100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

6 J. StachelFig. 2respectively. Furthermore, Newtonian gravitation theory is considered in itsmodern, four-dimensional formulation, which takes into account the equivalenceprinciple (see Sec. 11); I have adopted the name for this formulationof Newtonian theory introduced by Jürgen Ehlers – General Non-Relativity— which contrasts nicely with General Relativity. But the name should notbe taken to imply that the theory has no relativity (i.e., no symmetry groupof the space-time): indeed, the chronogeometry of this class of space-timesis invariant under a wider group than that of Galilei-Newtonian space-time,as discussed in Secs. 5 and 8.The upper right-hand corner of the cube, Quantum Gravity, also callsfor further comment. It is not the name of an already-existing theory, butrather of a hope: The goal of much current research in theoretical physics isto find a theoretical framework wide enough to encompass (in some sense)both classical general relativity and (special-relativistic) quantum field theory.Unfortunately, in the current state of this subject, the edges of the cubedo not commute (see Figs. 3, 4). Starting from quantum field theory on theroad to quantum gravity and attempting to incorporate the Newtonian constantG, most particle physicists believe that one will arrive at some versionI Figure 2