Neutrino Oscillations from Strings and Other Funny Things

I will discuss three related unconventional ways to generate neutrino oscillations (1)Equivalence principle violation by the string dilaton field (i2)Violation of Lorentz Invariance and (3) Equivalence principle violation through a non-universal tensor neutrino-gravity coupling. These unorthodox neutrino oscillation mechanisms are shown to be viable at the level of our present experimental knowledge and demonstrate that neutrino oscillations can probe very profound questions

Mapping Lorentz Invariance Violations into Equivalence Principle Violations

We point out that equivalence principle violations, while not dynamically equivalent, produce the same kinematical effects as Lorentz invariance violations for particle processes in a constant gravitational potential. This allows us to translate many experimental bounds on Lorentz invariance violations into bounds on equivalence principle violations. The most stringent bound suggests that a postive signal in an E\"otv\"os experiment may be at least seven orders of magnitude beyond current technology.Comment: 6 pages, late

Neutrino Tests of General and Special Relativity

We review the status of testing the principle of equivalence and Lorentz invariance from atmospheric and solar neutrino experiments.Comment: replaced incorrect abstract in earlier version; LaTeX, 10 pages; 1 postscript figure included at the end; to appear in the Proceedings of the 1999 Workshop on Neutrino Factories Based on a Muon Collider, Lyon, France, July 5-9, 199

Closing the neutrinoless double beta decay window into violations of the equivalence principle and/or Lorentz invariance

We have examined Lorentz invariance and equivalence principle violations in the neutrino sector as manifested in neutrinoless double beta decay. We conclude that this rare decay cannot provide a useful view of these exotic processes.Comment: 5 pages, RevTe

Neutrino Oscillations from String Theory

We derive the character of neutrino oscillations that results from a model of equivalence principle violation suggested recently by Damour and Polyakov as a plausible consequence of string theory. In this model neutrino oscillations will take place through interaction with a long range scalar field of gravitational origin even if the neutrinos are degenerate in mass. The energy dependence of the oscillation length is identical to that in the conventional mass mixing mechanism. This possibility further highlghts the independence of and need for more exacting direct neutrino mass measurements together with a next generation of neutrinoless double beta decay experiments.Comment: 7 pages LaTE

Pulsar Kicks Induced by Spin Flavor Oscillations of Neutrinos in Gravitational Fields

The origin of pulsar kicks is reviewed in the framework of the spin-flip conversion of neutrinos propagating in the gravitational field of a magnetized protoneutron star. We find that for a mass in rotation with angular velocity {\bbox \omega}, the spin connections entering in the Dirac equation give rise to the coupling term {\bbox \omega}\cdot {\bf p}, being ${\bf p}$ the neutrino momentum. Such a coupling can be responsible of pulsar kicks owing to the neutrino emission asymmetry generated by the relative orientation of ${\bf p}$ with respect to {\bbox \omega}. For our estimations, the large non standard neutrino magnetic momentum, $\mu_\nu \lesssim 10^{-11}\mu_B$, is considered.Comment: 8 pages, no figures. Changed content and references adde

The Solar Neutrino Problem in the Light of a Violation of the Equivalence Principle

We have found that long-wavelength neutrino oscillations induced by a tiny breakdown of the weak equivalence principle of general relativity can provide a viable solution to the solar neutrino problem.Comment: 3 pages, 1 eps figure, Talk given by R. Zukanovich Funchal at the VIth International Workshop on ``Topics in Astroparticle and Underground Physics'' (TAUP99), Sep. 6-10, 1999, College de France, Paris - Franc

Confronting Dilaton-exchange gravity with experiments

We study the experimental constraints on theories, where the equivalence principle is violated by dilaton-exchange contributions to the usual graviton-exchange gravity. We point out that in this case it is not possible to have any CPT violation and hence there is no constraint from the CPT violating measurements in the $K-$system. The most stringent bound is obtained from the $K_L - K_S$ mass difference. In contrast, neither neutrino oscillation experiments nor neutrinoless double beta decay imply significant constraints.Comment: 7 page

Neutrino Mixing due to a Violation of the Equivalence Principle

Massless neutrinos will mix if their couplings to gravity are flavor dependent, i.e., violate the principle of equivalence. Because the gravitational interaction grows with neutrino energy, the solar neutrino problem and the recent atmospheric neutrino data may be simultaneously explained by violations at the level of 1E-14 to 1E-17 or smaller. This possibility is severely constrained by present accelerator neutrino experiments and will be preeminently tested in proposed long baseline accelerator neutrino experiments.Comment: 13 page

When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the $n$-stage repeated version of the game exist if and only if both players have $\Omega(n)$ random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the $n$-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on "random-like" sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then $\Omega(n)$ random bits remain necessary for equilibria to exist