I’ve heard a lot about discreteness and energy levels and things in the various books I’ve read on the subject, however I’m a little hazy as to how (if at all) this applies to quantum fields. Because in classical physics you have the inverse square law sort of fields, where the effect of a disturbance in a field decreases with distance but never quite reaches zero, and so there is (theoretically) no place unaffected by that disturbance. This doesn’t seem to fit with discreteness, so if we look at a particle as a disturbance in a quantum field, then does the effect of this particle spread over the whole field because it never quite reaches zero, or does discreteness mean that the effect of the particle is only found near the particle and otherwise the field is at zero?
Also if the latter is true does this mean that unless a particle is directly interacting with another particle it might as well not exist for all the other particle is concerned? (sorry, I couldn’t help that personification but I’m not sure it helped. To rephrase: can a particle be isolated from the rest of the universe and have no effect whatsoever on it, and at the same time be completely unaffected by the rest of the universe?) As this would at least clarify a few things that I can’t make sense of in this utterly and beautifully bizarre area of science.
