In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interact...In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.展开更多
To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, the uncertainty component of the silicon sphere's volume introduced by the spherical harmonics method, which is usually used in deter...To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, the uncertainty component of the silicon sphere's volume introduced by the spherical harmonics method, which is usually used in determining the sphere's volume, is reevaluated. By means of representing the shape of the silicon sphere by an ellipsoid with Gaussian white noise in its diameters, the uncertainty of the current mapping methods based on the spherical harmonics theory can be estimated theoretically. It is evidenced that the uncertainty component attributed to the current mapping method is underestimated. To eliminate this effect as much as possible, the number of mapping points should be increased to more than before. Moreover, a new mapping method is proposed to accomplish the equal-area mapping with large number points on the silicon sphere.展开更多
The Planck constant h is one of the most significant constants in quantum physics. Recently, the precision measurement of the value of h has been a hot issue due to its important role for the establishment of both a n...The Planck constant h is one of the most significant constants in quantum physics. Recently, the precision measurement of the value of h has been a hot issue due to its important role for the establishment of both a new SI and a revised fundamental physical constant system. Up to date, two approaches, the watt balance and counting atoms, have been employed to determine the Planck constant at a level of several parts in 108. In this paper, the principle and progress on precision measurement of the Planck constant using watt balance and counting atoms at national metrology institutes are reviewed. Further improvement in determining the Planck constant and possible developments of a revised physical constant system in future are discussed.展开更多
This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating th...This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating the ratio <em>G/<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ћ</span></span></span></span></em> as an empirical constant of nature in its own right. This ratio is repre- sented by a new symbol, <em>N</em><sub><em>T</em></sub>. It turns out that the value of <em>N</em><sub><em>T</em></sub> (which is 6.32891937 × 10<sup>23</sup> m<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span></span></span></span></span>kg<sup>-2</sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span></span></span></span></span>s<sup>-1</sup>) is within 5% of Avogadro’s number<em> N</em><sub><em>A</em></sub>, although the units are clearly different. Nevertheless, substitutions of <em>N</em><sub><em>T</em></sub> or <em>N</em><sub><em>A</em></sub> into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE. The method described allows for quantum term EFE substitutions into Einstein’s gravitational constant <em>κ</em>. These terms include <em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ћ</span></span></span></span></em>, <em>α</em>, <em>m</em><sub><em>e</em></sub>, <em>m</em><sub><em>p</em></sub>, <em>R</em>, <em>k</em><sub><em>B</em></sub>, <em>F, e, M<sub>U</sub></em>, and <em>m</em><sub><em>U</em></sub>. More importantly, perhaps, one or more of the many new expressions given for <em>κ</em> may provide a more accurate result than <em>κ</em> incorporating <em>G</em>. If so, this may have important implications for additional forward progress towards unification. Whether any of these new expressions for Einstein’s field equation can move us closer to quantizing gravity remains to be determined.展开更多
The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a ...The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.展开更多
文摘In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.
基金Project supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No.2006BAF06B06)Tsinghua University Initiative Scientific Research Program,China (Grant No.2009THZ06057)
文摘To determine the Avogadro constant with a target relative uncertainty of 2 x 10-s, the uncertainty component of the silicon sphere's volume introduced by the spherical harmonics method, which is usually used in determining the sphere's volume, is reevaluated. By means of representing the shape of the silicon sphere by an ellipsoid with Gaussian white noise in its diameters, the uncertainty of the current mapping methods based on the spherical harmonics theory can be estimated theoretically. It is evidenced that the uncertainty component attributed to the current mapping method is underestimated. To eliminate this effect as much as possible, the number of mapping points should be increased to more than before. Moreover, a new mapping method is proposed to accomplish the equal-area mapping with large number points on the silicon sphere.
基金Project supported by the National Natural Science Foundation of China(Grant No.51477160)the National Department Public Benefit Research Foundation of China(Grant No.201010010)the National Key Technology R&D Program of China(Grant No.2006BAF06B01)
文摘The Planck constant h is one of the most significant constants in quantum physics. Recently, the precision measurement of the value of h has been a hot issue due to its important role for the establishment of both a new SI and a revised fundamental physical constant system. Up to date, two approaches, the watt balance and counting atoms, have been employed to determine the Planck constant at a level of several parts in 108. In this paper, the principle and progress on precision measurement of the Planck constant using watt balance and counting atoms at national metrology institutes are reviewed. Further improvement in determining the Planck constant and possible developments of a revised physical constant system in future are discussed.
文摘This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating the ratio <em>G/<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ћ</span></span></span></span></em> as an empirical constant of nature in its own right. This ratio is repre- sented by a new symbol, <em>N</em><sub><em>T</em></sub>. It turns out that the value of <em>N</em><sub><em>T</em></sub> (which is 6.32891937 × 10<sup>23</sup> m<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span></span></span></span></span>kg<sup>-2</sup><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">⋅</span></span></span></span></span></span>s<sup>-1</sup>) is within 5% of Avogadro’s number<em> N</em><sub><em>A</em></sub>, although the units are clearly different. Nevertheless, substitutions of <em>N</em><sub><em>T</em></sub> or <em>N</em><sub><em>A</em></sub> into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE. The method described allows for quantum term EFE substitutions into Einstein’s gravitational constant <em>κ</em>. These terms include <em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">ћ</span></span></span></span></em>, <em>α</em>, <em>m</em><sub><em>e</em></sub>, <em>m</em><sub><em>p</em></sub>, <em>R</em>, <em>k</em><sub><em>B</em></sub>, <em>F, e, M<sub>U</sub></em>, and <em>m</em><sub><em>U</em></sub>. More importantly, perhaps, one or more of the many new expressions given for <em>κ</em> may provide a more accurate result than <em>κ</em> incorporating <em>G</em>. If so, this may have important implications for additional forward progress towards unification. Whether any of these new expressions for Einstein’s field equation can move us closer to quantizing gravity remains to be determined.
基金Project supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(Grant No.2006BAF06B06)the Tsinghua University Initiative Scientific Research Program,China(Grant No.2009THZ06057)
文摘The effect of a spherical shape on the measurement result of spectroscopic ellipsometry (SE) is analyzed, and a method to eliminate this effect is proposed. Based on the simulation result of the SE measurement on a silicon sphere by ray tracking, we find that the sphere makes the parallel incident beam of the SE be divergent after reflection, and the measurement error of the SE caused by this phenomenon is explained by the mixed polarization theory. By settling an aperture in front of the detector of the SE, we can almost eliminate the error. For the silicon sphere with a diameter of 94 mm used in the Avogadro project, the thickness error of the oxide layer caused by the spherical shape can be reduced from 0.73 nm to 0.04 nm by using the proposed method. The principle of the method and the results of the experimental verification are presented.