[1] | De Maupertuis, P.-L. M. 1744, Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles. Mém. Ac. Sc. Paris 417–426. |
[2] | Thomson, W. 1851, On the dynamical theory of heat, with numerical results deduced from Mr Joule’s equivalent of a thermal unit, and M. Regnault’s observations on steam. Trans. R. Soc. Edinb. Excerpts §§1–14 & §§99–100. |
[3] | Griffiths, D. 1999, Introduction to Electrodynamics. Upper Prentice Hall, Saddle River, NJ. |
[4] | Chew, G. F., and Poénaru, V. 1980, Topological bootstrap prediction of three-"colored," eight-flavored quarks. Phys. Rev. Lett. 45, 229–231. |
[5] | Chew, G. F., and Poénaru, V. 1981, Topological bootstrap theory of hadrons. Z. Phys. C—Particles and Fields 11, 59–93. |
[6] | Jackiw, R. 1995, Diverse Topics in Theoretical and Mathematical Physics. Singapore: World Scientific. |
[7] | Heller, M., and Sasin, W. 1999, Origin of classical singularities. General Relativity and Gravitation 31, 555–570. |
[8] | Noether, E. 1918, Invariante Variationsprobleme. Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse 235–257. http://arxiv.org/abs/physics/0503066v1. |
[9] | Feynman, R. P. 1965, The Principle of Least Action. in The Feynman Lectures on Physics 2, Ch 19 Addison-Wesley. |
[10] | Annila, A. 2010, All in action. Entropy 12, 2333–2358. |
[11] | Du Châtelet, E. 1740, Institutions de Physique. Prault, Paris, France. |
[12] | Eddington, A. 1931, Preliminary note on the masses of the electron, the proton, and the universe. Proc. Cambridge Phil. Soc. 27, 15–19. |
[13] | Thouless, D. J. 1998, Topological quantum numbers in nonrelativistic physics. World Scientific, River Edge, NJ. |
[14] | Berry, M. V. 1984, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45–57. |
[15] | Avron, J. E., Osadchy, D., and Seiler, R. 2003, Topological quantum numbers in the Hall effect. Physics Today 56, 38–42. |
[16] | Silverman, J. H. 1992, The Arithmetic of Elliptic Curves. Springer-Verlag, New York, NY. |
[17] | Mahoney, M. S. 1994, The Mathematical Career of Pierre de Fermat, 1601-1665, 2nd ed. Princeton University Press, Princeton, NJ, p. 401. |
[18] | Annila, A. 2011, Least-time paths of light. MNRAS 416, 2944–2948. |
[19] | Koskela, M., and Annila, A. 2011, Least-time perihelion precession. MNRAS 417, 1742–1746. arXiv:1009.1571. |
[20] | Annila, A. Probing Mach’s principle. 2012 MNRAS (in press). |
[21] | Genz, H. 2002, Nothingness: The Science of Empty Space. Perseus, Cambridge, MA. |
[22] | Lambrecht, A. 2002, The Casimir effect: a force from nothing. Physics World September, 29–32. |
[23] | Moore, G. 1970, Quantum theory of the electromagnetic field in a variable-length one dimensional cavity. J. Math. Phys. 11, 2679–2691. |
[24] | Wilson, C. M., Johansson, G., Pourkabirian, A., Simoen, M., Johansson, J. R., Duty, T., Nori, F. and Delsing, P. 2011, Observation of the dynamical Casimir effect in a superconducting circuit. Nature 479, 376–379. |
[25] | Annila, A., and Kallio-Tamminen, T. 2010, Tangled in entanglement. arXiv:1006.0068. |
[26] | Aharonov, Y., and Bohm, D. 1959, Significance of electromagnetic potentials in quantum theory. Phys. Rev. 115, 485–491. |
[27] | Annila, A. 2012, Space, time and machines. Int. J. Theor. Math. Phys. in press arXiv:0910.2629. |
[28] | Anderson, J. D., Laing, P. A., Lau, E. L., Liu, A. S., Nieto, M. M., and Turyshev, S. G. 1998, Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys. Rev. Lett. 81, 2858–2861. |
[29] | Anderson, J. D., and Nieto, M. M. 2009, Astrometric solar-system anomalies. In Relativity in Fundamental Astronomy. Proceedings IAU Symposium 261, Klioner, S. A., Seidelman, P. K., and Soffel, M. H. (eds.) arXiv:0907.2469v2. |
[30] | Lorenz, L. 1867, On the identity of the vibrations of light with electrical currents. Philos. Mag. 34, 287–301. |
[31] | Sharma, V. and Annila, A. 2007 Natural process – Natural selection. Biophys. Chem. 127, 123–128. |
[32] | Tuisku, P., Pernu, T. K., and Annila, A. 2009, In the light of time. Proc. R. Soc. A 465, 1173–1198. |
[33] | Gauss, C. F. 1829, Ueber ein neues allgemeines Grundgesetz der Mechanik. J. Reine Angew. Math. (Crelle’s Journal) 4, 232–235. |
[34] | Hubble, E. 1929, A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl. Acad. Sci. USA 15, 168–173. |
[35] | de Broglie, L. 1932, C. R. Acad. Sci. (Paris) 195, 536, 577, 862. |
[36] | Ampère, A.-M. 1823, Détermination de l’action électrodynamique d’un fil d'acier aimanté curviligne faite. Mém. de l’Académie des Sciences 6, 175–388. |
[37] | Parson, A. L. 1915, A magneton theory of the structure of the atom. Smithsonian Miscellaneous Collection 65, 1–97. |
[38] | Urbantke, H. K. 2003, The Hopf fibration-seven times in physics. JGP 46, 125–150. |
[39] | Nakamura, K., et al. 2010, Particle Data Group, JPG 37, 075021. |
[40] | Peskin, M. E., and Schroeder, D. V. 1995, An Introduction to Quantum Field Theory. Addison-Wesley, Reading, MA. |
[41] | Irons, M. L. 2005, The curvature and geodesics of the torus. http://www.rdrop.com/~half/math/torus/index.xhtml. |
[42] | Milne, E. A. 1935, Relativity, Gravitation and World-structure. Clarendon Press, Oxford, UK. |
[43] | Jaakkola, S., Sharma, V., and Annila, A. 2008, Cause of chirality consensus. Curr. Chem. Biol. 2, 53–58. |
[44] | Cabibbo, N. 1963 Unitary symmetry and leptonic decays. Phys. Rev. Lett. 10, 531–533. |
[45] | Kobayashi, M., and Maskawa, T. 1973, CP-violation in the renormalizable theory of weak interaction. Progr. Theor. Phys. 49, 652–657. |
[46] | Crawford, F. S. 1968, Waves, Berkeley Physics Course 3. McGraw-Hill, New York, NY. |
[47] | Alonso, M., and Finn, E. J. 1983, Fundamental University Physics. Addison-Wesley, Reading, MA. |
[48] | Berry, M. 2001, Principles of Cosmology and Gravitation. Cambridge University Press, Cambridge, UK. |
[49] | Kepler, J. 1601, De Fundamentis Astrologiae Certioribus. Prague. Concerning the More Certain Fundamentals of Astrology, translated by Rossi, M. A. 2003. Kessinger Publishing. p. 7. |
[50] | Annila, A., and Kuismanen, E. 2009, Natural hierarchy emerges from energy dispersal. BioSystems 95, 227–233. |
[51] | Annila, A., and Salthe, S. 2010, Physical foundations of evolutionary theory. J. Non-equilb. thermodyn. 35, 301–321. |
[52] | Pernu, T.K., and Annila, A. 2012, Natural emergence. Complexity (doi: 10.1002/cplx.21388, in press). |
[53] | Lehto, A. 2009, On the Planck scale and properties of matter. Nonlin. Dyn. 55, 279–298. |
[54] | Penrose, R. 1969, Gravitational collapse: The role of general relativity. Nuovo Cimento Rivista, Numero Speciale 1, 252–276. |
[55] | Wardle, J. F. C., Homan, D. C., Ojha, R. and Roberts, D. H. 1998, Electron–positron jets associated with the quasar 3C279. Nature 395, 457–461. |
[56] | Kaiser, C. R., and Hannikainen, D. C. 2002, Pair annihilation and radio emission from galactic jet sources: the case of Nova Muscae. MNRAS 330, 225–231. |
[57] | Rivas, M. 2001, Kinematical Theory of Spinning Particles: Classical and Quantum Mechanical Formalism of Elementary Particles. Kluwer, Dordrecht, The Netherlands. |
[58] | Burinskii, A. 2011, Gravity beyond quantum theory: Electron as a closed heterotic string. arXiv:1109.3872 |
[59] | Annila, A., and Salthe, S. 2009, Economies evolve by energy dispersal. Entropy 11, 606–633. |
[60] | Annila, A., and Salthe, S. 2010, Cultural naturalism. Entropy 12, 1325–1343. |
[61] | Annila, A., 2010, The 2nd law of thermodynamics delineates dispersal of energy. Int. Rev. Phys. 4, 29–34. |
[62] | Carter, B., 1974, Large number coincidences and the anthropic principle in cosmology. IAU Symposium 63, Confrontation of Cosmological Theories with Observational Data. pp. 291–298. Reidel, Dordrecht, The Netherlands. |
[63] | Annila, A., and Annila, E. 2008, Why did life emerge? Int. J. Astrobio. 7, 293–300. |
[64] | Koskela, M., and Annila, A. 2012, Looking for LUCA. Genes 3, 81–87. |
[65] | Kaila, V. R. I., and Annila, A. 2008, Natural selection for least action. Proc. R. Soc. A 464, 3055–3070. |
[66] | Gödel, K. 1931, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Mathematik und Physik 38, 173–198. |
[67] | Feynman, R. P., Morinigo, F. B., Wagner, W. G., and Hatfield, B. 1995, Feynman Lectures on Gravitation. Addison-Wesley, Reading, MA. |
[68] | Kogut, A., et al. 1993, Dipole anisotropy in the COBE differential microwave radiometers first-year sky maps. ApJ 419, 1–6. |
[69] | Nordström, G. 1914, Über die Möglichkeit, das elektromagnetische Feld und das Gravitationsfeld zu vereinigen. Physikalische Zeitschrift 15, 504–506. |
[70] | Kaluza, T. 1921, Zum Unitätsproblem in der Physik. Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.) 966–972. |
[71] | Peebles, P. J. E., and Yu, J. T. 1970, Primeval adiabatic perturbation in an expanding universe. ApJ. 162, 815–836. |
[72] | Mäkelä, T., and Annila, A. 2010, Natural patterns of energy dispersal. Phys. Life Rev. 7, 477–498. |
[73] | Grönholm, T., and Annila, A. 2007, Natural distribution. Math. Biosci. 210, 659–667. |
[74] | Poincaré, J. H. 1890, Sur le problème des trois corps et les équations de la dynamique. Divergence des séries de M. Lindstedt. Acta Math. 13, 1–270. |
[75] | Sipser, M. 2001, Introduction to the Theory of Computation. Pws Publishing, New York, NY. |
[76] | Annila, A. 2012, Physical portrayal of computational complexity. ISRN Computational Mathematics 321372, 1–15. |
[77] | Annila, A., and Salthe, S. 2012, On intractable tracks. Physics Essays 2, 232-237. |