The concept of fundamental particles as zero-dimensional points is not a well-established or widely accepted notion in modern physics. The idea of particles being point-like in nature, without any internal structure or extension in space, arises from certain theoretical models, such as point particle models in classical physics or the concept of point-like particles in certain formulations of quantum field theory.
In classical physics, particles are often treated as point particles, meaning they are assumed to have no size or spatial extent. This approximation simplifies calculations and allows for straightforward mathematical descriptions of their motion and interactions.
In the context of quantum field theory, which is a framework that combines quantum mechanics with special relativity, particles are interpreted as excitations or quanta of underlying quantum fields. These fields are defined at every point in space and time, and particles can be thought of as localized disturbances or concentrations of energy within these fields. In some formulations of quantum field theory, particles are treated as zero-dimensional mathematical points, where the field value is non-zero.
However, it is important to note that this notion of particles as zero-dimensional points is an idealization within certain theoretical frameworks and should not be taken literally as a physical description of particles. In reality, our current understanding of fundamental particles is based on experimental evidence, such as high-energy collision experiments and observations of particle interactions, rather than on the assumption of particles as zero-dimensional points. The precise nature and structure of fundamental particles are still subjects of ongoing research and exploration in modern physics.