Valia Allori

This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by presenting the material with an original spin, guided by a particular understanding of fundamental physical theories, the so-called primitive ontology approach.

What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wave function, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wave function is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. That is, we need more structure than the one provided by the wave function. As a response, quantum theories about the wave function can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wave function ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wave function; 2- Even if the wave function is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time.

It has been argued that the transition from classical to quantum mechanics is an example of a Kuhnian scientific revolution, in which there is a shift from the simple, intuitive, straightforward classical paradigm, to the quantum, convoluted, counterintuitive, amazing new quantum paradigm. In this paper, after having clarified what these quantum paradigms are supposed to be, I analyze whether they constitute a radical departure from the classical paradigm. Contrary to what is commonly maintained, I argue that, in addition to radical quantum paradigms, there are also legitimate ways of understanding the quantum world that do not require any substantial change to the classical paradigm.

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world.