Abstract
In this paper, starting from Biot–Savart mechanics for entangled vortex-membranes, a new theory — knot physics — is developed to explore the underlying physics of quantum mechanics. Owning to the conservation conditions of the volume of knots on vortices in incompressible fluid, the shape of knots will never be changed and the corresponding Kelvin waves cannot evolve smoothly. Instead, the knot can only be split. The knot-pieces evolve following the equation of motion of Biot–Savart equation that becomes Schrödinger equation for probability waves of knots. The classical functions for Kelvin waves become wave-functions for knots. The effective theory of perturbative entangled vortex-membranes becomes a traditional model of relativistic quantum field theory — a massive Dirac model. As a result, this work would help researchers to understand the mystery in quantum mechanics.
Highlights
In pseudo-quantum mechanics, there are three conserved physical quantities for helical vortex-membranes: the energy H(pLamb) that is proportional to the volume of the vortex-membrane VP = volume(P ); the momentum pLamb that is proportional to the winding number along given direction w1D; and the (Lamb impulse) angular momentum that is proportional to the volume of the vortex-membrane in the 5D fluid VP · πr[02]
The quantization of Kelvin waves is similar to quantization of a matter wave in quantum mechanics: a constant JLamb plays the role of the Planck constant eff, mpseudo plays the role of mass in Schrodinger equation, and so on
In pseudo-quantum mechanics, there are three conserved physical quantities for entangled vortex-membranes: the total energy H(pLamb) that is proportional to the total volume of the two vortex-membranes VP = volume(P ); the total momentum pLamb that is proportional to the linking number between two vortex-membranes; and the total (Lamb impulse) angular momentum that is proportional to the total volume of the two vortex-membranes in the 5D fluid VP · r02
Summary
Kelvin found a transverse and circularly polarized wave[1] (called Kelvin wave), in which the vortex-lines twist around their equilibrium position forming a helical This is an Open Access article published by World Scientific Publishing Company. Kelvin and Toit tried to develop an early atomic theory that is linked to the existence and dynamics of knotted vortex-rings in ether. They failed — the fundamental structure of atoms is irrelevant to knots. We develop a new theory towards understanding quantum mechanics based on three-dimensional (3D) leapfrogging vortex-membranes in fivedimensional (5D) incompressible fluid. It is the 3D quantum Dirac model that characterizes the knot dynamics of leapfrogging vortex-membranes.
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