Born-Infeld Theory and Stringy Causality

Fluctuations around a non-trivial solution of Born-Infeld theory have a limiting speed given not by the Einstein metric but the Boillat metric. The Boillat metric is S-duality invariant and conformal to the open string metric. It also governs the propagation of scalars and spinors in Born-Infeld theory. We discuss the potential clash between causality determined by the closed string and open string light cones and find that the latter never lie outside the former. Both cones touch along the principal null directions of the background Born-Infeld field. We consider black hole solutions in situations in which the distinction between bulk and brane is not sharp such as space filling branes and find that the location of the event horizon and the thermodynamic properties do not depend on whether one uses the closed or open string metric. Analogous statements hold in the more general context of non-linear electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld action to second order might be obtained from higher-curvature gravity in Kaluza-Klein theory. Finally we point out some intriguing analogies with Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde

Causality and momentum conservation from relative locality

Theories with a curved momentum space, which became recently of interest in the quantum-gravity literature, can in general violate many apparently robust aspects of our current description of the laws of physics, including relativistic invariance, locality, causality and global momentum conservation. We here explore some aspects of the particularly severe pathologies arising in generic theories with curved momentum space for what concerns causality and momentum conservation. However, we also report results suggesting that when momentum space is maximally symmetric, and the theory is formulated (DSR-)relativistically, with the associated relativity of spacetime locality, momentum is globally conserved and there is no violation of causality.Comment: 20 pages, 6 figures, latex (V2: minor editing

Time-symmetry without retrocausality: how the quantum can withhold the solace

It has been suggested that some of the puzzles of QM are resolved if we allow that there is retrocausality in the quantum world. In particular, it has been claimed that this approach offers a path to a Lorentz-invariant explanation of Bell correlations, and other manifestations of quantum "nonlocality", without action-at-a-distance. Some writers have suggested that this proposal can be supported by an appeal to time-symmetry, claiming that if QM were made "more time-symmetric", retrocausality would be a natural consequence. Critics object that there is complete time-symmetry in classical physics, and yet no apparent retrocausality. Why should QM be any different? In this note I call attention to a respect in which QM is different, under some assumptions about quantum ontology. Under these assumptions, the option of time-symmetry without retrocausality is not available in QM, for reasons intimately connected with the fundamental differences between classical and quantum physics (especially the role of discreteness in the latter)

Grouping time series by pairwise measures of redundancy

A novel approach is proposed to group redundant time series in the frame of causality. It assumes that (i) the dynamics of the system can be described using just a small number of characteristic modes, and that (ii) a pairwise measure of redundancy is sufficient to elicit the presence of correlated degrees of freedom. We show the application of the proposed approach on fMRI data from a resting human brain and gene expression profiles from HeLa cell culture.Comment: 4 pages, 8 figure