Mach's principle and relativistic field theory

Dierck-E.Liebscher, Astrophysikalisches Institut Potsdam

Mach's principle is an unspecified demand to get rid of all notions of absolute space. It can be developed into different directions (Barbour & Pfister 1995). If we follow the road to relational mechanics, we end in stating that Mach's principle includes the breakdown of some larger telescopic group to the Galilei group, and that the instantaneity of gravitational interaction cannot be hidden by theoretical constructions from the detection in the post-Newtonian approximation of gravitation theory. Consequently, we should try a scheme where the telescopic group of the universe breaks down to the Lorentz group (Liebscher & Yourgrau 1979, Bleyer & Liebscher 1995). In such a scheme, Lorentz invariance is observed only locally, i.e., the distinction of a time coordinate or a lightcone exists only locally and it is due to the existence and the state of the surrounding universe. This implies to start a theory without metric a priori. We discuss the known purely affine field theory and new interpretations and programs (Aldrovandi et al. 1998, Wilczek 1998). We are led to expect final forms like the integral representation of the metric (Sciama et al. 1969, Gilman 1970, Raine 1975). The difference consists in that the metric properties are not supposed to exist in the constuction of the integral. The result should be more complicated than general relativity when the state of the universe is not quite ideal just as in relational mechanics where the Galilei invariance in small subsystems depends on and indicates the symmetry properties of the universe.

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