The vacuum expectation value of the stress-energy tensor 0 |T µν | 0 is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as R 3 × S 1 , R 2 × T 2 , R 1 × T 3 , the Möbius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether 0 |T µν | 0 diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass 0 |T µν | 0 remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.
Although the observed universe appears to be geometrically flat, it could have one of 18 global topologies. A constant-time slice of the spacetime manifold could be a torus, Möbius strip, Klein bottle, or others. This global topology of the universe imposes boundary conditions on quantum fields and affects the vacuum energy density via Casimir effect. In a spacetime with such a nontrivial topology, the vacuum energy density is shifted from its value in a simply-connected spacetime. In this paper, the vacuum expectation value of the stress-energy tensor for a massless scalar field is calculated in all 17 multiply-connected, flat and homogeneous spacetimes with different global topologies. It is found that the vacuum energy density is lowered relative to the Minkowski vacuum level in all spacetimes and that the stress-energy tensor becomes position-dependent in spacetimes that involve reflections and rotations.
In the absence of an adequate theory of quantum gravity, the search for a mechanism of "chronology protection" is currently focused on the vacuum energy divergence of quantized matter fields at chronology horizons and its back reaction on the metric via the semiclassical theory of gravity. The divergence of the vacuum energy at the chronology horizon was first demonstrated by Hiscock and Konkowski for a conformal massless scalar field in the Misner space. In this paper, we extend this earlier work to calculate the vacuum stress-energy tensor of a massive nonconformally coupled scalar field in Misner space. We find that the asymptotic behavior of ( T,,) as it diverges at the chronology horizon is, to leading order, independent of the curvature coupling and mass of the scalar field. Thus the vacuum energy of nonconformal and/or massive scalar fields diverges with the same strength as the massless conformal case. Since one important aspect of gravity is its nonconformal nature, this suggests that quantum gravity may be unable to act as the protector of chronology.PACS number(s): 04.62. + v, 04.20.G~
The electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (particle-like) or not (wave-like). It is shown that the localization of the electron at one of the slits is equivalent to choosing a particular object in the t-site and that the electron behaves as a wave when it passes through a double-slit because there are more than one object in the t-site. Also, the single-slit diffraction is interpreted as a result of the possibility of many different ways of factoring a morphism between two objects.
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