Gravitation and wave-particle duality revisited

This section discusses the case of micro-universe of atoms and elementary particles, and relationships to manage de Broglie matter waves.

Let us now try to construct or exercise what could be the macro-universe equivalent to de Broglie matter-waves concept. The idea here is to show that planets and similar macro objects are also respecting certain periodicity and “macro matter-waves packaging rules”, like de Broglie matter waves in a micro universe. The best for exercising such brainstorming is to start from the Kepler’s third law (of planetary orbital motions), which is also applicable to all satellite motions around certain planet or big mass. Let us temporarily focus our attention only to pure circular rotations, where radius of rotation is r, in order to use simpler mathematical expressions. Kepler’s third law is showing that period T of planetary (or satellite) orbiting around a mass M (or its sun) is given by (2.11.10),

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This paper is dealing with innovative aspects of particle-wave duality, gravitation and electromagnetic theory addressed from the point of view of electric and mechanical analogies united with continuous Symmetries. This is also a discussion document with objectives to initiate the revision of particle-wave dualism and gravitation theory, by presenting one specific system of overall electromechanical analogies (extended mobility type of analogies), which is established after:

1. Analogies taken from the similarity of relevant mathematical formula expressions and belonging differential equations;
2. Analogies coming from the same geometry or same topology of equivalent circuits or models;
3. Analogies created after comparing higher level of energy and force formulas, as well as comparing different Conservation Laws.

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Based on the established system of analogies, several innovative ideas are formulated, regarding possible generalization and unification of Gravitation, Maxwell Electromagnetic Theory and Quantum Theory in the frames of new understanding of Particle Wave Duality. Of course, we have to be conscious that any conclusion based (only) on analogies is at the same time very powerful, if correct, and very risky and weak if it is not correctly developed and applied, and this is the reason why analogies in this paper are taken only as initial new idea generators.

The “foggy concept” of Particle Wave Duality known from our contemporary physics (or Quantum Theory) is very much elaborated in this paper, becoming the concept of “Particle Wave Unity” (here formulated also as PWDC (=) Particle Wave Duality Code). It is also shown that all important wave equations and Uncertainty relations of Orthodox Quantum Theory can be logically, naturally and step by step developed without even knowing that Quantum Theory exist, and without any of “probability philosophy” backing.

The specific innovative achievements, or just creatively formulated hypothetical ideas and proposals of this paper, can be briefly summarized as contributions related to:

1. New ways of seeing Gravitation in the frames of stationary and resonant, standing-waves states of masses or energy agglomerations. Schrödinger type of wave equation is also applicable to Gravitation. In reality Gravitation is just a specific form of weak electromagnetic attractive force.
2. All matter in our universe can be seen in number of packaging or formatting states of matter waves, where de Broglie matter waves are just a small piece of the global picture. New definition of generalized matter waves’ periodicity is replacing old concept of matter waves.
3. Uncertainty Relations known in Physics and Mathematics can be significantly extended to all matter states, valid for micro and macro Universe. The elementary matter domains, like elementary particles, are well defined by different understanding of extended Uncertainty Relations, taking the shady and boundary space between mutually conjugated Original and Spectral domains.
4. And much more about waves, velocities and wave equations. All of that as a consequence of complementary nature of united linear and rotational motions, very much similar to complementary nature inside electromagnetic fields.

A wider and more general platform for extending and exploiting the analogies in physics is to be found in exploiting Symmetries. The following, supporting segment is taken from the book [10] written by Michio Kaku (see also [11], from the same author): “… we are beginning to realize that nature, at the fundamental level, does not just prefer symmetry in a physics theory, nature demands it. Physicists now realize that symmetry is the key to constructing physics laws without disastrous anomalies and divergences.”

Of course, we need to be extremely careful regarding correct foundations of relevant Symmetries, and author of this paper is proposing the self-correcting and self-supporting strategy of united multilevel Analogies and continuous Symmetries, as a basis for Physics managements, advances and generalizations.

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