Quantum mechanics doesn’t just challenge our intuition; it reshapes what counts as an object. Philosopher of science, Dennis Dieks, explains why at the fundamental level there are no discrete particles. Instead, objects like electrons or photons emerge only under special conditions, much like units of money appearing from a single bank balance. Our everyday world of things is a macroscopic illusion built on an undivided quantum reality.

The world we perceive every day is full of things, objects, which we can distinguish from one another, follow in time, and often grasp and manipulate. This experiential fact so imposes itself on us that it is hard to imagine a world without objects. How could we reach out and make contact with the external world if there were no things to touch and see? It is no wonder, then, that from the very beginning of natural science, objects have been considered fundamental constituents of reality. It was already suggested in classical antiquity that the gross objects of our everyday experience are composed of smaller more fundamental objects and finally of smallest “atoms.” These “elementary particles” posited by ancient natural science/philosophy should of course not be confused with those of modern physics. For one thing, they differed from each other in shape and size, contrary to modern views, as we will see in a moment. The quantum theory further complicates matters and, as I will argue, makes us reject the very idea of individual particles at the fundamental level. In its place comes the image of a whole from which individual particles can emerge under special conditions.

SUGGESTED VIEWING The quantum unknown With Matt O'Dowd, Sabine Hossenfelder

 Differences make it possible to distinguish things. If you have a number of different objects in front of you, at a certain instant, you can give them individual names; they thus have their own identity. Moreover, objects retain their identity over time, because of their different histories. Thus, if we have two distinct particles, A and B, we can after some time still identify which is A and which is B by looking at their paths in space (e.g., by filming them). So, objects not only differ at a given moment, but also possess “genidentity,” i.e. identity over time.

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Classically speaking, two different electrons will always be in different places, probably also possess different velocities; and follow different trajectories in space.

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In classical mechanics, which got its foundations in Isaac Newton's revolutionary Principia (1687), the concepts of “object” and “particle” play a central role. Classical mechanics is all about how distinguishable objects move under the influence of forces. Interestingly, a year before the Principia appeared, the German philosopher Leibniz (1646-1716) formulated a general principle regarding distinguishability and identity. According to Leibniz, if two things have exactly the same physical properties, then they must be one and the same thing (Leibniz’s Principle of the Identity of Indiscernibles). Accordingly, two different things cannot have all their attributes in common. Given how we conceptualize objects in everyday life and in classical physics, this seems an eminently reasonable principle. It proves, nevertheless, to be open to debate. Thus, one might wonder whether two things could share all their physical properties but yet differ in a non-empirical identity-bestowing property, “primitive thisness” or “haecceity” (from medieval Latin haecceitas, “thisness”). Such non-empirical “thisnesses” seem poorly compatible with modern scientific thinking. But the discussion has become topical again because of quantum mechanics.

Even before quantum mechanics, views on the fundamental building blocks of matter changed significantly. In the 19^th and early 20^th centuries, it became clear that so-called elementary particles occur in "kinds" (species), and that within each kind, characteristic properties such as mass and electrical charge are exactly the same. Thus, all electrons have the same charge and mass, and similarly for protons, neutrons and other elementary particles, each species of elementary particles having its own intrinsic properties. Nevertheless, in a classical picture, it remains possible to tell particles of the same kind apart via non-intrinsic properties. Thus, classically speaking, two different electrons will always be in different places, probably also possess different velocities; and follow different trajectories in space.

This classical picture of individual objects moving under the influence of forces matches intuition very well, but has been shockingly exposed to doubt by the advent of quantum mechanics. The mathematical formalism of quantum mechanics does not represent a particle by the combination of its position and velocity, as classical mechanics does. Instead, quantum mechanics characterizes a particle by a “wave function” ψ(x), which assigns a complex number to each point in space. This wave function evolves deterministically over time according to the Schrödinger equation. The description of a single particle by means of a function extended over space is in itself reason to wonder what “particle” can even mean anymore in quantum mechanics. This question becomes only more pressing when we consider the quantum treatment of two or more particles of the same kind. Quantum mechanics requires that the wave function of a collection of such particles be completely symmetric or antisymmetric. To illustrate, take two electrons, which we number in our minds as 1 and 2, and to which we would like to assign wave functions ψ and φ. The rules of quantum mechanics now say that the total state cannot be the product ψ₁φ₂ (electron 1 in state ψ and electron 2 in state φ) but must be antisymmetric, therefore proportional to (ψ₁φ₂ - φ₁ψ₂). Antisymmetry means that a minus sign appears before each permutation of single particle wave functions, symmetric wave functions show a plus sign. There are two families of elementary particles, “fermions” (electrons, for example) and “bosons” (e.g. photons). Quantum mechanics requires fermion states to be completely antisymmetric and boson states symmetric. Generally, the wave function assigned to a two-electron system will be even more complicated than (ψ₁φ₂ - φ₁ψ₂), because “superpositions” of antisymmetrized products are also possible, like  (ψ₁φ₂ - φ₁ψ₂  +  α₁β₂ - β₁α₂).

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Particles of the same kind share not only their intrinsic but also all their non-intrinsic physical properties—they are physically indistinguishable.

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In both symmetric and antisymmetric total wave functions, the labels 1 and 2 are not associated with a single one-particle state. Thus, in the state (ψ₁φ₂ - φ₁ψ₂), electrons 1 and 2 are both associated with ψ AND φ. A more extensive analysis confirms this result for any symmetric or antisymmetric state, for any number of particles: each single particle receives exactly the same description in such a total state, regardless of its label. In other words, according to the quantum formalism, particles of the same kind share not only their intrinsic but also all their non-intrinsic physical properties—they are physically indistinguishable. This doctrine of the indistinguishability of quantum particles of the same kind has become textbook wisdom and is known as the Received View of identical particles.

According to this Received View electrons are indistinguishable, yet do not coincide into a single particle. This contradicts Leibniz's principle. To rescue that principle and make intelligible that there can be a multiplicity of things that are physically completely the same, one might take recourse to the old concept of haecceity. In this case the particles can be made different after all, by giving them different haecceities. The minus side of this option is that it seeks to explain a mysterious multiplicity without distinguishability by appealing to an even more mysterious and inaccessible identity principle (haecceity). The most widely defended version of the Received View is therefore different. In it, it is argued that quantum particles of the same kind are a completely new kind of thing: entities without any identity. Since the concept of identity simply does not apply to them, neither does Leibniz's principle.

According to this proposal, the members of a set of particles of the same kind cannot be used to generate singleton sets of which they are the sole members—indeed, if this were possible each member would have its own identifying property, represented by its singleton set. This non-existence of singleton sets, however, is inconsistent with the axioms of mathematical set theory. Defenders of the view have therefore designed an alternative “quasi-set” theory, with new axioms. Systematic handling of these axioms leads to non-standard reasoning rules tailored to things without identity.

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There is a simpler view: accept that, in many cases, an (anti)symmetric total state does not represent a multitude of particles at all, but describes an undivided whole.

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A yet other approach is to maintain a classical particle concept, by extending the quantum formalism with extra quantities that distinguish particles from each other. Bohm's hidden-variable theory is an example of this possibility. In the Bohm theory each particle has a position, a velocity and a trajectory, just as in classical mechanics. But the equations of motion are not Newtonian: they have been adapted to exactly reproduce the predictions of quantum mechanics.

In contrast, I defend a position that respects Leibniz's principle, can do without deviant logic, and does not need additions to the standard formalism of quantum mechanics. The strategies that we just sketched all adhered to the idea that in an (anti)symmetric total state more than one particles must be present. These strategies then either went looking for properties that give substance to the individuality of those particles (haecceities, particle positions à la Bohm), or took the resigning stance that we are facing a mysterious new type of entities, things without identity.  But there is a simpler view: accept that, in many cases, an (anti)symmetric total state does not represent a multitude of particles at all, but describes an undivided whole.

According to this view, particles in an (anti)symmetric state may well be compared to units of money in a bank account. The balance in such an account could be built up by bringing physical units of money, say euros, to a bank branch. But an amount in the account does not consist of individual euros, each with its own identity. For example, it is impossible to trace which euro was last credited to the account. This is not a matter of ignorance because it is forbiddingly difficult to determine what is the case. Rather, it is a matter of principle: there are simply no individual euros in the total balance. The balance is one undivided whole, representing a certain purchasing power. That does not mean that individual euros, with their own identity, cannot be created from the total balance. When making a payment, I can transfer one euro to another, still empty account. From then on, that euro is distinguishable from the rest. If needed, I can withdraw it from the bank and keep it separate. Thus, a euro with its own identity is created. Therefore, under certain circumstances, euros with individual identities can emerge from the undifferentiated whole of the total balance. Analogously, my preferred view says that at the fundamental quantum level, there are no discrete particles. However, such particles can emerge when the overall wave function assumes a special form.  

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Physical reality at its more fundamental levels does not consist of thing-like entities at all.

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The relevant emergence conditions are often fulfilled in situations where there is a lot of interaction with the environment, which leads to “decoherence”. Decoherence, the influence of the environment, is omnipresent in the familiar world around us. Indeed, in our world everything is always surrounded by something else, such as atmospheric air and light (or other radiation), with which it interacts. These interactions with the environment are sensitive to position, as demonstrated, e.g., by the fact that we can see where things are. Apparently, the properties of light change depending on the position of that with which it interacts. That these interactions are position-dependent turns out to explain the special role that “position” plays for objects in our macroscopic world: things that emerge under the conditions in which we live are predicted to be localized.

This prediction is, of course, necessary for the viability of our heterodox view, since in everyday experience we are constantly surrounded by what seem to be unquestionably robust and localized objects. But quantum mechanics appears to reveal to us—and importantly, this is confirmed by even more fundamental theories, such as quantum field theory—that the picture of robust and localized objects is deceptive. Physical reality at its more fundamental levels does not consist of thing-like entities at all.