A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory

This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf--the topos quantum analogue of a classical state space. In the second part of the paper we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study `truth objects' in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism.Comment: 34 pages, no figure

Guarding the Tongue: A thematic analysis of gossip control strategies among orthodox Jewish women

This article describes the views and experiences of Strictly-Orthodox Jewish women with respect to the metapragmatic ethos of Shmiras HaLoshon (monitoring one's talk, literally 'guarding the tongue'). Eight extended interviews were conducted with Strictly-Orthodox women and teenagers in London, and salient themes were identified, namely: A. Loshon Hora ('evil talk') is the prime exemplar of bad talk. B. Loshon Hora is the hardest (one of the hardest) things to avoid, because it is so easy to do. C. The perceived consequences of Loshon Hora are very serious D. Great caution/various strategies are employed in order to not speak Loshon Hora E. Perceived gender differences exist in proneness to speak Loshon Hora. F. One is reponsible for monitoring others. G. Young children can be(come) aware of the issues. Subjects appeared to take this aspect of religious observance very seriously, and were taking active steps to promote observance. Social desirability bias may be an inappropriate concept for explaining our participants' behaviour. It is also suggested that the perceived importance of Shmiras HaLoshon may be important in helping to maintain community cohesion and preventing conflicts, by improving respect for privacy and reputation in a community where gossip is attractive but divisive

Is Gliese 581d habitable? Some constraints from radiative-convective climate modeling

The recently discovered exoplanet Gl581d is extremely close to the outer edge of its system's habitable zone, which has led to much speculation on its possible climate. We have performed a range of simulations to assess whether, given simple combinations of chemically stable greenhouse gases, the planet could sustain liquid water on its surface. For best estimates of the surface gravity, surface albedo and cloud coverage, we find that less than 10 bars of CO2 is sufficient to maintain a global mean temperature above the melting point of water. Furthermore, even with the most conservative choices of these parameters, we calculate temperatures above the water melting point for CO2 partial pressures greater than about 40 bar. However, we note that as Gl581d is probably in a tidally resonant orbit, further simulations in 3D are required to test whether such atmospheric conditions are stable against the collapse of CO2 on the surface.Comment: 9 pages, 11 figures. Accepted for publication in Astronomy & Astrophysic

A Geometrical Characterization of the Twin Paradox and its Variants

The aim of this paper is to provide a logic-based conceptual analysis of the twin paradox (TwP) theorem within a first-order logic framework. A geometrical characterization of TwP and its variants is given. It is shown that TwP is not logically equivalent to the assumption of the slowing down of moving clocks, and the lack of TwP is not logically equivalent to the Newtonian assumption of absolute time. The logical connection between TwP and a symmetry axiom of special relativity is also studied.Comment: 22 pages, 3 figure

Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3?

Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on $K3$, or on surfaces whose universal covering is $K3$.Comment: Misprints in eqs.(9-11) corrected. Submitted to Classical and Quantum Gravit

Increased insolation threshold for runaway greenhouse processes on Earth like planets

Because the solar luminosity increases over geological timescales, Earth climate is expected to warm, increasing water evaporation which, in turn, enhances the atmospheric greenhouse effect. Above a certain critical insolation, this destabilizing greenhouse feedback can "runaway" until all the oceans are evaporated. Through increases in stratospheric humidity, warming may also cause oceans to escape to space before the runaway greenhouse occurs. The critical insolation thresholds for these processes, however, remain uncertain because they have so far been evaluated with unidimensional models that cannot account for the dynamical and cloud feedback effects that are key stabilizing features of Earth's climate. Here we use a 3D global climate model to show that the threshold for the runaway greenhouse is about 375 W/m$^2$, significantly higher than previously thought. Our model is specifically developed to quantify the climate response of Earth-like planets to increased insolation in hot and extremely moist atmospheres. In contrast with previous studies, we find that clouds have a destabilizing feedback on the long term warming. However, subsident, unsaturated regions created by the Hadley circulation have a stabilizing effect that is strong enough to defer the runaway greenhouse limit to higher insolation than inferred from 1D models. Furthermore, because of wavelength-dependent radiative effects, the stratosphere remains cold and dry enough to hamper atmospheric water escape, even at large fluxes. This has strong implications for Venus early water history and extends the size of the habitable zone around other stars.Comment: Published in Nature. Online publication date: December 12, 2013. Accepted version before journal editing and with Supplementary Informatio

Drowning your sorrows? Attitudes towards alcohol in UK Jews and Protestants: a thematic analysis

Jewish culturally-supported beliefs may discourage drinking and drunkenness as ways of socialising and coping with stress. Thus Jewish men under stress may be relatively more likely to become depressed, and less likely to use and abuse alcohol. This study is the first qualitative comparison of Jews and Protestants, men and women. It examines whether alcohol-related beliefs are consistent with the alcohol-depression hypothesis, i.e. that positive beliefs about alcohol use and effects are associated with high alcohol use and low depression. Material and discussion: A thematic (interpretive phenomenological) analysis on open-ended question responses, from 70 Jews and 91 Protestants, and on semi-structured interviews with 5 Jews and 4 Protestants, identified three salient themes: the importance of retaining self-control, the pleasures of losing inhibitions, and the relations of alcohol-related behaviour to identity. Compared to Protestants, Jews described alcohol-related behaviour as threatening to self-control, loss of inhibition as unenjoyable and dangerous, and distinguished between the kinds of drinking behaviours appropriate for Jews and others. Sub-themes for Protestant men were denial that drinking threatens self-control, and appropriateness of going to the pub. Conclusions: The themes identified are not measurable using published research instruments. Alcohol-related behaviour may be a feature of Jewish identity. The beliefs identified are consistent with the alcohol-depression hypothesis

Topos theory and `neo-realist' quantum theory

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.Comment: 22 pages, no figures; contribution for Proceedings of workshop "Recent Developments in Quantum Field Theory", MPI MIS Leipzig, July 200

Ethnic-minority groups in England and Wales-factors associated with the size and timing of elevated COVID-19 mortality: a retrospective cohort study linking census and death records

BACKGROUND: We estimated population-level associations between ethnicity and coronavirus disease 2019 (COVID-19) mortality using a newly linked census-based data set and investigated how ethnicity-specific mortality risk evolved during the pandemic. METHODS: We conducted a retrospective cohort study of respondents to the 2011 Census of England and Wales in private households, linked to death registrations and adjusted for emigration (n = 47 872 412). The outcome of interest was death involving COVID-19 between 2 March 2020 and 15 May 2020. We estimated hazard ratios (HRs) for ethnic-minority groups compared with the White population, controlling for individual, household and area characteristics. HRs were estimated on the full outcome period and separately for pre- and post-lockdown periods. RESULTS: In age-adjusted models, people from all ethnic-minority groups were at elevated risk of COVID-19 mortality; the HRs for Black males and females were 3.13 (95% confidence interval: 2.93 to 3.34) and 2.40 (2.20 to 2.61), respectively. However, in fully adjusted models for females, the HRs were close to unity for all ethnic groups except Black [1.29 (1.18 to 1.42)]. For males, the mortality risk remained elevated for the Black [1.76 (1.63 to 1.90)], Bangladeshi/Pakistani [1.35 (1.21 to 1.49)] and Indian [1.30 (1.19 to 1.43)] groups. The HRs decreased after lockdown for all ethnic groups, particularly Black and Bangladeshi/Pakistani females. CONCLUSION: Differences in COVID-19 mortality between ethnic groups were largely attenuated by geographical and socio-demographic factors, though some residual differences remained. Lockdown was associated with reductions in excess mortality risk in ethnic-minority populations, which has implications for a second wave of infection

Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries

We extend the Mason-Newman Lax pair for the elliptic complex Monge-Amp\`ere equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the K\"ahler potential which directly leads to a Legendre transformation and to a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Amp\`ere equation and obtain hyper-K\"ahler metrics with anti-self-dual Riemann curvature 2-form that admit no Killing vectors.Comment: submitted to J. Phys.