Talks

Set theory provides foundations of mathematics in the sense that all the mathematical notions like numbers, functions, relations, structures are defined in the axiomatic set theory called ZFC. Quantum set theory naturally extends ZFC to quantum logic. Hence, we can expect that quantum set theory provides mathematics based on quantum logic. In this talk, I will show a useful application of quantum set theory to quantum mechanics based on the fact that the real numbers constructed in quantum set theory exactly corresponds to the quantum observables. The standard formulation of quantum mechanics answers the question as to in what state an observable A has the value in an interval I. However, the question is not answered as to in what state two observables A and B have the same value. The notion of equality between the values of observables will play many important roles in foundations of quantum mechanics. The notion of measurement of an observable relies on the condition that the observable to be measured and the meter after the measurement should have the same value. We can define the notion of quantum disturbance through the condition whether the values of the given observable before and after the process is the same. It is shown that all the observational propositions on a quantum system corresponds to some propositions in quantum set theory and the equality relation naturally provides the proposition that two observables have the same value. It has been broadly accepted that we cannot speak of the values of quantum observables without assuming a hidden variable theory. However, quantum set theory enables us to do so without assuming hidden variables but alternatively under the consist use of quantum logic, which is more or less considered as logic of the superposition principle. [1] M. Ozawa, Transfer principle in quantum set theory, J. Symbolic Logic 72, 625-648 (2007), online preprint: http://arxiv.org/abs/math.LO/0604349. [2] M. Ozawa, Quantum perfect correlations, Ann. Phys. (N.Y.) 321, 744--769 (2006), online preprint: LANL quant-ph/0501081.

I will comment on the prevailing atmosphere and attitudes that provoked the CJS theorem, aspects of the theorem itself, some features of the aftermath following the theorem and, finally, a critique of the relevance of the theorem based on my own research on position operators in Lorentz covariant quantum theory.

Observations of the Milky Way by the SPI/INTEGRAL satellite have confirmed the presence of a strong 511 KeV gamma-ray line emission from the bulge, which require an intense source of positrons in the galactic center. These observations are hard to account for by conventional astrophysical scenarios, whereas other proposals, such as light DM, face stringent constraints from the diffuse gamma-ray background. I will describe how light superconducting strings could be the source of the observed 511 KeV emission. The associated particle physics, at the ~ 1 TeV scale, is within reach of planned accelerator experiments, while the scenario has a distinguishing spatial distribution, proportional to the galactic magnetic field. I will also discuss how cosmic magnetic fields of nano-Gauss strength today could have been created at the time of baryogenesis. In addition to being astrophysically relevant, such magnetic fields, which are helical, can provide an independent probe of baryogenesis and CP violation in particle physics.