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- Born's rule for the QED electron violates causality.

**Summary:**Born's rule for the QED electron violates causality.

[Since the thread where some of this material was presented was closed for further discussion, I summarize here the main content relevant for the above topic.]

The free QED electron can be described in terms of a non-local single-parthicle Hamiltonian, as follows.

The single electron sector of renormalized QED including infrared dressing is invariant under Poincare transformations, since in this sector there is no scattering. Its Hilbert space carries a reducible unitary representation of the Poincare group. The generator of time defines the Hamiltonian ##H##. The resolvent ##(E-H)^{-1}## equals the renormalized electron propagator, and is given by the Kallen-Lehmann formula associated with some continuous mass density (due to infrared dressing effects) whose support extends from

the nominal electron mass to infinity.

The mass spectrum is nondegenerate and has a branch point at the nominal electron mass, where the continuous mass spectrum has a sharp peak. This means that the free QED electron has an additional mass degree of freedom, which formally behaves like an additional momentum degree of freedom. This mass degree of freedom generates the

continuous mass spectrum. Therefore the free QED electron is not an elementary particle in the sense of Wigner but a stable infraparticle.

- B. Schroer, Infrateilchen in der Quantenfeldtheorie, Fortschritte der Physik 11 (1963), 1-31.

- T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975), 2856--2861.

- D. Buchholz, The physical state space of quantum electrodynamics, Comm. Math. Phys. 85 (1982), 49--71.

- G.C. Hegerfeldt, Instantaneous spreading and Einstein causality in quantum theory, Annalen der Physik 7 (1998), 716-725.

''ensures either instantaneous spreading or confinement in a fixed bounded region for all times'' (quote from p.7).

In other words, a single QED electron prepared locally in an arbitrary state has - according to the Born rule, taken at face value - a nonzero probability of being immediately detected arbitrarily far away.

This violates causality.

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