Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity ...Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.展开更多
Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but ev...Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but even identical, or to rephrase the main statement of this work: A gravitational force does not exist. Rather, gravity is a fictitious force, or, more pointedly: Gravity is the centrifugal force which acts upon material bodies within the rotating S3-hypersphere of the Universe. These in turn warp the adjacent space-fabric, shaping it to the well-known field geometry of general relativity.展开更多
Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable wit...Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose-Einstein condensate. We also elaborate on the theoretical framework for atomic Bose-Einstein condensation, which includes statistical mechan- ics and the Gross-Pitaevskii equation. As an extension, we discuss Bose-Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck＇s law in statistical mechanics. Further, a comparison is made between photon condensateand laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.展开更多
文摘Planck’s radiation law provides an equation for the intensity of the electromagnetic radiation from a physical body as a function of frequency and temperature. The frequency that corresponds to the maximum intensity is a function of temperature. At a specific temperature, for the frequencies correspond to much less than the maximum intensity, an equation was derived in the form of the Lambert <em>W</em> function. Numerical calculations validate the equation. A new form of solution for the Euler’s transcendental equation was derived in the form of the Lambert <em>W</em> function with logarithmic argument. Numerical solutions to the Euler’s equation were determined iteratively and iterative convergences were investigated. Numerical coincidences with physical constants were explored.
文摘Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but even identical, or to rephrase the main statement of this work: A gravitational force does not exist. Rather, gravity is a fictitious force, or, more pointedly: Gravity is the centrifugal force which acts upon material bodies within the rotating S3-hypersphere of the Universe. These in turn warp the adjacent space-fabric, shaping it to the well-known field geometry of general relativity.
文摘Bose-Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose-Einstein condensate （BEC） in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose-Einstein condensate. We also elaborate on the theoretical framework for atomic Bose-Einstein condensation, which includes statistical mechan- ics and the Gross-Pitaevskii equation. As an extension, we discuss Bose-Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck＇s law in statistical mechanics. Further, a comparison is made between photon condensateand laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.
