The Bridge Theory that is based on the role that the transversal component of the Pointing vector has in the localisation in the neighbourhood of a dipole of an amount of energy and momentum equal to ones of a photon of same frequency, if applied at the collision of a pair of real particles is able to describe their travel in space in agreement with the Relativistic Quantum Theory. This result suggests that Relativity and Quantum Mechanics despite their apparent incompatibility they become compatible if we assume the existence of a deepest level of reality in which is the electromagnetism to produce the quantum and relativistic effects in the matter allowing in the same context a dualism wave-particle equivalent to that hypothesized by Louis de Broglie.
The Bridge Theory that is based on the role that the transversal component of the Pointing vector has in the localisation in the neighbourhood of a dipole of an amount of energy and momentum equal to ones of a photon of same frequency, if applied at the collision of a pair of real particles is able to describe their travel in space in agreement with the Relativistic Quantum Theory. This result suggests that Relativity and Quantum Mechanics despite their apparent incompatibility they become compatible if we assume the existence of a deepest level of reality in which is the electromagnetism to produce the quantum and relativistic effects in the matter allowing in the same context a dualism wave-particle equivalent to that hypothesized by Louis de Broglie.
In the framework of Special Relativity and in agreement with the electromagnetic approach used to connect Quantum and Relativistic effects in Bridge Theory, a first order wave-equation able to emulate the wave-particle duality in terms of local electromagnetic interactions is proposed. The equation is able to describe the propagation of a fermion as a de Broglie's wave and simultaneously to characterise the wave in motion with a mass energy as a particle. The solution of the wave-equation proposed is compatible with the de Broglie's idea of an empty pilot wave, carrying information about the dynamical properties of a particle materialising during each local interaction with the observers.
A hypothesis is put forward according to which the formulas of Relativity are a consequence of the laws of quantum physics and may be applied only to quantum objects. According to the wave - particle duality quantum bodies are simultaneously the waves and considered in the present research with a use of the wave equation and requirement of its Lorentz‘s invariance. The property of invariance with respect to the Lorentz’s transform is analysed in hyperbolic coordinates in an area of complex numbers. An examination showed that formulas of relativistic kinematics can be obtained based on the condition of equality of the amplitudes and phases of the wave, observed from different inertial frames. There is no need to introduce the concept of a unified entity of space-time, but the return to the idea of aether and matter waves de Broglie occurs. The physical model becomes borrowed partly from quantum field theory. It is assumed that the moving particle binds to a wave of the aether disturbance, and only this wave acts on the other particle like an electromagnetic field pushes an electrical charge. The model of colliding elastic balls becomes inapplicable, but equations of relativity mechanics remain the same, however, with a new interpretation. The mass of a particle in all coordinate systems is constant, in exchange the expressions of energy and momentum alter relative the classical case, include the property of aether – coefficient c of the wave equation, and acquire relativistic forms.
Wave-particle duality is widely regarded as one of the conceptual pillars of modern quantum theory, providing the framework through which the behavior of microscopic matter can be consistently interpreted. According to this principle, microscopic entities such as electrons, photons, atoms and even complex molecules exhibit both wave-like and particle-like properties depending on the experimental configuration used to observe them. This duality is quantitatively formalized through the De Broglie relation, which associates a wavelength with any particle possessing momentum. The present work provides a comprehensive theoretical analysis of the physical and mathematical foundations of wave-particle duality, focusing particularly on the De Broglie wavelength and the kinetic energy of the electron in both non-relativistic and relativistic regimes. The connection between the De Broglie hypothesis and Schrödinger’s equation is discussed in detail, highlighting the role of the kinetic energy operator and the interpretation of matter waves in terms of quantum wave packets. Experimental evidence supporting the wave nature of matter, including electron diffraction experiments and interferometry techniques, is also reviewed. Beyond their conceptual importance, these principles underpin several modern technologies, including electron microscopy, nanoscale semiconductor devices and quantum metrology. The analysis demonstrates that the De Broglie relation provides a unifying framework connecting momentum, wavelength and kinetic energy, thereby forming a fundamental bridge between classical mechanics, quantum theory and modern technological applications.
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.
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.