On the Existence of Undistorted Progressive Waves (UPWs) of Arbitrary Speeds 0 ≤ v < ∞ in Nature

Foundations of Physics

Volumn 27, Issue 3, 1997, Pages 435-508

  Rodrigues, Waldyr A ^a   Lu, Jian Yu ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b MAYO CLINIC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001824973     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02550165     Document Type: Article

References (88)

1. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II (Wiley, New York, 1966), pp. 760.
2. T. Waite, "The relativistic Helmholtz theorem and solitons," Phys. Essays 8, 60-70 (1995).
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," preprint, Dep. Eng. Phys. and Math., Cairo Univ., Egypt (1995).
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 in J. 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).
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.
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).
9. D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus (Reidel, Dordrecht, 1984).
10. B. Jancewicz, Multivectors and Clifford Algebras in Electrodynamics (World Scientific, Singapore, 1988).
11. H. Bateman, Electrical and Optical Motion (Cambridge University Press, Cambridge, 1915).
12. L. Mackinnon, "A non-dispersive de Broglie wave packet," Found. Phys. 8, 157-170 (1978).
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).
14. 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).
15. A. O. Barut, "E = hω," Phys. Lett. A 143, 349-352 (1990).
16. 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).
17. J. Durnin, "Exact solutions for non-diffracting beams I. The scalar theory," J. Opt. Soc. Am. 4, 651-654 (1987).
18. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
19. 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).
20. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
21. 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).
22. J.-Y. Lu and J. F. Greenleaf, "Ultrasonic nondiffracting transducer for medical imaging," IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37, 438-477 (1990).
23. J.-Y. Lu and J. F. Greenleaf, "Pulse-echo imaging using a nondiffracting beam transducer," Ultrasound Med. Biol. 17, 265-281 (1991).
24. J.-Y. Lu and J. F. Greenleaf, "Simulation of imaging contrast of non-diffracting beam transducer," J. Ultrasound Med. 10, 54 (1991) (Abstract).
25. 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).
26. M. S. Patterson and F. S. Foster, "Acoustic fields of conical radiators," IEEE Trans. Sonics Ultrason. SU-29(2), 83-92 (1982).
27. J.-Y. Lu, Z. Hehong, and J. F. Greenleaf, "Biomedical ultrasound beam forming," Ultrasound Med. Biol. 20, 403-428 (1994).
28. J. N. Brittingham, "Focus wave modes in homogeneous Maxwell's equations: Transverse electric mode," J. Appl. Phys. 54, 1179 (1983).
29. P. A. Bélanger, "Packet-like solutions of the homogeneous wave equation," J. Opt. Soc. Am. A 1, 723-724 (1986).
30. A. Sezginer, "A general formulation of focused wave modes," J. Opt. Soc. Am. A 1, 723-724 (1984).
31. R. W. Ziolkowski, "Exact solutions of the wave equation with complex source locations," J. Math. Phys. 26, 861-863 (1985).
32. 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).
33. I. 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).
34. R. W. Ziolkowski, "Localised transmission of electromagnetic energy," Phys. Rev. A 39, 2005-2033 (1989).
35. R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, "Experimental verification of the localized wave transmission effect," Phys. Rev. Lett. 62, 147 (1989).
36. 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).
37. P. Hillion, "More on focus wave modes in Maxwell equations," J. Appl. Phys. 60, 2981-2982 (1986).
38. P. Hillion, "Spinor focus wave modes," J. Math. Phys. 28, 1743-1748 (1987).
39. P. Hillion, "Nonhomogeneous nondispersive electromagnetic waves," Phys. Rev. A 45, 2622-2627 (1992).
40. P. Hillion, "Relativistic theory of scalar and vector diffraction by planar aperture," J. Opt. Soc. Am. A 9, 1794-1880 (1992).
41. E. C. de Oliveira, "On the solutions of the homogeneous generalized wave equation," J. Math. Phys. 33, 3757-3758 (1992).
42. 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).
43. 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).
44. J.-Y. Lu and J. F. Greenleaf, "Nondiffracting X-waves - Exact solutions to free-space scalar wave equations and their finite aperture realizations," IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19-31 (1992).
45. J.-Y. Lu and J. F. Greenleaf, "Experimental verification of nondiffracting X-wave," IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441-446 (1992).
46. 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).
47. R. Donnelly and R. Ziolkowski, "Designing localized waves," Proc. R. Soc. London A 460, 541-565 (1993).
48. A. O. Barut and H. C. Chandola, "Localized tachyonic wavelet solutions of the wave equation," Phys. Lett. A 180, 5-8 (1993).
49. 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.
50. 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).
51. 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.
52. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Measurement of the single photon tunneling time," Phys. Rev. Lett. 71, 708-711 (1993).
53. A. Enders and G. Nimtz, "Photonic tunneling experiments," Phys. Rev. B 47, 9605-9609 (1993).
54. 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).
55. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, 1975), Chap. 5.
56. 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.
57. 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.
58. H. Poincaré, "Sur la dynamique de l'électron, R. C. Circ. Mat. Palermo 21, 129-175 (1906).
59. P. Ehrenfest, "Die Translation deformierbarer Electron und der Flächensatz," Ann. Phys. (Leipzig) 23, 204-205 (1907).
60. D. Reed, "Archetypal vortex topology in nature," Spec. Sci. Tech. 17, 205-224 (1994).
61. M. W. Evans, "Classical relativistic theory of the longitudinal ghost fields in electromagnetism," Found. Phys. 24, 1671-1688 (1994).
62. R. K. Sachs and H. Wu, General Relativity for Mathematicians (Springer, New York, 1977).
63. 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).
64. 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).
65. N. Bourbaki, Théorie des Ensembles (Hermann, Paris, 1957), Chap. 4.
66. H. Reichenbach, The Philosophy of Space and Time (Dover, New York, 1958).
67. E. Recami, Classical Tachyons and Applications, Riv. Nuovo Cimento 9, 1-178 (1986).
68. W. A. Rodrigues, Jr., Q. A. G. de Souza, and Y. Bozhkov, "The mathematical structure of Newtonian spacetime: Classical dynamics and gravitation," Found. Phys. 25, 871-924 (1995).
69. W. A. Rodrigues and J. Tiomno, "On experiments to detect possible failures of relativity theory," Found. Phys. 15, 995-961 (1985).
70. R. M. Santilli, "Lie isotopic lifting of special relativity for extended particles," Lett. Nuovo Cimento 37, 545-555 (1983).
71. R. M. Santilli, "Nonlinear, nonlocal, and noncanonical isotopies of the Poincaré symmetry," J. Moscow Phys. Soc. 3, 255-280 (1993).
72. R. M. Santilli, "Limitations of the special and general relativities and their isotopic generalizations," Chinese J. Syst. Eng. Electr. 6, 157-176 (1995).
73. R. M. Santilli, in T. L. Giulli, ed., New Frontiers in Hadronic Mechanics (Hadronic Press, Palm Harbor, 1996), in press.
74. R. M. Santilli, Elements of Hadronic Mechanics, Vols. I and II, 2nd edn. (Naukova Dumka, Ukraine Acad. Sci., Kiev, 1995).
75. R. M. Santilli, Isospecial Relativity with Applications to Quantum Gravity, Antigravity, and Cosmology (Balkan Geom. Press, Budapest), in press.
76. G. Nimtz, "New knowledge of tunneling from photonic experiments," to appear in Proceedings, Adriatico Research Conference: Tunneling and Its Implications (07/30-08/02, 1996) (World Scientific, Singapore, 1997).
77. E. W. Otten, "Squeezing the neutrino mass with new instruments," Nucl. Phys. News 5, 11-16 (1995).
78. E. Gianetto et al., "Are neutrinos faster than light particles?," Phys. Lett. B 178, 115-118 (1986).
79. τ) ≃ 2.4 eV," Phys. Rev. Lett. 74, 2160 (1995).
80. E. T. Whittaker, A History of the Theories of Aether and Electricity, Vols. I and II (Humanities Press, New York, 1973).
81. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vols. I and II (McGraw-Hill, New York, 1953).
82. W. A. Rodrigues, Jr. and J. E. Maiorino, "A unified theory for construction of arbitrary speed (0 ≤ v ≤ ∞) solutions of the relativistic wave equations," Random Operators and Stochastic Equations 4, 355-400 (1996).
83. 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.
84. D. Hestenes, Spacetime Algebra (Gordon & Breach, New York, 1969).
85. P. Lounesto, "Clifford algebras and Hestenes spinors," Found. Phys. 23, 1203-1237 (1993).
86. 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).
87. 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).
88. I. Porteous, Topological Geometry (Van Nostrand, London, 1969).