I met a traveller from an antique land,
Who said—“Two vast and trunkless legs of stone
Stand in the desert. . . . Near them, on the sand,
Half sunk a shattered visage lies, whose frown,
And wrinkled lip, and sneer of cold command,
Tell that its sculptor well those passions read
Which yet survive, stamped on these lifeless things,
The hand that mocked them, and the heart that fed;
And on the pedestal these words appear:
`My name is Ozymandias, King of Kings:
Look on my works, ye mighty, and despair!'
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare,
The lone and level sands stretch far away".
Percy Bysshe Shelley
Space is the absence of anything. It may be one-dimensional, as for example, the space between words in a sentence; two-dimensional, as with a bullet hole in a signboard; or three-dimensional, like a hole in a Swiss cheese. But so far as we know, space cannot be more than three-dimensional, which puts the skids under string theory that demands five, six ... ten, eleven, or is it 25 dimensions of space. Time, moreover, although sometimes referred to as the fourth dimension, is not a spatial dimension but an index of the successive stages in the evolution of events in space.
Multiple instances of planar space
Space, in other words, is everywhere that nothing else is. Thus, before the Big Bang, an observer with a flashlight would have seen that space was not only cold and dark but that, like the lone and level sands of Shelley's poem, it stretched far away, and indeed, if our observer's flashlight had been powerful enough, he would have seen that it stretched, boundless and bare, to the furthest corners of infinity (except that, with nothing to illuminate, the flashlight would have revealed nothing at all, not even the boundaries of infinity unless these were helpfully sign-posted).
End of infinite space ahead
More conventionally, space is where there is room to put stuff. My attic, for example, which is "empty," notwithstanding the air, the dust, perhaps a dead spider, a stream of photons through a ventilator, electromagnetic radiation from a wi-fi router, the local radio and TV stations, and nearby cell-phone towers, plus alpha particles from the decay of radon atoms diffusing through the house from the concrete basement walls, muons created by the impact of cosmic rays on the upper atmosphere, and other particles you can see for yourself with the aid of a simple, home-built cloud chamber (for details see here).
But even a light year or two from Earth, in what is known as deep space, there's still lots of stuff. Looking around, you would see a billion points of light, each a star in our own galaxy. Which means that for every star in the Milky Way, there is a stream of photons, both visible and invisible, that would pass an aperture as small as the pupil of your eye, wherever in space that aperture might be located. And there is much else beside. The microwave background radiation is everywhere, as is the gravitational field, the electromagnetic field, and the Higgs field, all vibrating, or pulsating, or whatever it is that fields do, in every infinitesimally small volume of "space."
But despite all that stuff occupying what would otherwise be pure space — stuff that exerts force, confers mass on elementary particles, transmits energy — space itself does not pulsate or curve or form a fabric interwoven with time. It remains, what it is by definition, the absence of anything. This conclusion may seem controversial. Does it not refute the theory of relativity, which implies, so some have argued, the existence of a four-dimensional space-time continuum, which is subject to gravitational curvature and bending? So one might think from the popular literature. For example, according to one exponent of science for the masses:
... things that slip out of your hand accelerate toward the floor because Earth's mass warps time.*Wow, bendy time! But what does that mean? To the lay person, nothing, obviously, which means that it is no explanation at all, which in turn means that we can dismiss it as twaddle without implying anything whatever about the theory of relativity. Relativity seems weird because its premises are weird. In particular, relativity takes light waves, which bend under the influence of gravity, to measure distance and to read distant clocks; and it takes natural processes, such as the oscillations of a quartz crystal, the rates of which are slowed by acceleration or by the presence of energy or mass, to date-stamp events. Relativity theory then assumes all clocks, wherever located, however they are moving, and by whomever they are read, to be correct. It further considers all light waves to be equivalent to the straight lines of plane geometry. Furthermore, relativity accepts the verifiable postulate of the constant velocity of light, constant in velocity, that is, without regard to the relative velocity of the source and the observer. Such peculiar premises have strange implications as the theory of relativity confirms, but the results computed by that theory are undoubtedly correct. Bravo. But that does not prove that either time or space are real, let alone that they form a unified fabric that bends and warps. For as Einstein acknowledged:*
We may have to give up, by principle, the space-time continuum. It is not unimaginable that human ingenuity will some day find methods which will make it possible to proceed along such a path."————
* George Musser in "Spooky Action at a Distance." Scientific American/Farrar, Straus and Giroux, New York, 2015.
CanSpeccy: The Nature of Physical Reality, Part I: Time