Electrodynamics
EstablishedCharge Quantisation
Electric charge is quantised because torus knot winding numbers are integers. The Hopf charge maps the U(1) winding number of the fibre S¹ to the observed electric charge quantum.
A standard mystery in physics is why charge is quantised. In standard physics, it is treated as an empirical fact or follows from Dirac's monopole argument—which requires magnetic monopoles that haven't been found.
In the CPT framework, the explanation is topological. Electric charge corresponds to the Hopf winding number. It must be an integer because only integer windings are topologically stable on the fibre.
The Hopf charge formula
The elementary charge is defined by the torus knot, which has a winding number in the Hopf fibre. Quarks have fractional charge because they represent sub-knot configurations, where partial winding numbers are only stable when confined together to form an integer net charge.
Because topology is conserved, charge is conserved. A topologically stable knot can only be created or destroyed in pairs with its mirror image.
Classical electron radius
The winding can be expressed as for around the Hopf fibre.
Source Documents
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