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On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞ in nature

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Abstract

We present the theory, the experimental evidence and fundamental physical consequences concerning the existence of families of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞, which are solutions of the homogeneuous wave equation, the Maxwell equations, and Dirac, Weyl, and Klein-Gordon equations.

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References

  1. R. Courant and D. Hilbert,Methods of Mathermatical Physics, Vol. II (Wiley, New York, 1966), pp. 760.

    Google Scholar 

  2. T. Waite, “The relativistic Helmholtz theorem and solitions,”,Phys. Essays 8, 60–70 (1995).

    Article  Google Scholar 

  3. T. Waite, A. O., Barut, and J. R. Zeni, “The purely electromagnetic electron revisited,” in J. Dowling, ed.,Electron Theory and Quantum Electrodynamics (Nato ASI Series Volume) (Plenum, 1995).

  4. A. M. Shaarawi, “An electromagnetic charge-current basis for the de Broglie double solution,” peprint, Dep. Eng. Phys. and Math., Cairo Univ., Egypt (1995).

    Google Scholar 

  5. J.-Y. Lu and J. F. Greenleaf, “Limited diffraction solutions to Maxwell and Schrödinger equations,” preprint Biodynamics Res. Unity, Mayo Clinic and Foundation, Rochester (1995), submitted for publication inJ. Phys. (Paris).

  6. W. A. Rodrigues, Jr. and Q. A. G. de Souza, “The Clifford bundle and the nature of the gravitational field,”Found. Phys. 23, 1465–1490 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  7. Q. A. G. de Souza and W. A. Rodrigues, Jr., “The Dirac Operator and the Structure of Riemann-Cartan-Weyl Spaces,” in P. Letelier and W. A. Rodrigues, Jr., eds.,Gravitation: The Spacetime Structure, (World Scientific, Singapore, 1994), pp. 179–212.

    Google Scholar 

  8. W. A. Rodrigues, Jr., Q. A. G. de Souza, J. Vaz, Jr., and P. Lounesto, “Dirac-Hestenes spinor fields in Riemann-Cartan spacetime,”Int. J. Theor. Phys. 35, 1849–1900 (1996).

    Article  MATH  Google Scholar 

  9. D. Hestenes and G. Sobczyk,Clifford Algebra to Geometric Calculus (Reidel, Dordrecht, 1984).

    MATH  Google Scholar 

  10. B. Jancewiez,Multivectors and Clifford Algebras in Electrodynamics (World Scientific, Singapore, 1988).

    Google Scholar 

  11. H. Bateman,Electrical and Optical Motion, (Cambridge University Press, Cambridge, 1915).

    Google Scholar 

  12. L. Mackinnon, “A non-dispersive de Broglie wave packet,”Found. Phys. 8, 157–170 (1978).

    Article  ADS  Google Scholar 

  13. Ph. Gueret and J. P. Vigier, “De Broglie wave-particle duality in the stochastic interpretation of quantum mechanics: A testable physical assumption,”Found. Phys. 12, 1057–1083 (1982);38, 125 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  14. A. O. Barut, “E=hω,”Phys. Lett. A 143, 349–352 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  15. A. O. Barut and J. Bracken, “Particle-like configurations of the electromagnetic field: An extension of de Broglie's ideas,”Found. Phys. 22, 1267–1289 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  16. J. Durnin, “Exact solutions for non-diffracting beams I. The scalar theory,”J. Opt. Soc. Am. 4, 651–654 (1987).

    Article  ADS  Google Scholar 

  17. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,”Phys. Rev. Lett. 58, 1499–1501 (1987).

    Article  ADS  Google Scholar 

  18. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Experiments with non-diffracting needle beams,” Opt. Soc. Am., Washington, DC, available from IEEE Service Center (list. No. 87CH2391-1), Piscataway, New Jersey, pp. 208 (1987).

  19. J. A. Stratton,Electromagnetic, Theory (McGraw-Hill, New York, 1941).

    MATH  Google Scholar 

  20. D. K. Hsu, F. J. Margeton, and D. O. Thompson, “Bessel beam ultrasonic transducers: Fabrication method and experimental results,”Appl. Phys. Lett. 55, 2066–2068 (1989).

    Article  ADS  Google Scholar 

  21. J.-Y. Lu and J. F. Greenleaf, “Ultrasonic nondiffracting transducer for medical imaging,”IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37, 438–477 (1990).

    Article  Google Scholar 

  22. J.-Y. Lu and J. F. Greenleaf, “Pulse-echo imaging using a nondiffracting beam transducer,”Ultrasound Med. Biol. 17, 265–281 (1991).

    Article  Google Scholar 

  23. J.-Y. Lu and J. F. Greenleaf, “Simulation of imaging contrast of non-diffracting beam transducer,”J. Ultrasound Med. 10, 54 (1991) (Abstract).

    Google Scholar 

  24. J. A. Campbell and S. Soloway, “Generation of a non-diffracting beam with frequency-independent beam width,”J. Acoust. Soc. Am. 88, 2467–2477 (1990).

    Article  ADS  Google Scholar 

  25. M. S. Patterson and F. S. Foster, “Acoustic fields of conical radiators,”IEEE Trans. Sonics Ultrason. SU-29(2), 83–92 (1982).

    Google Scholar 

  26. J.-Y. Lu, Z. Hehong, and J. F. Greenleaf, “Biomedical ultrasound beam forming,”Ultrasound Med. Biol. 20, 403–428 (1994).

    Article  Google Scholar 

  27. J. N. Brittingham, “Focus wave modes in homogeneous Maxwell's equations: Transverse electric mode,”J. Appl. Phys. 54, 1179 (1983).

    Article  ADS  Google Scholar 

  28. P. A. Bélanger, “Packet-like solutions of the homogeneous wave equation,”J. Opt. Soc. Am. A 1, 723–724 (1986).

    Google Scholar 

  29. A. Sezginer, “A general formulation of focused wave modes,”J. Opt. Soc. Am. A 1, 723–724 (1984).

    Google Scholar 

  30. R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,”J. Math. Phys. 26, 861–863 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  31. A. M. Shaarawi, I. M. Besieris, and R. Ziolkowski, “Localized energy pulse trains launched from an open, semi-infinite circular waveguide,”J. Appl. Phys. 62, 805 (1988).

    Google Scholar 

  32. L. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation,”J. Math. Phys. 30, 1254 (1989).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,”Phys. Rev. A 39, 2005–2033 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  34. R. W. Ziolkowski, D. K. Lewis, and D. B. Cook “Experimental verification of the localized wave transmission effect,”Phys. Rev. Lett. 62, 147 (1989).

    Article  ADS  Google Scholar 

  35. A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, “A novel approach to the synthesis of non-dispersive wave packets solutions to the Klein-Gordon and Dirac equations”J. Math. Phys. 31, 2511–2519 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  36. P. Hillion, “More on focus wave modes in Maxwell equations,”J. Appl. Phys. 60, 2981–2982 (1986).

    Article  ADS  Google Scholar 

  37. P. Hillion, “Spinor focus wave modes,”J. Math. Phys. 28, 1743–1748 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  38. P. Hillion, “Nonhomogeneous nondispersive electromagnetic waves,”Phys. Rev. A 45, 2622–2627 (1992).

    Article  ADS  Google Scholar 

  39. P. Hillion, “Relativistic theory of scalar and vector diffractory by planar aperture,”J. Opt. Soc. Am. A 9, 1794–1880 (1992).

    ADS  MathSciNet  Google Scholar 

  40. E. C. de Oliveira, “On the solutions of the homogeneous generalized wave equation,”J. Math. Phys. 33, 3757–3758 (1992).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. W. Band, “Can information be transferred faster than light? I. A gedanken device for generating electromagnetic wave packets with superoptic group velocity,”Found Phys. 18, 549–562 (1988).

    Article  ADS  Google Scholar 

  42. W. Band, Can information be transferred faster than light? II. The relativistic Doppler effect on electromagnetic wave packets with suboptic and superoptic group velocities,Found Phys. 18, 625–638 (1988).

    Article  ADS  Google Scholar 

  43. J.-Y. Lu and J. F. Greenleaf, “NondiffractingX-waves—Exact solutions to free-space scalar wave equations and their finite aperture realizations,”IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992).

    Article  Google Scholar 

  44. J.-Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffractingX-wave,”IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992).

    Article  ADS  Google Scholar 

  45. R. Donnelly and R. Ziolkowski, “A method for constructing solutions of homogeneous partial differential equations: Localized waves,”Proc. R. Soc. London A 437, 673–692 (1992).

    ADS  MathSciNet  MATH  Google Scholar 

  46. R. Donnelly and R. Ziolkowski, “Designing localized waves,”Proc. R. Soc. London A 460, 541–565 (1993).

    ADS  Google Scholar 

  47. A. O. Barnt and H. C. Chandola, “Localized tachyonic wavelet solutions of the wave equation,”Phys. Lett. A 180, 5–8 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  48. W. A. Rodrigues, Jr. and J. Vaz, Jr., “Subluminal and superluminal solutions in vacuum of the Maxwell equations and the massless Dirac equation,” RP 44/95 IMECC-UNICAMP, in Advances in Appl. Clifford Algebras.

  49. J. Vaz, Jr. and W. A. Rodrigues, Jr., “On the equivalence of Maxwell and Dirac equations, and quantum mechanics,”Int. J. Theor. Phys. 32, 945–958 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  50. J. Vaz, Jr. and W. A. Rodrigues, Jr., “Maxwell and Dirac theories as an already unified theory,” RP 45/95 IMECC-UNICAMP, in Advances in Appl. Clifford Algebras.

  51. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single photon tunneling time,”Phys. Rev. Lett. 71, 708–711 (1993).

    Article  ADS  Google Scholar 

  52. A. Enders and G. Nimtz, “Photonic tunneling experiments,”Phys. Rev. B 47, 9605–9609 (1993).

    Article  ADS  Google Scholar 

  53. W. Heitman and G. Nimtz, “On causality proofs of superluminal barrier traversal of frequency band limited wave packets,”Phys. Lett. A 196, 154–158 (1994).

    ADS  Google Scholar 

  54. A. V. Oppenheim and R. W. Schafer,Digital Signal Processing (Prentice-Hall, Englewood Cliffs, 1975), Chap. 5.

    MATH  Google Scholar 

  55. A. Einstein,Sitzungsber. Preuss, Akad. Wiss. (1919), as translated in H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl,The Principle of Relativity (Dover, New York, 1952), p. 142.

  56. H. Poincaré, “Sur al dynamique de l'électron,R. C. Circ. Mat. Palermo 21, 129–175 (1906).

    MATH  Google Scholar 

  57. P. Ehrenfest, “Die Translation deformierbarer Electron und der Flächensatz,”Ann. Phys. (Leipzig)23, 204–205 (1907).

    Article  Google Scholar 

  58. D. Reed, “Archetypal vortex topology in nature,”Spec. Sci. Tech. 17, 205–224 (1994).

    Google Scholar 

  59. M. W. Evans, “Classical relativistic theory of the longitudinal ghost fields in electron-magnetism,”Found. Phys. 24, 1671–1688 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  60. R. K. Sachs and H. Wu,General Relativity for Mathematicians, (Springer, New York, 1977).

    MATH  Google Scholar 

  61. W. A. Rodrigues, Jr. and M. A. F. Rosa, “The meaning of time in relativity and Einstein's later view of the twin paradox,”Found. Phys. 19, 705–724 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  62. W. A. Rodrigues, M. E. F. Scanavini, and L. P. de Alcântara, “Formal structures, the concepts of covariance, invariance, equivalent reference frames, and the principle of relativity,”Found. Phys. Lett. 3, 59–79 (1990).

    Article  MathSciNet  Google Scholar 

  63. N. Bourbaki,Théorie des Ensembles (Hermann, Paris, 1957), Chap. 4.

    MATH  Google Scholar 

  64. H. Reichenbach,The Philosophy of Space and Time (Dover, New York, 1958).

    MATH  Google Scholar 

  65. E. Recami,Classical Tachyons and Applications, Riv. Nuovo Cimento 9, 1–178 (1986).

    MathSciNet  Google Scholar 

  66. W. A. Rodrigues, Jr., Q. A. G. de Souza, and Y. Bozhkov, “The mathematical structure or Newtonian spacetime: Classical dynamics and gravitation,”Found. Phys. 25, 871–924 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  67. W. A. Rodrigues and J. Tiomno, “On experiments to detect possible failtures of relativity theory,”Found. Phys. 15, 995–961 (1985).

    Article  MathSciNet  Google Scholar 

  68. R. M. Santilli, “Life lsotopic lifting of special relativity for extended particles,”Lett. Nuovo Cimento 37, 545–555 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  69. R. M. Santilli, “Nonlinear, nonlocal, and noncanonical isotopies of the Poincaré symmetry,”J. Moscow Phys. Soc. 3, 255–280 (1993).

    MathSciNet  Google Scholar 

  70. R. M. Santilli, “Limitations of the special and general relativities and their isotopic generalizations,”Chinese J. Syst. Eng. Electr. 6, 157–176 (1995).

    Google Scholar 

  71. R. M. Santilli, in T. L. Giulli, ed.,New Frontiers in Hadronic Mechanics (Hadronic Press, Palm Harbor, 1996), in press.

    Google Scholar 

  72. R. M. Santilli,Elements of Hadronic Mechanics, Vols. I and II, 2nd edn. (Naukova Dunka, Ukraine Acad. Sci., Kiev, 1995).

    Google Scholar 

  73. R. M. Santilli,Isospecial Relativity with Applications to Quantum Gravity, Antigravity, and Cosmology (Balkan Geom. Press, Budapest) in press.

  74. G. Nimtz, “New knowledge of tunneling from photonic experiments,” to appear inProceedings, Adriatico Research Conference: Tunneling and Its Implications (07/30-08/02, 1996) (World Scientific, Singapore, 1997).

    Google Scholar 

  75. E. W. Otten, “Squeezing the neutrino mass with new instruments,”Nucl. Phys. News 5, 11–16 (1995).

    Article  Google Scholar 

  76. E. Gianetto et al., “Are neutrinos faster than light particles?,”Phys. Lett. B 178, 115–118 (1986).

    Article  ADS  Google Scholar 

  77. J. R. Primack, J. Holtzman, A. Klypin, and D. O. Caldwell, “Cold + hot dark matter cosmology withm(v μ)-m(vτ)-2.4eVX,”Phys. Rev. Lett. 74, 2160 (1995).

    Article  ADS  Google Scholar 

  78. E. T. Whittaker,A History of the Theories of Aether and Electricity, Vols. I. and II (Humanities Press, New York, 1973).

    Google Scholar 

  79. P. M. Morse and H. Feshbach,Methods of Theoretical Physics, Vols. I and II (McGraw-Hill, New York, 1953).

    MATH  Google Scholar 

  80. W. A. Rodrigues, Jr. and J. E. Maiorino, “A unified theory for construction of arbitrary speed (0≤ϑ≤∞) solutions of the relativistic wave equations,”Random Operators and Stochastic Equations 4, 355–400, (1996).

    Article  MathSciNet  Google Scholar 

  81. W. A. Rodrigues, Jr., Q. A. G. de Souza, and J. Vaz Jr., “Spinor fields and superfields as equivalence classes of exterior algebra fields,” in R. Ablamowicz and P. Lounesto, eds.,Clifford Algebras and Spinor Structures (Kluwer Academic, Dordrecht, 1995), pp. 177–198.

    Google Scholar 

  82. D. Hestenes,Spacetime Algebra (Gordon & Breach, New York, 1969).

    Google Scholar 

  83. P. Lounesto, “Clifford algebras and Hestenes spinors,”Found. Phys. 23, 1203–1237 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  84. W. A. Rodrigues, Jr., and V. L. Figueiredo, “Real spin-Clifford bundles and the spinor structure of spacetime,”Int. J. Theor. Phys.,29, 413–424 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  85. W. A. Rodrigues, Jr., and E. C. de Oliveira, “Dirac and Maxwell equations in the Clifford and spin-Clifford bundles,”Int. J. Theor. Phys. 29, 397–412 (1990).

    Article  MATH  Google Scholar 

  86. I. Porteous,Topological Geometry (Van Nostrand, London, 1969).

    MATH  Google Scholar 

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Rodrigues, W.A., Lu, JY. On the existence of undistorted progressive waves (UPWs) of arbitrary speeds 0≤ϑ<∞ in nature. Found Phys 27, 435–508 (1997). https://doi.org/10.1007/BF02550165

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