Number theory as the ultimate physical theory

@article{Volovich1987NumberTA,
  title={Number theory as the ultimate physical theory},
  author={Igor V. Volovich},
  journal={P-Adic Numbers, Ultrametric Analysis, and Applications},
  year={1987},
  volume={2},
  pages={77-87}
}
At the Planck scale doubt is cast on the usual notion of space-time and one cannot think about elementary particles. Thus, the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings. In this paper the numbers are considered as the fundamental entities. We discuss the construction of the corresponding physical theory. A hypothesis on the quantum fluctuations of the number field is advanced for discussion. If these fluctuations actually take… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 10 REFERENCES

Danske Videnskab Selskab Mat .fi s . Medd . 12 , 1 ( 1933 )

Kgl.
  • Phys . Rev .
  • 1986

Quantum Cosmology,

S. W. Hawking
  • Years of Gravity (Cambridge Univ. Press,
  • 1986
VIEW 2 EXCERPTS

Superstring Theory (CUP, Cambridge, UK 1987); I. Ya

M. B. Green, J. H. Schwarz, E. Witten
  • Arefeva and I. V. Volovich, Usp. Fiz. Nauk 146,
  • 1985
VIEW 1 EXCERPT

a Short Course on Recent Work (Cambridge Univ

Introduction to p-Adic Numbers K. Mahler, 1973 Their Functions Cambridge Univ. Press, p-adic Numbers p-adic Analysis N. Koblitz, 1984 Zeta-Functions Springer Verlag, p-Adic Analysis N. Koblitz
  • Press, 1980); W. H. Schikhof, Ultrametric Calculus (Cambridge Univ. Press, 1984); S. Lang, Cyclotomic Fields
  • 1980
VIEW 1 EXCERPT

Schikhof, “Non-Archimedean monotone functions,

W H.
  • Report 7916 (Mathematisch Instituut, Nijmegen, The Netherlands,
  • 1979
VIEW 1 EXCERPT

an Introduction to Current Research, ed

Ann. Phys. 2 604 J.A. Wheeler, Nuovo Cimento 7 215 T. Regge, A. Peres, Phys. Rev. 118 335 N. Rosen, “The quantization of geometry” in Gravitation B. De Witt
  • L. Witten (John Wiley and Sons, New York and London 1962); M. A. Markov, Progr. Theor. Phys. Suppl. 85 (1965); H.-J. Treder, in Relativity, Quanta and Cosmology, ed. F. de Finis
  • 1979

Geometrodynamics (Academic Press, New York and London 1962)

J. A. Wheeler
  • Nucl. Phys. B 144,
  • 1978
VIEW 1 EXCERPT

Shafarevich, Number Theory

I.R.Z.I. Borevich
  • A Course in Arithmetic (Springer-Verlag,
  • 1973
VIEW 2 EXCERPTS

Pjatetski-Shapiro, Theory of Representations and Automorphic Functions (Nauka, Moscow, 1966) [in Russian

I. M. Gelfand, I.I.M.I. Graev
  • 1966
VIEW 1 EXCERPT

The quantization of geometry

L. Witten
  • Gravitation : an Introduction to Current Research
  • 1960