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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.24 n.2 Antofagasta ago. 2005

http://dx.doi.org/10.4067/S0716-09172005000200003 

 

Proyecciones
Vol. 24, No 2, pp. 121-152, August 2005.
Universidad Católica del Norte
Antofagasta - Chile

 

INERTIAL RELATIVITY - A FUNCTIONAL ANALYSIS REVIEW

 

NORBERTO SÁINZ

Universidad Católica de Valparaíso, Chile

Correspondencia a :


ABSTRACT

The theory of special relativity (TSR) exhibits an unquestionable success, at the expense of an unresolved axiomatic conflict with functional analysis and operator theory, as this paper demonstrates. These mathematical disciplines —amongst the newest developments in the field— could not possibly be incorporated into the original formulation of the TSR because they were in an incipient state at the turn of the 20th century when the TSR was being formulated, maturing only decades later.


 

4. REFERENCES

1. E. F. Taylor and J.A. Wheeler, "Spacetime Physics", 111. W. H. Freeman and Co. (1963).        [ Links ]

2. Robert M.Wald, "General Relativity", 61. The University of Chicago Press, Chicago and London, (1984).        [ Links ]

3. C. W. Misner et al., “Gravitation", 53. W.H. Freeman and Co., (1973).        [ Links ]

4. B. Z. Vulikh, "Introduction to Functional Analysis for Scientists and Technologists", 71. Pergamon Press, (1963).        [ Links ]

5. A.W. Naylor and G.R. Sell, "Linear Operator Theory", 47. Holt, Rinehart and Winston, Inc., (1971).        [ Links ]

6. Ibid. [2], 23.

7. Ibid. [3], 51.

8. Ibid. [2], 60.

9. R. Tabenski, "Relativity, Special" Encyclopedia of Applied Physics, Vol 16, 375, (1996).        [ Links ]

10. Ibid. [4], 77.

11. Ibid. [5], 70.

12. Albert Einstein, "Die Grundlage Der Allgemeinen Relativitätstheorie", Spanish translation by Fidel Alsina F. and Damián Canales F. of original paper published in Annalen der Physik 49, 769 (1916). La Relatividad, Emecé Editores, B. Aires, (1950).        [ Links ]

13. Ibid. [2], 9, 22-23.

14. Ibid. [3], 324-325.

15. Lars V. Ahlfors & Leo Sario, "Riemann Surfaces", 124. Princeton University Press, (1960).        [ Links ]

16. H.M. Farkas & I. Kra, "Riemann Surfaces", 198. Springer Verlag (1980).        [ Links ]

17. Encyclopaedia Britannica, "Riemannian Geometry," Vol. 19, p.323d, (1967).        [ Links ]

18. Shiing-shen Chern “General Relativity and Differential Geometry", in “Some Strangeness in the Proportion, a Centennial Symposium to Celebrate the Achievements of Albert Einstein", 271-280. Addison Wesley publishing Co., (1980).        [ Links ]

19. David O. Hestenes, “Spacetime Physics with Geometric Algebra", in American Journal of Physics, 71 (2.7), pp. 691 — 714, (July, 2003).        [ Links ]

20. David O. Hestenes, “Journal of Mathematical Analysis and Applications", 24 (2.2), 313 — 325, Academic Press, (1968).        [ Links ]

21. Walter Rudin, "Functional Analysis", 372. Mc Graw-Hill, (1973).        [ Links ]

22. Frédéric Riesz, "Über Lineare Funktionalgleichungen", Acta Math. 41. pp.71-98, (1917).        [ Links ]

23. S. Banach, "Fundamenta Math. vol 3, pp.133-181, (1922).        [ Links ]

24. Ibid. [17], "Mathematics, History of," Vol. 14, p. 1106b.

25. Ibid. [17], "Operators, Theory of," Vol. 16, p. 988d.

26. Ibid. [40], 67.

27. Ray Redheffer, “Men of Modern Mathematics. A history chart of mathematicians from 1000 to 1900", produced for IBM by the office of Charles Eames (1966).        [ Links ]

28. Ibid. [1], 40.

29. Ibid. [2], 14-17.

30. Ibid [3], 208-217, 226-235, 310.

31. Ibid. [3], 311.

32. André Lichnerowicz, “Topics on Space-Times", in “Battelle Rencontres",1967 Lectures in Mathematics and Physics, 108. W. A. Benjamin. (1968).        [ Links ]

33. Ibid. [1], 36-39.

34. Rolf Lingenberg, “Metric Planes and Metric Vector Spaces", 19-23. John Wiley & Sons (1979).        [ Links ]

35. Ibid. [5], 272-276.

36. Ibid [3], 22.

37. Roger Penrose, “Structure of Space-Time", in “Battelle Rencontres", 1967 Lectures in Mathematics and Physics, 121-134. W. A. Benjamin. (1968).        [ Links ]

38. Ibid. [2], 59-60.

39. Ibid. [3], 20-21.

40. John L. Kelley, “General Topology", 68. D. Van Norstrand and Co., Inc. (1955).        [ Links ]

41. Ibid. [40], 62.

42. Roger Penrose, “Techniques of Differential Topology in Relativity", Sect 1. Soc. for Industrial and Applied Mathematics (1972).        [ Links ]

43. Ibid. [40], 83.

44. Ibid. [40], 56.

45. Ibid. [40], 124-130.

46. Tom M. Apostol, “Calculus", 210. Reverté, S.A. (1967).        [ Links ]

47. Ibid. [46], 201 & 271.

48. Ibid. [46], 215-216

49. Ibid. [3], 47-63, 77, 79-81.

50. Andrei Linde, "Particle Physics and Inflationary Cosmology" Vol. 5. English translation by Marc Damashek, 271-272, 279. Harwood Academic Publishers, (1990).        [ Links ]

51. Stephen W. Hawking, "A Brief History of Time. From the Big Bang to Black Holes". Spanish translation by Miguel Ortuño, 178. Editorial Crítica, (1988).        [ Links ]

Received : Julio 2004. Accepted : June 2005

NORBERTO SÁINZ

Pontificia Universidad Católica de Valparaíso
Facultad de Ingeniería
Escuela de Ingeniería Industrial
Valparaíso
Chile
e-mail : norberto.sainz@ucv.cl

 

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