Christoph Schmid
We show that the dragging of axis directions of local inertial frames by a weighted average of the energy currents in the universe (Mach's principle) is exact for all linear perturbations of all Friedmann-Robertson-Walker universes and for all types of matter.
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We show that the dragging of the axis directions of local inertial frames by a weighted average of the energy currents in the universe is exact for all linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K = (+1, -1, 0) and of Einstein's static closed universe. This includes FRW universes which are arbitrarily close to the Milne Universe, which is empty, and to the de Sitter universe. Hence the postulate formulated by E. Mach about the physical cause for the time-evolution of the axis directions of inertial frames is shown to hold in cosmological General Relativity for l…
If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results on the dragging of inertial frames in closed, flat and open universe with and without a cosmological constant.
The axes of gyroscopes experimentally define local non-rotating frames, i.e. the time-evolution of axes of inertial frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed FRW cosmology with k=0 we consider linear cosmological vorticity perturbations and ask: Will cosmological vorticity perturbations exactly drag the axes of gyroscopes relative to the directions of geodesics to galaxies in the asymptotic FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of gravitomagnetism into a form showing the close correspon…
The axes of gyroscopes experimentally define non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? Starting from an unperturbed, spatially flat FRW cosmology, we consider cosmological vorticity perturbations (i.e. vector perturbations, rotational perturbations) at the linear level. We ask: Will cosmological rotational perturbations drag the axis of a gyroscope relative to the directions (geodesics) to galaxies beyond the rotational perturbation? We cast the laws of Gravitomagnetism into a form showing clearly the close correspondence with the laws of ordina…
The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary mag…
Mach Principle presents the absolute universe. For example, when Einstein stood on the ground and relaxed, his arms fell down naturally. However, if he rotated his body then his arms were lifted up as the rotation was faster and faster. Mach principle is that the matter of the whole universe can affect local dynamic systems. That is, the matter of the whole universe sets up the local absolute reference frames. However, Einstein's general theory of relativity is against the absolute reference frames of Mach Principle.
Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an alternative cosmological model, based on a linearly expanding universe with Omega=1, can fully account for these observations. This model is also able to resolve the other problems associated with the standard Big Bang model. A scale-invariant form of the field equations of General Relativity is postulated, based on the replacement of the Newtoni…
Maintaining the relativity of all motion, especially rotational motion, Mach denied the existence of absolute motion and absolute space. He maintained the equivalence of the Ptolemaic and the Copernican systems and the equivalence of a fixed bucket in a rotating universe with the converse. An analysis of the Foucault pendulum shows that there cannot be a fixed bucket in a rotating universe. Also, Mach's views violate the physics he espoused: non-inertial experiments, e.g. stellar aberration and electromagnetic effects, distinguish between a rotating bucket in a fixed universe and the converse,…
Linear perturbations of Friedmann-Robertson-Walker universes with any curvature and cosmological constant are studied in a general gauge without decomposition into harmonics. Desirable gauges are selected as those which embody best Mach's principle: in these gauges local inertial frames can be determined instantaneously via the perturbed Einstein field equations from the distributions of energy and momentum in the universe. The inertial frames are identified by their `accelerations and rotations' with respect to the cosmological frames associated with the `Machian gauges'. In closed spherical …
We introduce a new statistic to measure more accurately the cosmic sound speed of clusters of galaxies at different redshifts. This statistic is evaluated by cross-correlating cosmic microwave background (CMB) fluctuations caused by the Sunyaev-Zel'dovich effect from observed clusters of galaxies with their redshifts. When clusters are distributed in redshift bins of narrow width, one could measure the mean squared cluster peculiar velocity with an error σ_{C_S^2}\lsim (300{\rm km/s})^2. This can be done around z>0.3 with clusters of flux above 200 mJy which will be detected by PLANCK, coupled…
Over the past two decades or so, it has become increasingly appparent that, out to quite large distances, galaxies are distributed in a quasi-fractal fashion with fractal dimension $D \approx 2$. Whether or not this behaviour continues onto indefinitely large scales is a matter of live debate and is a question that can only be settled if, at some scale, there is an unambiguous transition to homogeneity. This point has not yet been reached and may never be. This paper has been written on the basis of the tentative hypothesis that quasi-fractal $D\approx 2$ behaviour is a persistent and fundamen…
If Mach's Principle explains the Newtonian inertial reaction to acceleration then the role of the 'fixed stars' should also be manifest through Hamilton's formulation of mechanics. This consistency may be achieved if the expression for relativistic energy contains a cosmological coefficient that is (currently) equal to one. The presence of the required cosmological term exactly identifies the rest energy of a body as its gravitational potential energy due to the mass of the Universe.
Recent discovery of the rate of expansion of the Universe (Reiss A.G. et al., 1998; Perlimutter S. et al., 1999) is connected with the vacuum energy in space which, in turn, can be considered (Gliner E.B., 1965) as the cosmological constant in Einstein's equation. In this article the cosmological term predicted by Einstein is interpreted in terms of World's mass required by Mach's principle. The Mach's principle itself is formulated as follows: inertia masses of bodies, including those of fundamental particles, are determined by the value of the cosmological term.
The effects that the present accelerating expansion of the universe has on the size and shape of Lorentzian wormholes and ringholes are considered. It is shown that, quite similarly to how it occurs for inflating wormholes, relative to the initial embedding-space coordinate system, whereas the shape of the considered holes is always preserved with time, their size is driven by the expansion to increase by a factor which is proportional to the scale factor of the universe. In the case that dark energy is phantom energy, which is not excluded by present constraints on the dark-energy equation of…
The oft-repeated claim that life is written into the laws of nature are examined and criticized. Arguments are given in favour of life spreading between near-neighbour planets in rocky impact ejecta (transpermia), but against panspermia, leading to the conclusion that if life is indeed found to be widespread in the universe, some form of life principle or biological determinism must be at work in the process of biogenesis. Criteria for what would constitute a credible life principle are elucidated. I argue that the key property of life is its information content, and speculate that the emergen…
In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the mass of an infinitely extended, homogeneously matter-filled and expanding universe. To answer this question we produce a space-like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added-up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric…
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