Discretization and Interaction of Fields via the Classical Kaluza-Klein Theory ()
Abstract
We show how the metric of a five-dimensional hyperspace-time can be used to model the quantum nature of electromagnetic interactions. The space-time neighborhood of the point where such an interaction takes place bends according to the curl and the derivative of the local electromagnetic four-potential, both calculated in the direction of the latter. In this geometric setting, the presence of a non-gravitational field is needed to induce the discretization of any gravitational field. We also exploit two variants of the classical Kaluza-Klein five-dimensional theory to obtain coupled generalizations of Einstein’s and Maxwell’s equations. The first variant involves an unspecified scalar field that may be related to the inflaton. The equations of the second variant show a direct interdependency of gravitation and electromagnetism that would emerge or be activated through the production of electromagnetic waves.
Share and Cite:
D. LaChance and C. Gauthier, "Discretization and Interaction of Fields via the Classical Kaluza-Klein Theory,"
Journal of Modern Physics, Vol. 4 No. 12, 2013, pp. 1608-1613. doi:
10.4236/jmp.2013.412199.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
T. Kaluza, “Zum Unitatsproblem in der Physik,” Sitzungsberichte der Koniglich Preußischen Akademie der Wissenschaften, 1921, pp. 966-972.
|
|
[2]
|
O. Klein, Zeitschrift für Physik, Vol. 37, 1926, pp. 895-906. http://dx.doi.org/10.1007/BF01397481
|
|
[3]
|
C. Gauthier and P. Gravel, Canadian Journal of Physics, Vol. 68, 1990, pp. 385-387.
http://dx.doi.org/10.1139/p90-061
|
|
[4]
|
C. Gauthier and P. Gravel, Nuovo Cimento A, Vol. 104, 1991, pp. 325-336.
http://dx.doi.org/10.1007/BF02799141
|
|
[5]
|
O. Ben Khalifa and C. Gauthier, Central European Journal of Physics, Vol. 5, 2007, pp. 151-164.
http://dx.doi.org/10.2478/s11534-007-0002-0
|
|
[6]
|
L. Schwartz, “Théorie des Distributions,” Hermann, Paris, 1978.
|
|
[7]
|
J. Overduin and P. Wesson, Physics Reports, Vol. 283, 1997, pp. 303-380.
http://dx.doi.org/10.1016/S0370-1573(96)00046-4
|