Fundamental Problems in the Unification of Physics

Heller, Michaël; Pysiak, Leszek; Sasin, Wiesław

doi:10.1007/s10701-011-9535-6

Cited by 3 publications

(4 citation statements)

References 30 publications

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“…On the other hand, some more of the completely covariant structure constants are now vanishing. In fact, formulae (6)(7)(8) imply that (v) Only the completely covariant structure constants of the form c {A}{B}{C} are nonzero.…”

Section: Model With a Simple Metricmentioning

confidence: 99%

“…The quantum sector of the model is given by the regular representation π : A Γ → B(H) of the algebra A Γ on a bundle H of Hilbert spaces. It turns out that the model has a rich mathematical structure [4], surprising conceptually unifying power [5], and throws some light on fundamental problems of physics [6].…”

Section: Introductionmentioning

confidence: 99%

“…Note that Hor A n possesses the structure of a commutative Lie algebra 6. For a given algebra (A, * ), its associated Lie algebra (A, [ ., . ])…”

mentioning

confidence: 99%

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Geometry and general relativity in the groupoid model with a finite structure group

Heller¹,

Miller

Pysiak

et al. 2015

Can. J. Phys.

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In a series of papers (M. Heller et al. ) we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra, A ⌫ , defined on a transformation groupoid ⌫ determined by the action of the Lorentz group on the frame bundle (E, M , M) over space-time M. In the present work, we construct a simplified version of the gravitational sector of this model in which the Lorentz group is replaced by a finite group, G, and the frame bundle is trivial E = M × G. The model is fully computable. We define the Einstein-Hilbert action, with the help of which we derive the generalized vacuum Einstein equations. When the equations are projected to space-time (giving the "general relativistic limit"), the extra terms that appear due to our generalization can be interpreted as "matter terms", as in Kaluza-Klein-type models. To illustrate this effect we further simplify the metric matrix to a block diagonal form, compute for it the generalized Einstein equations and find two of their "Friedman-like" solutions for the special case when G = Z 2 . One of them gives the flat Minkowski space-time (which, however, is not static), another, a hyperbolic, linearly expanding universe. ), nous proposions un modèle unifié de la relativité générale et de la mécanique quantique. L'idée était de déduire les deux à partir d'une algèbre non commutative, A ⌫ , définie par un groupoïde de transformation ⌫, déterminé par l'action du groupe de Lorentz sur le fibré principal (E, M , M) sur l'espace-temps M. Dans le présent article, nous construisons une version simplifiée du secteur gravitationnel de ce modèle dans laquelle le groupe de Lorentz est remplacé par un groupe fini G et le fibré principal est trivial E = M × G. Le modèle est complètement calculable. Nous définissons l'action de Einstein-Hilbert et, avec son aide, dérivons les équations d'Einstein généralisées du vide. Lorsque les équations sont projetées sur l'espace-temps (donnant la limite relativité générale), les termes additionnels, qui apparaissent à cause de notre généralisation, peuvent être interprétés comme termes de matière, comme c'est le cas dans les modèles de type Kaluza-Klein. Pour illustrer cet effet, nous simplifions encore plus la métrique à une forme diagonale par blocs, calculons les équations généralisées d'Einstein et trouvons leurs deux solutions de type Friedman pour le cas spécial où G = Z 2 . La première est l'espace-temps plat de Minkowski, qui n'est pas statique cependant et la deuxième correspond à un univers hyperbolique en expansion linéaire. [Traduit par la Rédaction]

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Section: Model With a Simple Metricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometry and general relativity in the groupoid model with a finite structure group

Heller¹,

Miller

Pysiak

et al. 2015

Can. J. Phys.

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“…There is overt discussion of a crisis in fundamental physics [ 65 , 66 ]. One reason for this harsh admission is the lack of a solution for the most protracted problem in modern physics: a model that unifies the atomic and cosmic realms [ 67 ]. From the early 20 th century, there have been two separate models for these two domains.…”

Section: Theorymentioning

confidence: 99%

Theory of the Origin, Evolution, and Nature of Life

Andrulis

2011

Life

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Life is an inordinately complex unsolved puzzle. Despite significant theoretical progress, experimental anomalies, paradoxes, and enigmas have revealed paradigmatic limitations. Thus, the advancement of scientific understanding requires new models that resolve fundamental problems. Here, I present a theoretical framework that economically fits evidence accumulated from examinations of life. This theory is based upon a straightforward and non-mathematical core model and proposes unique yet empirically consistent explanations for major phenomena including, but not limited to, quantum gravity, phase transitions of water, why living systems are predominantly CHNOPS (carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur), homochirality of sugars and amino acids, homeoviscous adaptation, triplet code, and DNA mutations. The theoretical framework unifies the macrocosmic and microcosmic realms, validates predicted laws of nature, and solves the puzzle of the origin and evolution of cellular life in the universe.

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