Current interpretations of quantum mechanics suggest that the classical concepts of space and time are not applicable to microscopic systems. Salecker and Wigner have recently proved that these concepts have no operational meaning for microsystems. Therefore, space-time descriptions may be valid only for macroscopic systems. It is here suggested that space and time themselves arise from, but do not have analogs in, the properties of microscopic particles, in the same way that thermodynamic properties arise as a result of interactions among the many actually existing particles of the universe. Neither the particles nor the interactions need to be described in spatial-temporal terms. This macroscopic interpretation of space-time seems compatible with the known properties of the physical world, suggests a more direct interpretation of the statistical nature of microscopic events, and offers a new approach to some physical problems.
Current interpretations of quantum mechanics suggest that the classical concepts of space and time are not applicable to microscopic systems. Salecker and Wigner have recently proved that these concepts have no operational meaning for microsystems. Therefore, space-time descriptions may be valid only for macroscopic systems. It is here suggested that space and time themselves arise from, but do not have analogs in, the properties of microscopic particles, in the same way that thermodynamic properties arise as a result of interactions among the many actually existing particles of the universe. Neither the particles nor the interactions need to be described in spatial-temporal terms. This macroscopic interpretation of space-time seems compatible with the known properties of the physical world, suggests a more direct interpretation of the statistical nature of microscopic events, and offers a new approach to some physical problems.
A physical picture of macroscopic and microscopic worlds is presented. In the space-time description, both the macroscopic and microscopic worlds are described simultaneously in space-time being a single boundless four dimensional continuum in which the motion of the observer is represented as a world line. In our picture, the space-time description is valid only for the macroscopic world and the microscopic world is local in the sense that it is described in a finite space associated with each point of the macroscopic space-time. In this case, space-time does not exist in the microscopic world in which the observer can not move. For the description of our picture, the language of the non-space-time description is necessary in which space-time is not presupposed. We can utilize the space-time description for the macroscopic world and, at the same time, we have a theory of finite degree of freedom describing creations and annihilations of elementary particles in the microscopic world free from the divergence difficulty, instead of the divergent quantum field theory in the space-time description which is considered in our picture a limit of an approximation like the ideal gas in gas theories. The finite degree of freedom is given by a one-particle state-vector space of a finite dimension from which the second quantization leads to a state-vector space of a countable dimension (a Hilbert space) for the theory of creations and annihilations of elementary particles describing a local microscopic world. The relation between microscopic worlds associated with different macroscopic space-time points is given by a dynamical principle up to a phase factor due to possible fluctuations of phases of local state-vector spaces. The experiment on interference of light performed recently by Franson and Potocki is interpreted in terms of fluctuation of the local phases and is considered to support the theory of finite degree of freedom which leads to the idea of local microscopic worlds.
This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement” to include all property-indicating facts. Intrinsically, space is undifferentiated: There are no points on which a world of locally instantiated physical properties could be built. Instead, reality is built on facts, in the sense that the properties of things are extrinsic, or supervenient on property-indicating facts. The actual extent to which the world is spatially and temporally differentiated (that is, the extent to which spatiotemporal relations and distinctions are warranted by the facts) is necessarily limited. Notwithstanding that the state vector does nothing but assign probabilities, quantum mechanics affords a complete understanding of the actual world. If there is anything that is incomplete, it is the actual world, but its incompleteness exists only in relation to a conceptual framework that is more detailed than the actual world. Two deep-seated misconceptions are responsible for the interpretational difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts. There nevertheless exists a “classical” domain in which language suggestive of nomological necessity may be used. Quantum mechanics not only is strictly consistent with the existence of this domain but also presupposes it in several ways.
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory, and four postulates that refer to simple concepts, derived concepts of time, space-time, reference frame, particle, fields, and interaction between fields are obtained. The problem of the "direction " of time is analyzed and a paradox whose solution goes against the idea that this direction is fixed by the increase of entropy prescribed by the second law of thermodynamics is examined. In our theory this direction is unique to each reference frame, and is an intrinsic property of time. Two kinds of particles are described as derived concepts, and it is shown that one of them fullfills the Bose-Einstein statistics, and the other one fullfills the Fermi-Dirac statistics. We also consider the analysis of the wave function concepts and particle detector as concepts derived from the mentioned theory. Using these concepts, the process of locating both a macroscopic body (typical location) as well as one of a microscopic scale (quantum localization) is analyzed, and the significance of the location is examined in both cases.
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.
In this chapter, we define a new interpretation of quantum physics, called the thermal interpretation. The thermal interpretation of quantum physics (including quantum mechanics, quantum field theory, quantum statistical mechanics, and their applications) allows a consistent and deterministic relativistic quantum description of the universe from the smallest to the largest levels of modeling, including its classical aspects, without having to introduce any change in the formal apparatus of quantum physics. The goal of the thermal interpretation is to provide foundations that match all requirements from Chapter 8. The thermal interpretation agrees with how one interprets measurements in statistical thermodynamics, the macroscopic part of quantum physics, derived via statistical mechanics. Extrapolating from the macroscopic case, the thermal interpretation considers the functions of the state (or of the parameters characterizing a state from a particular family of states) as the objective properties of what really exists. Some of these are accessible to experiment-namely the expectation values of quantities that have a small uncertainty and vary sufficiently slowly in time and space. Because of the law of large numbers, all thermodynamic variables are in this category. By its very construction, the thermal interpretation naturally matches the classical, in essence, thermodynamical properties of our quantum world.