J. M. Domingos’s research while affiliated with University of Coimbra and other places

In strict accordance with special relativity, locality is defined in terms of observed results. In a non-deterministic "hidden-parameter" theory, admitting "statistical independence" of the outcomes for a single pair, locality and a restriction ("primary locality") at the level of "primary probabilities", Bell's inequalities are recollected. Their violation is traced to the assumption of an algebraic structure defining relations between single-constituent "probabilistic" descriptions that cannot be interpreted as distinctive properties of the components. It is then concluded that the experimental violation of Bell's inequalities cannot be a test of non-locality, even if locality is interpreted at the unobservable level, in terms of "primary probabilities".

We comment on a recently published criticism of our analysis of the paradox of Einstein, Podolsky and Rosen.

The Einstein, Podolsky and Rosen paradox, in Bohm's version, is re-examined with emphasis on the spin correlation operators, which represent the correlations in the mathematical theory as created in our mind. It is justified, in this approach, that these spin correlation operators acquire the status of physical concepts only in the context of a specific coincidence electronic set up, involving joint measurements in both subsystems. The analysis concurs with Bohr's point of view and it is held that inside Copenhagen interpretation there is no paradox. Attention is drawn to some adjacent problems such as Copenhagen interpretation, measurement theory and the applicability of the ignorance interpretation to quantum mixtures. Resumo. É reexaminado o paradoxo de Einstein, Podolsky e Rosen na versão de Bohm, sendo realçado o papel dos operadores de correlação de spin, que representam as correlações da teoria matemática. Sugere-se que estes operadores de correlação de spin só adquiram significado físico no contexto de uma montagem experimental específica para medição de coincidências, envolvendo medidas conjuntas nos dois subsistemas. Esta análise está em acordo com o ponto de vista de Bohr. Mantém-se que, dentro da interpretação de Copenhaga, não há paradoxo. É chamada a atenção para alguns problemas adjacentes tais como a interpretação de Copenhaga e a teoria da medida.

Discusses, for a product of several operators and in relation to commutativity, the requirements for the establishment of meaningful expectation values. A published example relating to the product of spin operators, where not all pairs commute, is critically examined on the basis of the strict properties of the Pauli operators.

Hegerfeldt proved that the localization of a relativistic quantum particle in a finite-space regionV, at a given timet 0, implies that the probability of finding the particle, at a later timet, at a distance |a|>c(t−t 0), is nonzero. We show that this mechanism cannot be used in the transmission of signals and therefore there is no conflict with relativistic causality.

The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied.

The construction of the quantum-mechanical Hamiltonian by canonical quantization is examined. The results are used to enlighten examples taken from slow nuclear collective motion. Hamiltonians, obtained by a thoroughly quantal method (generator-coordinate method) and by the canonical quantization of the semiclassical Hamiltonian, are compared. The resulting simplicity in the physics of a system constrained to lie in a curved space by the introduction of local Riemannian coordinates is emphasized. In conclusion, a parallel is established between the result for various coordinates and a proposed procedure for quantizing the semiclassical Hamiltonian for a single coordinate.

Assuming the Gaussian overlap approximation, a Schrodinger equation, for the collective motion of a system described by various shape parameters, is derived from the Hill-Wheeler equation. In this way a properly quantized Hamiltonian is obtained. An application to the solvable model due to Moszkowski is studied and results of the calculations, in the transition region, are compared with other approximations.

A review of Wigner's time reversal is presented and some important aspects are emphasized. The subject is introduced via classical mechanics. Non-physical statements as time running backwards are avoided. Comments are made on the roles of time and of the operatori(/t) in quantum mechanics. The role of symmetries and conservation laws and some properties of the time-reversed states are discussed.