In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The id...In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is 展开更多
Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E<sup>2...Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E<sup>2</sup> = p<sup>2</sup>c<sup>2</sup> + m<sup>2</sup>c<sup>4</sup>. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon;while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, v<sub>p</sub>⋅v<sub>g</sub> = c<sup>2</sup> with v<sub>p</sub> ≥ c because v<sub>g</sub> ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for v<sub>p</sub> = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if v<sub>p</sub> is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy;h = Planck’s constant;ν = frequency;ω = angular momentum;p = momentum;λ = wavelength;k = wave vector;c = speed of light;m = particle rest mass;v<sub>p</sub> = phase velocity;v<sub>g</sub> = group velocity].展开更多
From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and...From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.展开更多
In packet switched communication networks, traffic between any source destination (SD) pair is expected to be transmitted over multiple paths. In this paper, we focus on the problem how to optimally distribute the l...In packet switched communication networks, traffic between any source destination (SD) pair is expected to be transmitted over multiple paths. In this paper, we focus on the problem how to optimally distribute the load on a set of paths so that the overall network performance is maximized. This problem is first formulated as a nonlinear programming problem and then we propose a neural network (NN) to solve it. The NN architecture is discussed in detail. At last, we verify the effectiveness of our approach by applying it to a specific network model. The experimental results demonstrate that our method can yield optimal solutions with good stability.展开更多
The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave func...The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics;the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.展开更多
Because magnetic moment is spatial in classical magnetostatics, we progress beyond the axiomatic concept of the point particle electron in physics. Orbital magnetic moment is well grounded in spherical harmonics in a ...Because magnetic moment is spatial in classical magnetostatics, we progress beyond the axiomatic concept of the point particle electron in physics. Orbital magnetic moment is well grounded in spherical harmonics in a central field. There, quantum numbers are integral. The half-integral spinor moment appears to be due to cylindrical motion in an external applied magnetic field;when this is zero , the spin states are degenerate. Consider lifting the degeneracy by diamagnetism in the cylindrical magnetic field: a uniquely derived electronic magnetic radius shares the identical value to the Compton wavelength.展开更多
Two problems in solid state physics and superconductivity are addressed by applications of dispersion dynamics. The first is the Hall effect. The dynamics of charges that yield positive Hall coefficients in material h...Two problems in solid state physics and superconductivity are addressed by applications of dispersion dynamics. The first is the Hall effect. The dynamics of charges that yield positive Hall coefficients in material having no mobile positive charges have always been problematic The effect requires both electric and magnetic response, but magnetic deflection is only possible in mobile charges. In high temperature superconductors, these charges must be electrons. Contrary to Newton’s second law, their acceleration is reversed in crystal fields that dictate negative dispersion. This is evident in room temperature measurements, but a second problem arises in supercurrents at low temperatures. The charge dynamics in material having zero internal electric field because of zero resistivity;and zero magnetic field because of the Meissner-Ochsenfeld diamagnetism;while the supercurrents themselves have properties of zero net momentum;zero spin;and sometimes, zero charge;are so far from having been resolved that they may never have been addressed. Again, dispersion dynamics are developed to provide solutions given by reduction of the superconducting wave packet. The reduction is here physically analyzed, though it is usually treated as a quantized unobservable.展开更多
变压器等电气设备的吊装、转运环节是疏于监控的薄弱环节,极易发生由机械冲击引起的二次损伤。对变压器轨道运输车行进过程中受路基振动引起的冲击响应开展研究。首先,建立了轨道运输车⁃变压器耦合分析模型,利用有限元分析得出轨道运输...变压器等电气设备的吊装、转运环节是疏于监控的薄弱环节,极易发生由机械冲击引起的二次损伤。对变压器轨道运输车行进过程中受路基振动引起的冲击响应开展研究。首先,建立了轨道运输车⁃变压器耦合分析模型,利用有限元分析得出轨道运输车⁃变压器耦合分析模型在路基振动作用下的核心响应区域。然后,提出了一种基于小波包散布熵的非周期瞬态响应特征提取方法。该方法通过小波包最优子带树结构对整个频带进行良好的稀疏性分割,将包含多种信息的一维数据分解到不同维度,实现信号的有效分解,通过Teager能量算子(Teager Energy Operator,TEO)增强子带信号的冲击特性,利用散布熵选取包含冲击响应特征的子带信号。最后,通过路基振动仿真信号验证了所提方法能够准确从耦合路径干扰中提取出非周期性瞬态冲击响应成分。展开更多
文摘In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is
文摘Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E<sup>2</sup> = p<sup>2</sup>c<sup>2</sup> + m<sup>2</sup>c<sup>4</sup>. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon;while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, v<sub>p</sub>⋅v<sub>g</sub> = c<sup>2</sup> with v<sub>p</sub> ≥ c because v<sub>g</sub> ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for v<sub>p</sub> = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if v<sub>p</sub> is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy;h = Planck’s constant;ν = frequency;ω = angular momentum;p = momentum;λ = wavelength;k = wave vector;c = speed of light;m = particle rest mass;v<sub>p</sub> = phase velocity;v<sub>g</sub> = group velocity].
文摘From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.
文摘In packet switched communication networks, traffic between any source destination (SD) pair is expected to be transmitted over multiple paths. In this paper, we focus on the problem how to optimally distribute the load on a set of paths so that the overall network performance is maximized. This problem is first formulated as a nonlinear programming problem and then we propose a neural network (NN) to solve it. The NN architecture is discussed in detail. At last, we verify the effectiveness of our approach by applying it to a specific network model. The experimental results demonstrate that our method can yield optimal solutions with good stability.
文摘The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics;the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.
文摘Because magnetic moment is spatial in classical magnetostatics, we progress beyond the axiomatic concept of the point particle electron in physics. Orbital magnetic moment is well grounded in spherical harmonics in a central field. There, quantum numbers are integral. The half-integral spinor moment appears to be due to cylindrical motion in an external applied magnetic field;when this is zero , the spin states are degenerate. Consider lifting the degeneracy by diamagnetism in the cylindrical magnetic field: a uniquely derived electronic magnetic radius shares the identical value to the Compton wavelength.
文摘Two problems in solid state physics and superconductivity are addressed by applications of dispersion dynamics. The first is the Hall effect. The dynamics of charges that yield positive Hall coefficients in material having no mobile positive charges have always been problematic The effect requires both electric and magnetic response, but magnetic deflection is only possible in mobile charges. In high temperature superconductors, these charges must be electrons. Contrary to Newton’s second law, their acceleration is reversed in crystal fields that dictate negative dispersion. This is evident in room temperature measurements, but a second problem arises in supercurrents at low temperatures. The charge dynamics in material having zero internal electric field because of zero resistivity;and zero magnetic field because of the Meissner-Ochsenfeld diamagnetism;while the supercurrents themselves have properties of zero net momentum;zero spin;and sometimes, zero charge;are so far from having been resolved that they may never have been addressed. Again, dispersion dynamics are developed to provide solutions given by reduction of the superconducting wave packet. The reduction is here physically analyzed, though it is usually treated as a quantized unobservable.
文摘变压器等电气设备的吊装、转运环节是疏于监控的薄弱环节,极易发生由机械冲击引起的二次损伤。对变压器轨道运输车行进过程中受路基振动引起的冲击响应开展研究。首先,建立了轨道运输车⁃变压器耦合分析模型,利用有限元分析得出轨道运输车⁃变压器耦合分析模型在路基振动作用下的核心响应区域。然后,提出了一种基于小波包散布熵的非周期瞬态响应特征提取方法。该方法通过小波包最优子带树结构对整个频带进行良好的稀疏性分割,将包含多种信息的一维数据分解到不同维度,实现信号的有效分解,通过Teager能量算子(Teager Energy Operator,TEO)增强子带信号的冲击特性,利用散布熵选取包含冲击响应特征的子带信号。最后,通过路基振动仿真信号验证了所提方法能够准确从耦合路径干扰中提取出非周期性瞬态冲击响应成分。
