In this chapter, we look in more detail at some of the traditional quantum experiments from the point of view of the thermal interpretation. An analysis of individual events on a screen leads in Section 13.1 to the picture of a quantum bucket for measuring a continuous variable with a device capable only of producing discrete results. The notion of quantum currents from Section 7.4 may be used to visualize in the thermal interpretation the finite time dynamics of particle decay (Section 13.2) and the Stern-Gerlach experiment (Section 13.3). Another analysis of the Stern-Gerlach experiment, now in terms of particles, is given in Section 13.4. The discrepancy between the thermal interpretation and traditional interpretations is seen to be of order O(ℏ). Finally, in the context of entanglement experiments, we discuss notions of causality (Section 13.5) and nonlocality (Section 13.6) and their relation to the thermal interpretation.
In this chapter, we look in more detail at some of the traditional quantum experiments from the point of view of the thermal interpretation. An analysis of individual events on a screen leads in Section 13.1 to the picture of a quantum bucket for measuring a continuous variable with a device capable only of producing discrete results. The notion of quantum currents from Section 7.4 may be used to visualize in the thermal interpretation the finite time dynamics of particle decay (Section 13.2) and the Stern-Gerlach experiment (Section 13.3). Another analysis of the Stern-Gerlach experiment, now in terms of particles, is given in Section 13.4. The discrepancy between the thermal interpretation and traditional interpretations is seen to be of order O(ℏ). Finally, in the context of entanglement experiments, we discuss notions of causality (Section 13.5) and nonlocality (Section 13.6) and their relation to the thermal interpretation.
This paper continues the discussion of the thermal interpretation of quantum physics. While Part II and Part III of this series of papers explained and justified the reasons for the departure from tradition, the present Part IV summarizes the main features and adds intuitive explanations and new technical developments. It is shown how the spectral features of quantum systems and an approximate classical dynamics arise under appropriate conditions. Evidence is given for how, in the thermal interpretation, the measurement of a qubit by a pointer q-expectation may result in a binary detection event with probabilities given by the diagonal entries of the reduced density matrix of the prepared qubit. Differences in the conventions about measurement errors in the thermal interpretation and in traditional interpretations are discussed in detail. Several standard experiments, the double slit, Stern--Gerlach, and particle decay are described from the perspective of the thermal interpretation.
This chapter presents the measurement problem from the point of view of the thermal interpretation of quantum physics. Everything physicists measure is measured in a thermal environment, for which statistical thermodynamics is relevant. The thermal interpretation agrees with how one interprets measurements in thermodynamics, the macroscopic part of quantum physics, derived via statistical mechanics. By its very construction, the thermal interpretation naturally matches the classical properties of our quantum world: The thermal interpretation assigns states-and a realistic interpretation for them-to individual quantum systems, in a way that large quantum systems are naturally described by classical observables. Since measurement devices are large quantum systems, this is the key to solving the measurement problem. We discuss the role played by macroscopic systems and the weak law of large numbers in getting readings with small uncertainty. Since quantum physics makes many deterministic predictions, for example regarding observed spectra, but also assertions about probabilities, we distinguish deterministic and statistical measurements. To clarify the meaning of the concept of measurement, we postulate (in Section 11.1) a measurement principle that defines what it means in the thermal interpretation to measure a quantity with a specified uncertainty. This turns the measurement problem from a philosophical riddle into a scientific problem in the domain of quantum statistical mechanics, namely how the quantum dynamics correlates macroscopic readings from an instrument with properties of the state of a measured microscopic system. The essence of scientific practice is the reproducibility of measurements, discussed in Section 11.2. Unlike in traditional interpretations, single, nonreproducible observations do not count as measurements, since this would violate the reproducibility of measurements-the essence of scientific practice. As a consequence, the measurement of a Hermitian quantity A is regarded as giving an uncertain value approximating the q-expectation {A} rather than (as tradition wanted to have it) as an exact revelation of an eigenvalue of A. This difference is most conspicuous in the interpretation of single discrete microscopic events. Except in very special circumstances, these are not reproducible. Thus, they have no scientific value in themselves and do not constitute measurement results. Scientific value is, however, in ensembles of such observations, which result in approximate measurements of q-probabilities and q-expectations. Sections 11.3 and 11.4 distinguish deterministic and statistical measurements, depending on whether a single observation is reproducible, and discuss the role played by macroscopic systems and the weak law of large numbers in getting readings with small uncertainty. How to measure the q-probabilities of events, described in terms of POVMs, is discussed in Section 11.5. Section 11.6 poses the measurement problem as a problem of the statistical mechanics of measurement devices, and discuss recent work by Allahverdyan, Balian, and Nieuwenhuizen on its resolution. Section 11.7 discusses the problem how, in the thermal interpretation, discrete events can arise, although qexpectations are by their very nature continuous. This is resolved by pointing to work by Breuer and Petruccione on piecewise deterministic processes (PDP). Section 11.8 sheds additional light on the origin of discrete events by an analysis of the role dissipative bistability plays in obtaining discreteness in classical physics.
While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.
Most textbooks introduce the concept of spin by presenting the Stern-Gerlach experiment with the aid of Newtonian atomic trajectories. However, to understand how both spatial and spin degrees of freedom evolve over time and how the latter influence experimental outcomes, it is essential to employ a quantum approach. In this paper, we offer two simple methods, the Baker-Campbell-Hausdorff formula and the direct integration of the Schrödinger equation in an interaction picture, to determine the corresponding evolution operator. We not only provide an interpretation of the individual terms within this operator but also establish connections with semiclassical calculations, when feasible. Moreover, we compute the wave function and touch upon the concept of position-spin entanglement to illustrate how a full quantum description of the Stern-Gerlach experiment can open doors to topics like quantum measurement and nonlocality.
The Stern–Gerlach (SG) experiment (1922) was one of the earliest experiments for which the result could not be explained using classical physics by any means. Hence it demonstrated unambiguously the importance of quantum effects. The SG experiment can be explained using the quantum theory for the spin-½ particle, which is a quantum system that can be represented simply by 2 × 2 matrices. We will use the spin-½ particle to introduce some of the basic concepts of quantum mechanics, such as state space, operators, measurement, the uncertainty principle, and the evolution equation. Furthermore, the theory for the spin-½ particle can be readily generalized to finite dimensional quantum systems, i.e., systems that can be represented by finite dimensional matrices.