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.
Schrödinger,E. (1950):
Space-Time Structure, Cambridge UP.
Sciama,D.W., Waylen,P.C., Gilman,R.C. (1969):
Generally covariant integral formulation of Einstein's field equations,
Phys.Rev. 187, 1762-1766.
Gilman,R.C. (1970):
Machian theory of inertia and gravitation,
Phys.Rev. D 2, 1400-1410.
Raine,D.J. (1975):
Mach's principle in General Relativity,
Monthly Notices RAS 171, 507-528.
D.-E.Liebscher, W.Yourgrau (1979):
Classical breakdown of symmetry and the induction of inertia,
Ann.d.Physik (Lpz.) 36, 20-24.
Barbour,J.B., Pfister,H. eds. (1995):
Mach's principle: From Newton's bucket to quantum
cosmology, Boston, Birkhäuser.
Bleyer,U., Liebscher,D.-E. (1995):
Mach's principle and local causal structure,
in: Barbour,J.B. & Pfister,H. 1995, 293-307.
Aldrovandi,R., Barbosa,A.L., Crispino,L.C.B., Pereira,J.G. (1998):
Non-Metric Spacetimes,
jpereira@ift.unesp.br, gr-qc/9801100.
Wilczek,Frank (1998):
Riemann-Einstein Structure from Volume and Gauge Symmetry,
wilczek@IAS.EDU, hep-th/9801184.