The paper "Physics on a Branched Knotted Spacetime Manifold" describes the core of the theory, and it gives necessary background for the rest of the papers. The other papers address specific topics in Knot Physics, and they can be read in any order.

This paper reproduces the dynamics of quantum mechanics with a four-dimensional spacetime manifold that is branched and embedded in a six-dimensional Minkowski space. Elementary fermions are represented by knots in the manifold, and these knots have the properties of the familiar particles. We derive a continuous model that approximates the behavior of the manifold's discrete branches. The model produces dynamics on the manifold that corresponds to the gravitational, strong, and electroweak interactions.

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Physics on a Branched Knotted Spacetime Manifold This paper reproduces the dynamics of quantum mechanics with a four-dimensional spacetime manifold that is branched and embedded in a six-dimensional Minkowski space. Elementary fermions are represented by knots in the manifold, and these knots have the properties of the familiar particles. We derive a continuous model that approximates the behavior of the manifold's discrete branches. The model produces dynamics on the manifold that corresponds to the gravitational, strong, and electroweak interactions. |
C. Ellgen & G. Biehle |

Knot Physics: Neutrino Helicity We use the assumptions of knot physics to prove that a collection of interacting neutrinos and antineutrinos maximize their quantum probability when all neutrinos are of the same helicity and all antineutrinos are of the opposite helicity. In a previous paper we showed that the geometry of gravity spontaneously breaks symmetry. We show here that the geometry of gravity couples the neutrino linear momentum to its quantum phase. Likewise, the quantum phase of an interacting neutrino couples to its spin angular momentum. Therefore, the symmetry breaking of gravity couples the linear momentum of an interacting neutrino to its spin angular momentum, producing consistent helicity. |
C. Ellgen |

Knot Physics: Deriving the Fine Structure Constant
Knot physics describes the geometry of particles and fields. In a previous paper we described the topology and geometry of an electron. From the geometry of an electron we can construct a mathematical model relating its charge to its spin angular momentum. From experimental data, the spin angular momentum is ℏ/2. Therefore the mathematical model provides a comparison of electron charge to Planck's constant, which gives the fine structure constant α. We find that using only electromagnetic momentum to derive the fine structure constant predicts a value for α |
C. Ellgen |

Knot Physics: Entanglement and Locality We describe entanglement and locality in knot physics. In knot physics, spacetime is a branched manifold. The quantum information of a system is encoded in the branches of the manifold. We show how that quantum information can persist despite the continual recombination of the branches of the manifold. We also note that the quantum collapse of state of the branches is non-local. That non-locality allows for non-local effects of entanglement without additional assumptions. We apply this description to the EPR paradox. |
C. Ellgen |

Knot Physics: Dark Energy We describe features of cosmology in knot physics that have the characteristics of dark energy. Knot physics assumes that spacetime is a branched 4-manifold embedded in a Minkowski 6-space. The cosmology of an embedded spacetime manifold is described by the expansion and contraction of the manifold in the embedding space. We show that the motion of the manifold in the embedding space contributes to the redshift of photons on the manifold. In this way, the embedded manifold model provides an alternative explanation for the redshift data that has been used as evidence for dark energy. |
C. Ellgen |

Knot Physics: Dark Matter
We describe dark matter in knot physics. Knot physics assumes that spacetime is a branched 4-manifold embedded in a Minkowski 6-space. The theory has three metrics. The Minkowski space has the standard Minkowski metric η |
C. Ellgen |