Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure

Compact Time and Determinism for Bosons: foundations

Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose fundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality. The non trivial classical dynamics of these periodic fields show remarkable overlaps with ordinary quantum field theory. This can be interpreted as a generalization of the AdS/CFT correspondence.Comment: For editorial reasons the present version (0903.3680v5 accepted for publication in Found. Phys.) is focused on the foundational points of 0903.3680v4 (par.1, par.2 and par.3.2). The remaining parts (par.3.1, app.A and app.B) will be extended and published in dedicated papers. 28 pages, 3 figure

MESURE DU PARAMETRE DE DEPOLARISATION D DANS LA DIFFUSION ELASTIQUE DE PROTONS

Une expérience de double diffusion d'un faisceau polarisé a permis la détermination du paramètre de dépolarisation "D" de Wolfenstein pour la diffusion élastique sur 27Al, 10B, 9Be. Une section efficace de diffusion avec renversement de spin faible, mais mesurable, a été ainsi trouvée.We describe a measurement of the depolarization of a proton beam elastically scattered by 27Al, 10B and 9Be. Experimental results indicate a small but measurable (?) spin-flip cross-section

Key Role of the Cation Interstitial Structure in the Radiation Resistance of Pyrochlores

International audienc

Étude de la diffusion inélastique de particules alpha de 44,4 MeV sur 58Ni, 60Ni, 64Ni

Using the 44.4 MeV alpha particle beam of the Saclay cyclotron, a study of the states preferentially excited in (α, α') experiments was made. The energies of these states and the angular distributions of the inelastically scattered α particles leaving the nucleus in these excited states are given. The application of the Blair inelastic diffractional calculations allows us to give parity assignment to some of the levels.Utilisant le faisceau analysé de particules α de 44,4 MeV du cyclotron de Saclay, une recherche des niveaux préférentiellement excités lors de la diffusion inélastique de ces particules sur 58Ni. 60Ni, 64Ni a été effectuée. Le dispositif expérimental de détection et sélection de particules est celui décrit par M. Chaminade. Le spectre énergétique des particules émises montre l'excitation préférentielle de niveaux vers 1,4 ; 4 ; 5 ; 6 et 10 MeV. Les courbes de distributions angulaires de particules α émises abandonnant le noyau dans ces différents états d'excitation sont données. Ces courbes présentent des oscillations caractéristiques de l'interaction de surface. Une interprétation préliminaire selon le modèle de Blair est donnée

On the Origin of the Green Colour of Archaeological Bone Artefacts of the Gallo-Roman Period

International audienceRecent findings in the city of Reims have lead to the discovery of manufactured bone objects coloured in green throughout their entire volume. In order to discover the intentional nature of the colouration and to propose a colouration mechanism, modern ox bones have been coloured in the laboratory. Bones with a hue similar to that of the archaeological artefacts have been obtained by boiling in an acidic brine in a copper vessel. A combination of infrared spectroscopy, X-ray diffraction and transmission electron microscope observations did not reveal the speciation of copper, but allowed us to validate the colouration process and to discuss the intentional origin of the colouration

Discordance of peripheral artery disease diagnosis using exercise transcutaneous oxygen pressure measurement and post-exercise ankle-brachial index

International audienceIn patients with exertional limb symptoms and normal ankle-brachial index (ABI) at rest, exercise testing can be used to diagnose lower extremity arterial disease (LEAD). Post-exercise ABI decrease or Exercise transcutaneous oxygen pressure measurement (Exercise-TcPO2) can be used to diagnose LEAD. Objectives were (i) to assess the agreement between both methods (ii) to define the variables associated with the discordance, and (iii) to present results of healthy subjects. In this prospective cross-sectional study, patients with exertional limb symptoms and normal rest ABI were consecutively included. ABI was measured at rest and after standardized exercise protocol as well as Exercise-TcPO2. A kappa coefficient with a 95% confidence interval was used to assess the agreement between the two methods. Logistic regression analysis was performed to outline variables potentially responsible for discordance. Ninety-six patients were included. The agreement between the tests was weak with a k value of 0.23 [0.04-0.41]. Logistic regression analysis found that a medical history of lower extremity arterial stenting (odds ratio 5.85[1.68-20.44]) and age (odds ratio 1.06[1.01-1.11]) were the main cause of discordance. This study suggests that post-exercise ABI and Exercise-TcPO2 cannot be used interchangeably for the diagnosis of LEAD in patients with exertional symptoms and normal rest ABI