A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. 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. In paper II, we studied the topos representations of the propositional language PL(S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language L(S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow \breve{\delta}^o(A):\Sig\map\SR, where \SR is the quantity-value object for this theory. The construction of $\breve{\delta}^o(A)$ is an extension of the daseinisation of projection operators that was discussed in paper II. The object \SR is a monoid-object only in the topos, $\tau_\phi$, of the theory, and to enhance the applicability of the formalism, we apply to \SR a topos analogue of the Grothendieck extension of a monoid to a group. The resulting object, \kSR, is an abelian group-object in $\tau_\phi$. We also discuss another candidate, \PR{\mathR}, for the quantity-value object. In this presheaf, both inner and outer daseinisation are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme.Comment: 38 pages, no figure

Impact Of Gravitational Waves From First-Order Phase Transitions On Structure Formation

In this thesis we investigate the possibility that gravitational waves emitted from a first-order phase transition exhibit enough power to alter or generate uctuations in the primordial plasma of the early universe and in turn imprint new features into the matter power spectrum. We approach this task by performing a second order perturbative expansion of two coupled non-linear equations that monitor the evolution of energy density gradients in the 1+3 covariant formulation of cosmology. As a result, we find that adiabatic density fluctuations at second order can be generated from inhomogeneities in the gravitational wave energy density on sub-horizon scales. We interpret these fluctuations as baryon acoustic oscillations seeded by gravity radiation and derive their transferfunction to study their impact on the matter power spectrum. Strength and scale of the imprinted signatures depend on three phase transition parameters, namely the latent heat, the duration and the time at which gravitational waves are released. The amplitude of the signatures is limited by the cosmic variance bound on the matter power spectrum. We use this constraint to deduce limits for these three parameters and translate them into a new exclusion region for the relic stochastic gravitational wave background today. Finally, we discuss our results in the context of first-order phase transitions occurring in particle models

A Topos Foundation for Theories of Physics: IV. Categories of Systems

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. 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. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.Comment: 38 pages, no figure

Topos quantum theory with short posets

Topos quantum mechanics, developed by Isham et. al., creates a topos of presheaves over the poset V(N) of abelian von Neumann subalgebras of the von Neumann algebra N of bounded operators associated to a physical system, and established several results, including: (a) a connection between the Kochen-Specker theorem and the non-existence of a global section of the spectral presheaf; (b) a version of the spectral theorem for self-adjoint operators; (c) a connection between states of N and measures on the spectral presheaf; and (d) a model of dynamics in terms of V(N). We consider a modification to this approach using not the whole of the poset V(N), but only its elements of height at most two. This produces a different topos with different internal logic. However, the core results (a)--(d) established using the full poset V(N) are also established for the topos over the smaller poset, and some aspects simplify considerably. Additionally, this smaller poset has appealing aspects reminiscent of projective geometry.Comment: 14 page

Factors influencing the effectiveness of serious gaming in the field of vocational orientation

This study investigates the effectiveness of the serious game like2be, which has been developed to support the individual career orientation process of adolescents by broadening their occupational horizon. In this paper, we present results from an intervention study with n = 809 adolescents in Swiss schools at the lower secondary education level. To analyze the extent to which cognitive, affective, and motivational factors are stimulated and what influence they have on expanding knowledge about occupations (measured learning outcome), we applied confirmatory factor analysis, multiple linear regression, and a structural equation model. The results indicate that the stimulation of cognitive processes through serious gaming has a statistically significant impact on learning outcome, although such factors as enjoyment, flow experience, or self-perceived benefits in playing like2be did not significantly impact gain in knowledge about occupations

The potential of Serious Games to foster learning among children and adolescents with disabilities: A systematic review

Serious Games for children and adolescents with disabilities can enhance their learning and respond to their needs in an inclusive educational setting. The aim of this systematic review is to analyze the potential of Serious Games for children and young people with disabilities, thereby providing an overview of effective Serious Games for schools and practitioners in the field of inclusive education. For this purpose, a systematic review of empirical literature found in the database Education Resources Information Centre (ERIC) was conducted, applying a qualitative content analysis. Findings from the 21 reviewed quantitative and qualitative studies indicate that Serious Games provide effective support for achieving learning objectives in certain school subjects and facilitate optimal conditions for learning. We found that Serious Games have strong potential and can make an important contribution to the inclusion of children and adolescents with disabilities in school

Astrophysical neutrino point sources as a probe of new physics

Recently, the IceCube collaboration observed a neutrino excess in the direction of NGC 1068 with high statistical significance. This constitutes the second detection of an astrophysical neutrino point source after the discovery of a variable emission originating from the blazar TXS~0506+056. Neutrinos emitted by these sources traverse huge, well-determined distances on their way to Earth. This makes them a promising tool to test new physics in the neutrino sector. We consider secret interactions with the cosmic neutrino background and discuss their impact on the flux of neutrino point sources. The observation of emission from NGC 1068 and TXS 0506+056 can then be used to put limits on the strength of the interaction. We find that our ignorance of the absolute neutrino masses has a strong impact and, therefore, we present limits in two benchmark scenarios with the sum of the neutrino masses around their lower and upper limits.Comment: 7 pages + appendix, 5 figure

Career Choice With the Serious Game Like2be

Choosing a career is an important biographical event for adolescents. Toward the end of compulsory education, they must decide which career path they want to pursue. The serious game like2be was developed to support adolescents in this individual career choice process. In a quasi-experimental intervention study with 809 adolescents, like2be was evaluated for its effectiveness in career choice classes at the lower secondary level. In addition, a teaching concept for the application of the serious game which included additional teaching materials was analyzed. The data show that like2be is an effective medium for broadening personal career choice horizons, especially when it is pedagogically well-founded and integrated into career choice classes. Although the effectiveness of like2be in stimulating intensive reflection on one's own vocational aptitude or a gender-sensitive attitude towards occupations is limited, the present study shows that like2be has major potential for supporting the process of career choice among adolescents

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