Space and Time in Particle and Field Physics

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Abstract

Textbooks present classical particle and field physics as theories of physical systems situated in Newtonian absolute space. This absolute space has an influence on the evolution of physical processes, and can therefore be seen as a physical system itself; it is substantival. It turns out to be possible, however, to interpret the classical theories in another way. According to this rival interpretation, spatiotemporal position is a property of physical systems, and there is no substantival spacetime. The traditional objection that such a relationist view could not cope with the existence of inertial effects and other manifestations of the causal efficacy of spacetime can be answered successfully. According to the new point of view, the spacetime manifold of classical physics is a purely representational device. It represents possible locations of physical objects or events; but these locations are physical properties inherent in the physical objects or events themselves and having no existence independently of them. In relativistic quantum field theory the physical meaning of the spacetime manifold becomes even less tangible. Not only does the manifold lose its status as a substantival container, but also its function as a representation of spacetime properties possessed by physical systems becomes problematic. ‘Space and time’ become ordering parameters in the web of properties of physical systems. They seem to regain their traditional meaning only in the non-relativistic limit in which the classical particle concept becomes approximately applicable.

Introduction

Are space and time fundamental categories in physics? One, traditional, way of interpreting this question is to see it as a query about the independent existence of a kind of container of particles and fields; an arena in which physical processes take place. The question can also be interpreted in a different way, without emphasis on the ontological aspect. Are space and time indispensable for the representation of physical systems? In other words, should physical systems in all circumstances be at least partly characterised by spacetime concepts, regardless of the question whether these concepts refer to independently existing physical entities? In this article I will discuss both questions.

Because direct observations pertain to physical objects and processes, and not to space and time themselves, arguments in favour of the independent existence of space and time must necessarily rely on theoretical considerations. We need to consider the question of whether physical theories have to invoke the notion of spacetime as a container of physical events. This is a question with a respectable history. In classical (pre-quantum) physics the notion of a container space was considered indispensable. As I will make clear, however, a closer look reveals that classical physics can do without space and time as independent entities. As a consequence, classical physics does not provide a convincing argument for spacetime substantivalism. I will argue that this conclusion only becomes stronger when quantum mechanics is taken into account. In fact, consideration of the quantum-mechanical theoretical framework gives a new twist to the discussion about the status of space and time because in quantum mechanics space and time not only lose their fundamental character as a pre-existing container, but also their role as indispensable representational devices. A spacetime manifold, whether it is something that exists independently or is just a tool to represent spatial relations among objects, becomes unnecessary to describe physical systems in quantum theory. I will argue that this is not only true for non-relativistic quantum mechanics but, perhaps surprisingly, also for relativistic quantum field theory.

Section snippets

Traditional Relationism

We do not have direct empirical access to spacetime points. Our observations are of material events: of physical objects located in a frame of reference consisting of rigid rods and clocks, of particles colliding with each other, and so on. In accordance with this, we cannot observe distances in space itself. Observed distances are always distances between physical objects. The same is true of motion: we cannot see that objects change their position with respect to space. We see only relative

Everything Has Position

The role assigned to space in traditional accounts of classical mechanics suggests that space is a physical entity—it is a causal agent—which exists prior to any material process. But although the debate about the status of space has been dominated by the corresponding scientific arguments, the prima facie, intuitive plausibility of the notion that space is fundamental does not derive from its role in mechanics. A factor that is at least equally important is that all objects that we observe

The Theory of Relativity

In his early career Einstein was influenced by Mach's ideas about space and time, and his work on relativity was motivated partly by the desire to develop a theory that would be in accordance with relationism. However, it is now well known that relativity theory does not fulfil these original relationist hopes. This is particularly evident in the special theory of relativity. Newton's bucket thought-experiment, performed in otherwise empty space has the same outcome in special relativity as in

Position as a Property of Classical Particles

The traditional Newtonian argument is that we need substantival spacetime for explanatory purposes; that we cannot understand inertial effects without the assumption that space and time exist as independent, causally effective, physical entities. But this conclusion is not warranted. There exists a rival explanatory scheme which does not need substantivalism. The core idea of this alternative scheme is to think of space and time as properties of physical systems. In the context of classical

The Explanatory Resources of Mechanics without Space

In traditional Newtonian theory we can explain the difference between the resting and the rotating bucket by pointing to their different relations to absolute space. How can we retain the same explanatory resources without invoking space? To answer this question, I first want to draw attention to the fact that the purported Newtonian explanation is not a mechanical explanation in the usual sense of the word. There is no mechanism or interaction specified by which space could exert an influence

A Refined Form of the Scheme

That our proposal as outlined thus far is so close to Newtonian mechanics has an obvious drawback: just as Newtonian mechanics operates with the empirically superfluous notion of absolute location, our account as explained thus far not only attributes absolute accelerations to particles, but also absolute positions and velocities. But mechanical theory itself tells us that these latter notions do not have empirical counterparts. It would therefore be a serious disadvantage if absolute position

Special Relativistic Particle Physics

We have not yet discussed time explicitly. In order to treat time as a direct property, on a par with position, it is natural to focus on particle events as the fundamental physical objects with which physical quantities are to be associated. A particle event is assigned three position values (three components of the position) and a time value. As before, symmetry considerations can subsequently be used to filter out what is conventional and what is not, in the sense of what is irrelevant and

Classical Fields

Thus far, we have been eliminating substantival space from classical particle physics. Can the same be done for field theory? The culmination of field theory in non-quantum physics is the general theory of relativity. However, as we already noted, the status of spacetime in general relativity is very different from that in Newtonian and special relativistic physics. In those earlier theories spacetime points were traditionally considered to stand in metrical, geometric, relations to each other

Quantum Theory

That quantum theory introduces new elements into the discussion about the status of space and time is not a new suggestion. According to Niels Bohr it is impossible to make a spatiotemporal picture of quantum mechanical processes. There is already a problem with such pictures in the so-called ‘Old Quantum Theory’ of 1913, because the processes in which an electron goes from one orbit around an atom's nucleus to another cannot be represented in space and time. In his interpretation of the

Space in Quantum Mechanics

We have seen that all pre-quantum theories, including relativity, can be formulated as spacetime theories: they describe physical systems as embedded in a manifold of spacetime points. Particles at all times possess positions, according to these theories, and fields are defined by assigning field quantities to points in the manifold. We already argued for the possibility of denying this manifold an independent physical existence. We can think of particle positions as properties inherent in the

Quantum Field Theory

What I had in mind in the preceding two sections was non-relativistic quantum mechanics. Of course, relativity has to be taken into account, so we have to move on to relativistic quantum theory. As soon as we move into the relativistic quantum domain, it becomes clear that our considerations about space and time have to be adapted. In particular, there are well-known difficulties in defining a satisfactory position operator in relativistic quantum mechanics. General, very plausible,

Spacetime in Quantum Field Theory

It follows from what was said in the foregoing section that it is not necessary to view Minkowski spacetime as a given substantival background in quantum field theory. Rather, the Minkowski manifold can be seen as a representational tool that is used to handle the relations between the algebras in the net, in a Hilbert space with state Ω. If we consider the algebras as describing the possible properties of physical (sub)systems, the situation is not very different from that in non-relativistic

Conclusion

Classical particle and field physics are traditionally presented as theories about physical systems that find themselves in a pre-existing spacetime arena. It turns out to be possible, however, to interpret these same theories in another way, in which there is no substantival spacetime. The traditional objection that such an alternative reading could not cope with the existence of inertial effects can be answered successfully. As a result of this re-interpretation, the spacetime manifold of

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