Relativistic Theory of Gravitation Based Solely on the Uniform Scaling of Physical Properties
[1]
Robert J. Buenker, Fachbereich C-Mathematik und Naturwissenschaften, University of Wuppertal, Wuppertal, Germany.
[2]
Heinz-Peter Liebermann, Fachbereich C-Mathematik und Naturwissenschaften, University of Wuppertal, Wuppertal, Germany.
The Equivalence Principle (EP) enunciated by Einstein in 1907 states that the effects of gravity are simulated by purely kinematic acceleration. One of his main conclusions was that the speed of light varies with gravitational potential, even though it should have a constant value of c (299792458 ms-1) according to the Special Theory of Relativity (STR) which he published two years earlier. He assumed on this basis that light rays would be bent when they pass close to the sun, but his attempt to verify this prediction quantitatively failed. Schiff later showed that an accurate value for the angle of displacement of star images during solar eclipses is obtained when one assumes that the speed of light moving radial to the gravitational field varies in a different manner than its transverse components. In the present work it is shown that the EP can be successfully modified by employing a uniform scaling of physical units which is different for changes in gravitational and kinematic acceleration. The respective conversion factors are integral powers of two fundamental quantities denoted as S and Q. The methodology of the Global Positioning System (GPS), for example, uses separate scaling factors to compute the required amount of adjustment of clock rates on satellites to make them equal to those of identical counterparts on the earth’s surface. The interpretation of the transverse Doppler measurements employing high-speed rotors is shown to be affected by these considerations. An analysis of Schiff’s simplified computational method for predicting the angle of displacement of star images during solar eclipses is given which is consistent with the present conclusions. Moreover, it is shown that the scaling of the acceleration of gravity g in Newton’s Universal Law of Gravitation, which was not foreseen in Schiff’s theory, allows for the quantitative prediction of the precession of Mercury’s perihelion. As a consequence, it is argued that the uniform scaling of physical units accomplishes the same objectives as the far more complicated General Theory of Relativity (GTR).
Equivalence Principle (EP), Special Theory of Relativity (STR), Global Positioning System (GPS), General Theory of Relativity (GTR), Newton's Universal Law of Gravitation, Schiff's Light Trajectory Method, Precession of Mercury’s Perihelion
[1]
A. Pais, ‘Subtle is the Lord…’ The Science and Life of Albert Einstein, Oxford: Oxford University Press, 1982, pp. 178-182.
[2]
R. D. Sard, Relativistic Mechanics, New York: W. A. Benjamin, 1970, p. 310.
[3]
W. Rindler, Essential Relativity, New York: Springer-Verlag, 1977, p. 15.
[4]
A. Einstein, “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen,” Jahrb. Rad.Elektr. vol. 4, pp. 411-462, 1907.
[5]
A. Einstein, “Zur Elektrodynamik bewegter Körper,” Ann. Physik , vol. 322 (10), pp. 891-921, June 1905.
[6]
A. Einstein, “Einfluss der Schwerkraft auf die Ausbreitung des Lichtes,” Ann. Physik, vol. 35, p. 898, 1911.
[7]
L. I. Schiff, “On experimental tests of the general theory of relativity,” Am. J. Phys. vol. 28, pp. 340-343, 1960.
[8]
A. Einstein, “Die Feldgleichungen der Gravitation,” Sitzber. Kgl. Preuss. Akad. Wiss. p. 831, 1915.
[9]
R. V. Pound and J. L. Snider, “Effect of gravity on gamma radiation ,” Phys. Rev., vol.140 (3B), p. B788, 1965.
[10]
R. J. Buenker, G. Golubkov, M. Golubkov, I. Karpov and M. Manzheily, “Relativity laws for the verification of rates of clocks moving in free space and GPS positioning errors caused by space-weather events, ISBN 980-307-843-9; InTech-China, pp. 1-12, 2013”.
[11]
A. Pais, ‘Subtle is the Lord…’ The Science and Life of Albert Einstein, Oxford: Oxford University Press, 1982, pp. 194-200.
[12]
W. Rindler, Essential Relativity, New York: Springer-Verlag, 1977, p. 21.
[13]
R. J. Buenker, “Gravitational and kinetic scaling of physical units,” Apeiron, vol. 15, pp. 382-413, 2008.
[14]
R. J. Buenker, Relativity Contradictions Unveiled: Kinematics, Gravity and Light Refraction, Montreal: Apeiron, 2014, pp. 116-120.
[15]
H. E. Ives and G. R. Stilwell, “An experimental study of the rate of a moving atomic clock,” J. Opt. Soc. Am. Vol. 28, pp. 215-226,1938.
[16]
H. I . Mandelberg and L. Witten, “Experimental verification of the relativistic Doppler effect,” J. Opt. Soc. Am., Vol. 52, pp. 529-536, 1962.
[17]
H. J. Hay, J. P. Schiffer, T. E. Cranshaw, and P. A. Egelstaff, “Measurement of the red shift in an accelerated system using the Mössbauer effect in Fe57,” Phys. Rev. Letters vol. 4, pp. 165-166,1960.
[18]
C. W. Sherwin, “Some recent experimental tests of the ‘clock paradox’,” Phys. Rev., vol. 120, pp. 17-21, 1960.
[19]
R. D. Sard, Relativistic Mechanics, New York: W. A. Benjamin, 1970, p. 319.
[20]
R. J. Buenker, “The sign of the Doppler shift in ultracentrifuge experiments,” Apeiron, vol. 19, pp. 218-237, 2012.
[21]
W. Kündig, “Measurement of the transverse Doppler effect in an accelerated system,” Phys. Rev., vol. 129, pp. 2371-2375, 1963.
[22]
D. C. Champeney, G. R. Isaak, and A. M. Khan, “Measurement of relativistic time dilatation using the Mössbauer effect,” Nature, vol. 198, pp. 1186-1187, 1963.
[23]
R. J. Buenker, “Time dilation and the concept of an objective rest system,” Apeiron, vol. 17, pp. 99-125, 2010.
[24]
R. J. Buenker, Relativity Contradictions Unveiled: Kinematics, Gravity and Light Refraction, Montreal: Apeiron, 2014, p. 50.
[25]
R. J. Buenker, “Huygens’ principle and computation of the light trajectory responsible for the gravitational displacement of star images,” Apeiron, vol. 15, pp. 338-357, 2008.
[26]
F. W. Dyson, A. S. Eddington, and C. Davidson, “A determination of the deflection of light by the sun's gravitational field, from observations made at the total eclipse of May 29, 1919,” Phil. Trans. Roy. Soc. (London), vol. 220A, pp. 291-333, 1920.
[27]
W. W. Campbell and R. J. Trumpler, Lick Observ. Bull. XIII, pp. 130-160, 1928.
[28]
R. J. Buenker, “Extension of Schiff’s gravitational scaling method to compute the precession of the perihelion of Mercury,” Apeiron, vol. 15, pp. 509-532, 2008.
[29]
R. D. Sard, Relativistic Mechanics, New York: W. A. Benjamin, 1970, p. 104.
[30]
R. J. Buenker and H.-P. Liebermann, Bergische Universität (2003).
[31]
S. Weinberg, in Gravitation and Cosmology, New York:, Wiley, 1972, p. 198.
[32]
A. Einstein, “The Foundation of the General Theory of Relativity,” Ann. Physik, vol. 49, p. 769, 1916.
[33]
R. H. Dicke, in The Theoretical Significance of Experimental Relativity, New York: Gordon and Breach, 1964, p. 27.
[34]
W. Rindler, Essential Relativity, New York: Springer-Verlag, 1977, p. 145.
[35]
R. J. Buenker, “Comparison of the phenomena of light refraction and gravitational bending,” Khim. Fyz. Vol. 24 (4), pp. 29-35, 2005; see also http://arxiv.org, 0904.3232.
[36]
I. I. Shapiro, “Fourth test of general relativity,” Phys. Rev. Letters, vol. 13, p. 789, 1964.
[37]
R. J. Buenker, Relativity Contradictions Unveiled: Kinematics, Gravity and Light Refraction, Montreal: Apeiron, 2014, pp. 97-155.
