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

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Publications (13)


Locality. Relativity and Bell's inequalities
  • Article

May 2006

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19 Reads

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J M Domingos

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".



EPR: Copenhagen interpretation has got what it takes

May 1996

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72 Reads

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3 Citations

European Journal of Physics

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.


Expectation values and non-commuting operators

November 1992

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17 Reads

European Journal of Physics

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.


Localization and noncausal behaviour of relativistic quantum particles

June 1991

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6 Reads

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3 Citations

Il Nuovo Cimento B

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.



Self-adjointness of momentum operators in generalized coordinates

February 1984

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26 Reads

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26 Citations

Foundations of Physics

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 quantization of the Hamiltonian in curved space

January 1984

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13 Reads

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5 Citations

Foundations of Physics

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.


Quantization of the Collective Hamiltonian in the Adiabatic Approximation

May 1979

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6 Reads

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3 Citations

Progress of Theoretical Physics

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.


Time reversal in classical and quantum mechanics

March 1979

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15 Reads

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8 Citations

International Journal of Theoretical Physics

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.


Citations (4)


... "The third related" EPR argument is thus not only a misrepresentation of the original EPR argument, but also lacks cogency: the simultaneous determination of two conjugate quantities it purports to establish has no predictive power; it cannot lead to a physical state in which the values of two conjugate 9 A recent coincidence-measurement presentation of the EPR argument by Domingos et al. [13] thus falls in this class also; this paper has been commented on critically in Ref. [14]. 10 Heisenberg discussed such retrospective measurements on an example of the time-of-flight method of velocity measurement already in 1930 [15], and Bohr commented on such a method of velocity measurement even earlier, in his historic Como paper (Ref. [16], p. 66 in Atomic Theory and the Description of Nature). ...

Reference:

Common Misrepresentation of the Einstein-Podolsky-Rosen Argument
EPR: Copenhagen interpretation has got what it takes
  • Citing Article
  • May 1996

European Journal of Physics

... The covariant and contravariant components of the familiar form of the momentum operator − iℏ∇ has been formulated directly by Leaf [11] for curvilinear coordinates in three-dimensional space. There is a detailed discussion about self-adjointness of generalized momentum operators and the behavior of these operators on the boundary conditions [12,13]. Also, as a straight application of the generalized momentum operator, these operators are applied on a compact manifold such as sphere [14]. ...

Self-adjointness of momentum operators in generalized coordinates
  • Citing Article
  • February 1984

Foundations of Physics

... PT -symmetric quantum systems [1][2][3][4][5] offer a new paradigm for constructing non-Hermitian physical theories. They have a discrete PT symmetry [3,6], where P is a linear operator such as parity and T is an antilinear operator such as time reversal [7][8][9]. Such quantum systems are candidates for theories of fundamental physics, when PT symmetry is unbroken, i.e., when observables have real eigenvalues [1,10] and time evolution is unitary [11][12][13][14]. 1 This last requirement is essential for unitarity and involves the construction of an inner product on the Hilbert space, which differs from the Dirac inner product used in Hermitian theories. ...

Time reversal in classical and quantum mechanics
  • Citing Article
  • March 1979

International Journal of Theoretical Physics

...   in spherical coordinates and also the radial coordinate r remains restricted to fixed radius rR  . The classical Hamiltonian function for a particle of mass M moving freely on this surface is then given by  describe the components of the angular momentum L with respect to the unit vectors k and  .The consistent quantum mechanical Hamiltonian to the equation (20) is as following[16,17] Comparing the equation(21)with the equation(20), we can identify the metric components ...

The quantization of the Hamiltonian in curved space
  • Citing Article
  • January 1984

Foundations of Physics