No abstract

This question is puzzling. For the wave function-the thing that's governed by the dynamical laws, the object whose evolution predicts the results of quantum mechanical experiments-occupies a space that is very different from the one we seem to live in. The wave function's space has many dimensions-many more than the three dimensions of ordinary space (or four dimensions of ordinary space-time ). Prima facie, realism about quantum mechanics seems to require realism about the wave function and the space it inhabits. But then there's a glaring question as to why, if our world is fundamentally quantum mechanical, we seem to live in a space of only three dimensions.

In a recent paper, Malament () employs a time reversal transformation that differs from the standard one, without explicitly arguing for it. This is a new and important understanding of time reversal that deserves arguing for in its own right. I argue that it improves upon the standard one. Recent discussion has focused on whether velocities should undergo a time reversal operation. I address a prior question: What is the proper notion of time reversal? This is important, for it will affect our conclusion as to whether our best theories are time-reversal symmetric, and hence whether our spacetime is temporally oriented.

I discuss the nature of the puzzle about the time-asymmetry of radiation and argue that its most common formulation is flawed. As a result, many proposed solutions fail to solve the real problem. I discuss a recent proposal of Mathias Frisch as an example of the tendency to address the wrong problem. I go on to suggest that the asymmetry of radiation, like the asymmetry of thermodynamics, results from the initial state of the universe.

It is often claimed, or hoped, that some temporal asymmetries are explained by the thermodynamic asymmetry in time. Thermodynamics, the macroscopic physics of pressure, temperature, volume, and so on, describes many temporally asymmetric processes. Heat flows spontaneously from hot objects to cold objects (in closed systems), never the reverse. More generally, systems spontaneously move from non-equilibrium states to equilibrium states, never the reverse. Delving into the foundations of statistical mechanics, this chapter reviews the many open questions in that field as they relate to temporal asymmetry. Taking a stand on many of them, it tackles questions about the nature of probabilities, the role of boundary conditions, and even the nature and scope of statistical mechanics.