Universal Space-time Research Articles

When time is not space: The social and linguistic construction of time intervals and temporal event relations in an Amazonian culture

AbstractIt is widely assumed that there is a natural, prelinguistic conceptual domain of time whose linguistic organization is universally structured via metaphoric mapping from the lexicon and grammar of space and motion. We challenge this assumption on the basis of our research on the Amondawa (Tupi Kawahib) language and culture of Amazonia. Using both observational data and structured field linguistic tasks, we show that linguistic space-time mapping at the constructional level is not a feature of the Amondawa language, and is not employed by Amondawa speakers (when speaking Amondawa). Amondawa does not recruit its extensive inventory of terms and constructions for spatial motion and location to express temporal relations. Amondawa also lacks a numerically based calendric system. To account for these data, and in opposition to a Universal Space-Time Mapping Hypothesis, we propose a Mediated Mapping Hypothesis, which accords causal importance to the numerical and artefact-based construction of time-based (as opposed to event-based) time interval systems.

A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity

A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards Non-Commutative Spacetime structures with remarkable asymmetries or broken symmetries, such as the CPT-symmetry violation, is proposed. This has the potential for novel applications of Higher Dimensional Algebra to SpaceTime structure determination in terms of universal, topological invariants of ‘hidden’ symmetry. Fundamental concepts of Quantum Algebra and Quantum Algebraic Topology, such as Quantum Groups, von Neumann and Hopf Algebras are first considered with a view to their possible extensions and future applications in Quantum Field theories. New, non-Abelian results may be obtained through Higher Homotopy, General van Kampen Theorems, Lie Groupoids/Algebroids and Groupoid Atlases, possibly with novel applications to Quantum Dynamics and Local-to-Global Problems, Quantum Logics and Logic Algebras. Many-valued Logics, Łukasiewicz–Moisil Logics lead to Generalized LM-Toposes as global representations of SpaceTime Structures in the presence of intense Quantum Gravitational Fields. Such novel representations have the potential to develop a Quantum/General Relativity Theory in the context of Supersymmetry, Supergravity, Supersymmetry Algebras and the Metric Superfield in the Planck limit of spacetime. Quantum Gravity and Physical Cosmology issues are also considered here from the perspective of multiverses, thus leading also to novel types of Generalized, non-Abelian, Topological, Higher Homotopy Quantum Field Theories (HHQFT) and Non-Abelian Quantum Algebraic Topology (NA-QAT) theories.

Birefringence of hard electromagnetic waves of a field with Lorentz invariance violation in the expanding universe space-time

The dependence of the systematic polarization of radiation from extragalactic sources, arising in the models with Lorentz invariance violation, on the red shift Z is analyzed.

The Sagnac effect in curved space-times from an analogy with the Aharonov-Bohm effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, G\{odel} universe and Schwarzschild space-time.

Chain propagator, mass, and universality in polymer solutions from Brownian relativity

A Lagrangian theory for single chains in polymer solutions is addressed via a recent Brownian relativity. By employing generalized diffusive coordinates, statements of covariance and diffusivity invariance result into free particle Lagrangians, where mass turns out to rise as a universal spacetime property. It descends from lowering diffusivity (or curving spacetime), so identifying a mechanism which conceptually resemble those ruling macromolecular scaling laws. An extended chain propagator recovers the Gaussian end-to-end distribution and, in the limits of time-like and space-like orbits, the dualism for diffusive paths and polymer random-walks.

Universal space-time properties of X waves.

Exact results concerning spatiotemporal universal features of three-dimensional propagation-invariant solutions of the wave equation (X waves) are derived. In particular, relations connecting the pulse transverse extension to the longitudinal coordinate and the propagation velocity to the spatial field distribution are obtained for the whole class of X waves.

On the design of algebraic space-time codes for MIMO block-fading channels

The availability of multiple transmit antennas allows for two-dimensional channel codes that exploit the spatial transmit diversity. These codes were referred to as space-time codes by Tarokh et al. (see ibid., vol.44, p.744-765, Mar. 1998) Most prior works on space-time code design have considered quasi-static fading channels. We extend our earlier work on algebraic space-time coding to block-fading channels. First, we present baseband design criteria for space-time codes in multi-input multi-output (MIMO) block-fading channels that encompass as special cases the quasi-static and fast fading design rules. The diversity advantage baseband criterion is then translated into binary rank criteria for phase shift keying (PSK) modulated codes. Based on these binary criteria, we construct algebraic space-time codes that exploit the spatial and temporal diversity available in MIMO block-fading channels. We also introduce the notion of universal space-time codes as a generalization of the smart-greedy design rule. As a part of this work, we establish another result that is important in its own right: we generalize the full diversity space-time code constructions for quasi-static channels to allow for higher rate codes at the expense of minimal reductions in the diversity advantage. Finally, we present simulation results that demonstrate the excellent performance of the proposed codes.

Null string evolution in black hole and cosmological spacetimes

We discuss the problem of the motion of classical strings in some black hole and cosmological spacetimes. In particular, the null string limit (zero tension) of tensile strings is considered. We present some new exact string solutions in Reissner-Nordstr\"om black hole background as well as in the Einstein Static Universe and in the Einstein-Schwarzschild (a black hole in the Einstein Static Universe) spacetime. These solutions can give some insight into a general nature of propagation of strings (cosmic and fundamental) in curved backgrounds.

Lightlike signals in general relativity and cosmology

The modelling of light-like signals in general relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the signal by its embedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de Sitter universe and Minkowskian space-time.

Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry

Cantorian spacetime E∞, with the continuous dimensional expectation <DIME∞>=4+φ∞ is shown to consist of hierachical self affine Penrose universes with noncommutative properties constituting a geometrical realization of the noncommutative formalism of orthodox quantum mechanics.

Poincaré-Invariant Structures in the Solution Manifold of a Nonlinear Wave Equation

The solution manifold M of the equation \phi + g\phi^3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal space-time.

Universal conventionalism and space-time

Geo-chronometric conventionalism (GC) is shown to be part of a more general thesis, universal conventionalism, stating that coordinative definitions are needed in order to compare two measurements of any physical quantity at different space-time points. Two fully elaborated examples of the use of non-standard coordinative definitions in physics are given, demonstrating that the use of these definitions can actually simplify the physical formalism.

Capacity of Classes of Gaussian Channels

Gaussian channels capacity, studying supremum of information transmission rates with small error probability

Excursus on the Carnot-Kelvin aspect of Thermodynamics

According to Carnot's postulate heat can give rise to work only by falling to lower temperature. This negation ensures that at each temperature a definite physical system possesses a work-function A, named by W. Thomson its available, energy at that temperature. This aspect of Carnot's postulate was enforced especially in Thomson and Tait's Nat. Phil. (1867). These available energies at different temperatures combine into one more general function, the isothermal available energy, which is a function of temperature θ as well as configuration. (Cf. the Minkowski condensation of personal spaces and times into a single universal space-time.) Thus we are entitled to assert the equationwhere Ψ1r is the force exerted by the coordinate ψr of configuration. The final term in δA though regular has not to do with ostensible work: and −η, as yet arbitrary, here equal to A/θ, may be described as the thermal capacity or specific heat of available energy.