The concept of a particle is arguably the single most fraught issue in quantum physics.
From a phenomenological perspective, massive fermion particles like an electron appear to exist as discrete, point-like entities, as discussed below in discrete particle trajectories. But these particles are described in the Standard Model using the Dirac wave equation, which is a spatially-distributed, wave-based entity. Furthermore, most of the calculations are done using the field theory framework that only represents the momentum (energy) of the particles, and completely ignores the spatial localization dimension.
Thus, some people have concluded that particles don’t exist in the Standard Model (Hobson, 2013; Sebens, 2022). Furthermore, most of the deep paradoxes associated with the Copenhagen interpretation surround the conversion of distributed probability-wave equations into a discrete particle localization measurement event.
However, it seems clear that discrete particles are explicitly represented in the form of the Feynman diagrams that drive the path-integral framework used to actually perform computations in the Standard Model. Thus, it is actually the interplay between these discrete, localized particle-based interactions depicted in these diagrams, and the wave-based nature of the underlying fields, that gives rise to the predictions made from the Standard Model. Thus, contrary to the above-cited interpretations, it seems that the wave-particle duality is in fact alive and well in this model.
In addition to massive fermion particles, the Standard Model describes the force-field bosons as particles (with spin 1) that carry forces to mediate interactions among massive particles. This is where things become more tenuous, because the phenomenological reality of such things as discrete, localized, point-like entities is entirely absent. All measurement events ultimately reduce to position as a universal basis, which is inevitably in terms of the massive fermion particles.
Furthermore, there are no strong particle-number conservation laws or other constraints on boson numbers, and the (rarely-used) quantum wave function describing the photon is just a complex version of the purely classical Maxwell wave equations, and it lacks many of the properties of the quantum wave functions for fermions. Indeed, even the spin 1 of the photon is not well defined, in the same way that it is for fermions – it is just the polarization of the EM field.
The massive weak force bosons, and the Higgs boson, are extremely short-lived, and only evident in terms of indirectly-measured cascades of discrete fermion particle transmutation events, further suggesting that they are just transient fluctuations in the underlying field at a specific energy level consistent with the ascribed rest mass, which then gives rise to other longer-lived particles that can actually be directly measured.
The pilot-wave and semiclassical frameworks provide alternative interpretations, where fermions have a distinct ontological status as discrete particles that are always localized to a specific 3D location, while force fields and quantum waves remain purely wave-based phenomena. See mechanisms for more discussion about this logic.
Discrete particle trajectories
The raw data in high-energy particle physics experiments, e.g., at the large hadron collider (LHC), consists of trajectories of particles recorded in advanced detector chambers, capturing the fallout of high-energy collisions of protons with each other. In older experiments dating from the early 1900’s, these trajectories were recorded in cloud chambers.
These trajectories inevitably form straight or curved lines, depending on the presence of magnetic fields and the charge of the relevant particles. Furthermore, the points of collision, and points of decay, inevitably show up as discrete spatial points along the trajectories, with clear discrete forks along the paths.
Thus, phenomenologically, and consistent with the double slit experiment, it seems as though there really are these discrete spatially localized particles somehow moving through space along these trajectories. The pilot wave framework reifies this as a foundational principle.
However, it was shown by Mott (1929) (see also Figari & Teta, 2013) that standard wave-based quantum physics frameworks also predict such trajectories, when you analyze the entire particle + detector system as one big configuration space quantum system. In effect, the straight trajectory is the only one that emerges with high probability across all of the particle interactions represented in this configuration space, because otherwise you would require some kind of reliable force to cause the particle to deviate from such a trajectory. In the end, the Schrodinger wave function does capture the basic Newtonian principles of momentum and force, which dictate the nature of the straight trajectory.
Thus, different calculational tools indeed can produce the same, observed result. But the pilot-wave model provides a physical model in the form of a discrete particle that explains more concretely how these spatially-localized discrete trajectories might naturally emerge, instead of requiring an entirely non-local, exponentially-explosive configuration space to produce the result as a kind of post-hoc coincidence distributed across many different individual configuration-space interactions.