Absolute Maximum Proper Time to an Initial Event, the Curvature of Its Gradient along Conflict Strings and Matter

Affiliation(s)

R&D Algorithms Department, ANB/ANT—Applied Neural Biometrics/Technology, Netanya, Israel.

R&D Algorithms Department, ANB/ANT—Applied Neural Biometrics/Technology, Netanya, Israel.

ABSTRACT

Einstein equation of gravity has on one side the momentum energy density tensor and on the other, Einstein tensor which is derived from Ricci curvature tensor. A better theory of gravity will have both sides geometric. One way to achieve this goal is to develop a new measure of time that will be independent of the choice of coordinates. One natural nominee for such time is the upper limit of measurable time form an event back to the big bang singularity. This limit should exist despite the singularity, otherwise the cosmos age would be unbounded. By this, the author constructs a scalar field of time. Time, however, is measured by material clocks. What is the maximal time that can be measured by a small microscopic clock when our curve starts at near the “big bang” event and ends at an event within the nucleus of an atom? Will our tiny clock move along geodesic curves or will it move in a non geodesic curve within matter? It is almost paradoxical that a test particle in General Relativity will always move along geodesic curves but the motion of matter within the particle may not be geodesic at all. For example, the ground of the Earth does not move at geodesic velocity. Where there is no matter, we choose a curve from near “big bang” to an event such that the time measured is maximal. Without assuming force fields, the gravitational field which causes that two or more such curves intersect at events, would cause discontinuity of the gradient of the upper limit of measurable time scalar field. The discontinuity can be avoided only if we give up on measurement along geodesic curves where there is matter. In other words, our tiny test particle clock will experience force when it travels within matter or near matter.

Cite this paper

E. Suchard, "Absolute Maximum Proper Time to an Initial Event, the Curvature of Its Gradient along Conflict Strings and Matter,"*Journal of Modern Physics*, Vol. 4 No. 6, 2013, pp. 791-806. doi: 10.4236/jmp.2013.46109.

E. Suchard, "Absolute Maximum Proper Time to an Initial Event, the Curvature of Its Gradient along Conflict Strings and Matter,"

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[1] S. Vaknin, “Time Asymmetry Revisited [microform],” Ph.D. Dissertation, Library of Congress, Microfilm, 1982.

[2] J. W. Milnor, “Topology from the Differentiable Viewpoint,” Princeton Landmarks in Mathematics, Princeton University Press, Princeton, pp. 32-41.

[3] J. N. Munday, F. Capasso and V. A. Parsegian, Nature, Vol. 457, 2009, pp. 170-173. doi:10.1038/nature07610

[4] V. Guillemin and A. Pollack, “Homotopy and Stability,” Differential Topology, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, pp. 33-35.

[5] Y. Avni and E. Suchard, “Apparatus for and Method of Pattern Recognition and Image Analysis,” US Patent No: 7424462.

[6] D. Lovelock and H. Rund, “The Numerical Relative Tensors,” Tensors, Differential Forms and Variational Principles, Dover Publications Inc., Mineola, pp. 113-114.

[7] D. Lovelock and H. Rund, “Tensors, Differential Forms and Variational Principles,” Dover Publications Inc., Mineola, pp. 323-325.

[8] D. Lovelock and H. Rund, “Tensors, Differential Forms and Variational Principles,” Dover Publications Inc., Mineola, p. 262.

[9] D. Lovelock and H. Rund, “Tensors, Differential Forms and Variational Principles,” Dover Publications Inc., Mineola, p. 261.

[10] E. Cartan, “The Theory of Spinors,” Dover Publications Inc. Mineola, p. 149.

[11] V. Guillemin, “Submersions, Local Submersion Theorem,” Differential Topology, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, p. 20.

[12] Rambam, “The Guide For The Perplexed By Moses Maimonides (Moreh Nevuchim), Part. II, Chapter 13,” Routledge and Kegan Paul Ltd., London, 1904.

[13] J. Albo, “Immeasurable Time-Maamar 18, measurable, Time by Movement,” Book of Principles (Sefer Haikarim), Chapter 2, Chapter 13, (Circa 1380-1444, unknown), The Jewish Publication Society of America 1946.

[14] S. Deser and B. Tekin, Physical Review Letters D, Vol. 67, 2003, Article ID: 084009. doi:10.1103/PhysRevD.67.084009

[15] M. Alcubierre, Classical and Quantum Gravity, Vol. 11, 1994, pp. L73-L77.

[16] Y. Friedman and T. Scarr, Physica Scripta, Vol. 86, 2012, Article ID: 065008. doi:10.1088/0031-8949/86/06/065008

[17] T. Datta, M. Yin, A. Dimofte, M. C. Bleiweiss and Z. Cai, “Experimental Indications of Electro-Gravity,” 2005. arXiv:physics/0509068 [physics.gen-ph]