Dynamics & Predictions in the Co-Event Interpretation

Sorkin has introduced a new, observer independent, interpretation of quantum mechanics that can give a successful realist account of the 'quantum microworld' as well as explaining how classicality emerges at the level of observable events for a range of systems including single time 'Copenhagen measurements'. This 'co-event interpretation' presents us with a new ontology, in which a single 'co-event' is real. A new ontology necessitates a review of the dynamical & predictive mechanism of a theory, and in this paper we begin the process by exploring means of expressing the dynamical and predictive content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein

The Generalized Second Law implies a Quantum Singularity Theorem

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. An introductory section describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.) A proof of the coarse-grained ordinary second law is given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised (4.1, 5.2), more comments on AdS. v3: major revisions including change of title. v4: similar to published version, but with corrections to plan of paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new footnote

Spacelike distance from discrete causal order

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly difficult to extract spacelike distances, because of the unique combination of discreteness with local Lorentz invariance in that approach. We propose a number of methods to overcome this difficulty, one of which reproduces the spatial distance between two points in a finite region of Minkowski space. We provide numerical evidence that this definition can be used to define a `spatial nearest neighbor' relation on a causal set, and conjecture that this can be exploited to define the length of `continuous curves' in causal sets which are approximated by curved spacetime. This provides evidence in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio

Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.Comment: 23 pages, Few changes and added references in v

Emergence of spatial structure from causal sets

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying discreteness. The causal set approach, in which the fundamental relation is based upon causality, finds it easy to reproduce timelike distances, but has a more difficult time with spatial distance, due to the unique combination of Lorentz invariance and discreteness within that approach. We describe a method to deduce spatial distances from a causal set. In addition, we sketch how one might use an important ingredient in deducing spatial distance, the `$n$-link', to deduce whether a given causal set is likely to faithfully embed into a continuum spacetime.Comment: 21 pages, 21 figures; proceedings contribution for DICE 2008, to appear in Journal of Physics: Conference Serie

Twistor form of massive 6D superparticle

The massive six-dimensional (6D) superparticle with manifest (n, 0) supersymmetry is shown to have a supertwistor formulation in which its “hidden” (0, n) supersymmetry is also manifest. The mass-shell constraint is replaced by Spin(5) spin-shell constraints which imply that the quantum superparticle has zero superspin; for n = 1 it propagates the 6D Proca supermultiplet.PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society.This is the final version of the article. It was first available from IOP Science via http://dx.doi.org/10.1088/1751-8113/49/2/02540

Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory

We present a computational tool that can be used to obtain the "spatial" homology groups of a causal set. Localisation in the causal set is seeded by an inextendible antichain, which is the analog of a spacelike hypersurface, and a one parameter family of nerve simplicial complexes is constructed by "thickening" this antichain. The associated homology groups can then be calculated using existing homology software, and their behaviour studied as a function of the thickening parameter. Earlier analytical work showed that for an inextendible antichain in a causal set which can be approximated by a globally hyperbolic spacetime region, there is a one parameter sub-family of these simplicial complexes which are homological to the continuum, provided the antichain satisfies certain conditions. Using causal sets that are approximated by a set of 2d spacetimes our numerical analysis suggests that these conditions are generically satisfied by inextendible antichains. In both 2d and 3d simulations, as the thickening parameter is increased, the continuum homology groups tend to appear as the first region in which the homology is constant, or "stable" above the discreteness scale. Below this scale, the homology groups fluctuate rapidly as a function of the thickening parameter. This provides a necessary though not sufficient criterion to test for manifoldlikeness of a causal set.Comment: Latex, 46 pages, 43 .eps figures, v2 numerous changes to content and presentatio

Substrate translocation involves specific lysine residues of the central channel of the conjugative coupling protein TrwB

Conjugative transfer of plasmid R388 requires the coupling protein TrwB for protein and DNA transport, but their molecular role in transport has not been deciphered. We investigated the role of residues protruding into the central channel of the TrwB hexamer by a mutational analysis. Mutations affecting lysine residues K275, K398, and K421, and residue S441, all facing the internal channel, affected transport of both DNA and the relaxase protein in vivo. The ATPase activity of the purified soluble variants was affected significantly in the presence of accessory protein TrwA or DNA, correlating with their behaviour in vivo. Alteration of residues located at the cytoplasmic or the inner membrane interface resulted in lower activity in vivo and in vitro, while variants affecting residues in the central region of the channel showed increased DNA and protein transfer efficiency and higher ATPase activity, especially in the absence of TrwA. In fact, these variants could catalyze DNA transfer in the absence of TrwA under conditions in which the wild-type system was transfer deficient. Our results suggest that protein and DNA molecules have the same molecular requirements for translocation by Type IV secretion systems, with residues at both ends of the TrwB channel controlling the opening?closing mechanism, while residues embedded in the channel would set the pace for substrate translocation (both protein and DNA) in concert with TrwA

Structural studies of T4S systems by electron microscopy

Abstract: Type IV secretion (T4S) systems are large dynamic nanomachines that transport DNA and/or proteins through the membranes of bacteria. Analysis of T4S system architecture is an extremely challenging task taking into account their multi protein organisation and lack of overall global symmetry. Nonetheless the last decade demonstrated an amazing progress achieved by X-ray crystallography and cryo-electron microscopy. In this review we present a structural analysis of this dynamic complex based on recent advances in biochemical, biophysical and structural studies

Antimetastatic gene expression profiles mediated by retinoic acid receptor beta 2 in MDA-MB-435 breast cancer cells

BACKGROUND: The retinoic acid receptor beta 2 (RARβ2) gene modulates proliferation and survival of cultured human breast cancer cells. Previously we showed that ectopic expression of RARβ2 in a mouse xenograft model prevented metastasis, even in the absence of the ligand, all-trans retinoic acid. We investigated both cultured cells and xenograft tumors in order to delineate the gene expression profiles responsible for an antimetastatic phenotype. METHODS: RNA from MDA-MB-435 human breast cancer cells transduced with RARβ2 or empty retroviral vector (LXSN) was analyzed using Agilent Human 1A Oligo microarrays. The one hundred probes with the greatest differential intensity (p < 0.004, jointly) were determined by selecting the top median log ratios from eight-paired microarrays. Validation of differences in expression was done using Northern blot analysis and quantitative RT-PCR (qRT-PCR). We determined expression of selected genes in xenograft tumors. RESULTS: RARβ2 cells exhibit gene profiles with overrepresentation of genes from Xq28 (p = 2 × 10(-8)), a cytogenetic region that contains a large portion of the cancer/testis antigen gene family. Other functions or factors impacted by the presence of exogenous RARβ2 include mediators of the immune response and transcriptional regulatory mechanisms. Thirteen of fifteen (87%) of the genes evaluated in xenograft tumors were consistent with differences we found in the cell cultures (p = 0.007). CONCLUSION: Antimetastatic RARβ2 signalling, direct or indirect, results in an elevation of expression for genes such as tumor-cell antigens (CTAG1 and CTAG2), those involved in innate immune response (e.g., RIG-I/DDX58), and tumor suppressor functions (e.g., TYRP1). Genes whose expression is diminished by RARβ2 signalling include cell adhesion functions (e.g, CD164) nutritional or metabolic processes (e.g., FABP6), and the transcription factor, JUN