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All these classical ideas are pointless and obsolete today, because in quantum mechanics, the particles are completely different objects, defined by quantum motion of fields, not by the location of classical points (at least not in a causal field picture). The notion of a point particle was replaced by the more subtle notion of a quantum point particle, which has a probability amplitude to be at various places. This quantum point particle can reproduce the quantum field if it is allowed to go backward and forward in time.
That was quoted by Ron Maimon. From this - Can I gather that in reality, particles travel backward and forward in time or, is this just a mathematical expression or model?