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arXiv:physics/0002048

Irreversibility and Measurement in Quantum Mechanics

Douglas Snyder

Published Feb 28, 2000• 5 citations
arXivHTMLPDF

Abstract

Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the part of the experimenter concerning how the experimental circumstances are structured. Second, how is irreversibility that occurs in making a measurement explained in terms of a neurophysiological mechanism where a macroscopic measuring instrument is not required in principle to make the measurement, as in macroscopic quantum tunneling? Third, how does irreversibility characterize a negative observation where there is no physical interaction in the measurement process?

DOI
10.48550/arxiv.physics/0002048

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Irreversibility is often considered to characterize measurements in quantum mechanics. Fundamental problems with this characterization are addressed. First, whether a measurement is made in quantum mechanics is an arbitrary decision on the part of the experimenter concerning how the experimental circumstances are structured. Second, how is irreversibility that occurs in making a measurement explained in terms of a neurophysiological mechanism where a macroscopic measuring instrument is not required in principle to make the measurement, as in macroscopic quantum tunneling? Third, how does irreversibility characterize a negative observation where there is no physical interaction in the measurement process?
This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.
Instruments are necessarily of macroscopic size because our sense organs—which can be considered as instruments occupying a certain rank in the von Neumann hierarchy—are of macroscopic size. It is only natural, therefore, that physicists should have attempted to make use of this property for constructing quantum measurement theories. Moreover, one of the remarkable properties possessed by most macroscopic systems, including all instruments, but lacking in microscopic systems is irreversibility. This simple observation suggests very strongly that the phenomenon of irreversibility and the phenomenon of "wave packet reduction," which is associated in some way or other with the measurement process, should somehow be correlated. The theories in the chapter show that it is in practice always possible to attribute definite macroscopic properties to the measuring instruments. The danger that the error we thus make will ever be detected has been proved to be vanishingly small.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).
The quantum measurement problem arises from a structural asymmetry in standard formulations of quantum mechanics: while unitary evolution is treated as fundamental, irreversible events are introduced only through ad hoc postulates. As a result, measurement, decoherence, and probability appear conceptually disconnected. In this work, we propose a minimal reformulation in which irreversible interaction events are taken as ontological primitives. An event is defined as a completely positive, trace-preserving map that is not equivalent to any unitary transformation. Unitary evolution emerges as an effective description valid between events. Within this framework, quantum measurement is not a special process but a particular class of irreversible events with outcome-resolving structure. The Born rule arises naturally from the statistical structure of event realizations, and environmental decoherence is reinterpreted as a high density of irreversible events. No collapse postulate, observer-dependent rule, or modification of quantum dynamics is required. This formulation provides a unified and physically grounded resolution of the measurement problem and establishes a conceptual foundation for event-based extensions connecting quantum theory with spacetime and gravity.
This paper focuses on the study of the functional relationships between the tools of neuroscience, neurofinance and psychology on the one hand, and quantum physics / quantum mechanics and neurophysiology on the other. Can physics / quantum mechanics help explain / understand human behavior through the Shrödinger cat platform (perhaps we can explain the most mysterious phenomena- human behavior - cerebral secretion?)? The concepts of quantum mechanics allow a good prediction of human decision making within Schrödinger's cat (two particles can talk to each other even at a distance of a galaxy, perhaps in this sense can help explain an extremely complex decision making system), and define the "connection of quantum models with neurophysiological processes in the brain “... which is a very complex problem.†(Haven and Khrennikov) The application of quantum physics and neuroscience in finance allows us to consider the complexity of financial decision making, while the connection between quantum physics and psychology manifests itself as the field of quantum physics seeks to understand the fundamental nature of particles. while the field of psychology seeks to explain human nature along with its inherent misconceptions.If decision-making is a process of gathering evidence in favor of different alternatives over time, the process is discontinued once the decision limit is reached, followed by choice of decision. e activity within the posterior parietal cortex several important questions remain unanswered. Neural mechanisms that support the accumulation of evidence record the activities of individual neurons in different parts of the prefrontal cortex (PFC) and the lateral intraparietal area (LIP).
The role played by irreversible processes, at the microscopic scale, in several examples of quantum measurements is studied within a "minimally realist" interpretation of the quantum formalism introduced in a recent publication. The analysis extends and confirms the basic results of the earlier work: separation of the collapse and amplification phases of the measurement, and decoherence and collapse happening already as a consequence of irreversible microscopic processes at the level of the "probe" itself (typically an atom in the examples considered). Additionally, the proposed interpretation of the formalism is shown to be consistent with previous interpretations, and a case for true irreversibility in physics is argued in some detail.