In the context of quantum mechanics, spin is an intrinsic property of elementary particles. It is often referred to as a type of angular momentum, but it is distinct from the familiar notion of classical angular momentum associated with macroscopic objects.
Mathematically, spin is described by a quantum number, denoted by "s," which determines the magnitude of the spin angular momentum. The value of the spin quantum number determines the behavior of the particle under rotations in space.
Contrary to the statement, there are indeed massive particles that possess spin. In fact, most elementary particles, including quarks, electrons, and neutrinos, have spin. The spin of these particles is quantized, meaning it can only take certain specific values, such as 1/2, 1, 3/2, and so on, depending on the particle.
The statement that there are no massive particles with spin might be a misunderstanding. It is true that there is a class of particles known as "spin-0" particles that have zero spin, such as the Higgs boson. However, there are also particles with non-zero spin, known as "spin-1/2" particles, which are massive, like electrons and quarks. Spin is not exclusive to massless particles.
It is important to note that spin is a fundamental property of particles, and it is not related to their physical size or shape. It is intrinsic to the nature of the particle itself. As of our current understanding of quantum mechanics, it is not possible for a massive particle to exist without any spin.