Matter, spacetime and the vacuum.

We distinguish three historical and scientific views of matter, spacetime, and the relationship between them: the absolute approach of Newton, the relational approach most often associated with Mach, and a third, geometrical approach which inspired Einstein and continues to drive efforts toward a unified theory of fundamental interactions today. Which is correct? We suggest that this is, to a large extent, an "ill-posed question," reminiscent of the wave/particle debate in earlier times. The boundary between matter and spacetime is no longer easy to draw, and it is likely that they are complementary aspects of the same reality. There is no clearer illustration of this than the modern view of the vacuum. We review the importance of this concept in cosmology, and explore the extent to which the old idea of an "empty" vacuum might still be maintained. If the real cosmological vacuum is far from empty, as observations now suggest, then it may be possible to achieve an even simpler goal: a Universe with a net energy of zero.