This idea of quantifying the energy of bodies orbiting the Sun is not new. We have identified that quantization applies well if we use the true quantum number associated with the true energy state of rotating bodies. ...This idea of quantifying the energy of bodies orbiting the Sun is not new. We have identified that quantization applies well if we use the true quantum number associated with the true energy state of rotating bodies. This quantum number is very high for the main bodies or planets (10<sup>~70 to 76</sup>). However, since quantum energy levels E are very high and ΔE very low we observe that bodies can in practice occupy all orbits. Thus, the current observed stable positions of the bodies are the results of the quantization and the sum of the effects of other perturbative phenomena. To find a quantum state starting with n = 1, we expressed the true integer quantum numbers as a function of that of the planet Mercury and we find an excellent correlation. However, the search for a correlation of prediction of the average orbital radius of bodies using the simple integer number n = 1, 2, 3, 4, 5, 6, 7, … is not excellent for bodies beyond the planet Pluto. Indeed, several trans-Neptunian bodies have similar integer quantum numbers, which poses a problem in the sequence of integer numbers beyond 10. Moreover, it appears that the trans-Neptunian bodies seem to be grouped for many of them according to relatively well-defined bands. The study made it possible to question the de Broglie wavelength of bodies (10<sup>~-58 to -65</sup> m). Indeed, with the hypothesis of Planck quantities that would apply to the scale of the universe, it is difficult to conceive that de Broglie wavelengths are less than the Planck length l<sub>p</sub>. This led to an expression of the modified de Broglie wavelength λ<sub>m</sub> that predicts an asymptotic lower limit value equal to πl<sub>p</sub>. This modified de Broglie wavelength makes it possible to obtain a better correlation for the prediction of the average orbital radius of bodies. Finally, this modified wavelength of de Broglie made it possible to put into perspective the concept of the quantification of space with the idea of the minimum wavelength associated with photon’s energies during the generation of the energy of the universe according to a model already presented in this review. This modified de Broglie wavelength also makes it possible to imagine that the quantification of the volume of space involves the geometry of the sphere and the cube.展开更多
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects...A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.展开更多
文摘This idea of quantifying the energy of bodies orbiting the Sun is not new. We have identified that quantization applies well if we use the true quantum number associated with the true energy state of rotating bodies. This quantum number is very high for the main bodies or planets (10<sup>~70 to 76</sup>). However, since quantum energy levels E are very high and ΔE very low we observe that bodies can in practice occupy all orbits. Thus, the current observed stable positions of the bodies are the results of the quantization and the sum of the effects of other perturbative phenomena. To find a quantum state starting with n = 1, we expressed the true integer quantum numbers as a function of that of the planet Mercury and we find an excellent correlation. However, the search for a correlation of prediction of the average orbital radius of bodies using the simple integer number n = 1, 2, 3, 4, 5, 6, 7, … is not excellent for bodies beyond the planet Pluto. Indeed, several trans-Neptunian bodies have similar integer quantum numbers, which poses a problem in the sequence of integer numbers beyond 10. Moreover, it appears that the trans-Neptunian bodies seem to be grouped for many of them according to relatively well-defined bands. The study made it possible to question the de Broglie wavelength of bodies (10<sup>~-58 to -65</sup> m). Indeed, with the hypothesis of Planck quantities that would apply to the scale of the universe, it is difficult to conceive that de Broglie wavelengths are less than the Planck length l<sub>p</sub>. This led to an expression of the modified de Broglie wavelength λ<sub>m</sub> that predicts an asymptotic lower limit value equal to πl<sub>p</sub>. This modified de Broglie wavelength makes it possible to obtain a better correlation for the prediction of the average orbital radius of bodies. Finally, this modified wavelength of de Broglie made it possible to put into perspective the concept of the quantification of space with the idea of the minimum wavelength associated with photon’s energies during the generation of the energy of the universe according to a model already presented in this review. This modified de Broglie wavelength also makes it possible to imagine that the quantification of the volume of space involves the geometry of the sphere and the cube.
文摘A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.
