The probabilistic analysis of Schrödinger's equation at some point resulted in the uncertainty principle of Quantum Mechanics, formulated in 1926 by Werner Heisenberg. This principle says that an electron, or any other particle, can not have its precise position known, or even specified. More exactly, Heisenberg formulated a formula that connects the uncertainty in location of a particle to the uncertainty of its momentum. So not only do we have wave-particle duality to deal with, we need to take care of particles that may be here or may be there, but we just can't say where. If the electron is truly a particle, then it only stands to reason that it should be someplace.
Resolution. In Quantum Field Theory there are no particles (stop me if you have indeed heard this before) and thus no location-- certain or uncertain. Alternatively there are blobs of field that are spread over space. As opposed to a particle that is either here or here or perhaps there, we have a field that is here and here and there. Spreading out is a thing that only a field can do; a particle can not do this. Actually Heisenberg's Uncertainty Principle is not very different from Fourier's Theorem (found in 1807) that relates the spatial spread of any wave to the spread of its wave length.
This does not suggest that there is no uncertainty in Quantum Field Theory. There is uncertainty in regard to field collapse, but field collapse is not explained by the formulas of QFT; Quantum Field Theory can just forecast possibilities of when it happens. Nevertheless there is a significant difference between field collapse in QFT and the corresponding wave-function collapse in QM. The former is an actual physical change in the fields; the latter is just a change in our understanding of where the particle is...
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