Stable Knots and Links in Electromagnetic Fields

Bode, Benjamin

doi:10.1007/s00220-021-04219-3

Cited by 4 publications

(4 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, it remains to demonstrate that the conclusions of astrophysicists are strongly backed up by the fundamental laws/principles of quantum mechanics and electrodynamics. This then will help us to strengthen the arguments by astrophysicists by accounting for the knotty nature of the Maxwellian electrodynamics [15,41,54,55,63,80]. The existing quantization for electromagnetic fields do not contain any information about knots/links.…”

Section: Chladni Patterns In the Sky Or How Topological Nature Of Mas...mentioning

confidence: 92%

“…Therefore, Equation ( 59) implies that such PEP's are all massive nonhyperbolic knots. In the presence of boundaries, the formation of hyperbolic knots is also possible, as discussed in detail in [55] and differently in [80]. However, the negativity of masses is unphysical and, therefore such (hyperbolic) knots must be discarded.…”

Section: Restoring Kelvin's/thompson's Vortex Atoms With Help Of Quan...mentioning

confidence: 99%

“…in Equation ( 77) converts this (Dirac) equation into the system of Maxwell's Equation ( 1) [101]. The wave function (80) is not the only one converting the massless Dirac equation into the system of source-free Maxwell's equations. Following [102], we write down the set of all wave functions accomplishing the same task.…”

Section: The Proof Of Bijectivity Of Maxwell-dirac Mappingmentioning

confidence: 99%

“…However, as it was extensively discussed in this work, it is because they are essential for the existence of Ranada's knotty charges. Furthermore, the stability of these knotty structures (or their ability to disintegrate) is also linked with the existence of null fields [80,157]. Moreover, stabilities of knots require applications of contact geometry and topology [37,158].…”

Section: From Projective Relativity To Knotty Geometrodynamicsmentioning

confidence: 99%

See 3 more Smart Citations

Maxwell-Dirac Isomorphism Revisited: From Foundations of Quantum Mechanics to Geometrodynamics and Cosmology

Kholodenko

2023

Universe

View full text Add to dashboard Cite

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein’s equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics” as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada’s work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler’s geometrodynamics. They were added to it in the 1960s by Geroch. Ranada’s solutions of source-free Maxwell’s equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole.

show abstract