Angular Momentum and the Quantum Gyroscope: The Emergence of Spin

Continuing with understanding the implications of the postulates in Chapter 7 and following the approach in Chapter 8 to use operators find solutions to the time independent Schrödinger equation, we return to the subject of angular momentum, of importance to many problems including the quantum gyroscope. Aside from playing a central role in any spherically symmetric quantum system, it plays a central role in inertial guidance systems from airplanes and rockets to autonomous vehicles. Working with only the operators of the angular momentum vector, L^=L^xx̌+L^yy̌+L^zž and L^2 and the corresponding commutation relations, a procedure similar to that used in Chapter 8 for the nano-vibrator is used to completely identify the eigenvectors and eigenvalues. However, in Chapter 6, we required that the magnetic quantum number, m where L^z|l.m〉=mℏ|l.m〉, be integer, because the eigenfunction Yl,m(l,m)∝eimϕ, and we required that a full rotation around the z-axis give the same result requiring, eimϕ=eim(ϕ+2π). In the operator approach, there is no such requirement, but there is still a constraint on m, namely that m is either integer or half integer. The requirements in Chapter 6 hold, so what is the meaning of half-integer? This was one of the first results to indicate the existence of intrinsic (not associated with real space rotation) angular moment known as spin.

Proton core behaviour inside magnetic field switchbacks

ABSTRACT During Parker Solar Probe’s first two orbits, there are widespread observations of rapid magnetic field reversals known as switchbacks. These switchbacks are extensively found in the near-Sun solar wind, appear to occur in patches, and have possible links to various phenomena such as magnetic reconnection near the solar surface. As switchbacks are associated with faster plasma flows, we questioned whether they are hotter than the background plasma and whether the microphysics inside a switchback is different to its surroundings. We have studied the reduced distribution functions from the Solar Probe Cup instrument and considered time periods with markedly large angular deflections to compare parallel temperatures inside and outside switchbacks. We have shown that the reduced distribution functions inside switchbacks are consistent with a rigid velocity space rotation of the background plasma. As such, we conclude that the proton core parallel temperature is very similar inside and outside of switchbacks, implying that a temperature–velocity (T–V) relationship does not hold for the proton core parallel temperature inside magnetic field switchbacks. We further conclude that switchbacks are consistent with Alfvénic pulses travelling along open magnetic field lines. The origin of these pulses, however, remains unknown. We also found that there is no obvious link between radial Poynting flux and kinetic energy enhancements suggesting that the radial Poynting flux is not important for the dynamics of switchbacks.

Advances of Relativity Theory

In this article, a bijective research methodology is applied where every element in the model corresponds to exactly one element in physical reality. An element in the physical reality X and the corresponding element in the model Y are related by the bijective function. A bijective research methodology confirms that the Lorentz factor has its origin in the variable density of universal space. A lower value of the space density corresponds to the higher value of the Lorentz factor. Universal space is not “empty”; space is the primordial energy of the universe. Universal space is the absolute frame of reference for all observers as confirmed experimentally by the GPS system, which demonstrates that the relative rate of clocks is valid for all observers. A planet's perihelion precession and the Sagnac effect are the results of the space rotation.

Longitudinal characterization of the wake and electron bunch in a laser wakefield accelerator

Energy chirp compensation of the electron bunch (e-bunch) in a laser wakefield accelerator, which is caused by the phase space rotation in the gradient wakefield, has been applied in many schemes for low energy spread e-bunch generation. We report the experimental observation of energy chirp compensation of the e-bunch in a nonlinear laser wakefield accelerator with a negligible beam loading effect. By adjusting the acceleration length using a wedge-roof block, the chirp compensation of the accelerated e-bunch was observed via an electron spectrometer. Apart from this, some significant parameters for the compensation process, such as the longitudinal dispersion and wakefield slope at the bunch position, were also estimated. A detailed comparison between experiment and simulation shows good agreement of the wakefield and bunch parameters. These results give a clear demonstration of the longitudinal characteristics of the wakefield in a plasma and the bunch dynamics, which are important for better control of a compact laser wakefield accelerator.

Automatic Derivation of Geometric Properties of Components From 3D Polygon Models

To detect errors or find potential for improvement during the CAD-supported development of a complex technical system like modern industrial machines, the system’s virtual prototype can be examined in virtual reality (VR) in the context of virtual design reviews. Besides exploring the static shape of the examined system, observing the machines’ mechanics (e.g., motor-driven mechanisms) and transport routes for the material transport (e.g., via conveyor belts or chains, or rail-based transport systems) can play an equally important role in such a review. In practice it is often the case, that the relevant information about transport routes, or kinematic properties is either not consequently modeled in the CAD data or is lost during conversion processes. To significantly reduce the manual effort and costs for creating animations of the machines complex behavior with such limited input data for a design review, we present a set of algorithms to automatically determine geometrical properties of machine parts based only on their triangulated surfaces. The algorithms allow to detect the course of transport systems, the orientation of objects in 3d space, rotation axes of cylindrical objects and holes, the number of tooth of gears, as well as the tooth spacing of toothed racks. We implemented the algorithms in the VR system PADrend and applied them to animate virtual prototypes of real machines.

Counting of oscillatory modes of valence quarks forming qqq baryons for three quark flavors u, d, s

We present the unique properties of oscillatory modes of [Formula: see text] light quarks — [Formula: see text], [Formula: see text], [Formula: see text] — using the [Formula: see text] broken symmetry classification. [Formula: see text] stands for the space rotation group generated by the sum of the three individual angular momenta of quarks in their c.m. system. The baryonic multiplets are shown to emerge from the picture of oscillating quarks in three space dimensions in the center-of-mass system of the baryons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of mass-square is calculated. This estimate is of relevance for the accounting of the missing states of unobserved hadrons, as the here estimated baryonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.