In quantum field theory (QFT), particles are described as excitations of their corresponding fields. According to QFT, particles are fundamental entities with no internal structure or size in the traditional sense. Instead, their properties, such as mass and charge, arise from interactions with the underlying fields.
It is true that in experiments, we can measure the size of particles with high precision. For example, in the case of electrons, experiments like electron scattering can provide information about the spatial distribution of the electron's charge. These measurements may give the impression that particles have a finite size.
However, it's important to understand that the concept of "size" in the context of particle physics is different from the macroscopic objects we encounter in everyday life. The size of a particle, as determined by experiments, is often related to its interaction cross-section or spatial distribution of its charge or energy density.
In QFT, particles are described by wave functions or probability amplitudes that extend throughout space. The precise mathematical description of particles in QFT is in terms of point-like entities. This concept is related to the uncertainty principle of quantum mechanics, which states that there is an inherent limit to how precisely we can simultaneously know the position and momentum of a particle. This uncertainty implies that particles do not have definite positions or sizes at all times.
Therefore, while experiments can provide information about certain measurable quantities related to a particle's size, it is important to interpret these results within the framework of quantum mechanics and QFT. The idea that particles have no size in QFT is a fundamental concept that arises from our current understanding of the quantum nature of particles and their interactions.