Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more ...Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.展开更多
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matte...In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.展开更多
Since the lasers at fixed wavelengths are unable to meet the requirements of the development of modern science and technology,nonlinear optics is significant for overcoming the obstacle.Investigation on frequency conv...Since the lasers at fixed wavelengths are unable to meet the requirements of the development of modern science and technology,nonlinear optics is significant for overcoming the obstacle.Investigation on frequency conversion in ferroelectric nonlinear photonic crystals with different superlattices has been being one of the popular research directions in this field.In this paper,some mature fabrication methods of nonlinear photonic crystals are concluded,for example,the electric poling method at room temperature and the femtosecond direct laser writing technique.Then the development of nonlinear photonic crystals with one-dimensional,two-dimensional and three-dimensional superlattices which are used in quasi-phase matching and nonlinear diffraction harmonic generation is introduced.In the meantime,several creative applications of nonlinear photonic crystals are summarized,showing the great value of them in an extensive practical area,such as communication,detection,imaging,and so on.展开更多
Initially, all that was known about diffraction in quasicrystals was its point group symmetry;nothing was known about the mechanism. The structure was more evident, and was called quasiperiodic. From mapping the Mn at...Initially, all that was known about diffraction in quasicrystals was its point group symmetry;nothing was known about the mechanism. The structure was more evident, and was called quasiperiodic. From mapping the Mn atoms by phase-contrast, optimum-defocus, electron microscopy, the progress towards identifying unit cell, cluster, supercluster and extensive hierarchic structure is evident. The structure is ordered and uniquely icosahedral. From the known structure, we could calculate structure factors. They were all zero. The quasi structure factor is an iterative procedure on the hierarchic structure that correctly calculates diffraction beam intensities in 3-dimensional space. By a creative device, the diffraction is demonstrated to occur off the Bragg condition;the quasi-Bragg condition implies a metric that enables definition and measurement of the lattice constant. The reciprocal lattice is the 3-dimensional diffraction pattern. Typically, it builds on Euclidean axes with coordinates in geometric series, but it also transforms to Cartesian coordinates.展开更多
文摘Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.
文摘In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φas the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φmay indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.
基金supported by the Fundamental Research Funds for the Central Universities(No.2018CUCTJ043).
文摘Since the lasers at fixed wavelengths are unable to meet the requirements of the development of modern science and technology,nonlinear optics is significant for overcoming the obstacle.Investigation on frequency conversion in ferroelectric nonlinear photonic crystals with different superlattices has been being one of the popular research directions in this field.In this paper,some mature fabrication methods of nonlinear photonic crystals are concluded,for example,the electric poling method at room temperature and the femtosecond direct laser writing technique.Then the development of nonlinear photonic crystals with one-dimensional,two-dimensional and three-dimensional superlattices which are used in quasi-phase matching and nonlinear diffraction harmonic generation is introduced.In the meantime,several creative applications of nonlinear photonic crystals are summarized,showing the great value of them in an extensive practical area,such as communication,detection,imaging,and so on.
文摘Initially, all that was known about diffraction in quasicrystals was its point group symmetry;nothing was known about the mechanism. The structure was more evident, and was called quasiperiodic. From mapping the Mn atoms by phase-contrast, optimum-defocus, electron microscopy, the progress towards identifying unit cell, cluster, supercluster and extensive hierarchic structure is evident. The structure is ordered and uniquely icosahedral. From the known structure, we could calculate structure factors. They were all zero. The quasi structure factor is an iterative procedure on the hierarchic structure that correctly calculates diffraction beam intensities in 3-dimensional space. By a creative device, the diffraction is demonstrated to occur off the Bragg condition;the quasi-Bragg condition implies a metric that enables definition and measurement of the lattice constant. The reciprocal lattice is the 3-dimensional diffraction pattern. Typically, it builds on Euclidean axes with coordinates in geometric series, but it also transforms to Cartesian coordinates.
