On Separation between Metric Observers in Segal’s Compact Cosmos

Affiliation(s)

^{1}
Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia.

^{2}
A. P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk, Russia.

ABSTRACT

A certain class K of GR homogeneous spacetimes is considered. For each pair*E*, of spacetimes from K, where conformal transformation *g* is from . Each *E* (being or its double cover, as a manifold) is interpreted as related to an observer in Segal’s universal cosmos. The definition of separation *d* between *E* and is based on the integration of the conformal factor of the transformation *g*. The integration is carried out separately over each region where the conformal factor is no less than 1 (or no greater than 1). Certain properties of are proven; examples are considered; and possible directions of further research are indicated.

A certain class K of GR homogeneous spacetimes is considered. For each pair

KEYWORDS

Separation between Spacetimes, Segal’s Universal Cosmos, Conformal Group Action on U(2), DLF-Theory

Separation between Spacetimes, Segal’s Universal Cosmos, Conformal Group Action on U(2), DLF-Theory

Cite this paper

Levichev, A. and Palyanov, A. (2015) On Separation between Metric Observers in Segal’s Compact Cosmos.*Journal of Modern Physics*, **6**, 2040-2049. doi: 10.4236/jmp.2015.614210.

Levichev, A. and Palyanov, A. (2015) On Separation between Metric Observers in Segal’s Compact Cosmos.

References

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[2] Levichev, A.V. (1989) On the Causal Structure of Homogeneous Lorentzian Manifolds. General Relativity & Gravity, 21, 1027-1045.

http://dx.doi.org/10.1007/BF00774087

[3] Levichev, A.V. (1993) The Chronometric Theory by I. Segal Is the Crowning Accomplishment of Special Relativity. Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, 8, 84-89. (In Russian)

[4] Levichev, A.V. (1995) Mathematical Foundations and Physical Applications of Chronometry. In: Hilgert, J., Hofmann, K. and Lawson, J., Eds., Semigroups in Algebra, Geometry, and Analysis, de Gryuter Expositions in Mathematics, Berlin, 77-103.

http://dx.doi.org/10.1515/9783110885583.77

[5] http://dedekind.mit.edu/segal-archive/index.php

[6] Levichev, A.V. (2011) Pseudo-Hermitian Realization of the Minkowski World through DLF Theory. Physica Scripta, 83, 1-9.

http://dx.doi.org/10.1088/0031-8949/83/01/015101

[7] Hameroff, S. and Penrose, R. (2014) Consciousness in the Universe: A Review of the “Orch OR” Theory. Physics of Life Reviews, 11, 39-78.

http://dx.doi.org/10.1016/j.plrev.2013.08.002

[8] Hameroff, S. and Penrose, R. (2014) Reply to Criticism of the “Orch OR Qubit”—“Orchestrated Objective Reduction” Is Scientifically Justified. Physics of Life Reviews, 11, 94-100.

http://dx.doi.org/10.1016/j.plrev.2013.11.013

[9] Penrose, R. (1992) Gravity and Quantum Mechanics. In: Gleiser, R.J., Kozameh, C.N. and Moreschi, O.M., Eds., General Relativity and Gravitation 13. Part 1: Plenary Lectures 1992. Proceedings of the 13th International Conference on General Relativity and Gravitation, Cordoba, 28 June-4 July 1992, 179-189.

[10] Levichev, A. and Palyanov, A. (2014) On a Modification of the Theoretical Basis of the Penrose-Hameroff Model of Consciousness. In: International Conference MM-HPC-BBB-2014, Abstracts, Sobolev Institute of Mathematics SB RAS, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 49.

[11] Levichev, V. and Palyanov, A.Yu. (2014) On a Notion of Separation between Space-Times. In: Geometry Days in Novosibirsk. Abstracts of the International Conference, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 110.

[12] Segal, I.E., Hans, P.J., Bent, Ø., Paneitz, S.M. and Speh, B. (1981) Covariant Chronogeometry and Extreme Distances: Elementary Particles. PNAS, 78, 5261-5265.

http://dx.doi.org/10.1073/pnas.78.9.5261

[13] Werth, J.-E. (1986) Conformal Group Actions and Segal’s Cosmology. Reports on Mathematical Physics, 23, 257-268.

http://dx.doi.org/10.1016/0034-4877(86)90023-6

[14] Segal, I.E. (1976) Mathematical Cosmology and Extragalactic Astronomy. Academic Press, New York.

[15] Branson, T.P. (1987) Group Representations Arising from Lorentz Conformal Geometry. Journal of Functional Analysis, 74, 199-291.

http://dx.doi.org/10.1016/0022-1236(87)90025-5

[16] Segal, I.E. (1984) Evolution of the Inertial Frame of the Universe. Nuovo Cimento, 79B, 187-191.

http://dx.doi.org/10.1007/BF02748970

[17] Kon, M. and Levichev, A. (2015) Towards Analysis in Space-Time Bundles Based on Pseudo-Hermitian Realization of the Minkowski Space. In Preparation.

[1] Guts, A.K. and Levichev, A.V. (1984) On the Foundations of Relativity Theory. Doklady Akademii Nauk SSSR, 277, 253-257. (In Russian)

[2] Levichev, A.V. (1989) On the Causal Structure of Homogeneous Lorentzian Manifolds. General Relativity & Gravity, 21, 1027-1045.

http://dx.doi.org/10.1007/BF00774087

[3] Levichev, A.V. (1993) The Chronometric Theory by I. Segal Is the Crowning Accomplishment of Special Relativity. Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, 8, 84-89. (In Russian)

[4] Levichev, A.V. (1995) Mathematical Foundations and Physical Applications of Chronometry. In: Hilgert, J., Hofmann, K. and Lawson, J., Eds., Semigroups in Algebra, Geometry, and Analysis, de Gryuter Expositions in Mathematics, Berlin, 77-103.

http://dx.doi.org/10.1515/9783110885583.77

[5] http://dedekind.mit.edu/segal-archive/index.php

[6] Levichev, A.V. (2011) Pseudo-Hermitian Realization of the Minkowski World through DLF Theory. Physica Scripta, 83, 1-9.

http://dx.doi.org/10.1088/0031-8949/83/01/015101

[7] Hameroff, S. and Penrose, R. (2014) Consciousness in the Universe: A Review of the “Orch OR” Theory. Physics of Life Reviews, 11, 39-78.

http://dx.doi.org/10.1016/j.plrev.2013.08.002

[8] Hameroff, S. and Penrose, R. (2014) Reply to Criticism of the “Orch OR Qubit”—“Orchestrated Objective Reduction” Is Scientifically Justified. Physics of Life Reviews, 11, 94-100.

http://dx.doi.org/10.1016/j.plrev.2013.11.013

[9] Penrose, R. (1992) Gravity and Quantum Mechanics. In: Gleiser, R.J., Kozameh, C.N. and Moreschi, O.M., Eds., General Relativity and Gravitation 13. Part 1: Plenary Lectures 1992. Proceedings of the 13th International Conference on General Relativity and Gravitation, Cordoba, 28 June-4 July 1992, 179-189.

[10] Levichev, A. and Palyanov, A. (2014) On a Modification of the Theoretical Basis of the Penrose-Hameroff Model of Consciousness. In: International Conference MM-HPC-BBB-2014, Abstracts, Sobolev Institute of Mathematics SB RAS, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 49.

[11] Levichev, V. and Palyanov, A.Yu. (2014) On a Notion of Separation between Space-Times. In: Geometry Days in Novosibirsk. Abstracts of the International Conference, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 110.

[12] Segal, I.E., Hans, P.J., Bent, Ø., Paneitz, S.M. and Speh, B. (1981) Covariant Chronogeometry and Extreme Distances: Elementary Particles. PNAS, 78, 5261-5265.

http://dx.doi.org/10.1073/pnas.78.9.5261

[13] Werth, J.-E. (1986) Conformal Group Actions and Segal’s Cosmology. Reports on Mathematical Physics, 23, 257-268.

http://dx.doi.org/10.1016/0034-4877(86)90023-6

[14] Segal, I.E. (1976) Mathematical Cosmology and Extragalactic Astronomy. Academic Press, New York.

[15] Branson, T.P. (1987) Group Representations Arising from Lorentz Conformal Geometry. Journal of Functional Analysis, 74, 199-291.

http://dx.doi.org/10.1016/0022-1236(87)90025-5

[16] Segal, I.E. (1984) Evolution of the Inertial Frame of the Universe. Nuovo Cimento, 79B, 187-191.

http://dx.doi.org/10.1007/BF02748970

[17] Kon, M. and Levichev, A. (2015) Towards Analysis in Space-Time Bundles Based on Pseudo-Hermitian Realization of the Minkowski Space. In Preparation.