Online research in philosophy

There exist well‐known conundrums, such as measure‐theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space‐time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space‐time.

Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be related to each other via Wigner's extensions of the spacetime symmetry group. Furthermore, their are subtle differences in causality as well as the possibilities for the existence and creation of time-reversed states depending on which time arrow is chosen.

I argue that in the many worlds interpretation of quantum mechanics time has no fundamental direction. I further discuss a way to recover thermodynamics in this interpretation using decoherence theory (Zurek and Paz 1994). Albert's proposal to recover thermodynamics from the collapse theory of Ghirardi et al. (1986) is also considered.

No one conception of time emerges from a study of physics. As science changes—over time or through varying interpretations at a time—our conception of physical time changes. Each of these changes and resulting theories of time has been the subject of philosophical scrutiny, so there are many philosophical controversies internal to particular physical theories. For instance, the move to special relativity radically transformed our understanding of time, but it also gave rise to debates about the nature of simultaneity within the theory itself. Nevertheless, there are some philosophical puzzles that appear at every stage of the development of physics. Perhaps most generally, there is the perennial question, Is there a ‘gap’ between the conception of time as found in physics and the conception of time as found in philosophy?

David Albert's Time and Chance (2000) provides a fresh and interesting perspective on the problem of the direction of time. Unfortunately, the book opens with a highly non-standard exposition of time reversal invariance that distorts the subsequent discussion. The present article not only has the remedial goal of setting the record straight about the meaning of time reversal invariance, but it also aims to show how the niceties of this symmetry concept matter to the problem of the direction of time and to related foundation issues in physics.

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).

A conclusion drawn after a conference devoted (in 1995) to the “arrow of time” was the following: “Indeed, it seems not a very great exaggeration to say that the main problem with “the problem of the direction of time” is to figure out exactly what the problem is supposed to be !” What does that mean? That more than 130 years after the work of Ludwig Boltzmann on the interpretation of irreversibility of physical phenomena, and that one century after Einstein’s formulation of Special Relativity, we are still not sure what we mean when we talk of “time” or “arrow of time”. We shall try to show that one source of this difficulty is our tendency to confuse, at least verbally, time and becoming, i.e. the course of time and the arrow of time, two concepts that the formalisms of modern physics are careful to distinguish.

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.

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.

While experience tells us that time flows from the past to the present and into the future, a number of philosophical and physical objections exist to this commonsense view of dynamic time. In an attempt to make sense of this conundrum, philosophers and physicists are forced to confront fascinating questions, such as: Can effects precede causes? Can one travel in time? Can the expansion of the Universe or the process of measurement in quantum mechanics define a direction in time? In this book, researchers from both physics and philosophy attempt to answer these issues in an interesting, yet rigorous way. This fascinating book will be of interest to physicists and philosophers of science and educated general readers interested in the direction of time.