MACH'S PRINCIPLE IN CLASSICAL AND RELATIVISTIC PHYSICS
To investigate whether the reference frames remaining at rest relative to the expanding system of galaxies are also dynamically preferred, McVittie's metric describing exactly the field of a singular mass point in an expanding universe is transformed into a suitably chosen coordinate system. It is found that, in the Newtonian approximation, the potential governing the motion of a test particle is given by the sum of a Newtonian gravitational potential and of a cosmic potential which is composed additively by a scalar potential and by the scalar product of the velocity of the test particle and of a vector potential. The total energy of the test particle does not vary if, and only if, it is situated at the origin of a coordinate frame remaining at rest relative to the expanding system of galaxies. If the force acting on this particle should vanish, the origin of coordinates must coincide with the center of gravity of a field galaxy, or of a cluster of galaxies, respectively. If the Hubble constant of cosmic expansion varies with the time, the conservation law of energy does not hold in our neighborhood with infinite accuracy. The existence of the centrifugal and Coriolis forces, appearing also in the case when a single material body is rotating in an infinite absolutely empty space, is explained by the hypothesis that this empty space-time is to be considered for a Minkowski universe, i.e., a world model with infinite total mass and vanishing mean-mass density. Other exact solutions of the field equations of general relativity with a vanishing matter tensor which are free of singularities, if they actually occur in nature, are to be considered for selfexcited states of the Minkowski universe. This assumption stands in a natural accord both with general relativity, and with the relativistic formulation of Mach's principle (expressed in the statement: The space-time does not exist without matter). It agrees also with the investigations of Honl and Dehnen who proved that the centrifugal and Coriolis forces of correct magnitude appear in every reference frame which is rotating relatively to the total mass of the world model, and explains the Thirring forces as the result of the simultaneous action of the rotating mass of the near-hollow sphere and of the nonrotating distant mass of the Minkowski universe. From the standpoint of the proposed hypothesis, the cosmological constant is to be interpreted not as a universal natural constant, but as the 8 pi -multiple of the mean-mass density, written in a geometrical system of units, of a very strange and highly hypothetical form of matter the density of which, due to creation or annihilation of matter should remain constant during the expansion or contraction of the cosmic space. (auth)
- Research Organization:
- Technical Univ., Prague
- NSA Number:
- NSA-18-000708
- OSTI ID:
- 4169896
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 132; Other Information: Orig. Receipt Date: 31-DEC-64
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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