Principles of Discrete Time Mechanics: IV. The Dirac Equation, Particles and Oscillons

We apply the principles of discrete time mechanics discussed in earlier papers to the first and second quantised Dirac equation. We use the Schwinger action principle to find the anticommutation relations of the Dirac field and of the particle creation operators in the theory. We find new solutions to the discrete time Dirac equation, referred to as oscillons on account of their extraordinary behaviour. Their principal characteristic is that they oscillate with a period twice that of the fundamental time interval T of our theory. Although these solutions can be associated with definite charge, linear momentum and spin, such objects should not be observable as particles in the continuous time limit. We find that for non-zero T they correspond to states with negative squared norm in Hilbert space. However they are an integral part of the discrete time Dirac field and should play a role in particle interactions analogous to the role of longitudinal photons in conventional quantum electrodynamics.Comment: 27 pages LateX; published versio

Representation in Westminster in the 1990s : The ghost of Edmund Burke

Why are 'trustee' notions of representation still invoked in the UK House of Commons in the 1990s? In answering this question this article analyses the premises of Burkean theory and the arguments that these premises are of little relevance in the late twentieth century. Despite these dismissals of trusteeship, Burkean ideas are still articulated in the Commons some 200 years after they were first voiced. The idea of trusteeship can prove extremely useful to justify the actions of representatives when those actions conflict with constituency 'opinion', party policy or the wishes of interest groups. Examples of the occasions when Burkean notions have been invoked in the 1990s are provided

Evidence for polar jets as precursors of polar plume formation

Observations from the Hinode/XRT telescope and STEREO/SECCHI/EUVI are utilized to study polar coronal jets and plumes. The study focuses on the temporal evolution of both structures and their relationship. The data sample, spanning April 7-8 2007, shows that over 90% of the 28 observed jet events are associated with polar plumes. EUV images (STEREO/SECCHI) show plume haze rising from the location of approximately 70% of the polar X-ray (Hinode/XRT) and EUV jets, with the plume haze appearing minutes to hours after the jet was observed. The remaining jets occurred in areas where plume material previously existed causing a brightness enhancement of the latter after the jet event. Short-lived, jet-like events and small transient bright points are seen (one at a time) at different locations within the base of pre-existing long-lived plumes. X-ray images also show instances (at least two events) of collimated-thin jets rapidly evolving into significantly wider plume-like structures that are followed by the delayed appearance of plume haze in the EUV. These observations provide evidence that X-ray jets are precursors of polar plumes, and in some cases cause brightenings of plumes. Possible mechanisms to explain the observed jet and plume relationship are discussed.Comment: 10 pages, 4 figures, accepted as APJ Lette

Comment on ``Superconducting PrBa_2Cu_3O_x''

Recently, Zou et al. (Phys. Rev. Lett. 80, 1074, 1998) reported the observation of bulk superconductivity (SC) for a PrBa_2Cu_3O_x (Pr123) single crystal grown by the traveling-solvent floating zone (TSFZ) method. The aim of this Comment is to show the inconsistency of the value of effective magnetic moment \mu_{eff} reported by Zou et al. (2.92\mu_B) with their magnetic susceptibility data. The estimation made directly from their data points gives a considerably smaller value of \mu_{eff}=2.09\mu_B. At the same time the values of mu_{eff}=2.9\mu_B and 3.1\mu_B were obtained for our Pr123 single crystals grown by flux method for H||ab-plane and H||c-axis, respectively. This suggests that Pr occupies only about a half of the RE sites in TSFZ crystal. The other half of the RE sites is occupied most probably by the nonmagnetic Ba. Noteworthy, SC with T_c=43 K was observed earlier for Pr_{0.5}Ca_{0.5}Ba_2Cu_3O_{7-y} thin films. Ba^{2+} has a larger ionic radius than Pr^{3+} and so the substitution of Ba for Pr could give a natural explanation not only for the SC in TSFZ Pr123 but also for the elongation of the distance between the CuO_2 planes observed by Zou et al.Comment: Slightly extended version of Comment accepted to Phys. Rev. Lett. (v.81, N24, 1998), tentatevely to be publ. 14Dec98. 1 page, REVTex; 1 EPS fi

Fly-by-light flight control system technology development plan

The results of a four-month, phased effort to develop a Fly-by-Light Technology Development Plan are documented. The technical shortfalls for each phase were identified and a development plan to bridge the technical gap was developed. The production configuration was defined for a 757-type airplane, but it is suggested that the demonstration flight be conducted on the NASA Transport Systems Research Vehicle. The modifications required and verification and validation issues are delineated in this report. A detailed schedule for the phased introduction of fly-by-light system components has been generated. It is concluded that a fiber-optics program would contribute significantly toward developing the required state of readiness that will make a fly-by-light control system not only cost effective but reliable without mitigating the weight and high-energy radio frequency related benefits

Energy Requirement of Control: Comments on Szilard's Engine and Maxwell's Demon

In mathematical physical analyses of Szilard's engine and Maxwell's demon, a general assumption (explicit or implicit) is that one can neglect the energy needed for relocating the piston in Szilard's engine and for driving the trap door in Maxwell's demon. If this basic assumption is wrong, then the conclusions of a vast literature on the implications of the Second Law of Thermodynamics and of Landauer's erasure theorem are incorrect too. Our analyses of the fundamental information physical aspects of various type of control within Szilard's engine and Maxwell's demon indicate that the entropy production due to the necessary generation of information yield much greater energy dissipation than the energy Szilard's engine is able to produce even if all sources of dissipation in the rest of these demons (due to measurement, decision, memory, etc) are neglected.Comment: New, simpler and more fundamental approach utilizing the physical meaning of control-information and the related entropy production. Criticism of recent experiments adde

Gap maps and intrinsic diffraction losses in one-dimensional photonic crystal slabs

A theoretical study of photonic bands for one-dimensional (1D) lattices embedded in planar waveguides with strong refractive index contrast is presented. The approach relies on expanding the electromagnetic field on the basis of guided modes of an effective waveguide, and on treating the coupling to radiative modes by perturbation theory. Photonic mode dispersion, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the case of self-standing membranes as well as for Silicon-on-Insulator structures. Photonic band gaps in a waveguide are found to depend strongly on the core thickness and on polarization, so that the gaps for transverse electric and transverse magnetic modes most often do not overlap. Radiative losses of quasi-guided modes above the light line depend in a nontrivial way on structure parameters, mode index and wavevector. The results of this study may be useful for the design of integrated 1D photonic structures with low radiative losses.Comment: 9 pages, 8 figures, submitted to Physical Review

One, two, or three stars? An investigation of an unusual eclipsing binary candidate undergoing dramatic period changes

We report our investigation of 1SWASP J234401.81-212229.1, a variable with a 18 461.6 s period. After identification in a 2011 search of the SuperWASP archive for main-sequence eclipsing binary candidates near the distribution's short-period limit of ~0.20 d, it was measured to be undergoing rapid period decrease in our earlier work, though later observations supported a cyclic variation in period length. Spectroscopic data obtained in 2012 with the Southern African Large Telescope did not, however, support the interpretation of the object as a normal eclipsing binary. Here, we consider three possible explanations consistent with the data: a single-star oblique rotator model in which variability results from stable cool spots on opposite magnetic poles; a two-star model in which the secondary is a brown dwarf; and a three-star model involving a low-mass eclipsing binary in a hierarchical triple system. We conclude that the latter is the most likely model

Principles of Discrete Time Mechanics: II. Classical field Theory

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate the methodology. Stationary solutions to the discrete time Schrodinger wave equation are found to be identical to standard energy eigenvalue solutions except for a fundamental limit on the energy. Then we apply the formalism to the free neutral Klein Gordon system, deriving the equations of motion and conserved quantities such as the linear momentum and angular momentum. We show that there is an upper bound on the magnitude of linear momentum for physical particle-like solutions. We extend the formalism to the charged scalar field coupled to Maxwell's electrodynamics in a gauge invariant way. We apply the formalism to include the Maxwell and Dirac fields, setting the scene for second quantisation of discrete time mechanics and discrete time Quantum Electrodynamics.Comment: 23 pages, LateX, To be published in J.Phys.A: Math.Gen: contact email address: [email protected]