Colour appearance is affected not only by perceptual but also by linguistic context

Terminology is a crucial problem in science, since quite often the terms used to denote theoretical concepts are directly taken from the vocabulary of common words, which usually have multiple meanings. To solve this problem, scientists must operationalize the theoretical concepts they use but, in psychology, sometimes, this can be a difficult task, since the meaning of the terms used to give the instructions to observers can interfere with the spontaneous meaning that observers give to those terms. Starting from some empirical observations, we show that colour appearance is affected not only by the perceptual but also by the linguistic context

Hopf-algebra description of noncommutative-spacetime symmetries

In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a large literature is already available, we propose a line of analysis of noncommutative-spacetime symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutative Minkowski) and of a compatible notion of integration in the noncommutative spacetime. We confirm (and we establish more robustly) previous suggestions that the commutative-spacetime notion of Lie-algebra symmetries must be replaced, in the noncommutative-spacetime context, by the one of Hopf-algebra symmetries. We prove that in kappaMinkowski it is possible to construct an action which is invariant under a Poincare-like Hopf algebra of symmetries with 10 generators, in which the noncommutativity length scale has the role of relativistic invariant. The approach here adopted does leave one residual ambiguity, which pertains to the description of the translation generators, but our results, independently of this ambiguity, are sufficient to clarify that some recent studies (gr-qc/0212128 and hep-th/0301061), which argued for an operational indistiguishability between theories with and without a length-scale relativistic invariant, implicitly assumed that the underlying spacetime would be classical.Comment: 20 pages, no figures, LaTex. This version has exactly the same technical content as version 1, but the observation reported in Section VII is discussed more pedagogicall

Dirac spinors for Doubly Special Relativity and κ\kappa-Minkowski noncommutative spacetime

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a "doubly-special relativity", a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spinors. We also show that our modified Dirac equation naturally arises in constructing a Dirac equation in the kappa-Minkowski noncommutative spacetime. Previous, more heuristic, studies had already argued for a possible role of doubly-special relativity in kappa-Minkowski, but remained vague on the nature of the consistency requirements that should be implemented in order to assure the observer-independence of the two scales. We find that a key role is played by the choice of a differential calculus in kappa-Minkowski. A much-studied choice of the differential calculus does lead to our doubly-special relativity Dirac equation, but a different scenario is encountered for another popular choice of differential calculus.Comment: 26 pages, LaTex. v2: Alessandra Agostini (contributing some results from her PhD thesis) is added to the list of authors. The results presented in v1 remain unchanged and are contained in Section 2. Sections 3,4,5 add results not present in v1, concerning the realization of the DSR-deformed Dirac equation in kappa-Minkowski noncommutative spacetime. Title changed accordingl

Covariant formulation of Noether's Theorem for translations on kappa-Minkowski spacetime

The problem of finding a formulation of Noether's theorem in noncommutative geometry is very important in order to obtain conserved currents and charges for particles in noncommutative spacetimes. In this paper, we formulate Noether's theorem for translations of kappa-Minkowski noncommutative spacetime on the basis of the 5-dimensional kappa-Poincare' covariant differential calculus. We focus our analysis on the simple case of free scalar theory. We obtain five conserved Noether currents, which give rise to five energy-momentum charges. By applying our result to plane waves it follows that the energy-momentum charges satisfy a special-relativity dispersion relation with a generalized mass given by the fifth charge. In this paper we provide also a rigorous derivation of the equation of motion from Hamilton's principle in noncommutative spacetime, which is necessary for the Noether analysis.Comment: LateX, 24 pages. This version includes the analysis of the case of massive fiel

The perceptual contrast of impossible shadow edges

Luminance ratios along shadow edges remain the same even when they cross reflectance borders. According to Gilchrist (1988, Perception & Psychophysics 43 415 ^ 424) this so-called ratio-invariance property is a crucial factor in the perception of shadows. However, Soranzo and Agostini (2004, Perception 33 1359 ^ 1368) suggested that in some conditions (named `impossible shadows'), a luminance pattern might still be perceived as a shadow even if the ratio-invariance property along its edge is violated. This can occur when an edge is collinear with another edge (contextual edge) which incorporates it, shares the same polarity, and generates a larger ratio. The hypothesis that impossible shadows are actually perceived as shadows is here tested by comparing the perceptual contrast of a luminance edge in the absence of a contextual edge (control condition) to that of both possible shadow edges (where the contextual and mediating edge share the same ratio) and impossible shadow edges (where the ratio of the contextual edge is larger rather than that at the mediating edge). We found that the perceived contrast of luminance edges shrinks in both possible and impossible shadow conditions rather than in the control condition. This evidence supports the hypothesis that a luminance pattern might be perceived as a shadow even when the ratio-invariance property is violated

Dirac spinors for doubly special relativity and -Minkowski noncommutative spacetime

We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a “doubly-special relativity”, a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spinors. We also show that our modified Dirac equation naturally arises in constructing a Dirac equation in the κ-Minkowski noncommutative spacetime. Previous, more heuristic, studies had already argued for a possible role of doubly-special relativity in κ-Minkowski, but remained vague on the nature of the consistency requirements that should be implemented in order to assure the observer-independence of the two scales. We find that a key role is played by the choice of a differential calculus in κ-Minkowski. A much-studied choice of the differential calculus does lead to our doubly-special relativity Dirac equation, but a different scenario is encountered for another popular choice of differential calculus

kappa-Minkowski representations on Hilbert spaces

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in kappa-Minkowski spacetime in terms of the usual trace of operators.Comment: 23 pag. Latex, correction of a couple of typos, reference added, title slightly change

Luminance gradients, perceived illumination, and lightnes perception

1nonenoneAGOSTINI T.; GALMONTE A.Agostini, Tiziano; Galmonte, Alessandr