The Invariant Set postulate: A new geometric framework for the foundations of quantum theory and the role played by gravity

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 465, Issue 2110, 2009, Pages 3165-3185

  Palmer, T N ^a  

^a EUROPEAN CENTRE FOR MEDIUM RANGE WEATHER FORECASTS   (United Kingdom)

Author keywords

Invariant set hypothesis; Quantum foundations; Quantum gravity

Indexed keywords

COMPUTATIONAL GEOMETRY; COSMOLOGY; DYNAMICAL SYSTEMS; FRACTALS; NONLINEAR DYNAMICAL SYSTEMS; QUANTUM THEORY;

COMPLEX NUMBER; CONTEXTUALITY; COSMOLOGICAL SCALE; EXPLORATORY ANALYSIS; FRACTAL GEOMETRY; GEOMETRIC FRAMEWORK; INVARIANT SET; INVARIANT SET HYPOTHESIS; MICRO-SCALES; NON-EUCLIDEAN GEOMETRY; NONLOCALITIES; PHYSICAL PRINCIPLES; PHYSICAL REALITY; QUANTUM FOUNDATIONS; QUANTUM GRAVITY; QUANTUM PHYSICS; QUANTUM THEORY OF GRAVITY; SCIENCE FICTIONS; SELF-SIMILARITIES; STATE-SPACE; UNIFIED THEORY;

SET THEORY;

EID: 70349655888     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0080     Document Type: Article

References (37)

1. Albeverio, S. & Khrennikov, A. Yu. 1998 A regularisation of quantum field Hamiltonians with the aid of p-adic numbers. Acta Appl. Math., 50, 225-251. (doi:10.1023/A:1005813632179)
2. Barbour, J. 1999 The end of time, 374 pp. London, UK: Phoenix.
3. beim Graben, P. & Atmanspacher, H. 2006 Complementarity in classical dynamical systems. Found. Phys. 36, 291-306. (doi:10.1007/s10701-005-9013-0) (Pubitemid 43910082)
4. Bell, J. S. 1995 Free variables and local causality. In Speakable and unspeakable in quantum mechanics. Cambridge, UK: Cambridge University Press.
5. Berry, M. V. 2002 Singular limits. Phys. Today 55, 10-11. (doi:10.1063/1.1485555)
6. Blum, L., Cucker, F., Shub, M. & Smale, S. 1997 Complexity and real computation, p. 453. New York, NY: Springer-Verlag.
7. Birman, J. S. & Williams, R. F. 1983 Knotted periodic orbits in dynamical systems I: Lorenz's equations. Topology 22, 47-82. (doi:10.1016/0040-9383 (83) 90045-9)
8. Bohm, D. & Hiley, B. J. 1995 The undivided universe, p. 397. Abingdon, UK: Routledge.
9. Bojowald, M. 2007 What happened before the big bang? Nat. Phys. 3, 523-525. (doi:10.1038/nphys654)
10. Cornish, N. J. 1997 Fractals and symbolic dynamics as invariant descriptors of chaos in general relativity. (http://arxiv.org/abs/gr-qc/9709036)
11. Dube, S. 1993 Undecidable problems in fractal geometry. Complex Syst. 7, 423-444.
12. Ehrendorfer, M. 2006 The Liouville equation and atmospheric predictability. In Predictability of weather and climate (eds T. Palmer & R. Hagedorn). Cambridge, UK: Cambridge University Press.
13. El Naschie, M. S. 2004 A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons Fractals 19, 209-236. (doi:10.1016/S0960-0779 (03) 00278-9)
14. Gilder, L. 2008 The age of entanglement. New York, NY: Knopf Publishing Group.
15. Hardy, G. H. & Wright, E. M. 1979 An introduction to the theory of numbers. Oxford, UK: Oxford University Press.
16. Hardy, L. 2004 Why is nature described by quantum theory? In Science and ultimate reality (eds John D. Barrow, Paul C. W. Davies & Charles L. Harper Jr.). Cambridge, UK: Cambridge University Press.
17. Hawking, S. 1975 Particle creation by black holes. Comm. Math. Phys. 25, 152-166. (doi:10.1007/BF01877517)
18. Hawking, S. & Penrose, R. 2000 The nature of space and time. Princeton, NJ: Princeton University Press.
19. Khrennikov, A. 1997 Non-Archimedean analysis: quantum paradoxes, dynamical systems and biological models. Dordrecht, The Netherlands: Kluwer.
20. Lapidus, M. L. & van Frankenhuijsen, M. 2006 Fractal geometry, complex dimensions and zeta functions. New York, NY: Springer.
21. Lind, D. & Marcus, B. 1995 An introduction to symbolic dynamics and coding. Cambridge, UK: Cambridge University Press.
22. Liouville, J. 1838 Sur la théorie de la variation des constants arbitraries. J. Math. Pure Appl. 3, 342-349.
23. Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141. (doi:10.1175/1520-0469 (1963) 020<0130:DNF>2.0. CO;2)
24. Misner, C. W., Thorne, K. S. & Wheeler, J. A. 1973 Gravitation. New York, NY: W. H. Freeman.
25. Nottale, L. & Schneider, J. 1984 Fractals and non-standard analysis. J. Math. Phys. 25, 1296-1300. (doi:10.1063/1.526285)
26. Ord, G. N. 1983 Fractal space-time: a geometric analogue of relativistic quantum mechanics. J. Phys. A 16, 1869-1884. (doi:10.1088/0305-4470/16/9/012)
27. Palmer, T. N. 1995 A local deterministic model of quantum spin measurement. Proc. R. Soc. Lond. A 451, 585-608. (doi:10.1098/rspa.1995.0145)
28. Palmer, T. N. 2004 A granular permutation-based representation of complex numbers and quaternions: elements of a possible realistic quantum theory. Proc. R. Soc. Lond. A 460, 1039-1055. (doi:10.1098/rspa.2003.1189) (Pubitemid 38406360)
29. Penrose, R. 1965 Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14, 57-59. (doi:10.1103/PhysRevLett.14.57)
30. Penrose, R. 1989 The emperor's new mind. Oxford, UK: Oxford University Press.
31. Penrose, R. 2008 Causality, quantum theory and Cosmology. In On Space and Time (ed. Shahn Majid). Cambridge, UK: Cambridge University Press.
32. Price, H. 1996 Time's arrow and Archimedes' point: new directions for the physics of time. Oxford, UK: Oxford University Press.
33. Rössler, O. E. 1976 An equation for continuous chaos. Phys. Lett. A 57, 397-398. (doi:10.1016/0375-9601 (76) 90101-8)
34. Sciamarella, D. & Mindlin, G. B. 1999 Topological structure of chaotic flows from human speech data. Phys. Rev. Lett. 82, 1450-1453. (doi:10.1103/PhysRevLett.82.1450)
35. 'tHooft, G. 2007 The free-will postulate in quantum mechanics. (http://arxiv.org/abs/quant-ph/0701097)
36. Takens, F. 1981 Detecting strange attractors in turbulence. In Dynamical systems and turbulence, vol. 898 of Springer Lecture Notes in Mathematics, pp. 366-381. New York, NY: Springer.
37. Weinstein, S. 2008 Nonlocality without nonlocality. (http://arxiv.org/ abs/0812.0349v2)