In symmetry there is force. First, the indistinguishability of quantum mechanical particles divides the world into bosons and fermions, force and matter. Interchange symmetry imposes an exclusionary influence on fermions that gives atoms their size and hardness, thereby creating the chemical differences that make life possible. Second, the symmetry of a wave function with respect to a shift in phase — a “gauge” symmetry enforced locally and relativistically all throughout space-time — stitches together the quantum mechanical universe. If two observers, separated in time and space, are to perceive a rotated wave function as doing essentially the same thing, then nature must supply a force field that communicates the difference in phase. A quantized field of messenger particles, bosons, arises to guarantee the local symmetry.
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