In physics, the concept of a "point particle" is an idealization used to simplify certain calculations and models. A point particle is treated as having zero size or radius and is assumed to be concentrated at a single mathematical point in space.
The idea of a point particle having infinite mass is not a concept supported by our current understanding of physics. In classical physics, the mass of a point particle is considered to be finite and non-zero. However, when we delve into the realm of quantum mechanics and consider particles at extremely small scales, our classical understanding breaks down, and the concept of mass itself can become more complex.
In quantum field theory, particles are described as excitations of underlying quantum fields that permeate space. These fields have associated energy and momentum, and the concept of mass emerges as a result of interactions between particles and these fields.
While a point particle is treated as having zero size in classical physics, quantum mechanics introduces the concept of particle wavefunctions, which describe the probability distributions of a particle's position. These wavefunctions can have spatial extent, even for point-like particles. However, it's important to note that the wavefunctions do not represent the physical size of the particle but rather the probability distribution of finding the particle in different regions of space.
In summary, the idea of a point particle with both infinite mass and zero radius is not consistent with our current understanding of physics. Point particles are idealizations used to simplify certain calculations, and at the quantum level, the concept of mass and the behavior of particles become more nuanced.