This chapter examines the reasons why measurement theory is a particularly controversial part of modern theoretical physics. The problem of measurement in quantum mechanics is considered as nonexistent or trivial by an impressive body of theoretical physicists and as presenting almost insurmountable difficulties by a somewhat lesser but steadily growing number of their colleagues. The law of evolution in time constitutes the essential part of the conventional measurement theory. In this theory, the existence of a Hamiltonian describing the instrument-system interaction is postulated, not derived. In other words, this assumption is considered as a legitimate idealization of the experimental facts. A wave packet reduction can be considered as a phenomenological procedure that, in many instances, can be applied in order to calculate the results of successive observations and the correlations between them without introducing into the formulas the complicated wave functions of the various instruments.
This chapter examines the reasons why measurement theory is a particularly controversial part of modern theoretical physics. The problem of measurement in quantum mechanics is considered as nonexistent or trivial by an impressive body of theoretical physicists and as presenting almost insurmountable difficulties by a somewhat lesser but steadily growing number of their colleagues. The law of evolution in time constitutes the essential part of the conventional measurement theory. In this theory, the existence of a Hamiltonian describing the instrument-system interaction is postulated, not derived. In other words, this assumption is considered as a legitimate idealization of the experimental facts. A wave packet reduction can be considered as a phenomenological procedure that, in many instances, can be applied in order to calculate the results of successive observations and the correlations between them without introducing into the formulas the complicated wave functions of the various instruments.
This paper explores a thought experiment: what would physics look like if quantum mechanics had not originated in the early 20th century from the exploration of the physical properties of microscopic particles (such as blackbody radiation and the particle and wave nature of electron orbits), but had instead been established first as a dynamics and probability theory about "physical measurement" itself? Through extrapolation from this historical turning point, this paper reconstructs a theoretical framework centered on "measurement dynamics," not on "particles," "wave functions," or "quantum fields" as fundamental ontology, but on a trinity of "system-measuring instrument-observer." Research shows that under this paradigm, the "measurement problem" is no longer a philosophical dilemma added after the theory's establishment, but rather the logical starting point for its construction; wave functions and quantum fields are relegated to derivative mathematical tools for calculating measurement probability distributions. This paper elaborates on the dynamics of measurement operators, the law of information evolution, and a systematic critique of counterfactual definiteness under this paradigm, providing a new and unified perspective for re-examining the fundamental interpretation of modern quantum mechanics.
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 'unreasonable effectiveness of mathematics in the natural sciences' may at times give the impression that natural science, especially modern theoretical physics, is all but a formal apparatus. However, a key challenge of physics remains to align everyday notions of experience -- be it directly or mediated through instruments of arbitrary sophistication -- with their mathematical formalisation. This applies in particular to quantum theory, arguably the most successful theory of physics ever invented. One of its core assumptions postulates: Observablescorrespondwithself−adjointoperators. Here, we argue that already this most basic premise about the quantum formalism falls apart under careful scrutiny, at least when understood for all observables at once. In other words, we challenge the role of the noncommutative algebra of bounded operators as an adequate formalisation of the 'algebra of observables', understood as (equivalence classes of) measurement procedures that admit a coherent empirical interpretation.
The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system interacting with the measuring device and show under which ideal conditions the measure process may ideally work. Our procedure leads to the conclusion that there is no hope that any experimental procedure will be able to lead to a clean solution of the process, except maybe in very specific cases. The reasons for this situation are deeply rooted in the fundamental properties of quantum theory.
The term measurement theory refers to that part of a physical theory in which the empirical and operational content of the concepts of the theory is determined. Measurements are analyzed both as operational procedures defining the → observables of the theory and as physical processes which are themselves subject to the laws of physics. In classical physics, measurements are performed in order to deter-mine the values of one or several observables of the physical system un-der consideration. Classical physics allowed the idealized notion that every physical quantity has a definite value at any time, and that this value can be determined with certainty by measurement without influ-encing the object system in a significant way. By contrast, in quantum mechanics both features fail to hold without strong qualifications. Ac-cordingly, in their seminal paper of 1935 [1], Einstein, Podolsky and Rosen used elements of this description as a sufficient criterion of phys-ical reality, applicable both in classical and quantum mechanics:
Scope of this book Quantum mechanics is a difficult subject, and this book is intended to help the reader overcome the main difficulties in the way to understanding it. The first part of the book, Chs. 2–16, contains a systematic presentation of the basic principles of quantum theory, along with a number of examples which illustrate how these principles apply to particular quantum systems. The applications are, for the most part, limited to toy models whose simple structure allows one to see what is going on without using complicated mathematics or lengthy formulas. The principles themselves, however, are formulated in such a way that they can be applied to (almost) any nonrelativistic quantum system. In the second part of the book, Chs. 17–25, these principles are applied to quantum measurements and various quantum paradoxes, subjects which give rise to serious conceptual problems when they are not treated in a fully consistent manner. The final chapters are of a somewhat different character. Chapter 26 on decoherence and the classical limit of quantum theory is a very sketchy introduction to these important topics along with some indication as to how the basic principles presented in the first part of the book can be used for understanding them. Chapter 27 on quantum theory and reality belongs to the interface between physics and philosophy and indicates why quantum theory is compatible with a real world whose existence is not dependent on what scientists think and believe, or the experiments they choose to carry out. The Bibliography contains references for those interested in further reading or in tracing the origin of some of the ideas presented in earlier chapters.