Abstract
A rotating disk with angular acceleration is given a relativistic description as observed from the rotating rest frameR of the disk. It is shown how a non-Euclidean intrinsic spatial geometry develops inR, as the disk gets an angular velocity. The explanation of this as given by anR-observer is discussed. A recent description of the geometry inR presented by Grünbaum and Janis is criticized. The motion of light as described by use of coordinate clocks inR is discussed in connection with some recent work by R. C. Jennison and coworkers. The significance of the difference between directed signals and circular waves when clocks inR are to be synchronized by means of light emitted from the axis inR is made clear.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Ehrenfest,Phys. Z. 10, 918 (1909).
M. Born,Ann. Phys. (Leipzig) 30, 1 (1909).
Von V. Varićak,Phys. Z. 12, 169 (1911).
M. Planck,Phys. Z. 11, 294 (1910).
H. A. Lorentz,Nature 106, 795 (1921).
A. S. Eddington,The Mathematical Theory of Relativity (Cambridge Univ. Press, Cambridge, 1923), p. 50.
G. L. Clark,Proc. R. Soc. Ed. 62A, 434 (1947).
G. Cavalleri,Nuovo Cimento 53B, 415 (1968).
W. H. McCrea,Nature 234, 399 (1971).
C. W. Berenda,Phys. Rev. 62, 280 (1942).
C. Møller,The Theory of Relativity (Oxford Univ. Press, Oxford, 1952), §90.
H. Arzeliés,Relativistic Kinematics (Pergamon, New York, 1956), Ch. IX.
V. Cantoni,Nuovo Cimento 57B, 220 (1968).
K. Kraus,Z. Naturforsch.25a, 792 (1970).
Ø. Grøn,Am. J. Phys. 43, 869 (1975).
A. Grünbaum and A. J. Janis,Synthèse 34, 281 (1977).
A. Einstein,The Meaning of Relativity (Princeton University Press, Princeton, 1921).
M. Strauss,Int. J. Theor. Phys. 11, 107 (1974).
Ø. Grøn,Int. J. Theor. Phys. 16, 603 (1977).
E. Dewan and M. Beran,Am. J. Phys. 27, 517 (1959).
E. Dewan,Am. J. Phys. 31, 383 (1963).
R. F. Marzke and J. A. Wheeler, inGravitation and Relativity, H. Y. Chiu and W. F. Hoffmann, eds. (Benjamin, New York, 1964).
J. L. Anderson and R. Gautreau,Phys. Rev. 185, 1656 (1969).
A. Harvey,Gen. Rel. Grav. 7, 891 (1976).
L. D. Landau and E. M. Lifschitz,The Classical Theory of Fields, 3rd. ed. (Pergamon Press, 1971), pp. 233, 234.
R. G. Newburgh,Nuovo Cimento 23B, 365 (1974).
E. J. Post,Rev. Mod. Phys. 39, 475 (1967).
A. Einstein, inThe Principle of Relativity (Dover, New York, 1952), pp. 41, 42.
P. A. Davies and R. C. Jennison,J. Phys. A 8, 1390 (1975).
R. C. Jennison,Nature 199, 739 (1963).
D. G. Ashworth and R. C. Jennison,J. Phys. A 9, 35 (1976).
P. A. Davies,J. Phys. A 9, 951 (1976).
R. C. Jennison and D. G. Ashworth,J. Phys. A 9, 1257 (1976).
R. C. Jennison,New Scientist 73, 283 (1977).
D. G. Ashworth and P. A. Davies,Int. J. Theor. Phys. 16, 845 (1977).
P. F. Browne,J. Phys. A 10, 727 (1977).
T. E. Phipps, Jr.,Nuovo Cimento Lett. 9, 467 (1974).
K. McFarlane and N. C. McGill,J. Phys. A 11, 2192 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grøn, Ø. Relativistic description of a rotating disk with angular acceleration. Found Phys 9, 353–369 (1979). https://doi.org/10.1007/BF00708527
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00708527