To begin with, let's take another look at these cloudlike images.

The fuzzy positions of the electron relative to the proton (or vice versa) in some stationary states of atomic hydrogen

You may be tempted to think of the black expanse as space. If this is indeed what you think, then you are not allowed to think of space as something that has parts — something that by itself is partitioned into smaller and smaller and smaller... regions.

Here is why. If these regions existed (or if the distinctions we make between them corresponded to something in the real world), then their boundaries would cut right through the electron's fuzzy position relative to the proton. As a result, the electron's fuzzy position would be divided into parts — one per "region of space" — and each part would have its own position.

But, clearly, this makes no sense. We may be able to divide a material object, and in the process produce as many positions as there are material parts, but we cannot divide a position — not even a fuzzy one. If the position of the electron appears to be "smeared out" over different "parts of space," this just means that these "different parts" correspond to nothing in the real world. They exist solely in our minds.

The bottom line: if we think of space as something that exists by itself (in philosophese: as a substantial expanse), then we are forced to think of it as undifferentiated; it lacks parts. In this case we are able to say, paradoxically yet to the point, that ultimately there is only one place, and that this is everywhere. Instead of separating things, space unites things by its utter lack of multiplicity.

But is it appropriate to think of space as a self-existent (that is, substantial) expanse?

Take (yet) another look at those cloudlike images. What you see in each image is a fuzzy relative position or spatial relation. The positions of material objects are possessed by pairs of objects. If space is made up of positions, it is made up of the positions of material objects relative to material objects. Another way of thinking of space, therefore, is as the totality of the spatial relations that exist between material objects.

If this is how we think of space, then the expanse we see in those images does not exist independently of the relations. It is a property — the property of spatial extension — and it is possessed by each spatial relation. Vanish the spatial relations, and the expanse that appears to contain them vanishes as well.

Which comes to saying that there is no such thing as empty space. Where the is nothing (no thing) there is no there.

The behavior of electrons in two-slit experiments leads to the same conclusions. Under the conditions stipulated by Rule B, the distinction between "through the left slit" and "through the right slit" is a distinction that the electron does not make, and the distinction between "electron through the left slit" and "electron through the right slit" is a distinction that Nature does not make. It follows that L and R cannot be intrinsic parts of space, and that space (qua expanse) cannot have any parts. The reason why an electron can pass through both slits as an undivided whole is that, as far as this electron is concerned, "both slits" exists as an undivided whole.