Abstract:
We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is put to use in the discussion of particular point particle dynamics and the transition to a first quantized theory.

Abstract:
Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational dynamics of all tensorial geometries on a smooth manifold that can carry predictive matter equations, are time-orientable, and allow to distinguish positive from negative particle energies.

Abstract:
Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet p-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.

Abstract:
We show that Dirac-Born-Infeld theory possesses a hidden invariance that enhances the local O(1,p) Lorentz symmetry on a Dirichlet p-brane to an O(1,p) x O(1,p) gauge group, encoding both an invariant velocity and acceleration (or length) scale. This enlarged gauge group predicts consequences for the kinematics of observers on Dirichlet branes, with admissible accelerations being bounded from above. An important lesson beyond string theory is that a fundamental length scale can be implemented into the kinematics of general relativity, whilst preserving both space-time as a smooth manifold and local Lorentz symmetry, contrary to common belief. We point out consequences for string phenomenology, classical gravity and atomic physics.

Abstract:
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a bi-refringent linear optical medium.

Abstract:
A generical formalism for the discussion of Brownian processes with non-constant particle number is developed, based on the observation that the phase space of heat possesses a product structure that can be encoded in a commutative unit ring. A single Brownian particle is discussed in a Hilbert module theory, with the underlying ring structure seen to be intimately linked to the non-differentiability of Brownian paths. Multi-particle systems with interactions are explicitly constructed using a Fock space approach. The resulting ring-valued quantum field theory is applied to binary branching Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The presented formalism permits the application of the full machinery of quantum field theory to Brownian processes.

Abstract:
The two essays included here are parts of a longer study of temporality, and the genesis of the “religious.” The first part, “Multiple Nows,” depicts a universe in which a present to past relation is establishable from any and every point in consciousness. The resulting perspective differs from that offered by the linear timeline of chronological history. Remembering where I put my glasses is an historicizing act, as fully as is remembering when the Battle of Zama was fought or who won there. On this alternate view of temporality the genesis of the historical perspective is the historicizing subject. The second essay, “The History of a House,” places the observer before an historical structure, then asks where the historicity in the structure is. We discover that the historicity is put there by the observer/subject. This discovery resembles our earlier discovery that historicity is generated by an infinite sequence of nows. The two essays converge on a description of historical cognition as subject-generated.

Abstract:
The gravitational model of the three elements theory is an alternative theory to dark matter. It uses a modification of Newton’s law in order to explain gravitational mysteries. The results of this model are explanations for the dark matter mysteries, and the Pioneer anomaly. The disparity of the gravitational constant measurements might also be explained. Concerning the Earth flyby anomalies, the theoretical order of magnitude is the same as the experimental one. A very small change of the perihelion advance of the planet orbits is calculated by this model. Meanwhile, this gravitational model is perfectly compatible with restricted relativity and general relativity, and is part of the three element theory, a unifying theory.

Abstract:
The color of the sky in day-time and at twilight is studied by means of spectroscopy, which provides an unambiguous way to understand and quantify why a sky is blue, pink, or red. The colors a daylight sky can take primarily owe to Rayleigh extinction and ozone absorption. Spectra of the sky illuminated by the sun can generally be represented by a generic analytical expression which involves the Rayleigh function , ozone absorption, and, to a lesser extend, aerosol extinction. This study is based on a representative sample of spectra selected from a few hundred observations taken in different places, times, and dates, with a portable fiber spectrometer.