A New Insight on Physical Phenomenology: A Review

After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the deformed Minkowski space lead to a plurality of potential physical phenomena that should occur, provided that the resulting formalisms can be considered as useful models for the description of some aspects of physical reality. A list is given of available experimental evidence not easy to be interpreted, at present, by means of the more established models, such as the standard model with its variants aimed at overcoming its descriptive limits; this evidence could be useful to verify the predictions stemming from the properties of the deformed Minkowski space. The list includes anomalies in the double-slit-like experiments, nuclear metamorphosis, torsional antennas, as well as the physical effect of the “geometric vacuum” (as defined in analogy with quantum vacuum), in the absence of external electromagnetic field, when crossing critical thresholds of energy parameter values, energy density in space and energy density in time. Concrete opportunities are suggested for an experimental exploration of phenomena, either already performed but still lacking a widely accepted explanation, or conceivable in the application of the approach here presented, but not tackled until now. A tentative list is given with reference to experimental infrastructures already in operation, the performances of which can be expanded with limited additional resources.

ANALYSIS ON q-DEFORMED QUANTUM SPACES

A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather complete and self-contained way. All relevant notions are introduced and explained in detail. The different possibilities to realize the objects of q-deformed analysis are discussed and their elementary properties are studied. In this manner attention is focused on star products, q-deformed tensor products, q-deformed translations, q-deformed partial derivatives, dual pairings, q-deformed exponentials, and q-deformed integration. The main concern of this work is to show that these objects fit together in a consistent framework, which is suitable to formulate physical theories on quantum spaces.

DOUBLY SPECIAL RELATIVITY VERSUS κ-DEFORMATION OF RELATIVISTIC KINEMATICS

We argue that the so-called doubly special relativity (DSR), recently proposed by Amelino-Camelia et al.1,2 with deformed boost transformations identical with the formulae for κ-deformed kinematics in bicrossproduct basis is classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed four-momenta as advocated in Refs. 1 and 2 implies that DSR is obtained by considering the nonlinear four-momenta basis of classical Poincaré algebra and it does not lead to noncommutative space–time. We also show how to construct two large classes of doubly special relativity theories — generalizing the choice in Refs. 1 and 2 and the one presented by Magueijo and Smolin.3 The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative κ-deformed Minkowski space is provided by quantum κ-deformation of Poincaré symmetries.

ENERGY-DEPENDENT METRIC FOR GRAVITATION FROM CLOCK-RATE EXPERIMENTS

We carry out a detailed analysis of the data on the comparison of clock rates between a flying clock and a clock at ground, performed by Alley and co-workers at the end of 1970's. The fit to such data is in favor of an energy-dependent metric for gravitation, whose time coefficient is at variance with the standard Einsteinian one in the weak-field approximation. By exploiting the formalism of a deformed Minkowski space–time, with metric coefficients dependent on the energy, we show that a possible lower limit on the propagation speed of gravitational effects is about 1010c, in agreement with a recent analysis by Van Flandern based on the acceleration of binary systems.