Skip to main content
SpringerLink
Log in

Uncertainty relations for light waves and the concept of photons

  • Chapter
Special Relativity and Quantum Theory

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 33))

  • 830 Accesses

Abstract

A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Δt)(Δω)≃l for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Clarendon, Oxford, 1954).

    MATH  Google Scholar 

  2. E. P. Wigner, inAspects of Quantum Theory, in Honour of P. A. M. Dirac’s 70th Birthday, edited by A. Salam and E. P. Wigner (Cambridge University Press, London, 1972).

    Google Scholar 

  3. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 114, 243, (1927); 114, 710(1927).

    Article  MATH  Google Scholar 

  4. T. D. Newton and E. P. Wigner, Rev. Mod. Phys. 21, 400 (1949);

    Article  MATH  Google Scholar 

  5. A. S. Wightman, ibid. 34, Ser. A 845 (1962)

    MathSciNet  Google Scholar 

  6. T. O. Philips, Phys. Rev. 136, B893 (1964).

    Article  MathSciNet  Google Scholar 

  7. J. M. Jauch and C. Piron, Helv. Phys. Acta 40, 559 (1967);

    MATH  Google Scholar 

  8. W. O. Amrein, ibid. 42, 149 (1969).

    MATH  Google Scholar 

  9. K. Kraus, Am. J. Phys. 38, 1489 (1970); Ann. Phys. (NY), 64, 311 (1971).

    Article  Google Scholar 

  10. H. Neumann, Commun. Math. Phys. 23, 100 (1971)

    Article  MATH  Google Scholar 

  11. H. Neumann, Helv. Phys. Acta 45, 881 (1972).

    Google Scholar 

  12. S. T. Ali and G. G. Emch, J. Math. Phys. 15, 176 (1974).

    Article  MathSciNet  Google Scholar 

  13. G. C. Hegerfeldt, Phys. Rev. D 10, 3320 (1974)

    Article  Google Scholar 

  14. K. Kraus, in Foundations of Quantum Mechanics and Ordered Linear Space, Vol. 29 of Lecture Notes in Physics, edited by J. Ehlers et al. (Springer-Verlag, Berlin, 1974), p. 206.

    Chapter  Google Scholar 

  15. For review papers on this subject, see R. Kraus, in The Uncertainty Principle and Foundations of Quantum Mechanics, edited by W. C. Price and S. S. Chissick (Wiley, New York, 1977)

    Google Scholar 

  16. S. T. Ali, Riv. Nuovo Cimento 8, 1 (1985).

    MathSciNet  Google Scholar 

  17. For early papers on this subject, see P. A. M. Dirac, Proc. R. Soc. London, Ser. A 183, 284 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  18. H. Yukawa, Phys. Rev. 91, 416 (1953).

    Article  MathSciNet  Google Scholar 

  19. M. Markov, Nuovo Cimento Suppl. 3, 760 (1956)

    Article  Google Scholar 

  20. T. Takabayasi, Nuovo Cimento 33, 668 (1964)

    Article  Google Scholar 

  21. S. Ishida, Prog. Theor. Phys. 46, 1570 (1971); 46, 1905 (1971).

    Article  Google Scholar 

  22. For some of the recent articles, see R. P. Feynman, M. Kislinger, and F. Ravndal, Phys. Rev. D 3, 2706 (1971)

    Article  Google Scholar 

  23. Y. S. Kim and M. E. Noz, ibid. 8, 3521 (1973).

    MathSciNet  Google Scholar 

  24. M. J. Ruiz, Phys. Rev. 10, 4306 (1974)

    Google Scholar 

  25. Y. S. Kim, Phys. Rev. D 14, 273 (1976).

    Article  Google Scholar 

  26. Y. S. Kim and M. E. Noz, Found. Phys. 9, 375 (1979).

    Article  Google Scholar 

  27. Y. S. Kim, M. E. Noz, and S. H. Oh, J. Math. Phys. 20, 1341; Am. J. Phys. 47, 892 (1979); J. Math. Phys. 21 1224

    Article  Google Scholar 

  28. D. Han, Y. S. Kim, and M. E. Noz, Found. Phys. 11, 895 (1980)

    Article  Google Scholar 

  29. D. Han and Y. S. Kim, Am. J. Phys. 49, 1157; 49, 348 (1981).

    Article  Google Scholar 

  30. D. Han, M. E. Noz, Y. S. Kim, and D. Son, Phys. Rev. D 25, 1740 (1982)

    Article  Google Scholar 

  31. D. Han, Y. S. Kim, and D. Son, ibid. 26, 3717 (1982)

    MathSciNet  Google Scholar 

  32. D. Han, M. E. Noz, Y. S. Kim, and D. Son, ibid. 27, 3032 (1983).

    Google Scholar 

  33. For review oriented articles comparing various early approaches to this problem, see T. Takabayasi, Prog. Theor. Phys. Suppl. 67, 1 (1979)

    MathSciNet  Google Scholar 

  34. D. Han and Y. S. Kim, Prog. Theor. Phys. 64, 1854 (1980).

    Article  MathSciNet  Google Scholar 

  35. The uncertainty relation applicable to the time separation between the constituent quarks is responsible for the peculiarities in Feynman’s parton picture universally observed in high-energy hadronic experiments. See, P. E. Hussar, Phys. Rev. D 23, 2781 (1981).

    Article  Google Scholar 

  36. For papers dealing with qualitative features of the parton picture, see Y. S. Kim and M. E. Noz, Phys. Rev. D 15, 335 (1977); J. Math. Phys. 22, 2289 (1981)

    Article  Google Scholar 

  37. P. E. Hussar, Y. S. Kim, and M. E. Noz, Am. J. Phys. 53, 142 (1985).

    Article  Google Scholar 

  38. For earlier papers dealing with the dependence of the quark-model wave function on the time-separation variable, see G. Preparata and N. S. Craigie, Nucl. Phys. B 102, 478 (1976)

    Article  Google Scholar 

  39. J. Lukierski and M. Oziewics, Phys. Lett. 69B, 339 (1977)

    Google Scholar 

  40. D. Dominici and G. Longhi, Nuovo Cimento 42A, 235 (1977)

    MathSciNet  Google Scholar 

  41. T. Goto, Prog. Theor. Phys. 58, 1635 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  42. H. Leutwyler and J. Stern, Phys. Lett. 73B, 75 (1978); Nucl. Phys. B 157, 327 (1979)

    Google Scholar 

  43. I. Fujiwara, K. Wakita, and H. Yoro, Prog. Theor. Phys. 64, 363 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  44. J. Jersak and D. Rein, Z. Phys. C 3, 339 (1980)

    Article  Google Scholar 

  45. I. Sogami and H. Yabuki, Phys. Lett. 94B, 157 (1980).

    Google Scholar 

  46. M. Pauri, in Group Theoretical Methods in Physics, Proceedings of the IX International Collo–quim, Cocoyoc, Mexico, edited by K. B. Wolf (Springer– Verlag, Berlin, 1980)

    Google Scholar 

  47. G. Marchesini and E. Onofri, Nuovo Cimento A 65, 298 (1981)

    Article  MathSciNet  Google Scholar 

  48. E. C. G. Sudarshan, N. Mukunda, and C. C. Chiang, Phys. Rev. D 25, 3237 (1982).

    Article  MathSciNet  Google Scholar 

  49. The uncertainty relation applicable to the time-separation between the quarks is not inconsistent with the proposition that the time–energy uncertainty is applicable only to the time separation between two independent events. See L. D. Landau and E. M. Lifschitz, Quantum Mechanics, 2nd ed. (Pergamon, New York, 1958).

    MATH  Google Scholar 

  50. Y. S. Kim and M. E. Noz, Theory and Applications of the Poincaré Group (Reidel, Dordrecht, 1986)

    Book  Google Scholar 

  51. E. Inonu and E. P. Wigner, Nuovo Cimento 9, 705 (1952)

    Article  MathSciNet  Google Scholar 

  52. M. Hamermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962).

    Google Scholar 

  53. E. P. Wigner, Ann. Math. 40, 149 (1939)

    Article  MathSciNet  Google Scholar 

  54. V. Bargmann and E. P. Wigner, Proc. Natl. Acad. Sci. U.S.A. 34, 211 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  55. E. P. Wigner, Z. Phys. 124, 665 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  56. E. P. Wigner, in Theoretical Physics, edited by A. Salam (International Atomic Energy Agency, Vienna, 1962).

    Google Scholar 

  57. Chou Kuang-Chao and L. G. Zastavenco, Zh. Eksp. Teor. Fiz. 35, 1417 (1958) [Sov. Phys—JETP 8, 990 (1959)]

    Google Scholar 

  58. M. Jacob and G. C. Wick, Ann. Phys. (NY) 7, 404 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  59. A. S. Wightman, in Dispersion Relations and Elementary Particles, edited by C. Ditt and R. Omnes (Hermann, Paris, 1960)

    Google Scholar 

  60. J. Kuperzstych, Nuovo Cimento 31B, 1 (1976); Phys. Rev. D 17, 629 (1978)

    Google Scholar 

  61. A. Janner and T. Jenssen, Physica 53, 1 (1971); 60, 292 (1972)

    Article  Google Scholar 

  62. J. L. Richard, Nuovo Cimento 8A, 485 (1972)

    MathSciNet  Google Scholar 

  63. H. P. W. Gottlieb, Proc. R. Soc. London, Ser. A 368, 429 (1979).

    Article  MathSciNet  Google Scholar 

  64. S. Weinberg, Phys. Rev. 134, B 882 (1964)

    MathSciNet  Google Scholar 

  65. S. Weinberg, Phys. Rev. 135, B1049 (1964)

    Article  MathSciNet  Google Scholar 

  66. J. Kupersztych, Phys. Rev. D 17, 629 (1978)

    Article  Google Scholar 

  67. D. Han, Y. S. Kim, and D. Son, ibid. 26, 3717 (1982)

    MathSciNet  Google Scholar 

  68. D. Han, Y. S. Kim, and D. Son, Phys. Lett. 131B, 327 (1983)

    MathSciNet  Google Scholar 

  69. D. Han, Y. S. Kim, M. L Noz, and D. Son, Am. J. Phys. 52, 1037 (1984).

    Article  Google Scholar 

  70. D. Han, Y. S. Kim, and D. Son, Phys. Rev. D 31, 328 (1985)

    Article  MathSciNet  Google Scholar 

  71. C. O. Alley, inQuantum Optics, Experimental Gravity, and Measurement Theory, edited by P. Meystre and M. O. Scully (Plenum, New York, 1983).

    Google Scholar 

  72. E. P. Wigner, Rev. Mod. Phys. 29, 255 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  73. D. Han, Y. S. Kim, and D. Son, J. Math. Phys. 27, 2228 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  74. For some of the latest papers on hadronic mass spectra, see N. Isgur and G. Karl, Phys. Rev. D 19, 2653 (1978)

    Article  Google Scholar 

  75. D. P. Stanley and D. Robson, Phys. Rev. Lett. 45, 235 (1980).

    Article  Google Scholar 

  76. For review articles written for teaching purposes, see P. E. Hussar, Y. S. Kim, and M. E. Noz. Am. J. Phys. 48, 1038, (1980); 48, 1043 (1980)

    Article  Google Scholar 

  77. See also O. W. Greenberg, Am. J. Phys. 50, 1074 (1982).

    Article  Google Scholar 

  78. For papers dealing with form factor behavior, K. Fujimura, T. Kobayashi, and M. Namiki, Prog. Theor. Phys. 43, 73 (1970)

    Article  Google Scholar 

  79. R. G. Lipes, Phys. Rev. D 5, 2849 (1972)

    Article  Google Scholar 

  80. Y. S. Kim and M. E. Noz, ibid. 8, 3521 (1973). See also Ref. 10.

    MathSciNet  Google Scholar 

  81. For papers dealing with the jet phenomenon, see T. Kitazoe and S. Hama, Phys. Rev. D 19, 2006 (1979)

    Article  Google Scholar 

  82. Y. S. Kim, M. E. Noz, and S. H. Oh, Found. Phys. 9, 947 (1979)

    Article  Google Scholar 

  83. T. Kitazoe and T. Morii, Phys. Rev. D 21, 685 (1980); Nucl. Phys. B 164, 76(1980).

    Article  Google Scholar 

  84. For continuing debates on the time-energy uncertainty relation, see Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  85. V. A. Fock, Zh. Eksp. Teor. Fiz. 42, 1135 (1962) [Sov. Phys.—JETP 15, 784 (1962)]

    Google Scholar 

  86. J. H. Eberly and L. P. S. Singh, Phys. Rev. D 7, 359 (1973)

    Article  Google Scholar 

  87. M. Bauer and P. A. Mello, Ann. Phys. (N.Y.) 11, 38 (1978)

    Article  Google Scholar 

  88. M. Bauer, ibid. 150, 1 (1975)

    Google Scholar 

  89. For some review papers on the time-energy uncertainty relation, see articles by J. Rayski and J. M. Rayski, Jr., E. Recami, and E. W. R. Papp, in The Uncertainty Principles and Quantum Mechanics, edited by W. C. Price and S. S. Chissick (Wiley, New York, 1977)

    Google Scholar 

  90. C. H. Blanchard, Am. J. Phys. 50, 642 (1982)

    Article  Google Scholar 

  91. For some of the recent articles on the subject, see E. A. Gislason, N. H. Sabelli, and J. W. Wood, Phys. Rev. A 31, 2078 (1985)

    Article  MathSciNet  Google Scholar 

  92. M. Hossein Partovi, Phys. Rev. Lett. 23, 2887(1986)

    Article  Google Scholar 

  93. R. P. Feynman, inHigh Energy Collisions, Proceedings of The Third International Conference, Stony Brook, New York, 1969, edited by C. N. Yang et al. (Gordon and Breach, New York, 1969)

    Google Scholar 

  94. J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969).

    Article  Google Scholar 

  95. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  96. D. Bohm, The Special Theory of Relativity (Benjamin/Cummings, Reading, Mass., 1965)

    Book  MATH  Google Scholar 

  97. Y. S. Kim and M. E. Noz, Am. J. Phys. 50, 721 (1982).

    Article  MathSciNet  Google Scholar 

  98. For earlier discussions on Lorentz-deformed hadrons, see N. Byers and C. N. Yang, Phys. Rev. 142, 976 (1966)

    Article  Google Scholar 

  99. T. T. Chou and C. N. Yang, ibid. 170, 1591 (1968)

    Google Scholar 

  100. J. D. Bjorken and E. A. Paschos, ibid. 185, 1975 (1969)

    Google Scholar 

  101. A. L. Licht and A. Pagnamenta, Phys. Rev. D 2, 1150, (1970); 2, 1156 (1970)

    Article  Google Scholar 

  102. V. N. Gribov, B. L. Ioffe, and I. Ya. Pomeranchuk, J. Nucl. Phys. (USSR) J 2, 768 (1965) [Sov. J. Nucl. Phys. 2, 549 (1966)]

    Google Scholar 

  103. B. L. Ioffe, Phys. Lett. B 30, 123 (1969)

    Article  Google Scholar 

  104. Y. S. Kim and R. Zaoui, Phys. Rev. D 4, 1738 (1971)

    Google Scholar 

  105. S. D. Drell and T. M. Yan, Ann. Phys. (N.Y.) 60, 578 (1971)

    Article  Google Scholar 

  106. Y. S. Kim and M. E. Noz, Found. Phys. 9, 375 (1979).

    Article  Google Scholar 

  107. This point has been extensively discussed in the literature. See35 Refs. 10, 12, 13, 14, 15, and 17

    Google Scholar 

  108. For a pedagogical discussion of the connection between photons and light waves, see E. Gordin, Waves and Photons (Wiley, New York, 1982)

    Google Scholar 

  109. For the role of the Klein-Gordon equation in the development of Schrödinger’s form of quantum mechanics, see P. A. M. Dirac, Development of Quantum Theory (Gordon and Breach, New York, 1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Aeronautics and Space Administration, Goddard Space Flight Center (Code 636), Greenbelt, Maryland, 20771, USA

    D. Han

  2. Department of Physics and Astronomy, University of Maryland, College Park, Maryland, 20742, USA

    Y. S. Kim

  3. Department of Radiology, New York University, New York, New York, 10016, USA

    Marilyn E. Noz

Authors
  1. D. Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. S. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marilyn E. Noz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Radiology, New York University, USA

    M. E. Noz

  2. Department of Physics and Astronomy, University of Maryland, USA

    Y. S. Kim

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Kluwer Academic Publishers

About this chapter

Cite this chapter

Han, D., Kim, Y.S., Noz, M.E. (1988). Uncertainty relations for light waves and the concept of photons. In: Noz, M.E., Kim, Y.S. (eds) Special Relativity and Quantum Theory. Fundamental Theories of Physics, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3051-3_38

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-3051-3_38

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7872-6

  • Online ISBN: 978-94-009-3051-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation