Planck Constant in the Special Theory of Relativity (Fast Wave–Wave–Particle Triality)

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.