Minkowski Spacetime and QED from Ontology of Time

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover the intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concept with the obvious conditions for the possibility of measurements. The derived consequences put the measurement problem of quantum mechanics and the Copenhagen interpretation of the quantum mechanical wavefunction into perspective. According to our (onto-) logic we find that spacetime can not be fundamental. We argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding Lie algebra and the representation of a Clifford algebra. Within this conceptional framework we derive the dimensionality of spacetime, the form of Lorentz transformations and of the Lorentz force and fundamental laws of physics as the Planck-Einstein relation, the Maxwell equations and finally the Dirac equation.Comment: 36 pages, 3 figures, several typos corrected, references with title

Old Game, New Rules: Rethinking The Form of Physics

We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wave-function in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.Comment: 23 pages, no figure

A New Look at Linear (Non-?) Symplectic Ion Beam Optics in Magnets

We take a new look at the details of symplectic motion in solenoid and bending magnets and rederive known (but not always well-known) facts. We start with a comparison of the general Lagrangian and Hamiltonian formalism of the harmonic oscillator and analyze the relation between the canonical momenta and the velocities (i.e. the first derivatives of the canonical coordinates). We show that the seemingly non-symplectic transfer maps at entrance and exit of solenoid magnets can be re-interpreted as transformations between the canonical and the mechanical momentum, which differ by the vector potential. In a second step we rederive the transfer matrix for charged particle motion in bending magnets from the Lorentz force equation in cartesic coordinates. We rediscover the geometrical and physical meaning of the local curvilinear coordinate system. We show that analog to the case of solenoids - also the transfer matrix of bending magnets can be interpreted as a symplectic product of 3 non-symplectic matrices, where the entrance and exit matrices are transformations between local cartesic and curvilinear coordinate systems. We show that these matrices are required to compare the second moment matrices of distributions obtained by numerical tracking in cartesic coordinates with those that are derived by the transfer a matrix method.Comment: 7 pages, 2 figure

California Health Care Market Report 2005

Examines relationships among providers, physicians, hospitals, and patients, differences in the way physicians and hospitals organize, and factors that have prompted hospitals, medical groups, and health plans to redefine their relationships

Israel\u27s Transboundary Water Disputes

As water is necessary to the function of life, it is imperative to understand the role of water in the politically turbulent Middle East. This paper will focus on Israel’s water disputes with her neighbors and how such disputes have either led to military confrontation, have been partially resolved, and otherwise continue to exist. As populations in the region are expected to increase, the need for water, already in short supply, will be magnified. Thus negotiations to settle water disputes and provide for equitable distribution of the water resources will become more contentious. This legal analysis of Israel’s water disputes will hopefully provide some guidance to the settlement of such issues in Israel’s future peace negotiations with the Syrians and Palestinians

A general constitutive model for dense, fine particle suspensions validated in many geometries

Fine particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Recent examination of these mixtures in simple flow geometries suggests inter-granular repulsion is central to this effect --- for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas, when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to two-dimensional, steady, simple shearing flows. In this work, we introduce a predictive and general, three-dimensional continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a micro-structural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, non-uniform flow configurations where it is shown to accurately capture a variety of key behaviors: (i) the continuous shear thickening (CST) and discontinuous shear thickening (DST) behavior observed in steady flows, (ii) the time-dependent propagation of `shear jamming fronts', (iii) the time-dependent propagation of `impact activated jamming fronts', and (iv) the non-Newtonian, `running on oobleck' effect wherein fast locomotors stay afloat while slow ones sink

Persistence of fractional Brownian motion with moving boundaries and applications

We consider various problems related to the persistence probability of fractional Brownian motion (FBM), which is the probability that the FBM $X$ stays below a certain level until time $T$. Recently, Oshanin et al. study a physical model where persistence properties of FBM are shown to be related to scaling properties of a quantity $J_N$, called steady-state current. It turns out that for this analysis it is important to determine persistence probabilities of FBM with a moving boundary. We show that one can add a boundary of logarithmic order to a FBM without changing the polynomial rate of decay of the corresponding persistence probability which proves a result needed in Oshanin et al. Moreover, we complement their findings by considering the continuous-time version of $J_N$. Finally, we use the results for moving boundaries in order to improve estimates by Molchan concerning the persistence properties of other quantities of interest, such as the time when a FBM reaches its maximum on the time interval $(0,1)$ or the last zero in the interval $(0,1)$.Comment: 13 page