Artículos con la etiqueta ‘Físico matemática’

Three Merry Roads to T-Violation

Por • 30 jun, 2013 • Category: Leyes

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are really just three approaches currently being explored. I show how each is characterized by a symmetry principle, which provides a template for detecting T-violating laws even without knowing the laws of physics themselves. Each approach is illustrated with an example, and the prospects of each are considered in extensions of particle physics beyond the standard model.

God and Physics: From Hawking to Avicenna

Por • 3 jun, 2013 • Category: Ambiente

The twin pillars of every civilization are religion and science. Contemporary cosmological theories, especially discourse about the origins of the universe, reveal the continuing encounter between physics and theology. It is a discourse which interests thinkers of our own age as much as it did those in the Middle Ages. I should like to sketch some of the current discussion in order to suggest how the contemporary world can learn a great deal from mediaeval analyses of the relationship among physics, metaphysics, and theology. In fact, to go from Stephen Hawking to Avicenna is, in an important sense, to go from confusion to clarity. Recent studies in particle physics and astronomy have produced dazzling speculations about the early history of the universe. Cosmologists now routinely entertain elaborate scenarios which propose to describe what the universe was like when it was the size of a softball, a mere 10-35 second after the Big Bang. The description of the emergence of four fundamental forces and twelve discrete subatomic particles is almost a common-place in modern physics. There is little doubt among scientists that we live in the aftermath of a giant explosion which occurred around 15 billion years ago — give or take a few billion.

Commuting and noncommuting infinitesimals

Por • 10 abr, 2013 • Category: Filosofía

Infinitesimals are natural products of the human imagination. Their history goes back to the Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs. They have stimulated strong opinions and even vitriol. Edwin Hewitt developed hyperreal fields in the 1940s. Abraham Robinson’s infinitesimals date from the 1960s. A noncommutative version of infinitesimals, due to Alain Connes, has been in use since the 1990s. We review some of the hyperreal concepts, and compare them with some of the concepts underlying noncommutative geometry.

The Euler-Lagrange and Hamilton-Jacobi actions and the principle of least action

Por • 26 feb, 2013 • Category: Crítica

We recall the main properties of the classical action of Euler-Lagrange Scl(x; t; x0), which links the initial position x0 and its position x at time t, and of the Hamilton-Jacobi action, which connects a family of particles of initial action S0(x) to their various positions x at time t. Mathematically, the Euler-Lagrange action can be considered as the elementary solution of the Hamilton-Jacobi equation in a new branch of nonlinear mathematics, the Minplus analysis. Physically, we show that, contrary to the Euler-Lagrange action, the Hamilton-Jacobi action satis?es the principle of least action. It is a clear answer on the interpretation of this principle. Finally, we use the relation-ship between the Hamilton-Jacobi and Euler-Lagrange actions to study the convergence of quantum mechanics, when the Planck constant tends to 0, for a particular class of quantum systems, the statistical semiclassical case.

Tomita-Takesaki Modular Theory vs. Quantum Information Theory

Por • 12 ene, 2013 • Category: Crítica

In this review article, we make an attempt to find out the relationship between separating and cyclic vectors in the theory of von Neumann algebra and entangled states in the theory of quantum information. The corresponding physical interpretation is presented as well.

Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics

Por • 24 nov, 2011 • Category: Ciencia y tecnología

Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed, which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model, two alternative proofs of Takeuti’s correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive, showing a direct relation with the Gelfand representation theorem, and revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation of quantum theory. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality in Quantum Mechanics also in close connection with the Deutsch-Everett perspective.