3.Wave–Particle Duality as a Classic Phenomenon

Abstract: 
The hypothesis that both the universe and particles have four spatial dimensions and the quantification of space allow the application of the equations of macroscopic classical physics to elementary particles, so that purely quantum phenomena such  as quantum entanglement, quantum tunnelling, and so on can be explained through classical physics. This paper explains wave–particle duality as a unique phenomenon; the particle produces disruption of the medium (space, atoms, and time), generating a wave in the same way that a wave is generated in water

Keywords: 4D universe, discrete space, Planck length.

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 1. Introduction
Special relativity shows that space and time should be considered as a single physical entity, space-time. As the universe has three spatial physical observable dimensions, it is common to refer to time as the "fourth dimension" and space-time as "four-dimensional space". The second principle of special relativity states that the speed of light in a vacuum c is a universal constant, independent of the movement of the observer.

In general relativity, Einstein described gravitation using four dimensions, which proved to be necessary and sufficient, such that gravity is due to the spatial curvature. In general relativity, all energy is curvature. The curvature is a fundamental concept used in general relativity and quantum mechanics.


 General relativity assumes that space-time is continuous. However, there is no experimental evidence for this. Are space and time continuous? Or do we just believe it due to the conditioning of education? In recent years, physicists and mathematicians have questioned whether it is possible that space and time are discrete.

Lee Smolin wondered whether, if it were possible to analyses sufficiently small space scales, we would see "atoms" of space: irreducible pieces of volume that could not be broken down into anything smaller [1]. Quantification of space-time preserves relativistic invariance [2] and causality and distinguishes elementary particles in a simple and natural way [3].

The minimum values of volume, length, or area are measured in Planck units [1]. The theories related to quantum gravity, such as strings theory, doubly special relativity, and black hole physics, predict the existence of a minimum length [4, 5], on the size of the Planck length.

“The familiar concept of a “space-time continuum” implies that it should be possible to measure always smaller and smaller distances without any finite limit. Heisenberg, who insisted on expressing quantum mechanical laws in terms of measurable observables, questioned already the validity of this postulate [6]. We should thus treat the ultimate limit a for the smallest measurable length as a yet unknown quantity. Actually, we learned already from the development of relativity and quantum mechanics that Nature can impose  restrictions on our measurements because of two universal constants: the velocity c and the quantum of action h. Could Nature impose a third restriction, resulting from the existence of a universally constant quantum of length a and a universally constant quantum of time a/c?” [3]

“… a fundamental (minimal) length scale naturally emerges in any quantum theory in the presence of gravitational effects that accounts for a limited resolution of space-time. As there is only one natural length scale we can obtain by combining gravity (G), quantum mechanics (ħ) and special relativity (c), this minimal length is expected to appear at the Planck scale.” [7] 
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7. Conclusion
Heisenberg said that physics must have a fundamental length scale, which together with the Planck constant and the speed of light, permits the derivation of the masses of particles.

The Einstein field equation has a geometric interpretation indicating, as Einstein believed, that physics is geometry. Not only does the geometry describe the physics, but all physics is based on geometry. The geometry of space-time explains the atomic scale and allows the intrinsic properties of the particles to be calculated. According to Einstein, "God does not play dice".

Simply with the rotation of the space and time atoms in space and time (or the fourth dimension), the properties of the particles such as mass, charge, spin, and so on can be deduced and calculated.

Particle: Assuming that space-time is discrete with a diameter equal to the Planck length (Fig. 1), equations of classical physics can be applied to the macroscopic particles. Specifically, applying the gravitational potential (Eq. (3)) and the speed of rotation (Eq. (4)), to the particle, like a flat disk, allow us to conclude that the energy (mass) of the particle is due to the rotation of the particle (Eq. (6)) and the electric charge (Eq. (15)) is due to the period of the particle. 

Wave: The rotating Planck atom causes that the adjacent atoms (attached by Planck force) also rotate, causing the perturbation in the environment and generate the observed wave. Not only the energy of the particle and the energy of the wave are equivalent, but also the rotation of the particle in the fourth dimension generates the mass and the charge of the electron

The hypothesis that space-time is discrete can explain what the mass and charge are and also allows the value of the two constants to be calculated.

The current universe consists of different particles, energy, and space-time vacuum; all these elements originated from the energy of the Big Bang. It is assumed that they were initially identical and remain identical. As Einstein believed, light is simultaneously a particle and a wave.

Einstein assumed that the electron is the most important particle of the universe. While the electron turns completely in a three-dimensional space, it turns just half lap into the fourth dimension, which causes the observed particle to look backwards, with spin ½. 

The old intuition that something has to be at "absolute rest" (the atom of space and time) was correct. According to Messeen “the system of highest possible rest-energy Eu has to be at rest“ [3].

"... It is very difficult even for the most daring thinkers to abandon the beliefs that have persisted for millennia."

Lee Smolin


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