In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

Periodical:

International Letters of Chemistry, Physics and Astronomy (Volume 48)

Pages:

68-86

Citation:

D.L. Bulathsinghala and K. A. I. L. Wijewardena Gamalath, "Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields", International Letters of Chemistry, Physics and Astronomy, Vol. 48, pp. 68-86, 2015

Online since:

March 2015

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

[1] R. Lévi, Journal de Physique et le Radium 8 (4) (1927) 182–198.

[2] H. Snyder, Phys. Rev. 71 (1947) 38–41.

[3] C.N. Yang, Phys. Rev. 72 (1947) 874.

[4] H. Margenau, The Nature of Physical Reality. (McGraw-Hill, 1950).

[3] P. Caldirola, Lett. Nuovo Cim. 27 (1980) 225–228.

[4] S. Vaknin, Time Asymmetry Revisited (Thesis (Ph. D. ), Pacific Western University (Encino, California, 1982).

[5] E.H. Suchard, J. of Modern Phys. 4 (2013) 791-806.

[6] William G. Tifft, Astrophysical Journal 206 (1976) 38–56.

[7] H. T Elze, Phys. Lett. A310 (2003) 110.

[8] J.F. Barbero, Guillermo A. Mena Marugan, E.J. S Villasenor. Time uncertainty in quantum gravitational systems. arXiv: grqc/0311073, (2003).

[9] J. J Halliwell, The Interpretation of Quantum Cosmology and the Problem of Time. arXiv: gr-qc/0208018, (2002).

[10] Hitoshi Kitada, Quantum Mechanical Clock and Classical Relativistic Clock. arXiv: gr-qc/0102057, (2001).

[11] N.D. George, A. P. Gentle, A. Kheyfets, W.A. Miller, The Issue of Time in Quantum Geometrodynamics arXiv: gr-qc/0302051, (2003).

[12] B. Russell. Our Knowledge of the External World as a Field for Scientific Method in Philosophy, (Open Court Publishing Co. 1914, Chicago).

[13] P. Lynds. Found. of Phys. Lett. 16 (4) (2003) 343-355.

[14] E. Schrodinger, Annalen der Physik 79 (1926) 361, 489.

[15] O. Klein, Z. Phys. 37 (1926) p.895–906.

[16] W. Gordon, Z. Phys. 40 (1926–1927) p.117–133.

[17] D. L. Bulathsinghala, K. A. I. L. Wijewardena Gamalath, ILCPA 9(2) (2013) 103-115.

[18] P. A. M. Dirac, Proc. Roy. Soc. Lond. A 117 (1928) 610-624.

[19] Aristotle. Physics VI part 9, 239b5-7.

[18] T. Aquinas, Commentary on Aristotle's Physics. (Dumb Ox Books, Trans. By R.J. Blackwell, R.J. Spath, W.E. Thirlkel, 1999).

[19] H. Reichenbach. The Philosophy of Space and Time. (Dover Pub. inc. U.S. A, 1958).

[20] L.I. Mandelshtam, I.E. Tamm Jour. phys. (USSR) 9 (1945) p.249–254.

[21] P.A. M Dirac, Proc. R. Soc. Lond. A 133, (1931) 60-72.

[22] E.C. G Stueckelberg, Helvetica Physica Acta 14 (1941) p.51–80. ( Received 12 May 2015; accepted 20 May 2015 ).

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