Obtaining the relativistic formula for the refraction of light and the practice of its application

The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to T10 -7h10 -5 in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

Obtaining the relativistic formula for the refraction of light and the practice of its application

The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to T10 -7h10 -5 in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

New dispersion formula and results of its application

The aim of the study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to a wide range of transparent substances. In the process of research on the basis of Einstein's relativistic formula, such a dispersion formula was obtained. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which was ±10 -7 − 10 -5 in the calculated wavelength ranges of more than 100 nm.The new dispersion formula is obtained on the basis of the mathematical dependence of the speed of propagation of photons in a transparent substance on the energy density of electron clouds of atoms of the substance. Energy is a universal category, therefore, it is possible to apply the basic version of the new formula (where instead of the wavelength there is the energy density of electron clouds) when conducting research in all areas of light generation, manipulation and detection.And, finally, the very fact of applying the adapted relativistic Einstein's formula to physical processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

«New dispersion formula and results of its application»

The aim of the study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to a wide range of transparent substances. In the process of research on the basis of Einstein's relativistic formula, such a dispersion formula was obtained. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which was ±10 -7-10 -5 in the calculated wavelength ranges of more than 100 nm. The new dispersion formula is obtained on the basis of the mathematical dependence of the speed of propagation of photons in a transparent substance on the energy density of electron clouds of atoms of the substance. Energy is a universal category, therefore, it is possible to apply the basic version of the new formula (where instead of the wavelength there is the energy density of electron clouds) when conducting research in all areas of light generation, manipulation and detection. And, finally, the very fact of applying the adapted relativistic Einstein's formula to physical processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

Gravity, the origin of the mass in the Cosmos

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

Gravity, the origin of the mass in the Cosmos.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

Gravity, the origin of the mass in the Cosmos.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

Gravity, the origin of the mass in the Cosmos.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

How close is our ΛCDM physical universe to de Sitter spacetime dS4?

We introduce a methodology for quantitatively measuring at all times in its evolution how close our physical spatially flat [Formula: see text] CDM universe with cosmological constant [Formula: see text] is to the de Sitter spacetime [Formula: see text] with de Sitter radius [Formula: see text]. The main idea in this study is to align the respective scale factors [Formula: see text] and [Formula: see text] of these two spacetimes, where de Sitter spacetime is taken with respect to a spatially flat foliation. This goal is accomplished by fine-tuning an adjustable parameter [Formula: see text] that arises naturally in the de Sitter scale factor by requiring that these scale factors be future-asymptotically convergent. Once this parameter is adjusted and the scale factors are aligned, we define a relative error function [Formula: see text] that computes as a function of time [Formula: see text] how close the scale factors of these two spacetimes are to one another. Our results quantify how close our physical [Formula: see text]CDM universe is to its corresponding de Sitter spacetime as both spacetimes converge as they expand. As an example of our results, we show that at the present time [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], and at [Formula: see text][Formula: see text]Gy, to an accuracy of [Formula: see text], we can use de Sitter spacetime to model our own [Formula: see text]CDM universe. Our results also show by statistical analysis that with a confidence level of 68.3%, for [Formula: see text][Formula: see text]Gy, the scale factor [Formula: see text] of our [Formula: see text] universe and the scale factor [Formula: see text] of the corresponding de Sitter spacetime are indistinguishable to within the accuracy of current cosmological measurements.

Coexisting Multi-Dynamics of a Physical SBT Memristor-Based Chaotic Circuit

This paper presents a new physical [Formula: see text] (SBT) memristor-based chaotic circuit. The equilibrium point and the stability of the chaotic circuit are analyzed theoretically. This circuit system exhibits multiple dynamics such as stable point, periodic cycle and chaos by means of Lyapunov exponents spectra, bifurcation diagrams, Poincaré maps and phase portraits, when the initial state or the circuit parameter changes. Specially, the circuit system exhibits coexisting multi-dynamics. This study provides insightful guidance for the design and analysis of physical memristor-based circuits.