Noncommutative closed Friedman universe

Heller, Michaël; Pysiak, Leszek; Sasin, Wiesław; Golda, Zdzislaw A.

doi:10.1007/s10714-008-0740-3

Cited by 4 publications

(3 citation statements)

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“…Mathematical aspects of the model were dealt with in [21], and its physical content in [22]. Details of the Friedman cosmological model were computed in [11,24]. Further works, especially regarding field theoretical and observational aspects of the model, are in progress.…”

Section: The Model and Its Motivationmentioning

confidence: 99%

Fundamental Problems in the Unification of Physics

2011

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We discuss the following problems, plaguing the present search for the "final theory": (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the "final theory" be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either "yes" or "not" answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of M. Heller correspondence address: ul. Powstańców Warszawy 13/94, Found Phys (2011) 41: 905-918 the present general relativity and quantum mechanics, is a "third answer" possible?Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues.

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Section: The Model and Its Motivationmentioning

confidence: 99%

Fundamental Problems in the Unification of Physics

2011

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“…In [3], we have shown that, for the closed Friedman model, the normal states on the von Neumann algebra M (restricted to M 0 ), are of the form…”

Section: Noncommutative Geometry Of the Closed Friedman Modelmentioning

confidence: 99%

“…The present paper is mainly based on reference [3]. Here I give only a rather sketchy presentation of our model, for technical details referring the reader to our original papers, my intention being to focus on the above signaled conceptual problems.…”

Section: Introductionmentioning

confidence: 99%

A noncommutative Friedman cosmological model

Heller

2010

Ann. Phys.

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The closed Friedman cosmological model, based on noncommutative geometry, is presented. Two global effects exhibited by the model are discussed. The first effect is the "generation of matter out of geometry". Gravitational field equation in this model has the form of the eigenvalue equation for the Einstein operator. It turns out that the eigenvalues of this operator reproduce components of the energy-momentum tensor. The second effect concerns the existence of the initial and final singularities. Because of the strongly probabilistic character of the noncommutative dynamics on the fundamental level, although singularities do exist, they are probabilistically irrelevant.

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A noncommutative Friedman cosmological model

Heller

2010

Annalen der Physik

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The closed Friedman cosmological model, based on noncommutative geometry, is presented. Two global effects exhibited by the model are discussed. The first effect is the “generation of matter out of geometry”. Gravitational field equation in this model has the form of the eigenvalue equation for the Einstein operator. It turns out that the eigenvalues of this operator reproduce components of the energy‐momentum tensor. The second effect concerns the existence of the initial and final singularities. Because of the strongly probabilistic character of the noncommutative dynamics on the fundamental level, although singularities do exist, they are probabilistically irrelevant.

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Noncommutative closed Friedman universe

Cited by 4 publications

References 20 publications

Fundamental Problems in the Unification of Physics

Fundamental Problems in the Unification of Physics

A noncommutative Friedman cosmological model

A noncommutative Friedman cosmological model

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