Papers

We use principles from the thermodynamics of spacetime to modify the path integral of quantum mechanics. Entropy of the vacuum is interpreted as microstates that correspond to the measure of the path integral. The result is a contribution to the action that is proportional to the Einstein-Hilbert action. Because the contribution is real, not imaginary, it is unlikely to cause convergence problems. Paths that minimize the Einstein-Hilbert action make the largest contribution to the path integral, implying that the maximum likelihood paths are solutions of the Einstein equation.

Garrett Biehle, Clifford Ellgen, Bassem Sabra, & Sebastian Zając

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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

(Minor updates made on 8/23/2021)

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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 \(\alpha\);. We find that using only electromagnetic momentum to derive the fine structure constant predicts a value for \(\alpha^{-1}\) that is about two orders of magnitude too small. However, the equations of Knot Physics imply that the electromagnetic field cusp must be compensated by a geometric field cusp. The geometric cusp is the source of a geometric field. The geometric field has momentum that is significantly larger than the momentum from the electromagnetic field. The angular momentum of the two fields together predicts a fine structure constant of \(\alpha^{-1} \approx 136.85.\) Compared to the actual value of \(\alpha^{-1} \approx 136.85,\) the error is \(0.13 \% .\) Including the effects of virtual particles may reduce the error further.

C. Ellgen

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Calculations as Mathematica files:

• Fine structure constant calculation: knot_fine_structure_calculate.nb
• Calculation function verification: fine_structure_function_verification.nb

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

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We assume that spacetime is embedded in a Minkowski space and the metric on spacetime is induced by the Minkowski metric. Expansion of spacetime causes a redshift that corresponds to the usual cosmological redshift of general relativity. Changing expansion velocity also affects the redshift and introduces an additional term that is not included in the redshift effect attributed to general relativity. This extra contribution may explain the difference between astronomical data and the redshift predictions of general relativity.

C. Ellgen

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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 \(\eta_{\mu\nu}.\) The second metric, \(\bar \eta_{\mu\nu},\) is just the restriction of \(\eta_{\mu\nu}\) to the spacetime manifold. In a previous work, we showed how mass and energy affect the curvature of \(\bar \eta_{\mu\nu}\) , reproducing results of general relativity. The third metric, \(g_{\mu\nu},\) is used to constrain the branches of the spacetime manifold. In this paper, we derive an approximate relationship between \(\bar \eta_{\mu\nu}\) and \(g_{\mu\nu}.\) The relationship implies \(\bar \eta_{\mu\nu}\) can have non-zero Ricci curvature without a massive source particle. We show how this result has many of the characteristics of dark matter.

C. Ellgen

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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

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In a previous work, we describe a branched four-dimensional spacetime manifold embedded in a six-dimensional Minkowski space. In this paper, we provide additional information about the geometry of the vacuum. In this description, the classical vacuum can be described as Lorentz invariant, and the quantum vacuum is best described as Lorentz isotropic. We provide evidence that the vacuum has properties corresponding to a vacuum energy and a vacuum temperature.

C. Ellgen & B. Sabra

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