Time asymmetry of the Universe

The entropy of the Universe is calculated within the Einstein and Logunov concepts. It is shown that the entropies of the Universe calculated within the foregoing concepts coincide at the Beginning and at the present time.     

The Arrow of Time: From Universe Time-Asymmetry to Local Irreversible Processes

In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the “arrow” is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper is to complete the global and non-entropic program by showing that our approach is able to account for irreversible local phenomena, which have been traditionally considered as the physical origin of the arrow of time.     

Absolute Spacetime: The Twentieth Century Ether

All gauge theories need somethingfixed even as something changes.Underlying the implementation of these ideas all majorphysical theories make indispensable use of anelaborately designed spacetime model as the something fixed,i.e., absolute. This model must provide at least thefollowing sequence of structures: point set, topologicalspace, smooth manifold, geometric manifold, base forvarious bundles. The fine structure ofspacetime inherent in this sequence is of courseempirically unobservable directly, certainly whenquantum mechanics is taken into account. This issue isat the basis of the difficulties in quantizing generalrelativity and has been approached in many differentways. Here we review an approach taking into account thenon-Boolean properties of quantum logic when forming a spacetime model. Finally, we recall how thefundamental gauge of diffeomorphisms (the issue ofgeneral covariance vs. coordinate conditions) raiseddeep conceptual problems for Einstein in his earlydevelopment of general relativity. This is clearlyillustrated in the notorious holeargument. This scenario, which does not seem to bewidely known to practicing relativists, is neverthelessstill interesting in terms of its impact for fundamental gaugeissues.     

The Global Arrow of Time as a Geometrical Property of the Universe

Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, the global arrow of time. In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the universe as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions.     

Thermodynamics of Universe with Time Varying Cosmological Term

The FRW-type cosmologies with time varying cosmological term is discussed within the frame work of a thermodynamic context. If at some cosmological time, the cosmological term begins increasing again, as presently observed, expansion will accelerate and matter and/or radiation will be transformed back into dark energy. It is shown that such accelerated expansion is a route towards a new kind of gravitational singular state, characterized by an empty, conformally transitive spacetime in which all energy is dark. We investigate whether dynamic dark energy cosmologies are compatible with the second law of thermodynamics. We examine also the total entropy evolution with time. We observed that the dynamic dark energy cosmology is less restricted with second law of thermodynamics. Some physical implications of these solutions are briefly discussed.     

Electrodynamics and Spacetime Geometry: Foundations

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.     

Spacetime code: Preliminaries and motivations

A review of the work of David Finkelstein and others on quantum topology is given, the intention being to present physical ideas and a progress report, which will help readers with the more detailed papers. Some new approaches involving walks on graphs are presented.     

The Non-unique Universe

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Gödel’s incompleteness theorem for theories of everything.Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model.     

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.     

Global Phase Time and Path Integral for the Kantowski-Sachs Anisotropic Universe

The action functional of the anisotropic Kantowski-Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum transition amplitude is obtained by means of the usual path integral procedure of Fadeev and Popov.     

Global Phase Time and Wave Function for the Kantowski-Sachs Anisotropic Universe

A consistent quantization with a clear notion of time and evolution is given for the anisotropic Kantowski–Sachs cosmological model. It is shown that a suitable coordinate choice allows to obtain a solution of the Wheeler–DeWitt equation in the form of definite energy states, and that the results can be associated to two disjoint equivalent theories, one for each sheet of the constraint surface.     

Contracted Representation of Yang's Spacetime Algebra and Buniy-Hsu-Zee's Discrete Spacetime

Motivated by the recent proposition by Buniy, Hsu, and Zee with respect to discrete spacetime and finite spatial degrees of freedom of our physical world with short- and long-distance scales, l _P and L, we reconsider the Lorentz-covariant Yang's quantized spacetime algebra (YSTA), which is intrinsically equipped with two such kinds of scale parameters, λ and R. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio R/λ, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, λ → 0 and R → ∓.     

Letter: The Real Scalar Field in Schwarzschild-de Sitter Spacetime

In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called polynomial approximation is introduced to derive the relation between the tortoise coordinate x and the radius r. This method is different from the tangent approximation [1] and leads to more accurate results. The Nariai black hole is then discussed in details. We find that the wave function is harmonic only near the horizons as I. Brevik and B. Simonsen [1] found. However the wave function is not harmonic in the region of the potential peak, with amplitude increasing instead. Furthermore, we also find that, when the cosmological constant decreases, the potential peak increases, and the maximum wave amplitude increases.     

Quantum Charges and Spacetime Topology: The Emergence of New Superselection Sectors

A new form of superselection sectors of topological origin is developed. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*–algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts’ cohomological analysis to the case where 1–cocycles bear non-trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in the case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1–cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1–cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part much resembles what in literature is known as geometric phases. Indeed, by the very geometrical origin of the 1–cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations. Dedicated to Klaus Fredenhagen on the occasion of his sixtieth birthday     

Bianchi-I Universe with Decaying Vacuum Energy Density and Time Varying Gravitational Constant

Anisotropic Locally Rotationally Symmetric Bianchi-I (LRSBI) cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein’s general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Λ are discussed. Our calculations for the Supernova constraints concerning the luminosity distance provide reasonable results.