a macroscopic observable (MAO) such as a current pulse, which carries the information of the SEVs in actuality. The measurement is complete when the MAO is obtained. By adopting the postulate of the MIJ and by discarding the PCA, we have constructed a measurement theory, which is consistent with standard quantum mechanics.
This paper extends the temporal concept of Sequential Time Theory (STT) to the problem of metrology in the quantum domain. In STT, a time interval Δt is constructed by a counter n representing the number of realizations of a standard displacement ΔQ_unit, while time t serves as a coordinate label assigned to this sequence. STT explicitly posits that "time is a scaling of physical change" and that "time is constructed solely by clock phenomena subject to the same conditions within a local system." Consequently, in regimes where ΔQ is indistinguishable, time does not "cease to exist" but becomes "unconstructible (undefined)." Based on these definitions and axioms, this paper (i) organizes criteria for distinguishing between science and metaphysics, (ii) identifies conceptual confusions arising from the implicit assumption of an external classical clock in quantum theory, and (iii) proposes a relativity principle regarding differences in observation scale (e.g., macroscopic observation of microscopic systems). We demonstrate that issues such as measurement, classicality, and tunneling time can be unifiedly organized as problems of "choice of clock (ΔQ)" and "recording (event-token) protocols."
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring system and a measured one. These properties result directly from the Schrödinger equation. They cannot be formulated in terms of observables, do not affect the wave functions themselves but express their history in an irreversible way. They carry a specific new kind of local probabilities, which evolve with a finite velocity under nonlinear wave equations. The second category of results extends these local properties to the case of a macroscopic system and its environment. Fluctuations in their interaction are predicted then and generate a specific incoherence in the quantum state of the system. These two kinds of effects act together when a macroscopic measuring system interacts with a measured system and with an environment. Their combination yields then an explicit and effective mechanism of collapse, with a random behavior resulting from random incoherence. Born's basic probability rule for the results of measurements turns out then simply a consequence of quantum dynamics. Some conjectures still enter into the derivation of these effects, which one may recognize to look hardly credible at first sight. They fit however so well together that one proposes a more thorough investigation of their approach as a promising strategy for a self-contained explanation of collapse.
The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is the integral wave equation with kernel in the form of a path integral. It is shown, that wave function collapse is the specific transformation which is fundamentally differ from Shrödinger's evolution. Specifically, a formal cause of the collapse is a local time derivative (infinite large) of the potential energy. Such transformation can not be described using mathematical apparatus of conventional quantum mechanics.