Space-time Interpretation Research Articles

Liouville theory beyond the cosmological horizon

The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description ---with a specific canonical pair--- and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.

Modified constraint algebra in loop quantum gravity and spacetime interpretation

Classically, the constraint algebra of general relativity, which generates gauge transformations, is equivalent to spacetime covariance. In LQG, inverse triad corrections lead to an effective Hamiltonian constraint, which can lead to a modified constraint algebra. We have shown, using example of spherically symmetric spacetimes, that a modified constraint algebra does not correspond to spacetime coordinate transformation. In such a scenario, the notion of black hole horizon, which is based on spacetime notions, also needs to be reconsidered. A possible modification to the classical trapping horizon condition leading to consistent results is suggested. In the case where the constraint algebra is not modified, a spacetime picture is valid and one finds mass threshold for black holes and small corrections to Hawking temperature.

Towards an Intelligent Predictive Model for Analyzing Spatio-Temporal Satellite Image Based on Hidden Markov Chain

Nowadays remote sensing is an important technique for observing Earth surface applied to different areas such as, land use, urban planning, remote monitoring, real time deformation of the soil that can be associated with earthquakes or landslides, the variations in thickness of the glaciers, the measurement of volume changes in the case of volcanic eruptions, deforestation, etc. To follow the evolution of these phenomena and to predict their future states, many approaches have been proposed. However, these approaches do not respond completely to the specialists who process yet more commonly the data extracted from the images in their studies to predict the future. In this paper, we propose an innovative methodology based on hidden Markov models (HMM). Our approach exploits temporal series of satellite images in order to predict spatio-temporal phenomena. It uses HMM for representing and making prediction concerning any objects in a satellite image. The first step builds a set of feature vectors gathering the available information. The next step uses a Baum-Welch learning algorithm on these vectors for detecting state changes. Finally, the system interprets these changes to make predictions. The performance of our approach is evaluated by tests of space-time interpretation of events conducted over two study sites, using different time series of SPOT images and application to the change in vegetation with LANDSAT images.

Twins’ Paradox and Closed Timelike Curves: The Role of Proper Time and the Presentist View on Spacetime

Relativity allegedly contradicts presentism, the dynamic view of time and reality, according to which temporal passage is conceived of as an existentially distinguished ‘moving’ now. Against this common belief, the paper motivates a presentist interpretation of spacetime: It is argued that the fundamental concept of time—proper time—cannot be characterized by the earlier-later relation, i.e., not in the B-theoretical sense. Only the presentist can provide a temporal understanding of the twins’ paradox and of universes with closed timelike curves.

Non-Grassmann mechanical model of the Dirac equation

We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both Γμ and Γμν-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.

Abelian-Higgs and vortices from ABJM: towards a string realization of AdS/CMT

We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to embed all the usual (multi-)vortex solutions of the latter into the ABJM model. By turning off the mass deformation at the level of the reduced model, we can also continuously deform to the massive $\phi^4$ theory in the massless ABJM case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT correspondence as a consistent truncation of ABJM. In this context, the mass deformation parameter $\mu$ and a field VEV $<\phi>$ act as $g$ and $g_c$ respectively, leading to a well-motivated AdS/CMT construction from string theory. To further this particular point, we propose a simple model for the condensed matter field theory that leads to an approximate description for the ABJM abelianization. Finally, we also find some BPS solutions to the mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending on a spherical M5-brane.

BMS/GCA redux: towards flatspace holography from non-relativistic symmetries

The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA, obtained from a linear combination of two copies of the Virasoro algebra, is generically non-unitary. The unitary subsector previously constructed had trivial correlation functions. We consider a representation obtained from a different linear combination of the Virasoros, which is relevant to the relation with the BMS algebra in three dimensions. This is realised by a new space-time contraction of the parent algebra. We show that this representation has a unitary sub-sector with interesting correlation functions. We discuss implications for the BMS/GCA correspondence and show that the flat space limit actually induces precisely this contraction on the boundary conformal field theory. We also discuss aspects of asymptotic symmetries and the consequences of this contraction in higher dimensions.

Coupling shape dynamics to matter gives spacetime

Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomporphisms and local spatial conformal transformations. In this paper we extend the construction of Shape Dynamics form pure gravity to gravity-matter systems and find that there is no obstruction for the coupling of gravity to standard matter. We use the matter gravity system to construct a clock and rod model for Shape Dynamics which allows us to recover a spacetime interpretation of Shape Dynamics trajectories.

Spacetime Interpretation of Torsion in Prismatic Bodies

A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl’s linear soap-film approximation and Nadai’s sand-pile model. Geometrically Prandtl’s soap film and Nadai’s wavefront are unified into a single smooth surface of constant mean curvature in three-dimensional Minkowski spacetime.

Electromagnetic Casimir effect and the spacetime index of refraction

In [M. Nouri-Zonoz and B. Nazari, Phys. Rev. D 82, 044047 (2010)], we investigated the response of vacuum energy to a gravitational field by considering a Casimir apparatus in a weak gravitational field. Our approach was based on a conjecture involving the interpretation of spacetime as a refractive medium and its effect on vacuum energy composed of virtual massless scalar particles. There it was shown how the case of virtual photons as the constituents of vacuum could be inferred from that of the massless scalar field. Here we explicitly show how the same conjecture applies to the electromagnetic vacuum composed of virtual photons. Specifically, we show that the boundary conditions imposed on the components of the vector field, decomposed into two scalar fields, result in the same frequency shift for photons. Using the same decomposition and employing our conjecture, we also calculate the electromagnetic energy density for the Casimir apparatus in a weak gravitational field.

Interpreting spacetimes of any dimension using geodesic deviation

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corresponding deformations caused by a generic higher-dimensional gravitational waves observed in such physical subspace, need not be tracefree.

Old issues and linear sigma models

Using mirror symmetry, we resolve an old puzzle in the linear sigma model description of the spacetime Higgs mechanism in a heterotic string compactification with (2,2) worldsheet supersymmetry. The resolution has a nice spacetime interpretation via the normalization of physical fields and suggests that with a little care deformations of the linear sigma model can describe heterotic Higgs branches.

On the arithmetic of D-brane superpotentials: lines and conics on the mirror quintic

Irrational invariants from D-brane superpotentials are pursued on the mirror quintic, systematically according to the degree of a representative curve. Lines are completely understood: the contribution from isolated lines vanishes. All other lines can be deformed holomorphically to the van Geemen lines, whose superpotential is determined via the associated inhomogeneous Picard-Fuchs equation. Substantial progress is made for conics: the families found by Mustat¸ya contain conics reducible to isolated lines, hence they have a vanishing superpotential. The search for all conics invariant under a residual Z2 symmetry reduces to an algebraic problem at the limit of our computational capabilities. The main results are of arithmetic flavor: the extension of the moduli space by the algebraic cycle splits in the large complex structure limit into groups each governed by an algebraic number field. The expansion coefficients ofthe superpotential around large volume remain irrational. The integrality of those coefficients is revealed by a new, arithmetic twist of the di-logarithm: the D-logarithm. There are several options for attempting to explain how these invariants could arise from the A-model perspective. A successful spacetime interpretation will require spaces of BPS states to carry number theoretic structures, such as an action of the Galois group.

Conservative unsteady aerodynamic simulation of arbitrary boundary motion using structured and unstructured meshes in time

SUMMARYSimulation of unsteady fluid behaviour with arbitrary boundary motion or topological change remains restricted owing to mesh deformation limitations, and usually requires the application of special techniques using overlapping meshes, sliding planes, remeshing or immersed boundaries. This work presents the application of a spacetime interpretation of the fluid conservation laws that unifies meshes in space and time. This effectively replaces the problem of mesh deformation with the problem of mesh generation and, because connectivity is no longer restricted to being constant in time, any motion or topological change may be simulated. Examples are given applying the method to a piston, a pitching NACA0012 aerofoil, an appearing/disappearing object, a two‐dimensional store separation and a rotation case to validate and then demonstrate the capabilities of the method. Results for the pitching aerofoil case are compared with a conventional moving mesh unsteady computation and shown to be consistent, whereas the demonstration cases show qualitatively correct behaviour and illustrate the general nature of the technique. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Conceptual aspects of the hydrological regime for the definition of environmental hydrograph

Considering the instruments established by the Brazilian National Policy for Water Resources (Law 9,433/1997), the water right concession has the aim to limit water use of surface and groundwater reservoirs. In this sense, the sum of all granted uptake rights must take into consideration the natural ecological flows. It has been a complex challenge to establish a trade off between the management of water and environmental resources since various aspects have to be considered involving many knowledge areas such as ecology and hydrology. This paper focuses on the need for a closer dialogue between these areas by considering the space-time interpretation of the restrictions on natural flow regimes of the water resources. These regimes can be observed in hydrographs, which are indispensable tools for better understanding the hydro-ecologic behavior of rivers.

Adiabaticity and emergence of classical space-time in time-dependent matrix theories

We discuss the low-curvature regime of time-dependent matrix theories proposed to describe non-perturbative quantum gravity in asymptotically plane-wave space-times. The emergence of near-classical space-time in this limit turns out to be closely linked to the adiabaticity of the matrix theory evolution. Supersymmetry restoration at low curvatures, which is crucial for the usual space-time interpretation of matrix theories, becomes an obvious feature of the adiabatic regime.

Unification of residues and Grassmannian dualities

The conjectured duality relating all-loop leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every residue is individually Yangian invariant, but does not have a local space-time interpretation--only a special sum over residues gives physical amplitudes. In this paper we show that the sum over residues giving tree amplitudes can be unified into a single algebraic variety, which we explicitly construct for all NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to have a "particle interpretation" in the Grassmannian, where higher-point amplitudes can be constructed from lower-point ones by adding one particle at a time, with soft limits manifest. We move on to show that the connected prescription for tree amplitudes in Witten's twistor string theory also admits a Grassmannian particle interpretation, where the integral over the Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These apparently very different theories are related by a natural deformation with a parameter t that smoothly interpolates between them. For NMHV amplitudes, we use a simple residue theorem to prove t-independence of the result, thus establishing a novel kind of duality between these theories.

There was movement that was stationary, for the four-velocity had passed around

Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving space is characterised by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply-connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world-lines. The contradiction in the multiply-connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology.

Time-dependence and holography in the c=1 matrix model This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

Ideas related to the study of time-dependence in two dimensional Liouville string theory using the c=1 matrix model are reviewed. Following an introduction to Liouville string theory, the matrix model and the relationship between the two, an example of an exact quantum mechanical time-dependent solution is given. There is a brief discussion of the holographic issues complicating the construction of the exact spacetime interpretation of such solutions. An attempt is made to include sufficient background material to make the presentation self-contained and accessible to a non-expert.