The Quantum Wave Theory of Relativity

Xiaogang Ruan

In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.

Léon Brillouin

Caio Lima Firme

This chapter presents the double-slit experiment and Davisson-Germer’s corresponding experiment that proved the wave-like nature of the electron in 1927. Next, it shows the basics of the special theory of relativity which is used by de Broglie to obtain the wave-particle duality. Afterwards, it displays the most important properties of a periodic wave along with the concepts of travelling wave, composite wave, group velocity, wave packet and single wave packet. These sections are the basis for understanding the de Broglie’s work where he used the special theory of relativity, Einstein’s quantum theory of light and the features of the periodic waves to obtain his famous constant relation of the product of linear momentum (of a particle) and wavelength (of a wave) which became the most important quantum concept used by Schrödinger to develop the quantum wave theory. In the end, a do-it-yourself activity is also given in order to plot several wave packets. (153 words).

J. Manuel Oliveira

Wave-particle duality, the revolutionary concept that particles can exhibit both wave-like and particle-like properties, was first proposed by Louis de Broglie. His equations connecting a particle's energy and momentum to the properties of its corresponding wave laid the groundwork for quantum mechanics. This fundamental principle explains the surprising results of the double-slit experiment and underlies many of quantum mechanics' unique behaviors.In this work, relying solely on Einstein's two postulates of special relativity, and the idea that time is single valued, we will demonstrate that a complete theory of relativity predicts a wave-like quantizable behavior for particle trajectories. We will prove that the theory of relativity predicts a first-order, spin-independent transport equation as an equation of motion for particles, in addition to the classical relativistic Hamiltonian.As key results, we will demonstrate that our theory provides an integrable solution for a free scalar particle, offering insights into the wave-particle duality observed in nature. For spinor particles, we will show that our theory generalizes Weyl theory to accommodate massive particles, while also allowing for modified Dirac-like particles.

Gleb Wataghin