Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) is shown to provide a unified origin for: i) the complex vector space formulation of Quantum Mechanics (QM); ii) the momentum and space commutation relations and the corresponding representations; iii) the Dirac Hamiltonian in the formulation of Relativistic Quantum Mechanics (RQM); iv) the existence of a self adjoint Time Operator that circumvents Pauli's objection.

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

Neurological Soft Signs and cognitive processes in Mexican schoolchildren aged 6 to 11 yearsAbstrac Neurological Soft Signs (NSS) are indicative of generalized disruptions in neurological networks of cortico-subcortical areas.Their presence leads to problems in children's cognitive development with future academic repercussions. The presence of NSS was assessed and compared in 144 children aged 6 to 11 years of low-medium socioeconomic status from Mexico City and the metropolitan area through the Infant Neuropsychological Maturity Questionnaire (CUMANIN, for its Spanish acronym) and the School Neuropsychological Maturity Questionnaire (CUMANES, for its Spanish acronym). Results indicate significant differences by sex. Girls showed better performance in word articulation. In groups by age, significant differences were found in leximetriccomprehension, visual perception and executive function-errors. Participants showed the presence of developmental NSS which include: language (articulation disorders, oral and written language disturbances, difficulty finding words), psychomotricity, visual perception and other cognitive functions. There are several factors related to those impairments such as age, socioeconomic context and critical stages in child´s development. Identification and early diagnosis can reduce the risk of school failure.

We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from quantum gravity. Specifically we consider a two-parameter class of twisted Poincaré algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces, and quantum effects that arise as noncommutativities. Starting from a universal differential algebra of forms based on the above-mentioned Lie-algebraic noncommutativities of the translations, we construct the noncommutative differential forms and inner and outer derivations, which are the noncommutative equivalents of the vector fields in the case of commutative differential geometry. Having established the essentials of this formalism, we construct a bimodule, which is required to be central under the action of the inner derivations in order to have well-defined contractions and from where the algebraic dependence of its coefficients is derived. This again then defines the noncommutative equivalent of the geometrical line-element in commutative differential geometry. We stress, however, that even though the components of the twisted metric are by construction symmetric in their algebra valuation, it is not so for their inverse, and thus to construct it, we made use of Gel’fand’s theory of quasi-determinants, which is conceptually straightforward but computationally quite complicated beyond an algebra of 3 generators. The consequences of the noncommutativity of the Lie-algebra twisted geometry are further discussed.

Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schrödinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s). Integrating developments are: a) entanglement of a microscopic system with its classical environment accords it a time evolution description, the time dependent Schrödinger equation, where t is the laboratory time measured by clocks; b) canonical quantization of Special Relativity yields both the Dirac Hamiltonian and a self adjoint "time" operator, restoring to position and time the equivalent footing accorded to energy and momentum in Relativistic Quantum Mechanics. It introduces an intrinsic time property τ associated with the mass of the system, and a basis additional to the usual configuration, momentum and energy basis. As a generator of momentum displacements and consequently of energy, it invalidates Pauli's objection to the existence of a time operator. It furthermore complies with the requirements to condition the other observables in the conditional interpretation of QG.As Pauli's objection figures explicit or implicitly in most current developments of QM and QG, its invalidation opens to research the effect of this new two times perspective on such developments."If you are receptive and humble, mathematics will lead you by the hand" "One must be prepared to follow up the consequences of theory, and feel that one just has to accept the consequences no matter where they lead" P. A. M. Dirac