Space is all in your head

You may remember [haha, no, of course not] when I dispensed with math as fictional [somewhere near the end of that rambling entry].

I had a similar epiphany about space and time. As one does. I mean I've known for a long time that space and time aren't what people naively assume they are, or even perceive they are. But it took some poking and prodding and internet tough guy arguing to really get a handle on it.

While conceding that space itself is not made of matter, someone was asking whether it was, nevertheless, a 'thing'. I was immediately leery of calling it a thing, but pressed on the issue ('how can nothing expand?') led to some deeper thinking.

Now the expansion of space is fraught with misunderstanding. All our standard analogies are really misleading: pennies taped to balloons, raisins in raisinbread dough. These treat space as though it really were a thing that stretched and expanded, carrying other things with it.

If you think that 'space streams' carry galaxies away on it, you're thinking of it wrong. If you think galaxies are pinned to space like they've been nailed into some stretchy jello, you're thinking of it wrong.

So what's right? What is space? What I ultimately came up with was:

"Space is, perhaps, our mental model of the world. We are betrayed by our senses into mapping objects into a three dimensional Euclidean space, and then implicitly reifying that model."

Temperature is modeled by a number that fits on a number line, but we are not tempted to reify that as a real physical dimension. It is only because distance behaves more or less like distance in Euclidean geometry that we assume that space is 'out there' for real, rather than just distance being a property shared between two objects, like the temperature difference between two objects. Well, not just that, it also seems to us in our perceptual visual field (or at least it does to me) like there's a three dimensional more-or-less-Euclidean space out there. Of course, all we really perceive are objects. We have no way of putting space-itself under the microscope, or look at it.

Anyway, so space is just a mental model and it isn't real. You all think I'm crazy. I think I'm crazy. My interlocutor thinks I'm crazy, and asks: "Would you say [space] has always been just a mental model? i.e. when Einstein first presented [GR], he had no intention of implying that space is a thing that actually bends and stretches?"

Oh crap, I'm in for it now. I'm a humble Physics lieutenant, and he's going over my head to the general.

Einstein thought a lot about the Problem of Space:

"It is characteristic of Newtonian physics that it has to ascribe independent and real existence to space and time ...

Newton himself and his most critical contemporaries felt it to be disturbing that one had to ascribe physical reality both to space itself as well as to its state of motion; but there was at that time no other alternative, if one wished to ascribe to mechanics a clear meaning.

It is indeed an exacting requirement to have to ascribe physical reality to space in general, and especially to empty space. ...

The psychological origin of the idea of space, or of the necessity for it, is far from being so obvious as it may appear to be on the basis of our customary habit of thought."

.......

On the basis of the general theory of relativity, on the other hand, space as opposed to "what fills space", which is dependent on the co-ordinates, has no separate existence. ...

Space-time does not claim existence on its own, but only as a structural quality of the field [i.e. the metric].

I honestly did not expect to find Al stating it so unambiguously. I'm not sure why it was so surprising to share the same view, since I had the advantage of standing on his shoulders, but it was still thrilling.