We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set theoretical level of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Król J. (2006). “A model for spacetime. The role of interpretations in some Grothendieck topoi,” to appear Found. Phys. 36(7): 1070–1098
S. Koppelberg, in Handbook of Boolean Algebras, Vol. 1, J. D. Monk, ed. (North-Holland, Amsterdam, New York, 1989).
Jech T. (2003) Set Theory . Springer, New York
Blass A.(1977) “End extensions, conservative extensions, and the Rudin-Frolik ordering”. Trans. Amer. Math. Soc. 225, 325–340
L. Crane, “Categorical geometry and the mathematical foundations of quantum gravity,” (2006), gr-qc/0602120.
Moerdijk I., Reyes G.E. (1991) Models for Smooth Infinitesimal Analysis. Springer, New York
Mc Kinsey J.C.C., Tarski A. (1944) “The algebra of topology”. Ann. Math. 45, 141–191
Król J. (2004) “Background independence in quantum gravity and forcing constructions”. Found. Phys. 34(3): 361–403
Król J. (2004) “Exotic smoothness and noncommutative spaces. The model-theoretical approach,” Found. Phys. 34(5): 843–869
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2 (1998), hep-th/9802150.
G. T. Horowitz and J. Polchinski, “Gauge/gravity duality,” gr-qc/0602037, (2006).
J. Król, “Model theory and the AdS/CFT correspondence,” Talk presented at the IPM String School and Workshop, Queshm Island, Iran, 05-14.01.2005 (2005) hep-th/0506003
Benioff P. (1976) “Models of ZF set theory as carriers for the mathematics of physics I and II”. J. Math. Phys. 19, 618–629
Benioff P. (2002). “Towards a coherent theory of physics and mathematics”. Found. Phys. 32, 989–1029
J. Baez, “Quantum quandaries: a category-theoretic perspective,” (2004), The Structural Foundations of Quantum Gravity, D. Rickles, S. French and J. T. Saatsi, eds. (Oxford University, Oxford, 2007), (To appear) quant-ph/0404040
A. K. Guts, “Topos-theoretic model of the Deutsch multiverse,” Math. Struct. Model. 8, 76–90, (2001) physics/0203071
Mac Lane S., Moerdijk I. (1992) Sheaves in Geometry and Logic. A First Introduction to Topos Theory. Springer, New York
M. Barr, “Toposes without points,” J. Pure Appl. Alg. 5(265) (1974).
D. Kazhdan, “Introduction to QFT,” in Quantum Fields and Strings: A Course for Mathematicians, P. Deligne and E. Witten, eds. (AMS, IAS, 1999).
J. Polchinski and M. J. Strassler, “The string dual of a confining four-dimensional gauge theory,” hep-th/0003136 (2000).
Witten E. (1994) “Monopoles and four manifolds”. Math. Res. Lett. 1, 769–796 hep-th/9411102
M. Arnsdorf and L. Smolin, “The Maldacena conjecture and Rehren duality,” hep-th/0106073, (2001).
P. Benioff, “Fields of iterated quantum reference frames based on gauge transformations of rational string states,” (2006) quant-ph/0604135.
T. Jech, Multiple Forcing, Cambridge Tracts in Math, Vol. 88 (Cambridge University, Cambridge, London, New York, 1986).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Król, J. A Model for Spacetime II. The Emergence of Higher Dimensions and Field Theory/Strings Dualities. Found Phys 36, 1778–1800 (2006). https://doi.org/10.1007/s10701-006-9087-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-006-9087-3