One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous approach away from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schrodinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. A well-known explanatory framework due to Ludwig Boltzmann traces the rarity of " abnormal" thermodynamic phenomena to the scarcity of the initial conditions that lead to it. After all, physical laws are no more than algorithms and these are expected to generate different results according to different initial conditions, hence Boltzmann's insight that violations of thermodynamic laws are possible but highly improbable. Yet Boltzmann introduces probabilities into this explanatory scheme, and since the latter is couched in terms of classical mechanics, these probabilities must be interpreted as a result of ignorance of the exact state the system is in. Quantum mechanics has taught us otherwise. Here the attempts to explain why we never observe macroscopic superpositions have led to different interpretations of the formalism and to different solutions to the quantum measurement problem. These solutions introduce additional interpretations to the meaning of probability over and above ignorance of the definite state of the physical system: quantum probabilities may result from pure chance. Notwithstanding the success of the Boltzmannian framework in explaining the thermodynamic arrow in time it leaves us with a foundational puzzle: how can ignorance play a role in scientific explanation of objective reality? In turns out that two opposing solutions to the quantum measurement problem in which probabilities arise from the stochastic character of the underlying dynamics may scratch this explanatory itch. By offering a dynamical justification to the probabilities employed in classical statistical mechanics these two interpretations complete the Boltzmannian explanatory scheme and allow us to exorcize ignorance from scientific explanations of unobserved phenomena. In this thesis I argue that the puzzle of the thermodynamic arrow in time is closely related to the problem of interpreting quantum mechanics, i.e., to the measurement problem. We may solve one by fiat and thus solve the other, but it seems unwise to try solving them independently. I substantiate this claim by presenting two possible interpretations to non-relativistic quantum mechanics. Differing as they do on the meaning of the probabilities they introduce into the otherwise deterministic dynamics, these interpretations offer alternative explanatory schemes to the standard Boltzmannian statistical mechanical explanation of thermodynamic approach to equilibrium. I then show how notwithstanding their current empirical equivalence, the two approaches diverge at the continental divide between scientific realism and anti-realism.
One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous approach away from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schrodinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. A well-known explanatory framework due to Ludwig Boltzmann traces the rarity of " abnormal" thermodynamic phenomena to the scarcity of the initial conditions that lead to it. After all, physical laws are no more than algorithms and these are expected to generate different results according to different initial conditions, hence Boltzmann's insight that violations of thermodynamic laws are possible but highly improbable. Yet Boltzmann introduces probabilities into this explanatory scheme, and since the latter is couched in terms of classical mechanics, these probabilities must be interpreted as a result of ignorance of the exact state the system is in. Quantum mechanics has taught us otherwise. Here the attempts to explain why we never observe macroscopic superpositions have led to different interpretations of the formalism and to different solutions to the quantum measurement problem. These solutions introduce additional interpretations to the meaning of probability over and above ignorance of the definite state of the physical system: quantum probabilities may result from pure chance. Notwithstanding the success of the Boltzmannian framework in explaining the thermodynamic arrow in time it leaves us with a foundational puzzle: how can ignorance play a role in scientific explanation of objective reality? In turns out that two opposing solutions to the quantum measurement problem in which probabilities arise from the stochastic character of the underlying dynamics may scratch this explanatory itch. By offering a dynamical justification to the probabilities employed in classical statistical mechanics these two interpretations complete the Boltzmannian explanatory scheme and allow us to exorcize ignorance from scientific explanations of unobserved phenomena. In this thesis I argue that the puzzle of the thermodynamic arrow in time is closely related to the problem of interpreting quantum mechanics, i.e., to the measurement problem. We may solve one by fiat and thus solve the other, but it seems unwise to try solving them independently. I substantiate this claim by presenting two possible interpretations to non-relativistic quantum mechanics. Differing as they do on the meaning of the probabilities they introduce into the otherwise deterministic dynamics, these interpretations offer alternative explanatory schemes to the standard Boltzmannian statistical mechanical explanation of thermodynamic approach to equilibrium. I then show how notwithstanding their current empirical equivalence, the two approaches diverge at the continental divide between scientific realism and anti-realism.
In discussing the fundamental sources of unpredictability, I shall concentrate on those indeterminacies that are definitely required by theory. Let me therefore begin \nby eliminating from consideration supposed indeterminacies stemming from doubts that some people may entertain about basic principles or from certain kinds of ignorance that I believe to be temporary and likely to be remedied in the relatively near future. I assume the following: \n1. Quantum mechanics is correct. The formulation and interpretation of quantum mechanics are still undergoing some necessary evolution, especially in order to accommodate quantum cosmology in a comfortable way, but the basic character of quantum mechanics has always been the same and we may suppose it will remain unchanged. \n2. The elementary particles and their interactions obey a definite dynamical law, discoverable by inquiring complex adaptive systems such as the human scientific enterprise. Although the process of discovery involves a sequence of \napproximate schemata, there is an endpoint to the process after a finite amount of research. (Of course, it can never be possible to prove that the resulting unified theory is perfect; one can only verify it in the usual way by comparing predictions to available observations.) Humans may already have found this unified quantum field theory in the form of superstring theory, which has, to begin with, no arbitrary parameters. (Of course, spontaneous symmetry \nbreaking may give rise to some parameters and even to a choice of solutions, with probabilities for the various alternatives. I will deal with that possibility further on.) This second assumption is equivalent to stating that there is no necessary fundamental unpredictability stemming from ignorance of the universal dynamical law. \n3. The density matrix (in the Schrödinger picture) of the universe near the beginning of its expansion is also knowable. It must in any case be comparatively simple and very far from equilibrium. The second law of thermodynamics and the other associated arrows of time are explained by these properties of the initial density matrix along with the fact that the universe is still very young—the interval of ten billion years is extremely short compared with the relaxation time from the special initial condition.
I. Prigogine has proposed, and the writings of N. S. Krylov to some extent suggest, a novel and unorthodox solution to foundational problems in statistical mechanics. In particular, the view claims to offer new insight into two interconnected problems: underst and ing the role of probability in physics, and that of reconciling the irreversibility of physical processes with the temporal symmetry (time reversal invariance) of dynamical theories. The approach in question advocates a conception of the state of a system which incorporates features of the quantum mechanical state concept in a context, classical statistical mechanics, where quantum considerations are generally considered to be irrelevant. I examine the plausibility of this new approach by offering an analysis of the various notions of state employed in modern physics. In the first chapter, I analyze the conceptual connections between dynamical laws and the nature of a system's state. I argue that laws and states are correlative. In constructing dynamical theories one does not start with a fixed or pre-determined state concept. Neither is one given the laws of the theory from which the conception of state is derived. Rather, we get the law/state structure as a "package." In light of this general analysis, I next examine the notion of state employed in the quantum theory. Here I consider a variety of conceptions of quantum states and assess their ability to answer the "paradoxes" of quantum theory. I pay particular attention to the role of probability and related restrictions on the realization of certain states. The new approach to statistical mechanics proposes to exploit similar restrictions on states in order to resolve the irreversibility problem. But is this unorthodox approach viable? In the final four chapters, I offer a detailed critique of this approach, examining the plausibility of the radical reworking of the state concept. I argue that while some important progress can be made, certain old puzzles remain, and new and difficult ones arise--ones which raise serious doubts about the ultimate success of this particular approach. I conclude, however, by arguing that such radical proposals are not unmotivated; and that novel and unorthodox proposals concerning the foundations of statistical mechanics must be taken seriously.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
In present-day physics the fundamental dynamical laws are taken as a time-translation-invariant and time-reversal-invariant one-parameter groups of automorphisms of the underlying mathematical structure. In this context-independent and empirically inaccessible description there is no past, present or future, hence no distinction between cause and effect. To get the familiar description in terms of causes and effects, the time-reversal symmetry of the fundamental dynamics has to be broken. Thereby one gets two representations, one satisfying the generally accepted rules of retarded causality (no effect can precede its cause). The other one describes the strange rules of advanced causality. For entangled (but not necessarily interacting) quantum systems the arrow of time must have the same direction for all subsystems. But for classical systems, or for classical subsystems of quantum systems, this argument does not hold. As a cosequence, classical systems allow the conceptual possibility of advanced causality in addition to retarded causality. Every mathematically formulated dynamics of statistically reproducible events can be extended to a description in terms of a one-parameter group of automorphisms of an enlarged mathematical structure which describes a fictitious hidden determinism. Consequently, randomness in the sense of mathematical probability theory is only a weak generalization of determinism. The popular ideas that in quantum theory there are gaps in the causal chain which allow the accommodation of the freedom of human action are fantasies which have no basis in present-day quantum mechanics. Quantum events are governed by strict statistical laws. Freedom of action is a constitutive necessity of all experimental science which requires a violation of the statistical predictions of physics. We conclude that the presently adopted first principles of theoretical physics can neither explain the autonomy of the psyche nor account for the freedom of action necessary for experimental science.
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.
On a very intuitive way of thinking, if it is already determined that some event will happen, then there is no non-trivial chance of it failing to happen, and if it is already determined that some event will not happen, then there is no non-trivial chance of it happening. A different sort of worry that arises for an actual frequentist analysis of deterministic chance is that such an analysis seems unsuited to theories like Boltzmannian statistical mechanics or Bohmian mechanics insofar as those theories are supposed to describe the evolution of the Universe as a whole. It should be clear, then, that there are options available for understanding deterministic chance that are in keeping with several of the leading metaphysical analyses of chance. It is widely accepted that whatever chances are, they are to be contrasted with individual credences . According to classical statistical mechanics, the fundamental laws are Newtonian and thus deterministic.