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Published online by Cambridge University Press: 21 January 2010
Einstein's GTR initiated a new programme for describing fundamental interactions, in which the dynamics was described in geometrical terms. After Einstein's classic paper on GTR (1916c), the programme was carried out by a sequence of theories. This chapter is devoted to discussing the ontological commitments of the programme (section 5.2) and to reviewing its evolution (section 5.3), including some topics (singularities, horizons, and black holes) that began to stimulate a new understanding of GTR only after Einstein's death (section 5.4), with the exception of some recent attempts to incorporate the idea of quantization, which will be addressed briefly in section 11.3. Considering the enormous influence of Einstein's work on the genesis and developments of the programme, it seems reasonable to start this chapter with an examination of Einstein's views of spacetime and geometry (section 5.1), which underlie his programme.
Einstein's views of spacetime and geometry
The relevance of spacetime geometry to dynamics
Generally speaking, a dynamical theory, regardless of its being a description of fundamental interactions or not, must presume some geometry of space for the formulation of its laws and interpretation. In fact a choice of a geometry predetermines or summarizes its dynamical foundations, namely, its causal and metric structures. For example, in Newtonian (or special relativistic) dynamics, Euclidean (or Minkowskian) (chrono-) geometry with its affine structure, which is determined by the kinematic symmetry group (Galileo or Lorentz group) as the mathematical description of the kinematic structure of space (time), determines or reflects the inertial law as its basic dynamical law. In these theories, the kinematic structures have nothing to do with dynamics.
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