Carl E. Wulfman^*

Show more
Department of Physics, University of the Pacific, Stockton, USA.
Show less

Abstract: Maxwell’s equations are obeyed in a one-parameter group of isotropic gravity-free flat space-times whose metric depends upon the value of the group parameter. An experimental determination of this value has been proposed. If it is zero, the metric is Minkowski’s. If it is non-zero, the metric is not Poincare invariant and local frequencies of electromagnetic waves change as they propagate. If the group parameter is positive, velocity-independent red-shifts develop and the group parameter play a role similar to that of Hubble’s constant in determining the relation of these red-shifts to propagation distance. In the resulting space-times, the velocity-dependence of red shifts is a function of propagation distance. If 2c times the group parameter and Hubble’s constant have approximately the same value, observed frequency shifts in radiation received from stellar sources can imply source velocities quite different from those implied in Minkowski space. Electromagnetic waves received from bodies in galactic Kepler orbits undergo frequency shifts which are indistinguishable from shifts currently attributed to dark matter and dark energy in Minkowski space, or to a non-Newtonian physics.

Keywords: Space-Time; Metric; Hubble; Dark Matter; Red Shift; Astrophysics; Electrodynamics

Cite this paper: C. Wulfman, "On the Metric of Space-Time," Journal of Modern Physics, Vol. 4 No. 11, 2013, pp. 1511-1518. doi: 10.4236/jmp.2013.411184.

References

[1]   H. Bateman, Proceedings London Mathematical Society, Vol. 8, 1909, pp. 223-264.

[2]   E. Cunningham, Proceedings London Mathematical Society, Vol. 8, 1909, pp. 77-98.

[3]   E. L. Hill, Physical Review, Vol. 68, 1945, pp. 232-233.
http://dx.doi.org/10.1103/PhysRev.68.232.2

[4]   Hoyle, F., et al., “A Different Approach to Cosmology,” Cambridge University Press, Cambridge, 2000.

[5]   L. M. Tomilchik, AIP Conference Proceedings, Vol. 1205, 2010, pp. 177-184. http://dx.doi.org/10.1063/1.3382326

[6]   H. A. Kastrup, Annals of Physics, Vol. 17, 2008, pp. 631-690. http://dx.doi.org/10.1002/andp.200810324

[7]   C. E. Wulfman, “Dynamical Symmetry,” World Scientific Publishing Co., Singapore, 2011, pp. 426-429.

[8]   C. E. Wulfman, AIP Conference Proceedings, Vol. 1323, 2010, pp 323-329. http://dx.doi.org/10.1063/1.3537862

[9]   M. Calixto, et al., Journal of Physics A: Mathematical and Theoretical, Vol. 45, 2012, pp. 244010-244026.
http://dx.doi.org/10.1088/1751-8113/45/24/244010

[10]   B. J. Cantwell, “Introduction to Symmetry Analysis,” Cambridge University Press, Cambridge, 2002.

[11]   P. Hydon, “Symmetry Methods for Differential Equation,” Cambridge University Press, Cambridge, 2000.
http://dx.doi.org/10.1017/CBO9780511623967

[12]   F. H. Stephani, “Differential Equations: Their Solution Using Symmetries,” Cambridge University Press, Cambridge, 1989.

[13]   C. E. Wulfman, “Dynamical Symmetry,” loc cit.

[14]   V. M. Slipher, Lowell Observatory Bulletin, Vol. 2, 1914, p. 66.

[15]   F. Zwicky, Helvetica Physica Acta, Vol. 6, 1933, pp. 110-125.

[16]   V. C. Rubin, W. K. Ford Jr. and N. Thonnard, Astrophysical Journal, Vol. 238, 1980, pp. 471-487.
http://dx.doi.org/10.1086/158003

[17]   P. J. E. Peebles, “Principles of Physical Cosmology,” Princeton University Press, Princeton, 1993.

[18]   T. S. van Albada and R. Sancisi, Philosophical Transactions of the Royal Society A, Vol. 320, 1986, pp. 447-464.
http://dx.doi.org/10.1098/rsta.1986.0128

[19]   S. G. Turyshev, et al., Physical Review Letters, Vol. 108, 2012, pp. 241101-241104.
http://dx.doi.org/10.1103/PhysRevLett.108.241101

[20]   T. Fulton, F. Rohrlich and L. Witten, Reviews of Modern Physics, Vol. 34, 1962, pp. 442-457.
http://dx.doi.org/10.1103/RevModPhys.34.442