Charge 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.

Reading this entry

This entry reads electric charge as a Hopf winding: only integer windings of the U(1) fibre are topologically stable, so seat charge comes in whole multiples of the elementary quantum e. The T(1,1) seat occupies the winding n = 1, and topology conserves that integer.

What this is used for

Later fine-structure and particle pages use this integer slot when they label a seat by its fibre winding and place the input e on that slot. Pair creation and charge conservation in the framework inherit the same rule that a stable knot appears with its mirror image.

Walk through

The Hopf charge on the page is Q=ne with n an integer, the winding number of the U(1) fibre. The electron seat T(1,1) occupies the winding n=1, naming the integer slot on which the input elementary charge sits, with sub-knot marks kept as packaging on the same Hopf story. A stable knot and its mirror image appear together, so the integer is conserved. The classical radius written next is r_e=ke²/(m_ec²)≈2.818×10⁻¹⁵ m, with the magnitude of e calibrated to the Weber coupling k. The same winding is the angle shift φ→φ+2πn around the Hopf fibre.

Integrity note: BQ does not derive

. Integer Hopf winding is a stability / quantisation story. The elementary charge remains an input on /status.

Structure package: Claims here are geometric/packaging results under named premises. They do not by themselves close absolute α, continuum hold, or the full SM mass spectrum. See /status.

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 seat is the winding in the Hopf fibre. That names the integer slot; it does not mint the value of . Fractional labels on sub-knot configurations are packaging, not a quark-charge derivation.

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.

[E]

This concept is established and rigorously mathematically verified within the CPT framework.

Source Documents

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Hopf Charge Quantisation

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