Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.

In support of a recent conjecture by Nielsen (1999), we prove that the phenomena of ‘incomparable entanglement’— whereby, neither member of a pair of pure entangled states can be transformed into the other via local operations and classical communication (LOCC)—is a generic feature when the states at issue live in an infinite-dimensional Hilbert space.  2002 Elsevier Science B.V. All rights reserved.

Several cases which have been considered by the courts in recent years have highlighted the legal dilemmas facing doctors whose decisions result in the ending of a patient's life. This paper considers the case of Dr Cox, who was convicted of attempting to murder one of his patients, and explores the roles of motive, diminished responsibility and consent in cases of "mercy killing". The Cox decision is compared to that of Tony Bland and Janet Johnstone, in which the patients were (...) in a persistent vegetative state. In all three cases, the doctors believed that their patients' quality of life was so poor that their continued existence was of no benefit to them, and decided that their lives should not be unduly prolonged, yet the doctor who was prosecuted was the one whose dying patient had requested that her death be hastened. The paper examines the law's seemingly contradictory approaches to such cases. (shrink)

Lily Ross Taylor in an interesting recent article on the proportion of freedmen to freeborn in the sepulchral inscriptions of Imperial Rome discusses the increasing omission of status nomenclature by freedmen in the first and second centuries A.D. and the consequent difficulty of determining the status of persons whose names appear in the epitaphs. One contributory factor to this decline in the traditional nomenclature which she mentions is the growing numbers and importance of the freedmen of the emperor, the Augusti (...) liberti. While non-imperial freedmen were anxious to record their acquisition of citizenship, but not their inferior status in the citizen body, the emperor's freedmen, on the other hand, increasingly formalized their status nomenclature so that the formula ‘Aug. lib.’ proclaimed not only the fact of their manumission within the Familia Caesaris but also the higher social status which they enjoyed. An examination of the nomenclature of the Imperial freedmen might help to throw some light on this process, particularly on the problem of dating. (shrink)

According to the causal interpretation of quantum mechanics, one can precisely define the state of an individual particle in a many-body system by its position, momentum, and spin. It is shown in the EPR spin experiment that the quantum torque brings about an instantaneous change in the state of one of the particles when the other undergoes a local interaction, but that such a transfer of “information” cannot be extracted by any experiment subject to the laws of quantum mechanics.

As COVID-19 emerged as a phenomenon of the total environment, and despite the intertwined and complex relationships that make humanity an organic part of the Bio- and Geospheres, the majority of our responses to it have been corrective in character, with few or no consideration for unintended consequences which bring about further vulnerability to unanticipated global events. Tackling COVID-19 entails a systemic and precautionary approach to human-nature relations, which we frame as regaining diversity in the Geo-, Bio-, and Anthropospheres. Its (...) implementation requires nothing short of an overhaul in the way we interact with and build knowledge from natural and social environments. Hence, we discuss the urgency of shifting from current to precautionary approaches to COVID-19 and look, through the lens of diversity, at the anticipated benefits in four systems crucially affecting and affected by the pandemic: health, land, knowledge and innovation. Our reflections offer a glimpse of the sort of changes needed, from pursuing planetary health and creating more harmonious forms of land use to providing a multi-level platform for other ways of knowing/understanding and turning innovation into a source of global public goods. These exemplary initiatives introduce and solidify systemic thinking in policymaking and move priorities from reaction-based strategies to precautionary frameworks. (shrink)

One of the gains to be reckoned from the study of nomenclature in the sepulchral inscriptions of the early empire is the gradual abandonment of attempts to distinguish between slave and freeborn on the basis of personal name or cognomen alone, especially when this is of Latin derivation. Nevertheless, one still finds personal cognomina in undated inscriptions adduced as sole evidence for the origin or status of individuals below senatorial rank. Thus in a standard work on freedmen in the early (...) empire, recently reprinted, names such as Agilis, Amandus, Auctus, Communis, Donatus, Faustus, Felix, etc., are said to be commonly servile, but others such as Aquila, Bassus, Capito, Cams, Celer, Crescens, etc., are taken as ingenuous. The criteria used in making such a distinction are subjective and arbitrary and the statistics based on them are largely valueless. It is the purpose of this note to consider briefly on this question the evidence of the personal nomenclature of the Imperial slaves and freedmen. In this group, the Familia Caesaris, no problem of status arises, and the fact that the majority of their inscriptions can be dated, at least approximately, makes it possible to trace the chronological development of the use of cognomina ingenua by one important group of servile origin from the first to the early third century A.D. Moreover, such a development is useful evidence for change in the social structure of the early empire. (shrink)

In recent times, a previously unchallenged and longstanding communis opinio concerning the extant manuscript tradition of Valerius Flaccus' Argonautica has been shattered by Prof. W.-W. Ehlers in his revelation that the fifteenth-century Laurentianus plut. 39.38, L, written by the Florentine scholar, Niccolò Niccoli, is independent of the much exalted oldest witness, Vaticanus Latinus 3277, V, copied in Fulda in the second quarter of the ninth century. With equally silent subservience to the hazardous and now discredited principle, vetustissimus et optimus, second (...) place in the tradition had commonly been given to a manuscript of similar age to that of V, namely S, discovered in 1416 at the monastery of St. Gall by three humanist scholars, Poggio Bracciolini, Cencio Rustici and Bartolomeo da Montepulciano, and subsequently lost, except through reconstruction from six extant fifteenth-century apographa, each instantly recognizable from the fact that they contain only 1.1–4.317. Between V and S, however, as Ehlers and others before him have argued, a common exemplar, a, must be deduced to exist. (shrink)

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the “natural state” of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined by the (...) quantum potential is introduced and the example of a screw dislocated wave is discussed. (shrink)

In his discussion of Virgilian imitations of Lucretian phraseology Cyril Bailey examines the phenomenon of what he terms the ‘doublet’, that is, the procedure whereby Virgil imitates separate elements of a Lucretian phrase at different points in his own work. Take, for example, De Rerum Natura 1. 210–12: esse videlicet in terris primordia rerum, quae nos fecundas vertentes vomere glebas terraique solum subigentes cimus ad ortus.