Bell’s Inequality: LIMA-QTE Violates It Exactly Like Nature
Bell’s theorem proves that no local hidden-variable theory can reproduce all predictions of quantum mechanics. Experiments have confirmed violation of Bell inequalities by many standard deviations.
LIMA-QTE is 100% compatible with these results — and violates local realism in exactly the same way and to exactly the same degree as standard quantum mechanics.
LIMA-QTE violates Bell inequalities for exactly the same physical reason every quantum field theory does:
When two electrons (two knots) become entangled — for example, a knot/anti-knot pair created from a single excited knot that then splits — their internal helical twists remain perfectly correlated even after they fly apart.
The internal circulation direction (the “smoke ring” spin) of one knot is physically tied to the circulation direction of the other by topology that was set at the moment of pair creation. That correlation is encoded in the global configuration of the electromagnetic field across both knots, not in any local hidden variable carried by each knot separately.
When Alice measures her knot in one basis, she instantly changes the global field configuration, which immediately affects what Bob will measure on his knot — no matter how far away — because the two knots are still part of the same extended field structure until the measurement disturbs it.
The CHSH form of Bell's inequality for local realism:
\[ \left| \langle AB \rangle + \langle AB' \rangle + \langle A'B \rangle - \langle A'B' \rangle \right| \leq 2 \]where A,A' are Alice's measurements, B,B' Bob's.
In LIMA-QTE (and QM), the correlation for entangled knot pairs is
\[ \langle AB \rangle = -\cos\theta, \]where θ is the angle between measurement bases, yielding maximum violation
\[ 2\sqrt{2} \approx 2.828 > 2. \]This comes from the topological phase difference accumulated in the shared EM field configuration during pair creation and separation.
In one sentence:
Entanglement in LIMA-QTE is real, physical correlation of the internal smoke rings of two knots that were once part of the same field configuration — exactly the non-local correlation that Bell showed must exist.
There is no faster-than-light signalling (no-signalling theorem holds), but genuine non-locality in the global EM field — precisely the kind required to violate Bell by $2\sqrt{2}$ (Tsirelson's bound).
LIMA-QTE is local in the Lagrangian, but once extended, topologically non-trivial objects (knots) are created together, their states remain globally correlated until measured.
Local realism fails for the same reason as in every QFT — and LIMA-QTE reproduces the failure perfectly, with no hidden variables.
Bell’s theorem is satisfied — and explained — by real knots of light that remember they were once the same knot.