According to our current understanding in physics, two or more particles cannot have exactly the same mass without being identical. The mass of a particle is considered to be one of its intrinsic properties, and each particle is characterized by its unique set of intrinsic properties, including mass, charge, spin, and other quantum numbers.
In quantum mechanics, particles are described by their wave functions, which encapsulate their properties and behavior. The principle known as the Pauli exclusion principle states that no two identical fermions (particles that obey Fermi-Dirac statistics) can occupy the same quantum state simultaneously. This principle applies to particles like electrons, protons, and neutrons, which are fermions. As a consequence, fermions with the same intrinsic properties, such as mass, cannot occupy the same quantum state simultaneously.
This principle is fundamental to the stability and structure of matter. It ensures that electrons, for example, occupy different energy levels in an atom, resulting in the diverse and complex arrangements of electrons that give rise to the properties of different elements in the periodic table.
However, it's worth noting that particles of the same type, such as electrons or protons, are considered indistinguishable. That means if two electrons have the same mass, charge, and other intrinsic properties, they are considered identical particles and cannot be distinguished from each other. But this does not imply that two particles with different masses can be considered the same.
It's important to keep in mind that our understanding of particles and their properties is based on current theories and experimental observations. As scientific knowledge advances, new discoveries or theories may provide further insights that could refine or expand our understanding in this area.