Aims: The Planck’s constant has two parts; one part shows the 'rest action', 'rest energy' of waves and another part shows the 'kinetic action', 'kinetic energy' of waves. These two parts change in a synchronized manner and they make possible a superluminal velocity of the particle in tunneling. Particles (waves) with superluminal velocity are fast waves. Methodology: The de Broglie wavelength describes wave-particle duality. The de Broglie wavelength formula and Planck’s law seem to be contradicted in tunneling. Tunneling fast waves have longer wavelengths than waves. According to the de Broglie formula, a longer wavelength means smaller momentum (smaller energy). But fast waves have the same amount of energy as normal waves, since they can be transformed into each other. The barrier in tunneling cannot be seen as an optical medium, rather a special kind of space made out of matter that other matter is able to use as space. Here we show that the 'rest actions', 'rest energies' of fast waves in different spaces can resolve the contradiction. This 'rest action' of the wave is a new concept that hasn't been considered. It is hidden in the Planck constant. Planck’s constant doesn’t change, but it has two changing parts. The two parts of Planck’s constant work together. The values of these parts depend on the velocity of the fast wave. Comparing these two parts, we can introduce the moving indicator of the particle called ő. (Pronunciation is ɜː like her). Calculating ő, we are able to say how fast the particle (fast wave) travels compared to the given space. Results: Fast waves are made out of normal waves (or particles). The fast wave is the same particle in a different form. The Fast Wave–Wave–Particle Triality describes a new kind of metamorphosis of matter—how tunneling electrons travel faster than light without violating special relativity. Using the Fast Wave–Wave–Particle Triality, we realize that the speed of light is not a speed limit for particles with mass, since they can be transformed into fast waves. The Fast Wave–Wave–Particle Triality shows the border of scope of the special theory of relativity.
Aims: The Planck’s constant has two parts; one part shows the 'rest action', 'rest energy' of waves and another part shows the 'kinetic action', 'kinetic energy' of waves. These two parts change in a synchronized manner and they make possible a superluminal velocity of the particle in tunneling. Particles (waves) with superluminal velocity are fast waves. Methodology: The de Broglie wavelength describes wave-particle duality. The de Broglie wavelength formula and Planck’s law seem to be contradicted in tunneling. Tunneling fast waves have longer wavelengths than waves. According to the de Broglie formula, a longer wavelength means smaller momentum (smaller energy). But fast waves have the same amount of energy as normal waves, since they can be transformed into each other. The barrier in tunneling cannot be seen as an optical medium, rather a special kind of space made out of matter that other matter is able to use as space. Here we show that the 'rest actions', 'rest energies' of fast waves in different spaces can resolve the contradiction. This 'rest action' of the wave is a new concept that hasn't been considered. It is hidden in the Planck constant. Planck’s constant doesn’t change, but it has two changing parts. The two parts of Planck’s constant work together. The values of these parts depend on the velocity of the fast wave. Comparing these two parts, we can introduce the moving indicator of the particle called ő. (Pronunciation is ɜː like her). Calculating ő, we are able to say how fast the particle (fast wave) travels compared to the given space. Results: Fast waves are made out of normal waves (or particles). The fast wave is the same particle in a different form. The Fast Wave–Wave–Particle Triality describes a new kind of metamorphosis of matter—how tunneling electrons travel faster than light without violating special relativity. Using the Fast Wave–Wave–Particle Triality, we realize that the speed of light is not a speed limit for particles with mass, since they can be transformed into fast waves. The Fast Wave–Wave–Particle Triality shows the border of scope of the special theory of relativity.
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on
Louis-Victor de Broglie secured his place in the history of quantum physics by proposing the existence of matter waves. Following the concept accepted early in the twentieth century that light waves could display properties characteristic of particles (photons), de Broglie suggested the complementary principle that particles could display properties characteristic of waves. Within a few years, this far-reaching proposal was experimentally verified. The well-known formula for the wavelength λ of the wave associated with a particle of momentum p, namely λ=h/p, does not appear in de Broglie’s original paper, which was published in this journal in 1924. What is derived from the starting assumption that the frequency of the wave is the rest energy of the particle divided by Planck’s constant h, is the wave's velocity, which turns out to be c2/v, where v is the particle’s velocity. This velocity, being superluminal, means that the wave cannot transport energy. De Broglie called it a phase wave and postulated a group of such waves having virtually, but not exactly, the same velocity and wavelength. The group velocity of such a large number of almost identical phase waves is then shown, very satisfactorily, to be equal to the velocity of the particle. The proposal by de Broglie inspired Schrödinger to develop the mathematical foundations of wave mechanics. Whereas in conventional quantum theory, phase waves are considered fictional, de Broglie considered them to have a certain physical reality, renaming them pilot or guiding waves – a concept developed later by Bohm in 1952.
In this paper we demonstrate duality between matter and light. Through mathematical derivation we show that every fundamental matter particle with non-zero rest mass can be represented by a pair of photons. The photons in the representation are not normal photons but a special kind of continuously generating and annihilating virtual photons, whose wave functions super impose to give the wave function of the non-zero rest mass particle and the representation is in agreement with the spin of the particle. We use this duality to derive De Broglie wavelength. We show that a moving matter wave has two frequency components, one of it is with De-Broglie wavelength h/P and the other one is with wavelength hc/E. We also correct the De-Broglie wavelength for v = 0 where we show that there is only one frequency component for v = 0 with wavelength hc/E. Later in the paper we derive that every photon can be represented by a non-zero rest mass particle pair, one going below the speed of light and the other going above the speed of light.
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. According to the special relativity theory, the group velocity with which the overall envelope shape of the wave, namely the related particle’s propagation and information convey speed is changeable with its energy and related wavelength, among which only the energy exceeds over the minimum value, the propagation can be starting and the velocity is not allowed to surpass the maximum value i.e. the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 8.187×10ˉᴵ⁴J and the related wavelength is shorter than around 5.316×10ˉᴲnm, the matter wave can start to propagate.
In this article, it is shown that if a particle is at rest and has some harmonic oscillation, then a traveling particle with a constant speed corresponds to a De Broglie Wave.In 1924, De Broglie proposed that particles of matter exhibit wave like behavior, the expression for which became fundamental in the creation of wave mechanics (quantum mechanics).The main equation for this is the Schrödinger equation, which in the case of free motion of a particle becomes the expression for the De Broglie wave.This hypothesis is supported by many early experiments on the diffraction of electrons, and later the development of modern physics.However until now, the origin of this hypothesis remains unclear.We show that the expression for the De Broglie wavelength can be obtained from a more general well-known concept, that any particle at rest has a corresponding harmonic oscillation that transforms into a wave of a moving particle with the help of relativistic change of coordinates (the Lorentz transformations).In this way, a De Broglie wave can be explained as a spacetime wave.