Dear Daryl
You said: people accepted it for centuries...
I don't think so, most people (including Newton himself) knew that totally empty space was an absurdity, but we have to understand the reason why Newton left space totally empty in his theory. Newton mostly agreed with Descartes' view of space. For Newton space was a substance and the medium that convey gravity between celestial bodies was the aether, but he realized that Descartes' view was so complicated to put it in mathematical terms that he decided to leave space in his theory as an empty container. As we all know, the empty container view of space is mathematically represented by Euclidean space. This is space, as we all know, has no substantial or material properties per se and the same occurs with any other geometrical space (you should check Riemann's original paper on this subject). The view that space was an empty container was always seen as an anomaly of Newton's theory but the anomaly remained for centuries because that was the only game in town since nobody could come up with a better formulation of space until Minkowski arrived in 1908. Similar to Euclidean space, Minkowski space-time represented emptiness although its metrical properties are certainly different (the discussion of Minkowski space-time as a real space is still a hot topic among the philosophers of science and some physicists, Veselin Pektov is one of the advocates of the physical existence of Minkowski space-time). When the aether was rejected in 1905, Einstein left space again totally empty, just as in Newton's theory. According to Newton's theory celestial bodies were interacting at a distance in totally empty space, which for Newton himself was an absurdity. At this point, it is convenient to quote Newton's opinion about this topic, I'd like to show you that he was basically following Descartes' view. The quote was taken from one of his letters sent to Bentley in 1692:
It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter, without mutual contact, as it must do if gravitation in the sense of Epicurus be essential and inherent in it. And this is one reason why I desired you would not ascribe 'innate gravity' to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
So, as we all know, the discovery of Minkowski space-time didn't and doesn't solve the problem of how celestial bodies interact. Minkoswki space-time continues to be an empty container. At first, Einstein disliked Minkowski's formulation but later he recognized its scientific value. He realized that treating inertial frames in terms of space-time could be useful to extend his SR to non-inertial frames. Since, it is assumed that GR is an extension of SR, at some point the metrics in GR should reduce to the Minkowskian metric. He then argued that the Minkowskian metric is a special case of the general case g_ik where the gravitational potentials are contained. Einstein said that even if the energy-momentum tensor were zero, we still have the gravitational potentials contained in the metric tensor which at the end gives meaning to space. Minkowski metric, is then a special kind of gravitational potential with constant coefficients. According to Einstein, empty space is inconceivable, for him the g_ik tensor gives physical meaning to space, this object in Einstein view is the new "aether". But we should not mix the concepts, this is the metric of space not space itself. In Newton's theory the mathematical object that represents the notion of physical space is the Euclidean manifold not its metric. Similarly, in GR what represents space-time is not the g_ik but the pseudo-Riemannian manifold. And a manifold has no intrinsic material or substantial properties associated with it. In GR, space is not a medium as Descartes' aether was. Space-time is still a container with metrical properties defined by its material content but the manifold itself doesn't represent a substance.
Now, Einstein said that g_ik is the fundamental field, but what is a field made of? If we ask this question to Maxwell, he would certainly reply that an electromagnetic field is a state of a material medium, in his time, such medium was the aether which filled the empty space. I must make clear that I don't follow this dichotomy, for me aether and space are the same thing, therefore, a field is a state of space, understanding space as a material substance and so one can say that space is a material field. The fact that the permeability and permittivity of the vacuum are not zero tells us that the vacuum behaves as a paramagnetic medium and only material substances have these electromagnetic properties. If space were Minkowskian these properties would be zero. In contrast, for Einstein, an electromagnetic field is a different entity from space, is a physical reality that fills and propagates through space. And for him the properties of space itself are defined by the metric tensor that gets its "substantiality" from the gravitational potentials. But again, this is not a medium in the sense of Descartes, Newton or Maxwell because a medium is material and has no curvature. It is absurd to talk of a curvature of a medium, that term only makes sense only for geometrical spaces (manifolds). I hope I had made clear why I don't follow the notion of geometrical space-time. I have read your discussion with John and I support's John's view. I think you are getting it in the wrong direction.
Best regards
Israel
