The Uncertainty Principle

Uncertainty Principle, Fields of Color

The probabilistic translation of Schrödinger’s formula ultimately brought about the uncertainty principle of Quantum Mechanics, formulated in 1926 by Werner Heisenberg. This principle specifies that an electron, or any other particle, can not have its specific position known, or even pointed out. More exactly, Heisenberg derived a formula that relates the uncertainty in position of a particle to the uncertainty of its momentum. So not only do we have wave-particle duality to take care of, we must take care of particles that might be here or may be there, but we just can’t say where. If the electron is actually a particle, then it only stands to reason that it must be someplace.

Resolution. In Quantum Field Theory there are no particles (stop me if you have indeed heard this before) and hence no position– 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. Extending out is one thing that only a field can do; a particle cannot do this. Actually Heinsenberg’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 mean that there is no uncertainty in Quantum Field Theory. There is uncertainty in relation to field collapse, but field collapse is not explained by the equations of QFT; Quantum Field Theory can just predict probabilities of when it happens. Nevertheless there is a significant distinction 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 only a change in our understanding of precisely where the particle is….

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