Related papers: Kelvin Waves and Dynamic Knots on Vortex-Membrane
We extend our earlier study of the electroweak interactions of quantum knots to their gravitational and strong interactions. The knots are defined by appropriate quantum groups and are intended to describe all knotted field structures that…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate the probability of a trivial knot formation on the lattice…
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and…
Quantum oscillations (QO) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface…
The measurement problem of quantum mechanics concerns the question under which circumstances coherent wave evolution becomes disrupted to produce eigenstates of observables, instead of evolving superpositions of eigenstates. The problem…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
We analytically investigate the diffusive motion inferred from experimental observations of active particles driven by quantum vortices on the surface of superfluid helium. We first study the dynamical behavior of an active particle subject…
We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…