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But even a classical field, extends to infinity, the electric field around an electron extends to infinity. The strength of the fields vary and at some small distance from the peak, it becomes infinitesimal but not zero. So most of the energy is concentrated into a small place. That also explains particles "poping in and out of existence" from "nothing ".Also there is no propagatin wave between entangled particles to carry information. Another thing, instead of thinking about particles in a superposition of being at certain positions according to the wavefunction, it is easier to think of a field and probabilities of an interaction of the field as a independent unit. QFT makes more sense in physics, QM uses a mathematical model that is quite weird because it tries to adapt the classical model of a particle as a corpuscle to quantum world which may not be a good idea.