Special Problems in High Energy Physics pp 288-306 | Cite as

# Mach’s Principle and Elementary Particles

## Abstract

There are at least three different formulations of this principle which is named after Ernst Mach. The most specific is in terms of the Foucault pendulum which, according to the principle [1], moves in a constant plane with respect to the fixed stars, rather than to the absolute space, as Newton had thought. The second formulation, obviously closely related, but more general than the first, is the statement by Mach, that all motion is motion relative to other bodies [2]. Finally, one may consider the statement that inertia depends on the other bodies in the universe, as Mach’s principle, although it was formulated in this general form by Einstein [3]. The three formulations emphasize different aspects of Mach’s principle, and therefore require different criticism. It is clear that rotational motions considered in the first formulation will appear differently when the theory of relativity is taken into account; one need only recall the problem of the rotating disk. According to Newtonian ideas, two Cartesian coordinate frames in rotation relative to each other are “metrically” equivalent, since simultaneity has the same meaning for both observers, and distances of simultaneous events will thus be expressed in the same way. But the two observers are not dynamically equivalent, since in one or in both frames inertial forces will appear. A priori, one could think of two specific coordinate frames; one in which the Foucault pendulum remains in a constant plane, and another one in which the fixed stars remain at rest and it seems quite remarkable that these frames are in fact identical.

## Keywords

Cosmological Constant Inertial Force Coordinate Frame Absolute Space Cosmological Principle## Preview

Unable to display preview. Download preview PDF.

## References and Footnotes

- 1.see for instance H. Bondi, Cosmology, Cambridge University Press,1961, 2nd edition.Google Scholar
- 2.Ernst Mach, Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt, 2. verbesserte Auflage, Leipzig,F. A. Brockhaus;especially pp. 481, Mach emphasizes there that not only translational motion, but also rotational motion is relative.Google Scholar
- 3.A. Einstein, The Meaning of Relativity, Methuen Co. London, 5th edition, 1951, pp. 95.Google Scholar
- 4.Einstein, ibid. p. 94. The occurrence of inertial forces in a frame in which the “stars” represented by a spherical mass-shell, are rotating, has been demonstrated by H. Thirring, Phys. Z. 19,’33,(1918); ibid. 22, 29(1921). The comments made by L. Bass and F. A. E. Pirani, Phil. Mag. 46, 850(1955), though important should not change the fundamental features of the conclusions. See also H. Hönl and A. W. Maue, Z. Phys. 114, 152 (1956) and Ch. Soergei-Fabricius, Z. Phys, 159, 541 (1960).Google Scholar
- 5.The action at a distance theories may serve to prove the point since the inclusion of all particles of the universe is contrary to the spirit of a physicist.Google Scholar
- 6.W. Thirring, Fortschritte d. Phys. 7, 79 (1959).ADSCrossRefGoogle Scholar
- 7.A. Einstein, loc. Cit., p. 96, see also W. Davidson, Monthly No. Royal Astron. Soc. 117, 212 (1957).Google Scholar
- 8.loc. Cit. p. 98.Google Scholar
- 9.D. W. Sciama, Monthly Not.Royal Astr. Soc. 113, 34, (1953); also “The Unity of the Universe”, Dorbleday Anchor, 1961.Google Scholar
- 10.Only exploratory papers have been published: O. Bergmann, Am. J. Phys. 24, 38 (1956); Phys. Rev. 107, 1157 (1957). It was not proposed as a substitute for the general theory of relativity nor as interpreted by H. A. Buchdahl, Phys. Rev. 115, 1325 (1959) as a theory of “scalar charges”.Google Scholar
- 11.I. Ozvath and E. Schücking, Nature 193, 1108 (1962).Google Scholar
- 12.H. Dehnen and H. Hönl, Nature, 196, 362 (1962); H. H.nl and H. Dehnen, Zeits.f. Phys. 171, 178 (1963).MATHCrossRefGoogle Scholar
- 13.compare H. Hönl, Zeitschr.f. Naturf. 8a, 2 (1953).Google Scholar
- 14.The equation (6) follows easily from the H.Thirring’s argument (Ref. 4). The Coriolis forces will depend on the masses and the radius of the rotating mass shell, and if these inertial forces should in fact be independent of these quantities, the equation (6) must be postulated.Google Scholar
- 15.A preliminary report was presented at the Autumn Meeting of the American Physical Society in Nashville, Tenn.,Bull. Am. Phys. Soc. 11, 819(1966). For other interpretations of the cosmological constant see F. M. Gomide, Nuovo Cim. 30, 672 (1963).Google Scholar
- 16.G. C. McVittie, General Relativity and Cosmology, The University of Illinois Press, Urbana,1965.Google Scholar
- 17.In a more sophisticated version of the theory the constant b may depend on a higher power of a, and the desire to have the masses vanish in the limit of vanishing gravitational constant could be satisfied assuming m = o (see page 301).Google Scholar
- 18.op. cit. p. 203.Google Scholar
- 19.H. Hönl and H. Dehnen, Z. f. Phys. 156, 382 (1959).ADSMATHCrossRefGoogle Scholar
- 20.C. Fronsdal, Rev. Mod. Phys. 37, 221 (1965);P. Roman and J. J. Aghassi,Nuovo Cim. 152, 193 (1966); and other papers in preparation, W. Thirring, these proceedings;0. Nachtmann,to be published in Comm. Math. Phys.Google Scholar
- 21.L. P. Eisenhart,Riemannian Geometry,Princeton Univ. Press,(1963).Google Scholar