Thinking about what I have learned about GR I think I find it mentally useful to think of spacetime as a kind of aether. Thinking about it this way helps to emphasise that spacetime is a ‘real thing’ and not just ‘space’ (in the non-technical meaning of the word ‘space’).
The word ‘aether’ is not in vogue, I suppose because everyone knows that Einstein showed that Lorentz’s aether was an unnecessary postulate about 100 years ago. I have also noticed that Lorentz Ether Theory is the bette noire of the forums, no doubt with good reason. But if we can get beyond the allergy to this word it seems to me that the general idea of an aether gives the right general mental picture of something real which things can be measured against to determine invariant proper acceleration and the various invariant quantities we associate with rotation. Of course this GR aether is not the same as that envisaged by Lorentz – it is four dimensional and has a geometry determined by the distribution of mass and energy.
Do you think this is a reasonable way of looking at it?The idea of thinking about spacetime as an aether was suggested to me by Einstein’s writings. He gave a speech in 1920 entitled Ether and the Theory of Relativity which is here
https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity an extract of which follows:
“Certainly, from the standpoint of the special theory of relativity, the ether hypothesis appears at first to be an empty hypothesis. In the equations of the electromagnetic field there occur, in addition to the densities of the electric charge, only the intensities of the field. The career of electromagnetic processes
in vacua appears to be completely determined by these equations, uninfluenced by other physical quantities. The electromagnetic fields appear as ultimate, irreducible realities, and at first it seems superfluous to postulate a homogeneous, isotropic ether-medium, and to envisage electromagnetic fields as states of this medium.
But on the other hand there is a weighty argument to be adduced in favour of the ether hypothesis. To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. For the mechanical behaviour of a corporeal system hovering freely in empty space depends not only on relative positions (distances) and relative velocities, but also on its state of rotation, which physically may be taken as a characteristic not appertaining to the system in itself. In order to be able to look upon the rotation of the system, at least formally, as something real, Newton objectivises space. Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space "Ether"; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real.
The ether of the general theory of relativity is a medium which is itself devoid of
all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events...
What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same...
Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.”