I don't assume that I'm an expert on any of this, so if there are pertinent mistakes in what is written, please correct me. The idea of these posts is simply to give a very rough and very shoddy idea of non-existential Space and Time (for existential notions we've really got to deal with Heidegger, Foucault et al). Hopefully these entries will be short enough to deal with in one sitting but give a general idea of the discourse conducted over the last few centuries. If it isn't working, or you think this kind of thing is redundent, please, let me know.

Okay...

Part I

By the seventeenth century, it was already understood that velocity (the rate of motion in a specific direction: distance divided by time) was a relative concept. From your perspective the hot-air ballon is drifting by, but from the ballon’s perspective, you are going by and both are equally valid points of view. Velocity, then, can only be specified in relation to another object. We all move in relation to other things. It was also understood that velocity, if it is constant, generally goes unfelt but if there’s a sudden change in speed / direction then there is acceleration and acceleration is felt.

Newton’s Absolutism

Newton was one of the first to ask himself what are the meanings of these concepts we've just been using such as velocity, motion and what do they refer to?

To try and answer these questions he came up with a rather profound thought experiment. Imagine there’s a bucket of water and the water is still, and yet as the bucket begins to spin the water’s surface becomes concave and remains so even as the spinning bucket slows and stops. But why is this so? Why does spinning water take this shape?

That’s easy: because it is spinning, water is somehow pressed against the side of the bucket.

But what does spinning mean? Spinning with respect to what?

1. The bucket? No, because when there is relative motion, the water starts out as flat, becomes concave and when the bucket stops spinning the water continues to spin. So the bucket cannot be the reference for the motion of water.
   

1. The stuff around us, space? Well let’s take the imaginary bucket out to space, what then would serve as the reference, the something with respect to which the water is spinning? Well, for Newton, here lay the answer. If it wasn’t the bucket it had to be Absolute Space. Absolute Space was the reference. When an object is at rest or in motion, accelerating or constant, it is so with reference always to Absolute Space.
   

But what is Absolute Space? For Newton it was god-like: eternal, permanent and unchangeable.

Leibniz’s Relationism

Newton’s contemporary, Leibniz declared that all this talk of some god-like Absolute Space was nonsense. He asked himself, if Newton is right where is the universe within his Absolute Space and how are we going to know whether that given answer is true or not if we are unable to detect space or changes within it without access to objects? Indeed, how can we say space even exists without implicitly referring to other things?

Unable to find significant answers to these questions, Leibniz declared that space simply did not exist. Without objects space has no independent meaning or existence. Space is merely a useful language term used to indicate where things are in relative position and movement to each other. Space, in other words, has no meaning beyond providing a semiotic sign for discussing the relationship between things.

Mach’s Relationism

Mach raised another interesting question: why in Newton’s theory was velocity relative to another object whereas acceleration was fixed to an unmoving absolute? Might it be that Newton was mistaken and acceleration was also relative?

Imagine you’re floating in the skies; if you begin to spin the distant earth will no longer appear stationary. You will feel a force on your body and you will witness motion. But if you’re in absolute empty space, Mach argued, and you start spinning you are not going to feel any force on your body and you won’t have any distant object to reference your motion. Thus, how are you able to know whether you are spinning or not?

It follows that Leibniz was on to something. In absolute empty space there will be no conception of velocity or acceleration because there will be no reference to your motions. In empty space motionlessness and spinning will be indistinguishable. So, if there is no notion of movement in empty space, there cannot be any justification for Newton’s absolute space.

But we’re still left with a problem: how can we explain the bucket’s water shape if we throw out Absolute Space?

The solution was that if in empty space there was no concept of spinning or non-spinning, then in our universe, a universe with matter, the force of motion, velocity and acceleration will be relative or proportional to the amount of matter/mass in the universe. The force felt by acceleration, for example, arises simply due to the influence of all the matter in the cosmos. The more matter there is, the more force you will experience.

Thus, Mach’s universe is the universe of Leibniz. Velocity and acceleration are relative terms and space does not enjoy some independent, god-like existence but is relative only to matter in the universe.

And here the story will rest until Part II when Einstein will come along and radically transform both the absolutists’ and relationists’ centuries old arguments and critique.