Supersymmetry and Polytopes

We make an imaginative comparison between the Minimal Supersymmetric Standard Model and the 24-cell polytope in four dimensions, the Octacube.Comment: Presented to the Workshop on Geometry and Physics: Supersymmetry. Bilbao, Spain. May 200

Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1.913-25, to the Lichtquanten hypothesis of Einstein. Some episodes with H.A. Kramers, J.C. Slater and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavour to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.Comment: 15 page

Quantum gravity and minimum length

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.Comment: 23 pages, RevTeX, few minor changes, published versio