Relativistic short range phenomena and space-time aspects of pulse measurements. (English) Zbl 1163.83319

Summary: Particle physics is increasingly being linked to engineering applications via electron microscopy, nuclear instrumentation, and numerous other applications. It is well known that relativistic particle equations notoriously fail over very short space-time intervals. This paper introduces new versions of Dirac’s equation and of the Klein-Gordon equation that are suitable for short-range phenomena. Another objective of the paper is to demonstrate that pulse measurement methods that are based on the wave nature of matter do not necessarily correlate with physical definitions that are based on the corpuscular nature of particles.


83C10 Equations of motion in general relativity and gravitational theory
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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[1] E. Bakhoum, “Fundamental disagreement of wave mechanics with relativity,” Physics Essays, vol. 15, no. 1, pp. 87-100, 2002. · Zbl 1118.65133
[2] P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, Oxford, UK, 1958. · Zbl 1118.65133
[3] R. Feynman, The Feynman Lectures on Physics, vol. 2, Addison Wesley, Reading, Mass, USA, 1964. · Zbl 1118.65133
[4] Y. Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Physical Review, vol. 115, no. 3, pp. 485-491, 1959. · Zbl 0099.43102
[5] Y. Imry and R. A. Webb, “Quantum interference and the Aharonov-Bohm effect,” Scientific American, vol. 260, no. 4, pp. 56-62, 1989. · Zbl 1118.65133
[6] A. P. French and E. F. Taylor, An Introduction to Quantum Physics, Norton Publications, New York, NY, USA, 1978. · Zbl 1118.65133
[7] L. de Broglie, New Perspectives in Physics, Basic Books, New York, NY, USA, 1962. · Zbl 1118.65133
[8] L. de Broglie, The Current Interpretation of Wave Mechanics: A Critical Study, Elsevier, Amsterdam, The Netherlands, 1964. · Zbl 1118.65133
[9] D. Grifiths, Introduction to Elementary Particles, John Wiley & Sons, New York, NY, USA, 1987. · Zbl 1118.65133
[10] C. Morarescu, “Inner potential of generating pulses as a consequence of recurrent principles and specific computing architecture,” in Computational Science and Its Applications, vol. 3980 of Lecture Notes in Computer Science, pp. 814-820, Springer, Berlin, Germany, 2006. · Zbl 05497908
[11] C. Toma, “A connection between special relativity and quantum theory based on non-commutative properties and system-wave interaction,” Balkan Physics Letters, vol. 5, pp. 2509-2513, 1997. · Zbl 1118.65133
[12] M. Takeda, Sh. Inenaga, and H. Bannai, “Discovering most classificatory patterns for very expressive pattern classes,” in Discovery Science, vol. 2843 of Lecture Notes in Computer Science, pp. 486-493, Springer, Berlin, Germany, 2003. · Zbl 1118.65133
[13] C. Toma, “The advantages of presenting special relativity using modern concepts,” Balkan Physics Letters, vol. 5, pp. 2334-2337, 1997. · Zbl 1118.65133
[14] C. Cattani, “Harmonic wavelets towards the solution of nonlinear PDE,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1191-1210, 2005. · Zbl 1118.65133
[15] M. Simeonidis, S. Pusca, G. Toma, A. Toma, and T. Toma, “Definition of wave-corpuscle interaction suitable for simulating sequences of physical pulses,” in Computational Science and Its Applications, vol. 3482 of Lecture Notes in Computer Science, pp. 569-575, Springer, Berlin, Germany, 2005. · Zbl 05377783
[16] P. Sterian and C. Toma, “Methods for presenting key concepts in physics for MS students by Photon-MD program,” Bulgarian Journal of Physics, vol. 27, no. 4, pp. 27-30, 2000. · Zbl 1118.65133
[17] C. Toma, “The use of the cuadridimensional interval-the main possibility for improving the Lorentz formulae interpretation,” in Proceedings of the European Conference on Iteration Theory (ECIT /97), vol. 2, p. 202, Pitesti, Romania, November 1997. · Zbl 1118.65133
[18] M. Olteanu, V.-P. Paun, and M. Tanase, “The analysis of the time series associated to sem microfractographies of Zircaloy-4,” Revista de Chimie, vol. 56, no. 7, pp. 781-784, 2005. · Zbl 1118.65133
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