To study the orientation-dependence of the diffraction patterns of the reflective grating, we utilize the cylindrical screen. Experiments show the curved, expanded and inclined diffraction patterns. The textbook-screen in the grating experiments is a planar screen and the diffraction orders distribute linearly in one dimension. The cylindrical screen visually shows that the diffraction orders of a rotating reflective grating distribute in two dimensions. The CCD can be placed at the accurate locations of each order to collect data. By using the cylindrical screen, only two coordinates are needed to describe the curved/expanded/inclined diffraction patterns of the rotating reflective grating. The cylindrical screen may be used to test the theories of the grating rotating around 3 axes.

Special Relativity (SR) is the cornerstone for modern physics and variety of applications. SR is based on two postulates, the principle of relativity (the first postulate) and the principle of constancy of speed of light (the second postulate). Recently we have (1) shown that the light propagate as particles/photons in the “pure” wave experiments, such as double slit and grating experiments; (2) proposed experiments to measure the speed of the photons by an observer moving relative to the source and thus, to test the second postulate for photons. In this article we propose a classroom experiment to test the second postulate. If the experiments show the existence of interference pattern (the negative result), the constancy of the speed of the photons holds, namely the second postulate of SR is experimentally confirmed. If the experiments show no interference pattern (positive result), then the propagation speed of photons is not constant, namely, the second postulate of SR is disproved. Either negative result or positive results would be profoundly significant.

In this article we propose a Photon chamber to detect the traces of the light beam in the grating experiments, namely to visualize the passage of light beam. The experiments show that the light beam behaves as particles moving through the Photon chamber, while still distributes as waves. The Photon chamber is inexpensive and discloses novel phenomena.

The common gratings contain transmission gratings and reflective gratings. Recently it has been shown that a transmission grating produces not only a transmission diffraction pattern but also a reflective diffraction pattern (dual pattern) simultaneously in the same experiment. Namely the transmission grating behaves not only as a transmission grating but also as a reflective grating simultaneously (dual-grating) in the same experiment. To study the orientation-dependence of the dual-patterns of the dual-grating experiments, in this article, we proposed the novel cylindrical screen.The cylindrical screen visually shows the location of each diffraction order in dual-grating experiments, such that the CCD/telescope can be placed at the accurate location to collect data. One of the benefits is that, by using the planar screen, three coordinates are needed to describe either the dual-pattern or the curved/expanded/inclined patterns, while by using the cylindrical screen, only two coordinates are needed to describe either the dual-pattern or the curved/expanded/inclined patterns.

The common gratings contain transmission gratings and reflective gratings. The orientation-dependence of the diffraction patterns of the transmission grating experiments have been systematically studied by rotating the grating around three axes. In this article, we show the novel phenomena that the transmission grating plays dual-roles of a transmission grating and a reflective grating.Indeed, the transmission grating produces simultaneously the transmission diffraction patterns and the reflective diffraction patterns respectively. This rather ancient grating experiment continues to surprise.

The orientation-dependence of the diffraction patterns of the 1D-grating experiments have been systematically studied by utilizing the 3-axis-rotation apparatus. It is shown that the spacings between adjacent diffraction orders are non-uniform. Namely, from “one end” of the pattern to “other end”, the spacings between adjacent diffraction orders gradually increase. In this article, we systematically study the orientation-dependence of the diffraction patterns of the 2D-cross-grating. The experiments show that the diffraction patterns are non-uniform as that of the 1D-grating experiments. This extraordinary phenomenon challenges the existing theoretical description of the grating experiments. The above observed phenomena provide the comprehensive phenomena to theoretical study of the grating experiments. We suggest that the complete mathematical model should contain three rotation angles as parameters and should be able to describe the phenomena of the non-uniform-spacing, curved, expanded, inclined and mirror-symmetric diffraction patterns consistently.

The phenomena of the rotating grating have been studied and have the varieties application. The diffraction normal order that is at the intersection of the grating’s normal vector and the screen is introduced and is the function of the incident angle of light, the grating spacing and wavelength. We suggest the following: (1) the diffraction normal order and the zeroth order () divide a diffraction pattern into three portions; each portion corresponds to a range of diffraction orders, , , , and is described by specific equation, respectively; (2) the number of the diffraction orders “m” in each portion is determined by the incident angle of light, the grating spacing, and wavelength; (3) the diffraction angles and positions of the diffraction orders of each portion can be presented in terms of and ; (4) the diffraction pattern of a rotating grating is non-uniform.

A Universal Mathematical Field Theory (UMFT) is established, which states that the combination of the operations of both gradient and divergence of vector fields, such as electric field and velocity field, create the curl of an axial vector field, such as magnetic field. Utilizing UMFT, we mathematically: (1) derive the Extended-Maxwell equations and the Lorentz force from Coulomb’s law and the velocity of the source; (2) establish Maxwell-type gravitational equations and Lorentz-type gravitational force (Gravito-EM) from Newton’s law and velocity of gravitational source; (3) establish Classical-Spin-Electromagnetism (Spin-EM) from the Coulomb’s law and the spin of the spin angular velocity; (4) predicate the Spin related force. For a source moving with non-spatially-varying velocity the Extended-Maxwell equations reduce to Maxwell equations, which justifies UMFT and shows that the experiments-based Maxwell equations have mathematical origin. This derivation mathematically explains how a moving electric charge creates magnetic field, and shows that there is no magnetic monopole charge. UMFT shows that mathematical identities lead to physical dualities including duality between EM and Gravito-EM. The concepts, effects and phenomena of EM may be directly converted to that of gravity. The Gravito-EM are employed to study the accelerating universe, rotation curve and gravitation waves. The Gravito-EM can be quantized, along the line of quantizing EM, and unified with EM force. We derive, for the first time, the Spin-Lorentz-type force and Lagrangian-Lorentz-type force. If experimentally proved, the Spin-related force may be the 5th force. UMFT provides mathematical origins of physical dualities between Extended EM, Gravito-EM and Spin-EM.

Young’s double slit experiments, which represent the mystery of quantum mechanics (Feynman), have been described by optics, electromagnetic wave theory, quantum wave theory and Bohm’s trajectory theory. The double slit has the varieties of the applications. To test the description theories, we perform the comprehensive double slit experiments, which show that (1) before passing through the double slit/cross-double slit and before landing on the screen, the laser light behaves as particles, not as waves; (2) the experiments challenge the computer simulation of the trajectory theory at near field, however support the trajectory theory at far field. Those novel phenomena provide the comprehensive information for further theoretical development and applications.

The phenomena of the rotating grating have been studied and have the varieties application. In this article, we show in detail how to break the diffraction pattern of a rotating grating into three portions corresponding to different diffraction orders “m”, and each portion is described by an equation. Grating CCW rotation CW rotation

The gratings contain transmission gratings and reflective gratings. The textbook-screen in the grating experiments is a planar screen. To study the orientation-dependence of the 2-dimention diffraction patterns of the grating, we proposed the cylindrical screen. Then utilizing the cylindrical screen in both transmission grating experiments and reflective grating experiments. Experiments show the 2-dimention curved, expanded and inclined diffraction patterns. The cylindrical screen visually shows that the diffraction orders of the rotating gratings distribute in two dimensions. The CCD can be placed at the precise locations of each order to collect data. By using the cylindrical screen, two coordinates are needed to describe the curved, expanded and inclined diffraction patterns of the rotating grating. The cylindrical screen may be used to test the theories of the grating rotating around 3 axes.

A document by Hui Peng. Click on the document to view its contents.