What does research say about the Special and General Relativity Theory Teaching?

Na literatura da área de Ensino de Física encontramos diversos argumentos em defesa da inclusão, nos currículos escolares do Ensino Médio, de conteúdos de Física Moderna e Contemporânea. A Teoria da Relatividade Especial e Geral (ao lado da Mecânica Quântica) é um dos pilares da Física Moderna. Consideramos significativo e oportuno obter um panorama da produção acadêmica sobre o ensino e aprendizagem deste tópico. Nosso objetivo é sintetizar os avanços, as convergências e sinalizar perspectivas, com o intuito de contribuir para um avanço e defesa dos trabalhos futuros. Assim, procuramos resposta para a questão: Quais as contribuições da pesquisa em Ensino de Física para que a Teoria da Relatividade Especial e Geral (TREG) possa ser abordada no Ensino Médio?

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.

Introdução matemática aos modelos cosmológicos

Pós-graduação em Matemática Universitária - IGCE

Introdução aos monopolos magnéticos de t’Hooft e Polyakov

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O grupo de estudos e discussão como subsídio ao desenvolvimento de interações discursivas entre professores de física sobre a temática teoria da relatividade

Based on the assumption that the exchange of knowledge can support a process of self-organized interactions of the involved in the process, we present the results of a study about how happen the dialogue between physics teachers involved in a group of study of Modern and Contemporary Physics. With the support of the propositions of Bakhtin about the potential of the discourse and discursive interactions studies, we identified interesting regularities in how organize discussions among teachers, identifying a scheme that allows us to infer the effectiveness of the enforcement of this form of lead and mediate the discussions in groups of continuous formation of physics teachers to other topics, as well as adding arguments in defense of the groups of discussion as a strategy for continuing formation of teachers.

On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one stal ts fi om the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.

Teleparallel equivalent of non-Abelian Kaluza-Klein theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

Spin 1 fields in Riemann-Cartan space-times via Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.

de Sitter special relativity

A special relativity based on the de Sitter group is introduced, which is a theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincare group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime-modified by the presence of the de Sitter horizon-are briefly discussed.

Interacting spin 0 fields with torsion via Duffin-Kemmer-Petiau theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KO field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenbock manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.

De Sitter Special Relativity: Effects on cosmology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

De Sitter Relativity: a New Road to Quantum Gravity?

The Poincar, group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincar, as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant I > is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of I > and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem.

Weak-field approximation of effective gravitational theory with local Galilean invariance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

General relativity in two dimensions: A Hamilton-Jacobi analysis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Consistent gravitationally coupled spin-2 field theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)