Is the Space-Time a Superconductor?

Wenceslao Santiago-Germán

Manuel Sandoval Vallarta Institute for Theoretical Physics, Chetumal, México.

DOI: 10.4236/jmp.2013.410174                

Abstract

At the fundamental level, the 4-dimensional space-time of our direct experience might not be a continuum and discrete quantum entities might “collectively” rule its dynamics. Henceforth, it seems natural to think that in the “low-energy” regime some of its distinctive quantum attributes could, in principle, manifest themselves even at macroscopically large scales. Indeed, when confronted with Nature, classical gravitational dynamics of spinning astrophysical bodies is known to lead to paradoxes: to untangle them, dark matter or modifications to the classical law of gravity are openly considered. In this article, the hypothesis of a fluctuating space-time acquiring “at large distances” the properties of a Bose-Einstein condensate is pushed forward: firstly, it is shown that a natural outcome of this picture is the production of monopoles, dyons, and vortex lines of “quantized” gravitomagnetic—or gyrogravitational—flux along the transition phase; the minimal supported “charge” (and multiples of it) being directly linked with a nonzero (minimal) vacuum energy. Thus, a world of vibrating, spinning, interacting strings whose only elements in their construction are our topological concepts of space and time is envisioned, and they are proposed as tracers of the superfluid features of the space-time: the archetypal embodiment of these physical processes being set by the “gravitational roton”, an analogue of Landau’s classic higher-energy excitation used to explain the superfluid properties of helium II. The far and the near field asymptotics of string line solutions are presented and used to deduce their pair-interaction energy. Remarkably, it is found that two stationary, axis-aligned, quantum space-time vortices with the same sense of spin not only exhibit zones of repulsion but also of attraction, depending on their relative geodetic distance.

Keywords

Modified Gravity; Superconductivity; Kinematics; Dynamics; Rotation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	F. Hoyle, “Frontiers of Astronomy,” New American Library, New York, 1957, pp. 255-256.
[2]	B. Lindblad, Stockholms Observatoriums Annaler, Vol. 13, 1941, pp. 10.1-10.50.
[3]	C. C. Lin and F. H. Shu, Astrophysical Journal, Vol. 140, 1964, pp. 646-655.
[4]	C. C. Lin and F. H. Shu, Proceedings of the National Academy of Sciences, Vol. 55, 1966, pp. 229-234. http://dx.doi.org/10.1073/pnas.55.2.229
[5]	J. Binney and S. Tremaine, “Galactic Dynamics,” Princeton Series in Astrophysics, Princeton University Press, Princeton, 1950, p. 318.
[6]	W. Santiago-Germán, “Theory of Superconductivity of Gravitation and the Dark Matter Problem,” Unpublished.
[7]	G. G. Byrd, T. Freeman, S. Howard and R. J. Buta, The Astronomical Journal, Vol. 135, 2008, pp. 408-413.
[8]	B. L. Davies, et al., The Astrophysical Journal, Vol. 199, 2012, p. 33.
[9]	S. Kendall, R. C. Kennicutt and C. Clarke, MNRAS, Vol. 414, 2011, pp. 538-564.
[10]	E. E. Martínez-García, The Astrophysical Journal, Vol. 744, 2012, p. 92.
[11]	E. J. Wilczynski, The Astrophysical Journal, Vol. 3, 1986, pp. 97-100.
[12]	P. Goldreich and D. Lynden-Bell, Monthly Notices of the Royal Astronomical Society, Vol. 130, 1965, p. 125.
[13]	W. H. Julian and A. Toomre, The Astrophysical Journal, Vol. 146, 1966, pp. 810-830.
[14]	K. Foyle, H.-W. Rix, C. L. Dobbs, A. K. Leroy and F. Walter, The Astrophysical Journal, Vol. 735, 2011, p. 101. http://dx.doi.org/10.1088/0004-637X/735/2/101
[15]	P. Kapitza, Nature Vol. 141, 1938, p. 74.
[16]	J. F. Allen and A. D. Misener, Nature, Vol. 141, 1939, p. 75.
[17]	S. M. Christensen, “Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. DeWitt,” Adam Hilger Ltd., Bristol, 1984.
[18]	C. DeWitt-Morette, “The Pursuit of Quantum Gravity: Memoirs of Bryce DeWitt from 1946 to 2004,” Springer-Verlag, Berlin, 2011, p. 6.
[19]	M. Born, “The Statistical Interpretation of Quantum Mechanics: Nobel Lecture,” 1954, pp. 259-266.
[20]	W. Pauli, “Theory of Relativity,” Dover, New York, Translated from the German Original of 1921, 1981.
[21]	H. Weyl and S. B. Preuss, Annalen der Physik, Vol. 364, 1918, p. 465.
[22]	H. Weyl, Mathematische Zeitschrift, Vol. 2, 1918, p. 384.
[23]	H. Weyl, Annals of Physics, Lpz., Vol. 59, 1919, p. 101.
[24]	R. Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe,” Alfred A. Knopf, New York, 2005, pp. 449-455, 782-868.
[25]	J. M. Bardeen, B. Carter and S.W. Hawking, “The Four Laws of Black Hole Mechanics,” Communications in Mathematical Physics, Vol. 31, 1973, pp. 161-170. http://dx.doi.org/10.1007/BF01645742
[26]	A. Lichnerowicz, Journal de Mathématiques Pures et Appliquées, Vol. 23, 1944, pp. 37-63.
[27]	Y. Choquet-Bruhat and J. W. York, “The Cauchy Problem: In General Relativity and Gravitation,” A. Held Plenum, New York, 1980.
[28]	H. Hopf, Mathematische Annalen, Vol. 95, 1925, pp. 313-339.
[29]	W. Killing, Ibid, Vol. 39, 1891, p. 257.
[30]	I. Newton, “Opticks,” Dover, New York, 1952.
[31]	A. Koyré, I. B. Cohen and A. Whitman, “Philosophiae Naturalis Principia Mathematica,” Harvard University Press, Cambridge, 1972.
[32]	H. M. Macdonald, Proceedings London Mathematical Society, Vol. 30, 1899, pp. 165-179.
[33]	G. Giacomelli and L. Patrizii, “Magnetic Monopole Searches: Lectures given at the Summer School on Astroparticle Physics and Cosmology,” Trieste, 17 June-5 July 2002, pp. 125-146.
[34]	H. Kragh, “Dirac, a Scientific Biography,” Cambridge University Press, New York, 1990.
[35]	P. A. M. Dirac, Proceedings of the Royal Society of London, Vol. A133, 1931 pp. 60-72.
[36]	P. A. M. Dirac, Physical Review, Vol. 74, 1948, pp. 817-30.
[37]	G. ‘t Hooft, Nuclear Physics B, Vol. 79, 1974, pp. 276 284. http://dx.doi.org/10.1016/0550-3213(74)90486-6
[38]	A. M. Polyakov, JETP Letters, Vol. 20, 1974, pp. 194-195.
[39]	V. A. Rubakov, JETP Letters, Vol. 33, 1981, pp. 644-646.
[40]	C. G. Callan Jr., Nuclear Physics B, Vol. 212, 1983, pp. 391-400. http://dx.doi.org/10.1016/0550-3213(83)90677-6
[41]	J. Preskill, Vol. 34, Annual Review of Nuclear and Particle Science, 1984, pp. 461-530.
[42]	J. Schwinger, Science, Vol. 165, 1969, pp. 757-761. http://dx.doi.org/10.1126/science.165.3895.757
[43]	M. F. Atiyah and N. J. Hitchin, Physics Letters, Vol. 197A, 1985, pp. 21-25.
[44]	A. H. Taub, Annals of Mathematics, Vol. 53, 1951, pp. 472-490. http://dx.doi.org/10.2307/1969567
[45]	E. Newman, L. Tamburino and T. Unti, “Empty-Space Generalization of the Schwarzschild Metric,” Journal of Mathematical Physics, Vol. 4, 1963, p. 915. http://dx.doi.org/10.1063/1.1704018
[46]	S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Space-Time,” Cambridge University Press, Cambridge, 1973.
[47]	B. Russell “Human Knowledge: Its Scope and Limits,” George Allen and Unwin, London, 1948.
[48]	L. Bombelli, J. Lee, D. Meyer and R. D. Sorkin, Physical Review Letters, Vol. 59, 1987, p. 521.
[49]	A. Ashtekar, Acta Cosmologica, Fasc, Vol. 21, 1995, pp. 85-110.
[50]	D. Finkelstein, International Journal of Theoretical Physics, Vol. 27, 1988, pp. 473-519. http://dx.doi.org/10.1007/BF00669395
[51]	Y. Nambu, Physical Review D, Vol. 10, 1974, pp. 4262-4268. http://dx.doi.org/10.1103/PhysRevD.10.4262
[52]	J. Scherk and J. H. Schwarz, Nuclear Physics B, Vol. 8, 1974, pp. 118-144. http://dx.doi.org/10.1016/0550-3213(74)90010-8
[53]	A. Einstein, Gedenkboek aangeb. aan H. Kamerlingh Onnes, eaz. Leiden, E. IJdo, 1922, p. 435; translated in ArXiv e-prints, arXiv:0510251.
[54]	L. D. Landau, The Journal of Physics, USSR, Vol. 5, 1941, p. 71.
[55]	R. P. Feynman, “Statistical Mechanics: A Set of Lectures,” Addison-Wesley Publishing Company, Massachusetts, 1972, pp. 312-350.