The requirement for force-mediating particles to have integer spin is a consequence of the principles of quantum mechanics and the symmetries of the laws of nature. It is known as the spin-statistics theorem, which establishes a connection between the spin of a particle and its statistical behavior under particle exchange.
According to quantum mechanics, particles can be classified into two broad categories based on their statistical behavior: bosons and fermions. Bosons have integer values of spin (0, 1, 2, etc.), while fermions have half-integer values of spin (1/2, 3/2, 5/2, etc.).
The spin-statistics theorem states that bosons follow Bose-Einstein statistics, which allows an unlimited number of particles to occupy the same quantum state. This property leads to phenomena like the formation of Bose-Einstein condensates and the ability of bosons to occupy the same energy state, leading to the concept of bosonic fields and particles.
On the other hand, fermions obey Fermi-Dirac statistics, which impose the Pauli exclusion principle, stating that no two identical fermions can occupy the same quantum state simultaneously. This leads to the observed behavior of matter particles, where electrons, protons, and neutrons, for example, each have distinct quantum states and form the basis of matter as we know it.
Force-mediating particles, such as photons (mediating electromagnetism) or gluons (mediating the strong nuclear force), are bosons. Their integer spin allows multiple copies of these particles to occupy the same quantum state, enabling the exchange and transmission of forces between particles without violating the exclusion principle.
In summary, the requirement for force-mediating particles to have integer spin arises from the spin-statistics theorem, which connects the statistical behavior of particles with their spin values and is rooted in the fundamental principles of quantum mechanics.