Classical interpretation and derivation of wave particle duality relation has been done very recently usingNewtonian mechanics which is termed as Bag's wave of a particle.According to Bag's wave particle duality, wavelength of a moving particle is λ = b / p , instead of λ = h / p which is for de Broglie wave length of a particle.The constant 'b' is a function of opposition field and spin momentum of the particle.So far b is not characterized completely and not used for experimental purpose.In this article an approximate value of b is presented which is calculated using few assumptions.Calculated value of b differs from value of h.This discrepancy is addressed.It is also shown that at T = 4.8 × 10 -11 K, b and h become equal.This temperature is termed as equivalence temperature.
Classical interpretation and derivation of wave particle duality relation has been done very recently usingNewtonian mechanics which is termed as Bag's wave of a particle.According to Bag's wave particle duality, wavelength of a moving particle is λ = b / p , instead of λ = h / p which is for de Broglie wave length of a particle.The constant 'b' is a function of opposition field and spin momentum of the particle.So far b is not characterized completely and not used for experimental purpose.In this article an approximate value of b is presented which is calculated using few assumptions.Calculated value of b differs from value of h.This discrepancy is addressed.It is also shown that at T = 4.8 × 10 -11 K, b and h become equal.This temperature is termed as equivalence temperature.
In the particle-wave duality interpretation of matter and radiation (Topic G3) a particle moving in space can also be described as a wave in space with a wavelength related to the particle momentum by de Broglie’s equation, λ=h/p. In quantum mechanics, the notion of a particle moving in defined trajectories in a system is replaced entirely by this description of the system in terms of its wavefunctions, ψ. The wavefunction simultaneously describes all regions of space in which the particle it represents can be found. This, in turn, introduces the idea of uncertainty into quantum mechanics because the exact position of the particle at each point in time is not defined, only the region of space of all its possible positions. The exact shape of the wavefunction is important because the probability of finding the particle at each point is proportional to ψ2 at that point; a greater amplitude in the wavefunction corresponds to a greater probability density in the particle’s distribution.
The discovery of the Planck relation is generally regarded as the starting point of quantum physics. Planck’s constant h is now regarded as one of the most important universal constants. The physical nature of h , however, has not been well understood. It was originally suggested as a fitting constant to explain the black-body radiation. Although Planck had proposed a theoretical justification of h , he was never satisfied with that. To solve this outstanding problem, we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet. We find that the energy of the wave packet is indeed proportional to its oscillation frequency. This allows us to derive the value of Planck’s constant. Furthermore, we show that the emission and transmission of a photon follows the all-or-none principle. The “strength” of the wave packet can be characterized by ζ , which represents the integrated strength of the vector potential along a transverse axis. We reason that ζ should have a fixed cut-off value for all photons. Our results suggest that a wave packet can behave like a particle. This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck’s law.
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.
The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.
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.