An experiment aimed at detecting a DC voltage across a conductor induced by the steady magnetic field of a coil, carried out in 1998, provided a positive (although preliminary) evidence for such an effect, which might be interpreted as a breakdown of local Lorentz invariance. We repeated in 1999 the same experiment with a different experimental apparatus and a sensitivity improved by two orders of magnitude. The results obtained are discussed here in detail. They confirm the findings of the previous (...) experiment, and show, among the others, that the effect is independent of the direction of the current. A possible interpretation of the results is given in terms of a geometric description of the gravitational and the electromagnetic interactions by means of phenomenological, energy-dependent metrics. (shrink)

In a short section on the semantics of programs within his discussion of program correctness, Primiero seems to endorse the received view on the Scott-Strachey approach to denotational semantics as directly related to correctness. While this is true to some extent, I argue that the mathematical entities associated with programs play a lesser role in reasoning on program correctness, while the mathematical foundations of denotational semantics, namely the theory of domains, have contributed significantly to the conceptual understanding of programming and (...) of computation in general. (shrink)

We discuss the possible breakdown of Lorentz invariance—at distances greater than the Planck length—from both the theoretical and the phenomenological point of view. The theoretical tool to deal with such a problem is provided by a “deformation” of the Minkowski metric, with parameters dependent on the energy of the physical system considered. Such a deformed metric realizes, for any interaction, the “solidarity principle” between interactions and spacetime geometry (usually assumed for gravitation), according to which the peculiar features of every interaction (...) determine—locally—its own spacetinie structure. The generalized theory of relativity, based on the locally deformed Minkowski spacetime, is called “deformed special relativity” (DSR). In the first part of the paper, we give the foundations and the basic laws of DSR. In the second part, we analyze some experimental data, which admit an interpretation in terms of the DSR formalism and are, therefore, candidates for displaying a breakdown of the Lorentz symmetry. They are (i) the superluminal propagation of evanescent electromagnetic waves in waveguides, (ii) the meanlife of the KS 0, (iii) the Bose-Einstein correlation in pion production and (iv) the comparison of clock rates in the gravitational field of Earth. Such analysis provides us with the explicit forms of the related deformed metrics as functions of the energy, thus putting in evidence, in all four cases (and therefore for all four fundamental interactions), departures from the usual Minkowski metric. This preliminary evidence for a broken Lorentz invariance may be regarded as the signature of possible nonlocal effects involved in the processes examined. Moreover, the corresponding deformed metrics obtained by our analysis provide an effective dynamical description of the interactions (at least in the energy range considered). (shrink)

Continuity is perhaps the most familiar characterization of the finitary character of the operations performed in computation. We sketch the historical and conceptual development of this notion by interpreting it as a unifying theme across three main varieties of semantical theories of programming: denotational, axiomatic and event-based. Our exploration spans the development of this notion from its origins in recursion theory to the forms it takes in the context of the more recent event-based analyses of sequential and concurrent computations, touching (...) upon the relations of continuity with non-determinism. (shrink)

We present a type inference system for pure λ-calculus which includes, in addition to arrow types, also universal and existential type quantifiers, intersection and union types, and type recursion. The interest of this system lies in the fact that it offers a possibility to study in a unified framework a wide range of type constructors. We investigate the main syntactical properties of the system, including an analysis of the preservation of types under parallel reduction strategies, leading to a form of (...) the subject-reduction property. We describe a model for this system where types are special subsets of a D∞ model for λ-calculus, without imposing any formal contractiveness constraint on types of the kind considered for a closely related system by MacQueen, Plotkin and Sethi. (shrink)

We expose some basic elements of a style of programming supported by functional languages like Haskell by relating them to a coherent set of notions and techniques from Curry’s work in combinatory logic and formal systems, and their algebraic and categorical interpretations. Our account takes the form of a commentary to a simple fragment of Haskell code attempting to isolate the conceptual sources of the linguistic abstractions involved.

In this paper, we introduce the concept of N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. This is the first of a series of papers devoted to the investigation of the Killing symmetries of generalized Minkowski spaces. In particular, we discuss here the infinitesimal-algebraic structure of the space-time rotations in such spaces. It is shown that the maximal Killing group of these spaces is the direct product (...) of a generalized Lorentz group and a generalized translation group. We derive the explicit form of the generators of the generalized Lorentz group in the self-representation and their related, generalized Lorentz algebra. The results obtained are specialized to the case of a 4-dimensional, “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\widetilde M}$$ \end{document}4, i.e., a pseudoeuclidean space with metric coefficients depending on energy. (shrink)

In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit general form of the (...) finite rotations and boosts in different parametric bases. (shrink)

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde M_4 $$ \end{document}.

A torsional-antenna and a log-periodic antenna are used as a source and an analyzer, respectively, to investigate the possible anomalies of an electro-magnetic field. An unexpected isotropic signal has been detected using those torsion angles, which correspond to a breakdown of the Local Lorentz Invariance, which was found in the past. This coincidence is interpreted as the recovery of a lost symmetry by torqueing the antenna, thus putting in evidence that this Lorentz violation is of angular nature. Introducing a new (...) physical dimension—not only a mathematical dimension as a way to rearrange some equations—is here proposed as a general rule to recover the lost symmetry. (shrink)