The concept of strong and weak virtual reality

We approach the virtual reality phenomenon by studying its relationship to set theory, and we investigate the case where this is done using the wellfoundedness property of sets. Our hypothesis is that non-wellfounded sets (hypersets) give rise to a different quality of virtual reality than do familiar wellfounded sets. We initially provide an alternative approach to virtual reality based on Sommerhoff's idea of first and second order self-awareness; both categories of self-awareness are considered as necessary conditions for consciousness in terms of higher cognitive functions. We then introduce a representation of first and second order self-awareness through sets, and assume that these sets, which we call events, originally form a collection of wellfounded sets. Strong virtual reality characterizes virtual reality environments which have the limited capacity to create only events associated with wellfounded sets. In contrast, the more general concept of weak virtual reality characterizes collections of virtual reality mediated events altogether forming an entirety larger than any collection of wellfounded sets. By giving reference to Aczel's hyperset theory we indicate that this definition is not empty, because hypersets encompass wellfounded sets already. Moreover, we argue that weak virtual reality could be realized in human history through continued progress in computer technology. Finally, we reformulate our characterization into a more general framework, and use Baltag's Structural Theory of Sets (STS) to show that within this general hyperset theory Sommerhoff's first and second order self-awareness as well as both concepts of virtual reality admit a consistent mathematical representation.Comment: 17 pages; several edits in v

Constraints On The Delayed Transition to Detonation in Type Ia Supernovae

We investigate the possibility of a delayed detonation in a type Ia supernova under the assumption that the transition to detonation is triggered by turbulence only. Our discussion is based on the Zeldovich mechanism and suggests that typical turbulent velocities present during the explosion are not strong enough to allow this transition to occur. Although we are able to show that in carbon-rich matter (e.g., $X(^{12}$C$) = 0.75$) the possibility of a deflagration to detonation transition (DDT) is enhanced, even in this case the turbulent velocities needed are larger than the expected value of $u'(L) \approx 10^7 {cm s}^{-1}$ on a length-scale of $L \approx 10^6$ cm. Thus we conclude that a DDT may not be a common event during a thermonuclear explosion of a Chandrasekhar-mass white dwarf.Comment: 18 pages, 5 figures, accepted for publication in the Ap

Fluid Dynamics of Relativistic Quantum Dust

The microscopic transport equations for free fields are solved using the Schwinger function. Thus, for general initial conditions, the evolution of the energy-momentum tensor is obtained, incorporating the quantum effects exactly. The result for relativistic fermions differs from classical hydrodynamics, which is illustrated for Landau and Bjorken type initial conditions in this model of exploding primordial matter. Free fermions behave like classical dust concerning hydrodynamic observables. However, quantum effects which are present in the initial state are preserved.Comment: 5 pages; LaTe