"Whether or not time travel could ever become a practical proposition, just thinking about it, in the context of the Everett interpretation of quantum mechanics, is very illuminating. The fact that going back in time invariably means going sideways in actuality highlights an important truth: namely, that the parallel realities that arise within the Everett interpretation of quantum mechanics are not discrete entities... Studying the geometry of this continuum should prove a fruitful and fascinating line of research for the more avant-garde physicists of the twenty-first century." Michael Lockwood, The Labyrinth of Time. |
The quest for a quantum gravity theory began more than fifty years ago; but so far, despite the hard efforts of some of the greatest minds of the twentieth century, a quantum theory of time and gravity remains a tantalizing and elusive problem. Numerous lines of research have been proposed, some of them involving the work of a considerable number of scientists within the physicists and mathematicians community; however, none of these dominant approaches have provided conclusive answers or any new fundamental insights about our classical theories. The situation results even more dramatic if we consider that there is not experimental evidence that can guide our search or that can be used to confront the new proposals... read more.
The Limits of Classical Formalism:
Causality Violations, Quantum Computation and Quantum Geometry:
Causality violations as black holes are one of the most intriguing predictions of classical relativistic formalism. These phenomena have been normally considered as unphysical mainly because, within the classical formalism, causality violations seem to impose more initial data constraints than those normally required in causality respecting spacetimes. These initial constrains, for which we do not have experimental evidence, apparently are revealing the unphysical character of these phenomena. We are interested to know whether causality violations should be ignored because in conflict with our physical theories or have to be considered seriously in relation, for instance, with gravitational collapse scenarios... read more
Logic, Physics and Geometry:
The first of the 10 problems that Hilbert posed in his famous conference the 1900 in Paris; the problem of the Continuum Hypothesis (CH for short), which asserts that every subset of the real numbers is either enumerable or has the cardinality of the Continuum; was the origin of probably one of the greatest achievements in mathematics of the second half of the XXth century, that is the forcing technique created by P. Cohen during the sixties. Using this technique Cohen showed that the CH is independent (i.e. it cannot be proved or disproved) from the axioms of Zermelo-Fraenkel plus the Axiom of Choice (ZFC) . A couple of years later, in 1965, Scott and Solovay gave a more constructive version of Cohen’s technique based on models ruled by a boolean-valued logic. Based on this latter approach, in 1975, Takeuti showed that in a boolean valued model of set theory constructed over a complete boolean algebra of projector operators acting over a Hilbert space, there is a correspondence between the continuum of the model and the self-adjoint operators that can be expressed by the projectors of the algebra. The connection of this surprising result with interpretational issues in quantum theory was explored by Davis hypothesizing the possibility to introduce a relativistic principle in quantum theory. However, no conclusive results were obtained in this direction and maybe due to the fact that the mathematics of these constructions were based on advanced methods of set theory and model theory, these results did not reach the attention of the physicists community... read more
