Modern physics began with Isaac Newton, and it was Newton's time where a handful of epistemic shifts took place. In this particular post I will be concentrating on the philosophical shift that took place regarding the ontology of phase-space diagrams.
At the time of Descartes, we see the beginnings of people making little or no distinction between mathematics and the real world.
(I link this only to give examples of arguments of area versus length, and the "impossibility" of x^4 https://en.wikipedia.org/wiki/Ren%C3%A9 ... cal_legacy )
Throw a baseball straight upwards and then catch it again. You can graph the height of the baseball against time, giving a phase space diagram, which looks like a curve on the graph paper. Common sense would tell you that this curve is not real. It is merely the collection of positions occupied by the baseball at certain time slices, collated together onto a graph paper, with no deeper meaning than that. You draw a line between these moments and a curve results, incidentally. This curve is "surely" not real.
It was Newton who began to say that these curves are physically real. Newton began to reason geometrically about these curves as if they were geometric objects themselves of their own right -- (not mere "collections of moments"). In a funny sense, Newton was faced with a question, "Do these phase space diagrams commit to an ontology?" Newton's answer was unambiguous, "Yes they do". This broke with all common sense, but the calculus and the physics that resulted from this craziness, gave rise to the scientific and industrial revolutions of Europe.
This foundational cornerstone, (the idea that phase space diagrams are real, and not just "collection of moments") dominated all thinking in physics all the way up until the 1920s, where only radical versions of quantum theory really split from it in any serious manner.
General Relativity was first published by Einstein in 1915. It represents the highest historical apotheosis of the Phase-space-diagrammatic ontology. This idea had been built into physics from the start and had only become more entrenched as the centuries passed. As you will see, our modern parlance about gravity, space, the cosmos, and whatnot have borrowed heavily from Einstein's notions of spacetime. Even in modern science fiction, you will see the characters talk as if spacetime were a substance and not just a "phase space diagram on a chalkboard" !
You may even see people on this very forum (!) talk about spacetime as an object of its own ontological status .. not merely a mathematical collection of moments. People speaking in these terms are committing to the same ontology that Newton did with his diagrammatic curves of objects undergoing forces in time.
What follows will be obvious to the reader, but it must be said to frame the discussion correctly and succinctly express the idea. "Spacetime" is the notion that there is a 4-dimensional stretched-out snakelike tube of an object corresponding to that object passing through space. Imagine a minivan passing by on a road. Spacetime is the minivan stretched like a snake over the entire course of its passage over many minutes. The subtle mental trick is that the stretched-out minivan is not stretched in three dimensions, it is stretched out over four dimensions. The minivan is not stretched "down the road" in our regular three-dimensional space. Rather a 3D minivan is stretched into a 4D spacetime. From now on, refer to this stretched out snake in four dimensions as a "4D manifold".
General Relativity says that there is a timeless 4D manifold which sits, timelessly as a singular object. The shape ("curvature") of this manifold is determined by the locations of masses within it. General Relativity says nothing but this. Everything else you may have heard about it is an extrapolation of this claim. This timeless manifold does not stretch and curve through time like putty. It is a timeless, solid object whose shape is absolutely determined at every point. Most people cannot visualize in their mind what it "looks like" for a 4D manifold to have a curved shape, and neither can I. But we can play along since the math works out quite well on paper.
(To aid visualization, consider the very early video game called Pong. The ball bounced on a 2D screen. Now stretch out the screen into 3 dimensions, where the 3rd dimension is time. The ball, which was formerly a circle, is now a three dimensional tube through this 3D diagram).
It is this timelessness which is the key characteristic of physics from Newton to Einstein. For Newton, there was no apple, only a curve of the apple's trajectory through time. For Einstein, there is no universe, only a 4D manifold frozen forever, curved by 3D masses embedded within it.
In regards to this thing we all call time in our regular lives, Einstein replied,
There is no "now" in a phase space diagram, and there is no "now" in a frozen 4D manifold. There is no time at all. It is here that I hope the reader will be feeling the pangs of Scientific Recoil --- that sinking feeling in the stomach that this theory can't be true because all of everything you ever knew and loved is being turned upside down and dashed to pieces on the floor. Your whole life is a smear on a gigantic curved 4D canvas. Sitting there motionless like a super cosmic painting awaiting some 5-dimensional art critic to come along and gawk at it.Confirming the existence of a present moment is just outside the boundaries of science.
Is the cosmos some frozen four-dimensional "chunk" suspended motionless in a timeless reality? Or is spacetime a mere mathematical tool to aid in the quantification of gravity and its effects? A mere bunch of helpful symbols on a chalkboard? If you have kept up with this post long enough then you know what is at stake here. And if you have followed the above words, then you understand this next question perfectly:
Does General Relativity commit to an ontology?