In the past, MACH’S PRINCIPLE has been considered a central cosmological issue .Mach’s principle is an ill-defined concept but broadly speaking asserts that our local physical laws are influenced by the large scale distribution of matter. An often-quoted example that illustrates this is that of the Foucault Pendulum. If a pendulum is set up by suspending a ball on a string from the ceiling, and then sets swinging back and forth, the ball traces a straight line on the Moor. The plane in which the pendulum swings rotates once every twenty-throe hours, fifty-six minutes and four seconds. This is just shorter than the length of the day, so it is not the Sun that drags the pendulum around. In fact the plane of the swing of the pendulum is fixed relative to the distant stars and galaxies. Accordingly, we attribute the rotation of the plane of the pendulum directly to the influence (presumably gravitational) of the most distant matter in the Universe. At least, that is what Mach did. One of Einstein’s hopes when thinking about the general I theory of relativity had been to rediscover Mach’s principle as a consequence of a proper theory of gravitation. However, it is not clear to what extent Einstein’s theory achieves this. For example there are solutions to Einstein’s equations in which the Universe rotates. ^ hat is meant by the rotation of the Universe here is that an observer sitting in a terrestrial inertial frame sees the Universe rotating relative to this particular frame. Thus, such a Universe is not Machian in the sense that the coordinate system in which the distant stars are fixed is not an inertial frame.

It is possible to turn this doubt concerning Mach’s principle and Einstein’s general relativity into a strong cosmological principle by asserting that the only physical cosmological solutions to the Einstein equations are those which are Machian. Enunciated in this form. Mach’s principle immediately excludes rotating cosmological models as physically acceptable models for the Universe. The principle also excludes the curious vacuum universes which have no matter at all, and yet display the cosmological redshift phenomenon. Most importantly, it seems that the simple homo¬geneous and isotropic cosmological models are Machian. Thus if we add Mach’s Principle to the general theory of relativity, we may go part of the way to explaining the isotropy of the Universe.

Attempts have been made to modify General Relativity so as to incorporate Mach’s principle explicitly. It is possible to construct cosmological models from these modified theories of gravitation and so test the theories indirectly by seeing if these models are observationally validated. Since these Machian cosmologies behave somewhat differently near the cosmic singularity from the Einstein-theory models, the nucleosynthesis arguments may be used to eliminate some of them as being inconsistent with cosmology. More direct tests of non-Einstein gravitation theories will be possible using satellite-borne gyroscopes.

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