The concept of particles would seem to be a given. From grade school to graduate school we are told that matter is made up of particles—electrons, protons, neutrons, photons. On the other hand, in quantum mechanics there is the idea of wave-particle duality; sometimes matter acts like it is made of particles, sometimes it acts like it is made of waves (the wave function). But what is matter? Is it actually sometimes a particle and then, in different circumstances it becomes a wave?

To answer, we start from principle [P3]—one version of reality in the wave function always corresponds exactly to our perceptions. From this result (ignoring our cultural heritage concerning particles), our first hypothesis would be that matter consists of the wave function alone. So we will assume this and then investigate whether there are any observations or experiments that require the existence of particles for their explanation. If there are not, if we find that all the particle-like properties of matter can be explained by properties of the wave function, then the concept of particles is superfluous. In that case, we can presume that matter consists of wave functions alone.

There are many experiments that one could use to reputedly show the necessity for particles, but all the arguments depend on just a few properties (which all turn out to be invalid). They are:

(1) The classical particle-like properties of mass, energy, momentum, spin and charge are presumed to be properties of particles.
(2) The conservation and addition laws for energy, momentum, spin (angular momentum), and charge were established in classical, particle-based physics so their experimental verification is presumed to imply the existence of particles.
(3) Particles produce localized effects, so experimentally observed localized effects are presumed to imply the existence of particles.
(4) A small part of a classical wave, say a light or sound wave, carries a correspondingly small part of the energy and momentum of the wave, so the same is presumed to hold for the wave function.
(5) Because quantum mechanics gives several version of reality, it is presumed that we would perceive several versions of reality if there were no particles.

Particle-like properties of the wave function. We have seen in the section on Mass, Spin, and Charge that mass, energy, momentum, spin, and charge are properties of the wave function. So property (1) cannot be used to infer the existence of particles. Ditto for property (2). In the section on Localization, we showed that (spread out) wave functions produce perceptually localized effects, so property (3) also cannot be used to infer the existence of particles. The ‘small part of the wave function’ of property (4) is shown not to hold in the section on Small Parts; each small part carries the full properties. And finally, we have seen from the Classical Perception in Quantum Mechanics section that more than one version of reality cannot be perceived in quantum mechanics. Thus particles are not needed to explain the only-one perception of property (5) either.

So we see that all the underlying properties of matter which are used to infer the existence of particles can be explained by the properties of the wave function alone. This means there is no evidence for particles (because the wave function can account for all the particle-like properties).

[P15] There is no evidence for the existence of particles.

The seemingly paradoxical wave-particle duality of matter is resolved by the observation that the wave functions alone can account for both the wave-like and particle-like properties of matter. That is, the wave function has both classical wave-like properties and classical particle-like properties. So the dichotomy is in the properties of the wave function rather than in the ‘actual nature’ of matter.

Nomenclature. Even though there is no evidence for particles, it is not necessary to give up the very useful names. So we can agree that an ‘electron’ refers to an electron-like wave function, having mass m_e, spin , charge, -e; a ‘proton’ refers to a proton-like wave function, having mass m_p, spin , charge, -e; and a ‘photon’ refers to a photon-like wave function having mass 0, spin 1, and charge 0. But we must keep in mind that these names do not (if there is no collapse) refer to entities that objectively exist in a unique state; there can be several versions of them simultaneously existing in different states.

Related experiments. There are several experiments that, if one assumes particles exist, give perplexing results. Bell-like experiments on non-locality seem to show that particles interact instantaneously at a distance. And Wheeler’s delayed-choice experiment and the quantum eraser experiment seem to imply that causality can sometimes work backwards in time. But if one assumes there are no particles, the very peculiar inferences about the nature of reality simply evaporate. In a no-particle world, there is (to the best of my knowledge) no evidence for backwards causality. And while there are non-local effects in quantum mechanics, built into the theory by entanglement (Schrödinger’s cat), there is no faster-than-light signaling required to explain the results; it is just quantum mechanics as usual.