We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summa...We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summation of the kinetic angular momentum (J<sub>kin</sub>) and the intrinsic quantum flux dependent terms. In terms of the z-components this can be written as . For a free electron (e<sup>-</sup>) and a positron (e<sup>+</sup>) depending on the spin orientation we find that:;;and respectively. Similarly for a gamma (γ) photon, propagating in z direction with an angular frequency ω, the canonical angular momentum is found to be: , here the (+) and (-) signs stand for the right and left hand circular helicity respectively.展开更多
The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the gene...The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show tha...We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show that a photon propagating in z direction with an angular frequency ω carries a magnetic moment of μz = ±(ec/ω) along the propagation direction. Here, the (+) and (-) signs stand for the right hand and left circular helicity respectively. Because of these two symmetric values of the magnetic moment, we expect a splitting of the photon beam into two symmetric subbeams in a Stern-Gerlach experiment. The splitting is expected to be more prominent for low energy photons. We believe that the present result will be helpful for understanding the recent attempts on the Stern-Gerlach experiment with slow light and the behavior of the dark polaritons and also the atomic spinor polaritons.展开更多
文摘We calculate the canonical angular momentum of a free electron, positron and gamma photon. We show that for any particle with charge q the canonical angular momentum (J<sub>c</sub>) is written as the summation of the kinetic angular momentum (J<sub>kin</sub>) and the intrinsic quantum flux dependent terms. In terms of the z-components this can be written as . For a free electron (e<sup>-</sup>) and a positron (e<sup>+</sup>) depending on the spin orientation we find that:;;and respectively. Similarly for a gamma (γ) photon, propagating in z direction with an angular frequency ω, the canonical angular momentum is found to be: , here the (+) and (-) signs stand for the right and left hand circular helicity respectively.
文摘The SI system of units in rotational mechanics yields correct numerical results, but it produces physically incorrect units of measure in many cases. SI units also violate the principle of general covariance—the general rule for defining continuous coordinates and units in mathematics and mathematical physics. After 30+ years of wrestling with these problems, the ultimate authority on units of measure has declared that Newton–meter and Joule are not equivalent in rotational mechanics, as they are in the rest of physics. This article proposes a simple modification to SI units called “Nonstandard International units” (“NI units”) until a better name is agreed upon. NI units yield correct numerical results and physically correct units of measure, and they satisfy the principle of general covariance. The main obstacle to the adoption of NI units is the consensus among users that the radius of rotation should have the unit meter because the radius can be measured with a ruler. NI units assigned to radius should have units meter/radian because the radius is a conversion factor between angular size and circumferential length, as in arclength = rθ. To manage the social consensus behind SI units, the author recommends retaining SI units as they are, and informing users who want correct units that NI units solve the technical problems of SI units.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
文摘We have calculated the intrinsic magnetic moment of a photon through the intrinsic magnetic moment of a gamma photon created as a result of the electron-positron annihilation with the angular frequency ω. We show that a photon propagating in z direction with an angular frequency ω carries a magnetic moment of μz = ±(ec/ω) along the propagation direction. Here, the (+) and (-) signs stand for the right hand and left circular helicity respectively. Because of these two symmetric values of the magnetic moment, we expect a splitting of the photon beam into two symmetric subbeams in a Stern-Gerlach experiment. The splitting is expected to be more prominent for low energy photons. We believe that the present result will be helpful for understanding the recent attempts on the Stern-Gerlach experiment with slow light and the behavior of the dark polaritons and also the atomic spinor polaritons.
