Particle physics isn’t really about particles. Nor, it turns out, is it about fields—at least not in any traditional sense, argues NYU philosopher Jon Bain. Despite the name, the theories at the heart of modern physics describe a reality where the classical idea of discrete, localizable, countable particles collapses—and fields fare no better. For Bain, making sense of particle physics means abandoning these outdated intuitions and embracing a more radical view: the properties we associate with particles or fields don’t exist absolutely, but emerge only in specific regimes. What, then, underlies reality? Not objects, but structure—relations, observables, mathematical frameworks. If there’s anything fundamental, it may not be a thing at all.
To what extent is particle physics about particles? This is an important question for a naturalist who looks to science for the answers to philosophical questions about the nature of reality. When a philosopher asks “What is the nature of matter?” a naturalist will look to our current best scientific theories about matter; namely, those theories that make up the field of particle physics, and if particle physics is about particles, then the answer to the philosopher's question will be “matter consists of particles.” This seems straightforward: in order for it to be called particle physics, it must, surely, be about particles. But alas, it's not as simple as this. There is a consensus among philosophers that particle physics is not fundamentally about particles. In fact, the theories of matter that go under the rubric “particle physics” are relativistic quantum field theories (RQFTs), which are mathematical frameworks that are the result of combining Einstein's special relativity with a quantum version of classical field theory, and which, under a naive interpretation, are about quantum fields that sometimes exhibit particle-like excitations. But, as we will see, a standard argument against a particle interpretation of RQFTs also works against a field interpretation. So a naturalist seems to have her work cut out for her: why call it “particle physics” if it isn't about particles? Why can't it be about particles? If it isn't about particles, or fields, what is it about?
1. Particles in Classical Physics
Why use the phrase “particle physics” to refer to the collection of RQFTs that purport to describe the fundamental nature of matter? I blame Isaac Newton. Newton's theory of motion (described in his 1687 Mathematical Principles of Natural Philosophy) was, in part, a critique of Descartes’ earlier theory of motion (described in his 1644 Principles of Philosophy). In a Cartesian cosmos (apart from humans and God), there are no active principles, no occult forces acting across vast distances in a vacuum; rather, there are only extended bodies acting mechanistically on each other through direct contact and ultimately individuated by their motion in a continuous plenum. In contrast, in a Newtonian cosmos, matter consists of discrete particles moving in an infinite void and governed by a single active principle (i.e. gravity). The conceptual origins of Newton's cosmos go back to ancient Greek atomism, and slightly less ancient Neoplatonism, and center stage is given to what we might call a Newtonian particle.
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It turns out that, while particle intuitions have changed since Newton, they haven't changed all that much.
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Newtonian particles have three essential properties. First, they are always localizable: of any Newtonian particle, we can say that, at any instant in time, it is here, now, as opposed to there, now. Second, they are always countable: it is possible to begin with two here, now, add one here, now, and obtain three here, now. Both localizability and countability make sense in a Newtonian cosmos in which space and time are absolute. Finally, Newtonian particles are distinguishable: if a physical system consists of a collection of Newtonian particles, then exchanging any two of them makes an observable difference. This can be made a bit more precise by means of the concept of permutation invariance: we say that a multi-particle state is permutation invariant just when exchanging any two of its single-particle substates does not affect the expected value of an observable with respect to the state. So to say Newtonian particles are distinguishable is to say that a multi-particle system made up of Newtonian particles is not permutation invariant.
But why blame Newton for the phrase “particle physics?” Surely Newtonian intuitions about the concept of a particle have changed over the past ~340 years. In particular, haven't these intuitions been overturned by quantum mechanics? It turns out that, while particle intuitions have changed since Newton, they haven't changed all that much.
2. Particles in Non-Relativistic Quantum Mechanics
Let's be clear: even the simplest version of quantum mechanics (the version that describes non-relativistic physical systems with finite degrees of freedom) has changed some intuitions about particles, but arguably not in the way that most popularized accounts suggest. That way tells a story about strange experiments in the early 20th century involving electrons aimed at two slits, the outcomes of which suggest that an electron exhibits both wave-like and particle-like properties. This “wave-particle duality,” we are told, is unlike anything in classical physics. But this view depends on one particular way of interpreting (non-relativistic, finite-dimensional) quantum mechanics, and this is not the only way. Suffice it to say that there are alternative interpretations that support a particle ontology. For instance, one can maintain a particle ontology by interpreting quantum mechanics to entail that a quantum particle can exhibit “indefinite” properties, including “indefinite” position; and, arguably, this doesn't make it any less of a particle.
Thus it's perfectly consistent to interpret a composite (finite-dimensional, non-relativistic) quantum system as consisting of localizable and countable particles. On the other hand, the evidence suggests that, unlike Newtonian particles, quantum particles are not distinguishable: exchanging any two quantum particles in a multi-particle quantum system does not have an observable effect on the state of the system. To make this more precise, one can refer to the statistics, or “group rule,” that multi-particle systems obey. The group rule that multi-particle Newtonian systems obey is called Maxwell-Boltzmann statistics, which is characterized, in part, by a failure of permutation invariance—meaning that swapping the particles makes an observable difference. On the other hand, multi-particle quantum systems obey two types of group rule (depending on their spin properties); namely, Bose-Einstein statistics or Fermi-Dirac statistics, both of which are characterized, in part, by permutation invariance—you cannot tell when particles have been swapped.
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A realistic RQFT (of the type found in particle physics) cannot be formulated in a way that makes sense of localizability and countability.
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A lot has been written about the implications of the indistinguishability of quantum particles with respect to issues concerning identity and individuality. But we can set aside these debates since our interest here lies only in whether a particle concept makes sense in the context of quantum mechanics. And if particles are minimally taken to be localizable and countable, and we put aside the question of indistinguishability, then the answer seems to be “yes.”
3. No Particles in Relativistic Quantum Field Theories?
The argument is fairly straightforward: it claims that a realistic RQFT (of the type found in particle physics) cannot be formulated in a way that makes sense of localizability and countability. More precisely, it cannot be formulated using a standard way of mathematically representing the properties of localizability and countability. That way uses mathematical objects called a local number operator and a total number operator, and it turns out that in a realistic RQFT, these objects cannot be defined. (The gory details involve pointing out that the Reeh-Schlieder theorem entails that there are no local number operators in any RQFT, realistic or otherwise, while Haag's theorem entails that there is no total number operator in any realistic RQFT.) And what's worse, this argument against minimal Newtonian particle interpretations of particle physics also works against field interpretations: it turns out that the sort of mathematical structure that supports a minimal Newtonian particle interpretation (a “Fock space” structure) is mathematically equivalent to the sort of mathematical structure that supports a field interpretation.
If particle physics can't be said to be about minimal Newtonian particles or their field equivalents, then what is it about? One option is to adopt a form of instrumentalism: perhaps all we can say about particle physics is what is contained in the structure associated with its observable content. Some physicists have fleshed this out in terms of the slogan “particles are what particle detectors detect.” Alternatively, some philosophers reject this instrumentalist approach, but retain a focus on the structure of observables and hold out hope that the ontology of RQFTs can be expressed in terms of this structure (it turns out that very simple, and typically unrealistic, RQFTs can be rigorously formulated in an algebraic formalism in which algebras of observables play a central role).
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Philosophers have recently proposed a “selective” form of realism according to which what is real is scale-relative, and this is consistent with viewing minimal Newtonian particles as part of the ontology of particle physics.
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Another option is to replace the concept of an always localizable, always countable, minimal Newtonian particle with a different particle concept. Perhaps it’s our Newtonian intuitions that are getting in the way. In fact, one can show that the existence of local and total number operators (which are supposed to represent the properties of localizability and countability) depends on the existence of Newtonian spacetime structure (in the form of an absolute temporal metric). And since the spacetime structure of particle physics is relativistic and not Newtonian, it's not all that surprising that particle physics doesn't admit a minimal Newtonian particle interpretation. So perhaps localizability and countability should be understood as flexible, as opposed to absolute, properties of a particle. Maybe particles manifest these properties only in certain regimes, but not in others. And maybe what it means to be a particle in particle physics is just that—namely, having the property of manifesting localizability and countability in certain scenarios.
Yet another option is to retain a minimal Newtonian concept of a particle, but acknowledge that this concept is not a fundamental feature of particle physics; rather, it emerges at an appropriate level (in an appropriate energy regime, say). Philosophers have recently proposed a “selective” form of realism according to which what is real is scale-relative, and this is consistent with viewing minimal Newtonian particles as part of the ontology of particle physics. This is in keeping with the view among physicists that the realistic RQFTs that make up particle physics are not fundamental theories; rather, they are “effective” theories that are accurate only when restricted to appropriate energy scales.
4. Conclusion
So is particle physics about particles? I think the answer to this question is a qualified “yes.” In particular, I'm drawn to the last two options described at the end of the previous section. On the one hand, I think questions of ontology (e.g. what is the nature of a particle?) cannot help but be influenced by past theories in physics (e.g. Newton's theory of motion). But the history of physics suggests that there's a lag time between our intuitions and theories in physics. (One reason, perhaps, that most people don't have an intuitive grasp of quantum mechanics is because their intuitions have been informed by Newtonian mechanics.) So it seems eminently reasonable to think that intuitions about particles have not yet quite caught up with particle physics. What this suggests is that we should look to our current theories to inform us about the nature of particles; and this, in turn, suggests that, yes, particle physics can be said to be about particles, provided that we either give up minimal Newtonian intuitions about particles, or provided that we are willing to adopt an “effective” view of theories in physics, and, perhaps, a corresponding selective realism about the nature of matter.
27th June 2025
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