Mathematics of Particle-Wave Mechanical Systems

The existence of dark energy and matter suggests that conventional mechanical accounting is lacking. This monograph proposes a novel proposal to account for mass and energy through a combined particle-wave theory, which replaces Newtons second law of motion with a fully Lorentz invariant reformulation. Dark matter and energy emerge as special or privileged states occurring for alignments of spatial forces with the force in the direction of time, both propagating at the speed of light. The model includes special relativistic mechanics and Schrödingers quantum mechanics and may lead to faster than light travel.

Format: Hardback
Length: 378 pages
Publication date: 01 December 2022
Publisher: Springer International Publishing AG

Despite the remarkable achievements of modern physics, the presence of dark energy and matter suggests that conventional mechanical accounting is insufficient. At its core, the most fundamental principle of mechanical theory is Newton's second law, which states that energy is simply energy, whether it manifests as particle or wave energy. In this monograph, we explore Louis de Broglie's concept of the simultaneous existence of both particles and associated waves, proposing a novel approach to account for mass and energy through a combined particle-wave theory.

Newton's second law of motion is replaced by a fully Lorentz invariant reformulation that encompasses both particles and waves. This model originates from continuum mechanics and serves as a natural extension of special relativistic mechanics. It introduces the notion of "force in the direction of time," where each particle possesses both particle and wave energies, arising as properties of space and time, respectively. Dark matter and energy then emerge as special or privileged states that occur when spatial forces align with the force in the direction of time.

Dark matter is essentially a backward wave, while dark energy is a forward wave, both propagating at the speed of light. The model incorporates special relativistic mechanics and Schrödinger's quantum mechanics, encompassing the significant advancements in mechanics and quantum physics. However, our current understanding of particles and waves remains incomplete, largely tied to the speed of light as an extreme limit and the distinction between particle-wave demarcation. Sub-luminal particles possess an associated superluminal wave, suggesting the possibility of faster-than-light travel with profound implications for the future of humanity.

This monograph is carefully structured to delve into the complexities of special relativity and quantum mechanics, providing a comprehensive exploration of the mathematical foundations underlying the proposed particle-wave theory. By unraveling the mysteries of dark energy and matter, we aim to shed light on the fundamental nature of the universe and open up new avenues for scientific inquiry and technological advancement.

Weight: 752g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031197925
Edition number: 1st ed. 2022