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A Mathematicians' View of Geometrical Unification of General Relativity and Quantum Physics  [PDF]
Michel Vaugon
Mathematics , 2015,
Abstract: This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-time, no general principle is supposed. The properties we impose to some domains of (M, g) are only simple geometric constraints, essentially based on the concept of "curvature". These geometric properties allow to define, depending on considered cases, some objects (frequently depicted by tensors) that are similar to the classical physics ones, they are however built here only from the g tensor. The links between these objects, coming from their natural definitions, give, applying standard theorems from the pseudo-riemannian geometry, all equations governing physical phenomena usually described by classical theories, including general relativity and quantum physics. The purely geometric approach introduced hear on quantum phenomena is profoundly different from the standard one. Neither Lagrangian nor Hamiltonian are used. This document ends with a quick presentation of our approach of complex quantum phenomena usually studied by quantum field theory.
Deriving general relativity from considerations on quantum information  [PDF]
Thomas G?rnitz
Physics , 2010,
Abstract: From a theory of an abstract quantum information the theory of general relativity can be deduced by means of few and physically good founded reasons. "Abstract" quantum information means that primarily no special meaning is connected with it. Therefore it is named with a new denotation: Protyposis. From the Protyposis and by using group-theoretical methods follows a cosmological model, which has an isotropic and homogeneous metric and solves the so-called cosmological problems. The Protyposis is subject to an equation of states for energy density and pressure that fulfils all the energy conditions and that also gives an explanation for the "dark energy". If it is demanded that the relations between spacetime structure and the material content should remain valid for variations from this ideal cosmology, then general relativity results from this quantum theoretical considerations as a description for local inhomogenities.
General Relativity in the Undergraduate Physics Curriculum  [PDF]
James B. Hartle
Physics , 2005, DOI: 10.1119/1.2110581
Abstract: Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the case for a `physics first' approach to introducing general relativity to undergraduate physics majors.
Conformal Unification of General Relativity and Standard Model  [PDF]
M. Pawlowski,V. V. Papoyan,V. N. Pervushin,V. I. Smirichinski
Physics , 1998, DOI: 10.1016/S0370-2693(98)01394-X
Abstract: The unification of general relativity and standard model for strong and electro-weak interactions is considered on the base of the conformal symmetry principle. The Penrose-Chernikov-Tagirov Lagrangian is used to describe the Higgs scalar field modulus and gravitation. We show that the procedure of the Hamiltonian reduction converts the homogeneous part of the Higgs field into the dynamical parameter of evolution of the equivalent reduced system. The equation of dynamics of the "proper time" of an observer with respect to the evolution parameter reproduces the Friedmann-like equation, which reflects the cosmological evolution of elementary particle masses. The value of the Higgs field is determined, at the present time, by the values of mean density of matter and the Hubble parameter in satisfactory agreement with the data of cosmological observations.
Hamiltonian Unification of General Relativity and Standard Model  [PDF]
L. A. Glinka,V. N. Pervushin
Physics , 2007, DOI: 10.2478/v10005-007-0030-y
Abstract: The Hamiltonian approach to the General Relativity and the Standard Model is studied in the context of its consistency with the Newton law, the Higgs effect, the Hubble cosmological evolution and the Cosmic Microwave Background radiation physics. The version of the Higgs potential is proposed, where its constant parameter is replaced by the dynamic zeroth Fourier harmonic of the very Higgs field. In this model, the extremum of the Coleman--Weinberg effective potential obtained from the unit vacuum--vacuum transition amplitude immediately predicts mass of Higgs field and removes tremendous vacuum cosmological density. We show that the relativity principles unambiguously treat the Planck epoch, in the General Relativity, as the present-day one. It was shown that there are initial data of the Electro-Weak epoch compatible with supposition that all particles in the Universe are final products of decays of primordial Higgs particles and W-, Z-vector bosons created from vacuum at the instant treated as the "Big-Bang".
Noncommutative Unification of General Relativity with Quantum Mechanics and Canonical Gravity Quantization  [PDF]
M. Heller,W. Sasin
Physics , 2000,
Abstract: The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its (commutative) subalgebra, which determines the space-time slicing, an algebraic counterpart of superspace (space of 3-metrics) can be obtained. It turns out that when this space-time slicing emerges the universe is already in its commutative regime. We explore the consequences of this result.
Noncommutative Unification of General Relativity and Quantum Mechanics  [PDF]
Michael Heller,Leszek Pysiak,Wieslaw Sasin
Mathematics , 2005, DOI: 10.1063/1.2137720
Abstract: In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra A defined on a transformation groupoid given by the action of a group G on a space E. Owing to the fact that G was assumed to be finite it was possible to compute the model in full details. In the present paper we develop the model in the case when G is a noncompact group. It turns out that also in this case the model works well. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model ``collapses'' to the usual quantum mechanics.
Process Physics: From Quantum Foam to General Relativity  [PDF]
Reginald T. Cahill
Physics , 2002,
Abstract: Progress in the new information-theoretic process physics is reported in which the link to the phenomenology of general relativity is made. In process physics the fundamental assumption is that reality is to be modelled as self-organising semantic (or internal or relational) information using a self-referentially limited neural network model. Previous progress in process physics included the demonstration that space and quantum physics are emergent and unified, with time a distinct non-geometric process, that quantum phenomena are caused by fractal topological defects embedded in and forming a growing three-dimensional fractal process-space, which is essentially a quantum foam. Other features of the emergent physics were: quantum field theory with emergent flavour and confined colour, limited causality and the Born quantum measurement metarule, inertia, time-dilation effects, gravity and the equivalence principle, a growing universe with a cosmological constant, black holes and event horizons, and the emergence of classicality. Here general relativity and the technical language of general covariance is seen not to be fundamental but a phenomenological construct, arising as an amalgam of two distinct phenomena: the `gravitational' characteristics of the emergent quantum foam for which `matter' acts as a sink, and the classical `spacetime' measurement protocol, but with the later violated by quantum measurement processes. Quantum gravity, as manifested in the emergent Quantum Homotopic Field Theory of the process-space or quantum foam, is logically prior to the emergence of the general relativity phenomenology, and cannot be derived from it.
Affine metrics and algebroid structures: Application to general relativity and unification  [PDF]
N. Elyasi,N. Boroojerdian
Physics , 2011, DOI: 10.1007/s10773-012-1197-4
Abstract: Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the associated algebroid bundle that is similar to Einstein field equation but contain Einstein field equation and Maxwell equations simultaneously and contain a new equation that may have new results.
Instants in physics - point mechanics and general relativity  [PDF]
Domenico Giulini
Physics , 2013,
Abstract: Theories in physics usually do not address ``the present''or ``the now''. However, they usually have a precise notion of an ``instant'' (or state). I review how this notion appears in relational point mechanics and how it suffices to determine durations - a fact that is often ignored in modern presentations of analytical dynamics. An analogous discussion is attempted for General Relativity. Finally I critically remark on the difference between relationalism in point mechanics and field theory and the problematic foundational dependencies between fields and spacetime.
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