Online research in philosophy

Many physicists believe that time constitutes a serious problem in quantum mechanics. We show nevertheless that quantum mechanics does not involve a special problem for time, and that there is no fundamental asymmetry between space and time in quantum mechanics over and above the asymmetry that already exists in classical physics. The apparent problem of time arises when the time parameter is put on a par with dynamical position variables rather than with the coordinates of space. The commutation relations and uncertainty relations are generally considered to embody the essential content of elementary quantum mechanics, but the traditional mathematical expression of the uncertainty principle it shown to be quite unsatisfactory. It is the total energy that decrees whether or not the time variables of a system can be sharply determined.

We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability rule in the many worlds theory. Our conclusion is that the many worlds theory fails to account for the probabilistic statements of standard (collapse) quantum mechanics.

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.

The frequencies with which photons pass through half-silvered mirrors in the forward direction of time is always approximately 1/2, whereas the frequencies with which photons pass through mirrors in the backward direction in time can be highly time-dependent. I argue that whether one should infer from this time-asymmetric phenomenon that time has an objective direction will depend on one's interpretation of quantum mechanics.

The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.

In a previous paper (Hemmo and Shenker 2003) we discussed a recent proposal by Albert (2000, Ch. 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the quantum state of Ghirardi, Rimini and Weber (1986). We proposed an alternative way to explain thermodynamics within no collapse interpretations of quantum mechanics. In this paper some difficulties faced by both approaches are discussed and solved: the spin echo experiments, and the problem of extremely light gases. In these contexts, we point out several ways in which the above quantum mechanical approaches as well as some other classical approaches to the foundations of statistical mechanics may be distinguished experimentally.

Can we explain the laws of thermodynamics, in particular the irreversible increase of entropy, from the underlying quantum mechanical dynamics? Attempts based on classical dynamics have all failed. Albert (1994a,b; 2000) proposed a way to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wavefunction of Ghirardi, Rimini and Weber (1986). In this paper we propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems, e.g. Joos and Zeh (1985) and Zurek and Paz (1994).

We discuss a recent proposal by Albert (1994a; 1994b; 2000, ch. 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function by Ghirardi, Rimini, and Weber (1986). We propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems (e.g., Joos and Zeh 1985; Zurek and Paz 1994). This paper presents the two approaches and discusses their advantages. The problems faced by both approaches will be discussed in a sequel (Hemmo and Shenker 2003).

We discuss a recent proposal by Albert (1994a,b; 2000, Chapter 7) to recover thermodynamics on a purely dynamical basis, using the quantum theory of the collapse of the wave function of Ghirardi, Rimini and Weber (1986). We propose an alternative way to explain thermodynamics within no-collapse interpretations of quantum mechanics. Our approach relies on the standard quantum mechanical models of environmental decoherence of open systems, \eg Joos and Zeh (1985) and Zurek and Paz (1994). This paper presents the two approaches and discusses their advantages. The problems they face will be discussed in a sequel (Hemmo and Shenker 2002b).

I consider the question of the direction of time in the context of the Everett interpretation of quantum mechanics. I focus on the special role of decoherence in the recovery of time asymmetric behaviour, such as the collapse of the quantum state and the thermodynamic regularities. The discussion is based on results in the consistent histories approach (Gell-Mann and Hartle 1993) and in decoherence theory (Zurek and Paz 1994). Finally, I compare the status of the direction of time in Everett and in a recent proposal by Albert (2001) based on the collapse theory of Ghirardi, Rimini and Weber (1986).