Spin and Quantization of Gravitational Space

Affiliation(s)

College of Mathematics and Physics, Chongqing University of Post and Telecommunication, Chongqing, China.

College of Mathematics and Physics, Chongqing University of Post and Telecommunication, Chongqing, China.

ABSTRACT

According to the formula of translational motion of vector along an infinitesimal closed curve in gravitational space, this article shows that the space and time both are quantized; the called center singularity of Schwarzschild metric does not exist physically, and Einstein’s theory of gravity is compatible with the traditional quantum theory in essence; the quantized gravitational space is just the spin network which consists of infinite quantized loops linking and intersecting each other, and that whether the particle is in spin eigenstate depends on the translational track of its spin vector in gravitational space.

According to the formula of translational motion of vector along an infinitesimal closed curve in gravitational space, this article shows that the space and time both are quantized; the called center singularity of Schwarzschild metric does not exist physically, and Einstein’s theory of gravity is compatible with the traditional quantum theory in essence; the quantized gravitational space is just the spin network which consists of infinite quantized loops linking and intersecting each other, and that whether the particle is in spin eigenstate depends on the translational track of its spin vector in gravitational space.

Cite this paper

B. Liang, "Spin and Quantization of Gravitational Space,"*Journal of Modern Physics*, Vol. 3 No. 11, 2012, pp. 1757-1762. doi: 10.4236/jmp.2012.311218.

B. Liang, "Spin and Quantization of Gravitational Space,"

References

[1] S. Weinberg, “Gravitation and Cosmology,” Section 6-3, John Wiley & Sons, Inc., New York, 1972.

[2] Landau and Lifshitz, “Field Theory,” Section 11-1, Гостехиздат, Moscow, 1948;

[3] Landau and Lifshitz, “Field Theory,” Section 1-6, Гостехиздат, Moscow, 1948;

[4] Liao Liu and Zheng Zhao, “General relativity,” Higher Education Press, Beijing, 1987, p. 55.

[5] S. Weinberg, “Gravitation and Cosmology,” Section 6-3, John Wiley & Sons, Inc., New York,1972;

[6] L. Liu and Z. Zhao, “General Relativity,” Higher Education Press, Beijing, 1987, p.145.

[7] C. Rovelli,“Black Hole Entropy from Loop Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, pp. 3288-3291. doi:10.1103/PhysRevLett.77.3288

[8] L. Smolin, “Three Roads to Quantum Gravity,” chapter 8-10, Basic Book, New York, 2001.

[9] C. Rovell, “Quantum Gravity,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511755804

[10] A. Ashtekar, “Gravity and the Quantum,” New Journal of Physics, Vol. 7, No. 1, 2005, pp. 198-200. doi:10.1088/1367-2630/7/1/198

[11] C. Rovelli, “Loop Quantum Gravity,” Encyclopedia of Mathematical Physics 5, Jean-Pierre Francoise, 2006; Gregory L Naber, Tsou Sheun Tsun, Elsevier Inc, p265 Photocopy, Science Press, China, 2007.

[12] R. Gambini, “Knot Invariants and Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, p. 247.

[13] L. H. Kauffman, “Knot Theory and Physics,” Physical Review Letters, Vol. 77, No. 16, 1996, p.253.

[14] H. Sahlmann, “Quantum Dynamics in Loop Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, p. 276.

[15] V. Bonzom and M. Smerlak, “Gauge Symmetries in Spin-Foam Gravity: The Case for Celluler Quantization,” Physical Review Letters, Vol. 108, No. 24, 2012, p. 241303. doi:10.1103/PhysRevLett.108.241303

[1] S. Weinberg, “Gravitation and Cosmology,” Section 6-3, John Wiley & Sons, Inc., New York, 1972.

[2] Landau and Lifshitz, “Field Theory,” Section 11-1, Гостехиздат, Moscow, 1948;

[3] Landau and Lifshitz, “Field Theory,” Section 1-6, Гостехиздат, Moscow, 1948;

[4] Liao Liu and Zheng Zhao, “General relativity,” Higher Education Press, Beijing, 1987, p. 55.

[5] S. Weinberg, “Gravitation and Cosmology,” Section 6-3, John Wiley & Sons, Inc., New York,1972;

[6] L. Liu and Z. Zhao, “General Relativity,” Higher Education Press, Beijing, 1987, p.145.

[7] C. Rovelli,“Black Hole Entropy from Loop Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, pp. 3288-3291. doi:10.1103/PhysRevLett.77.3288

[8] L. Smolin, “Three Roads to Quantum Gravity,” chapter 8-10, Basic Book, New York, 2001.

[9] C. Rovell, “Quantum Gravity,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511755804

[10] A. Ashtekar, “Gravity and the Quantum,” New Journal of Physics, Vol. 7, No. 1, 2005, pp. 198-200. doi:10.1088/1367-2630/7/1/198

[11] C. Rovelli, “Loop Quantum Gravity,” Encyclopedia of Mathematical Physics 5, Jean-Pierre Francoise, 2006; Gregory L Naber, Tsou Sheun Tsun, Elsevier Inc, p265 Photocopy, Science Press, China, 2007.

[12] R. Gambini, “Knot Invariants and Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, p. 247.

[13] L. H. Kauffman, “Knot Theory and Physics,” Physical Review Letters, Vol. 77, No. 16, 1996, p.253.

[14] H. Sahlmann, “Quantum Dynamics in Loop Quantum Gravity,” Physical Review Letters, Vol. 77, No. 16, 1996, p. 276.

[15] V. Bonzom and M. Smerlak, “Gauge Symmetries in Spin-Foam Gravity: The Case for Celluler Quantization,” Physical Review Letters, Vol. 108, No. 24, 2012, p. 241303. doi:10.1103/PhysRevLett.108.241303