For something to exist it must, hypothetically, in some way, either directly or indirectly, affect us. Or if it possibly exists then its existence would have to imply that it might possibly affect you. Otherwise its existence has no meaning because, with no possible way to be affected by it even in principle, it has no properties. Such is the case with space. It can’t be seen, felt, heard, touched, or tasted, and it can’t in itself affect anything, even in principle. It’s not a causal agent, it’s not a part of our universal matrix of cause and effect. You can’t measure it itself with any scientific instrument. I wrote more about why something must be able to affect you in order to be said to exist here, and also in a couple of other essays in this blog.
Surely you can measure distances, but distances are no less abstract than any other subtracted difference between values. Position can be accounted for as a property belonging to material objects, and distances are merely the differences between those properties’ values. A part of empty space is just the potential for an object to exist with a particular position-property that doesn’t currently exist. It’s just the lack of something. It’s analogous to a shadow, a hole, or the concept of “nothing,” is that it’s easy to think of it as something that exists, but technically it doesn’t.
Yes, materiality behaves in a way as to make it intuitive/obvious/useful to see distances as very real things, and to see space as an extant container, but metaphysically distance and space are superfluous as real things. This has to be true because there is no possible way, even in theory, that you can interact with, affect or be affected by or measure space in itself. You take measurements of actual objects, and based on the differences in those measurements you can abstract space. Because you can’t do anything more than that even in principle, the existence of physical objects makes space superfluous. Consider Occam’s razor. Space is merely our way of conceptualizing an aspect of nature’s mechanism by which objects affect each other with respect to their individual position-properties.
It’s not as if space would not be superfluous if there were no matter; on the contrary, if there were no matter, if you were a bodiless point of perception “in the center of the universe” and there were no matter anywhere to be seen, you would never dream up such a concept as space. The concept would have no application. You would not see space; if you had the sense organs of a human, you would simply be seeing black.
“But,” you might argue, “The theory of relativity indicates that space-time is curved; and if it’s curved, and especially if can even detect that it’s curved, then it must be real.” No, all it really shows is that mass/energy interacts with other, remote mass/energy in a way described by the relativistic equations. The equations are such that it is convenient to think of the process as involving curved space-time, but that is only an interpretation; space itself is not being measured and used as a point of data input for the formulae, and if you tried to measure space itself you would, by logically necessity, actually be measuring the atomic movements, electrical impulses, etc. within your measuring device, because there is no action/reaction feedback loop between your measuring device and “space.” There can’t be, because if there were, it wouldn’t be space, it would be an local, invisible entity, because space, being the concept of locality itself (more or less; maybe the concept of a universal container?), has no local behavior, and if the matter in your measuring device indicating something extant behaves the same way at all points “in space” then we’d understand that that simply a property of matter itself.
Also, Einstein himself didn’t even come up with the idea that space-time is curved as a part of the theory of relativity. Minkowski did, and Einstein originally called the idea “superfluous erudition.” See EINSTEIN DIDN’T SAY THAT! – Quantum Field Theory and Paul Mainwood’s answer to What is spacetime? What did Einstein mean when he said it was curved?. In fact, Einstein also said, in “On the generalized theory of gravitation,” ”According to general relativity, the concept of space detached from any physical content does not exist.” And he said, in notes on the fifteenth edition of Relativity, “Physical objects are not in space, but these objects are spatially extended. In this way the concept ’empty space’ loses its meaning.”
However, does it suggest something about metaphysics that the theory of relativity is made simpler by imagining space-time as curved? Maybe, but I know that to imagine empty space is to imagine nothing except for specific possibilities involving movement, so whatever it suggests about metaphysics, it’s not that space exists as a thing-in-itself.
The question then arises, “If space does not exist, what causes matter to behave in the way it does: to have the properties of locality, to interact in three dimensions of motion, etc.—basically, to act in such a way that it behooves us to think in terms of there being space?”, and the answer is as it has always been: “We don’t know.” We don’t know anything about why matter/energy behaves in the way it does on the lowest levels. We’ve struggled just to make models to predict it, let alone explain it and why it has the fundamental properties it does. My observation that space does not exist doesn’t change the fact that we don’t know and have never known what all this means metaphysically; it only sheds new light on the question. Not that the point of this essay is to shed new light on our metaphysical questions, the point is only that it’s illogical to think of space as having its own existence.
Note, by the way, that we can now say that the answer to the age-old question, “Does space extend outward infinitely?” is “No, but it extends outward indefinitely,” because it doesn’t really extend in itself, being in-itself non-existent, but it’s true we that may, theoretically, send any physical object outward as far from the rest of the universe as we could imagine.