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A never ending story

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Hans van LeunenRSS Feed of this column.

I am a retired Physicist (born in 1941) with experience in chemistry, Fourier optics, image intensifiers, quantum logic, quantum physics, modular software. Stumbled into the quaternion waltz (c=ab/a)... Read More »

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The medium in which light propagates is space. This space can curve. The curvature is not static. So, this space moves. Its behavior can be analyzed by a kind of fluid dynamics. Let us call this method quantum fluid dynamics. It differs from conventional fluid dynamics in the medium that is treated. In conventional fluid dynamics this is a gas or a fluid. Fluid dynamics concerns density distributions and currents. In quantum fluid dynamics these are space density distributions and space current density distributions. They can be combined in quaternionic distributions, where the real part is the space density distribution and the imaginary part is the space current density distribution.

People can already count since several millennia. Arithmetic is improved over time. Usually we count by using integers. If we want to get more accurate results, then we better use rational numbers. Sometimes we also use numbers that are not expressible in a fraction, such as the number π (pi) and the square root of two . These are real numbers. The square root of a negative number delivers more problems. For this task it is necessary that we move to a two-dimensional number system. The better calculators under us can also handle this problem fluently. The so-called complex numbers are discovered in the sixteenth century by the Italian mathematician Gerolamo Cardano and are now used for all kinds of applications.


Introduction

It is a mathematical fact that both the real numbers and the rational numbers contain an infinite amount of elements. It is possible to devise a procedure that assigns a label containing a different natural number to every rational number. This is not possible for the real numbers. Technically this means that the set of real numbers has a higher cardinality than the set of rational numbers. In simple words it means that there are far more real numbers than there are rational numbers. Still both sets can densely cover a selected continuum, such as a line. However, the rational numbers leave open places,because infinite many real numbers fit between each pair of rational numbers.

This article eliminates the need for the Higgs.

The quaternionic equation of motion of an elementary particle is in fact a continuity equation in which another quaternionic flavor ψʸ of the transporting field ψˣ is coupled with that transporting field via a source term. The coupling factor acts as the mass of the corresponding particle.

This fact comes into the foreground when the Dirac equation is converted from its spinor based form to the much cleaner quaternionic form. After stripping away the matrices and reducing the spinors to a single element, the quaternionic Dirac equation for a free particle runs:

  ∇ψ = m ψ*

or

  ∇*ψ* = m ψ

A derived equation is

  ∇(ψ ψ) = m (ψ ψ*) = 2 m|ψ|²

This paper introduces a new model of physics. It is based on logic. It uses the congruence between the logic of quantum physics and a mathematical construct that got its name from David Hilbert. The Hilbert book model extends this construct such that fields and dynamics also fit in the new model.

Introduction

Every time when I read an article about the phenomena, which occur far from us in the universe, I'm surprised about the attention that this Farawayistan gets compared to the phenomena in the world of the smallest. Everything that happens there is dismissed with collective names such as “quantum mechanics” and “field theory”. Rarely or never the treatise goes deeper. In this sub-nano-world spectacular images, such as appear in stories about the cosmos are not available.

In its first years the development of quantum physics occurred violently. As a consequence some cracks sneaked into the fundaments of this branch of physics. A careful investigation brings these cracks to the foreground. The endeavor to repair these cracks delivers remarkable results.

In the early days of quantum physics much attention was given to equations of motion that were corrections of classical equations of motion. The Schrödinger approach was one and the Heisenberg approach was another. Schrödinger used a picture in which the state of a particle changes with time. Heisenberg uses a picture in which the operators change with time. For the observables this difference makes no difference.