# Philosophy and Particle Physics

# PHILOSOPHY AND PARTICLE PHYSICS

There are many claims in the literature about the impact of modern particle physics on the way philosophers conceptualize the world. The issues are complex and the conclusions not as decisive or clear-cut as is sometimes supposed.

## Individuality and Quantum Statistics

First, there is the question of what confers individuality on the particles, or indeed whether they are individuals at all in the sense of being particulars that transcend in some sense the properties (universals) they exhibit. Arguments from quantum statistics are often adduced to show how one would simply get the wrong (Boltzmannian) statistics if the particles possessed individuality in the classical sense. The argument here is persuasive but by no means decisive. The assignments of statistical weights may just reflect limitations on the accessibility of certain states rather than nonindividuality. Pursuing the nonindividuality route, however, chimes in with the view that particles are really quantized excitations of a field, and this is of course the point of view taken in quantum field theory (QFT). One of the big advantages of QFT is that the evanescent character of elementary particles, their creation and annihilation in high-energy collision experiments for example, seems a great deal less mysterious than the creation and annihilation of particles conceived of as individual particulars in their own right. The philosophical origins of Greek atomism, the ancient precursor of modern atomic theories, was quite at odds with such possibilities.

## Quantum Field Theory

However, the ontological status of a quantum field is somewhat problematic. In classical physics, field theories were sharply distinguished from particle theories. In the former, the role of the individual was played by the space-time points that were endowed with or in some sense associated with the properties of exhibiting a field amplitude or excitation. Notice that the role of space-time is quite different in field theories as opposed to particle theories, where spatiotemporal location is treated as a property of the particle.

Quantum fields come in two varieties, those like the electron field associated with matter, and those like the electromagnetic field associated with interactions. The interaction fields obey Bose-Einstein statistics, or in the language of QFT the fields satisfy microcausality conditions, expressing the fact that they cannot transmit influences faster than the speed of light. Their interpretation in terms of discrete quantized excitations or "quanta" as surrogate "particles" seems clear enough, setting aside all the interpretational problems of quantum mechanics itself. But the matter fields obey Fermi-Dirac statistics, and in the language of QFT they fail to satisfy the microcausality condition imposed by the special theory of relativity, so the matter fields are not observable; they belong to the so-called surplus mathematical structure. In a sense the matter fields don't "exist"! In particular, the classical limit of such a quantum field theory is not a classical field! Of course one can construct quantities like charge and current densities out of the fields, which do satisfy micro-causality, and are observable, but the point is that these constructions are not the fields themselves. The upshot of this discussion is that QFT does not in any simple way resolve the ancient philosophical puzzles of particle versus field, of atom versus plenum.

## Relativistic Particle Theories

Returning to the particle option, there is, however, another quite distinct difficulty. The elementary particles are usually thought of as unextended points (this is modified in string theory but will be ignored for present purposes). Considered as point particles, they should have precise spatial locations. But the apparently innocuous condition that if a particle is localized at one spatial point there must be zero probability for finding it at that very moment located at a different point turns out to be inconsistent in relativistic theories with the objectivity of localization in the sense that observers in different states of uniform relative motion will not agree on whether the particles are in fact localized at all! This is closely related to the fact that relativistic wave packets that are sharply localized in one reference frame disperse superluminally relative to that frame. These unpleasant features of relativistic particle localization have generally militated after all in favor of the quantum field approach.

## The Quantum Vacuum

Particular interest, philosophically speaking, attaches to the concept of the vacuum in relativistic QFT. In nonrelativistic theories the global vacuum identified with the absence of unlocalized particles (quanta with a definite momentum) implies a local vacuum in the sense of the absence of localized particles. This is no longer true in the relativistic vacuum, where the global vacuum actually implies the violation of a local vacuum. This violation is often described in terms of the creation and annihilation of so-called virtual particles that indeed violate energy conservation provided their lifetimes are governed by the time-energy uncertainty relations of quantum mechanics. Virtual particles of mass *m* exist for a time bounded by *h/mc*^{2}, where *h* is Planck's constant and *c* the velocity of light.

The properties of virtual particles show how far removed the particle concept is from any classical picture. Talking of classical pictures reminds one that the dynamics of elementary particles, whether conceived as field excitation or as "true" particles, is governed by the laws not of classical mechanics but of quantum mechanics.

## Quantum Mysteries

Physical magnitudes on the orthodox or so-called Copenhagen interpretation only have sharp definite values in special states called eigenstates. In general, the formulation of quantum mechanics provides rules for calculating the probabilities that possible values will turn up on measurement. In particular, so-called conjugate quantities have reciprocally related spreads of possible values governed by the famous Heisenberg uncertainty relations. As a result the particle theories no longer allow a notion of spatiotemporally continuous trajectories. The notion of causality as mediated by continuous processes has to be significantly revised. Essentially it is reduced to conservation laws for energy and momentum. Determinism survives in the time-development of the quantum-mechanical state in accordance with the time-dependent Schrödinger equation. The failure of determinism comes in with measurement interactions which play a privileged role in the theory. The sorts of questions that can be posed and answered are relativized to specific experimental setups. This leads to a form of perspectivalism, in which perspectives may be incompatible, but all are necessary for a complete conspectus of reality. All of this makes for a heady revision of traditional realist metaphysics.

But again the arguments are not decisive. There are other interpretations of quantum mechanics in which hidden variables are introduced, and it is our ignorance of these variables which allow for epistemic rather than ontic probabilities in the interpretation of the theory. So it is possible to restore determinism at the level of the hidden variables. But all this comes at a severe price. John Bell in 1964 showed that any such theory must exhibit nonlocality in the sense that mysterious changes in possessed values of local observables must be produced by operations carried out even at spacelike separation from the local observables. This causes prima facie problems for a relativistic theory of such hidden variables. But the exact interpretation of this nonlocality is a subtle matter that has been the subject of much philosophical debate. Under some interpretations the nonlocality is better described in terms of nonseparability, that the properties of composite systems in so-called entangled states cannot be analyzed in terms of local attributes of the constituents, thus introducing a holistic aspect to the interpretation of multiparticle states. Indeed this holistic aspect of quantum phenomena is also emphasized in the orthodox Copenhagen interpretation. The upshot of such arguments is that quantum mechanics may ultimately be inimical to the reductionist philosophy of understanding wholes in terms of their parts. It is ironic that particle physics that seems so conducive to reductionism may actually provide a counterexample to it!

## The Mathematization of Nature

As previously noted fermionic fields do not have direct physical significance. They belong to the mathematical "surplus structure," as it is often called, that has become endemic in modern theoretical particle physics. This is particularly true of the popular gauge theories of particle interactions where the physically significant quantities are invariant under transformations of the gauge symmetry, but these transformations can themselves only be specified in terms of quantities which are *not* gauge invariant. Much modern particle theory works with surplus structure which elegantly "controls" the physically significant magnitudes, rather than formulating the theories directly in terms of the physical magnitudes themselves. This situation has led to much philosophical debate ranging from a revival of Pythagorianism (that reality *is* mathematical) to an uneasy reflection that modern particle physics may have entered a decadent phase, losing touch with its empirical roots, and attempting Theories of Everything guided to a large extent by purely mathematical considerations.

*See also:*Influence on Science; Metaphysics; Universe

## Bibliography

Redhead, M. L. G. "A Philosopher Looks at Quantum Field Theory" in *Philosophical Foundation of Quantum Field Theory,* edited by H.R. Brown and R. Harré (Clarendon Press, Oxford UK, 1988).

Redhead, M. L. G. *From Physics to Metaphysics* (Cambridge University Press, Cambridge, UK, 1995).

Sklar, L. *Philosophy of Physics* (Oxford University Press, Oxford, UK, 1992).

Teller, P. *An Interpretive Introduction to Quantum Field Theory* (Princeton University Press, Princeton, NJ, 1995).

*Michael L. G. Redhead*

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