We can directly feel the effects of gravitational and electromagnetic fields because the quanta of these fields have zero mass, and they are particles of a type (known as bosons) that in large numbers can occupy the same state. These properties allow large numbers of photons to build up to form states that we observe as electric and magnetic fields that seem to obey the rules of classical (that is, non-quantum) physics. Electrons, in contrast, have mass and are particles of a type (known as fermions) no two of which can occupy the same state, so that electron fields are never apparent in
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