The Einstein-Podolsky-Rosen Argument and the Bell Inequalities

In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called ``Reality Criterion'' imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will

Helly dimension of algebraic groups

It is shown that for a linear algebraic group G over a field of characteristic zero, there is a natural number \kappa(G) such that if a system of Zariski closed cosets in G has empty intersection, then there is a subsystem consisting of at most \kappa(G) cosets with empty intersection. This is applied to the study of algebraic group actions on product varieties.Comment: 18 page

Target selection of classical pulsating variables for space-based photometry

In a few years the Kepler and TESS missions will provide ultra-precise photometry for thousands of RR Lyrae and hundreds of Cepheid stars. In the extended Kepler mission all targets are proposed in the Guest Observer (GO) Program, while the TESS space telescope will work with full frame images and a ~15-16th mag brightness limit with the possibility of short cadence measurements for a limited number of pre-selected objects. This paper highlights some details of the enormous and important work of the target selection process made by the members of Working Group 7 (WG#7) of the Kepler and TESS Asteroseismic Science Consortium.Comment: 4 pages, 1 figure, proceedings of the RRL2015 - High-Precision Studies of RR Lyrae Stars conference, to appear in the Communications from the Konkoly Observator

A modulated RRd star observed by K2

We report the analysis of the double-mode RR Lyrae star EPIC 205209951, the first modulated RRd star observed from space. The amplitude and phase modulation are present in both modes.Comment: 2 pages, 3 figures, proceedings of the Joint TASC2-KASC9-SPACEINN-HELAS8 Conference "Seismology of the Sun and the Distant Stars 2016", to be published in EPJ Wo

A local hidden variable theory for the GHZ experiment

A recent analysis by de Barros and Suppes of experimentally realizable GHZ correlations supports the conclusion that these correlations cannot be explained by introducing local hidden variables. We show, nevertheless, that their analysis does not exclude local hidden variable models in which the inefficiency in the experiment is an effect not only of random errors in the detector equipment, but is also the manifestation of a pre-set, hidden property of the particles ("prism models"). Indeed, we present an explicit prism model for the GHZ scenario; that is, a local hidden variable model entirely compatible with recent GHZ experiments.Comment: 17 pages, LaTeX, 7 eps figures, computer demo: http://hps.elte.hu/~leszabo/GHZ.html, an improper figure is replace

Mapping a star with transits: orbit precession effects in the Kepler-13 system

Kepler-13b (KOI-13.01) is a most intriguing exoplanet system due to the rapid precession rate, exhibiting several exotic phenomena. We analyzed $Kepler$ Short Cadence data up to Quarter 14, with a total time-span of 928 days, to reveal changes in transit duration, depth, asymmetry, and identify the possible signals of stellar rotation and low-level activity. We investigated long-term variations of transit light curves, testing for duration, peak depth and asymmetry. We also performed cluster analysis on $Kepler$ quarters. We computed the autocorrelation function of the out-of-transit light variations. Transit duration, peak depth, and asymmetry evolve slowly, due to the slowly drifting transit path through the stellar disk. The detected transit shapes will map the stellar surface on the time scale of decades. We found a very significant clustering pattern with 3-orbit period. Its source is very probably the rotating stellar surface, in the 5:3 spin-orbit resonance reported in a previous study. The autocorrelation function of the out-of-transit light variations, filtered to 25.4 hours and harmonics, shows slow variations and a peak around 300--360 day period, which could be related to the activity cycle of the host star.Comment: 7 pages, 7 figures, accepted in MNRA

Metal-rich or misclassified? The case of four RR Lyrae stars

We analysed the light curve of four, apparently extremely metal-rich fundamental-mode RR Lyrae stars. We identified two stars, MT Tel and ASAS J091803-3022.6 as RRc (first-overtone) pulsators that were misclassified as RRab ones in the ASAS survey. In the case of the other two stars, V397 Gem and ASAS J075127-4136.3, we could not decide conclusively, as they are outliers in the period-Fourier-coefficient space from the loci of both classes, but their photometric metallicities also favour the RRc classification.Comment: 5 pages, 2 figures, published in IBVS: http://ibvs.konkoly.hu/cgi-bin/IBVS?617

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure