For philosophers of space and time, Newton’s Scholium is the Old Testament. Even after Einstein revealed the New Testament of relativity theory, the deep framework of Newton’s vision remains basic to all of physics. It was Newton who made the key terms “relative” and “absolute” central to classical theories of space and time. The word “absolute” means “independent” in the sense that a thing is absolute when it does not depend on other things, is free from interference and makes itself what it is (“to absolve” means “to set free”). A king has absolute power when he exercises it himself, independently of a constitution, legislature or foreign allies.

Invariance is, here, a property of appearances. If all measurements of a spacetime interval yield the same result, then the observed interval is invariant. For Newton, “absolute” is a metaphysical term, and describes the reality behind appearances. A thing is absolute when it exists in its own right, when no other thing can alter it.

Newton began the Scholium with a definition of absolute time:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration; relative, apparent, and common time, is some sensible and external measure of duration . . .

Newton’s metaphor here is very important. He says that time “flows”, perhaps as a river does. He further asserts that the passage of time has a constant “speed”, that is, that it flows “equably” and uniformly. This seems reassuring, but is also very puzzling. A river flows past its banks. What does time flow past? The speed of a water flow can be measured in units of, say, kilometres per hour. At what speed does time flow? One hour per hour? Newton does not answer these questions.

For Newton, a “relative space” depends on something else. The hold of a ship is an enclosed volume that moves with the ship and depends on it, and is thus merely a relative space. By contrast, Newton thought that empty outer space did not depend on anything,and was therefore an “absolute” space. Relative spaces can move; absolute spaces are immobile:
Absolute space . . . remains always the same and immovable. Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to other bodies . . . Absolute and relative spaces are the same in shape and size; but they do not remain always one and the same. For if the earth, for instance, moves, a space of our air . . . will at one time be one part of the absolute space, and at another time it will be another part of the same. And so, absolutely understood, it will be continually changed.
Thus a relative space is part of absolute space. But if the boundaries of the relative space move, then the relative space moves with them. An absolute space is not dependent on anything. 

Bodies move in space from one place to another, that is, from one part of space to another. But because there are two kinds of spaces, there are two kinds of motions. In a key paragraph, Newton says:
Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship or the hold which the body fills, and which therefore moves with the ship. But real, absolute rest is the continuance of the body in the same part of immovable, absolute space.

This can be a bit tricky. All motion is in or through or towards or away from something else. All motion is relative to something. Thus absolute motion is actually a kind of relative motion. Absolute motion is motion relative to absolute space.  

Newton loudly takes a stand in the Scholium that was at odds with his old reputation. He was often hailed as the father of strict empiricism. This philosophy insists on limiting research to what can be observed and measured. Thus empiricists refuse to investigate God or angels, what makes a poem beautiful or what happened before the beginning of the universe. These are not open to observation and measurement and therefore, they say, should not be part of science.

Modern empiricism has been so enormously fruitful that its advocates sometimes pushed the idea to an extreme. They rejected discussion of anything that could not be directly observed, and attacked those philosophers who championed conceptual or linguistic investigations. In these controversies, Newton was used as an emblem of strict empiricism, as a scientist whose great discoveries stemmed from his adoption of empiricism. This image is, of course, completely outdated now. What is peculiar is that even Newton’s published papers proclaimed that he was a moderate empiricist. He made a great contribution by emphasizing observation and measurement, and even constructed his own telescopes and other instruments. But Newton thought of himself as a philosopher and also balanced his empiricism with a sense of its limitations.

The Scholium contains a passage in which Newton suggests that science must go beyond what can be directly observed, must go beyond strict empiricism:
But because the parts of absolute space cannot be seen, or distinguished from one another by our senses, we use sensible measures of them. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things in themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.
Those who confound real quantities with their relations and sensible measures defile the purity of mathematical and philosophical truths. Relative spaces are directly observable because their boundaries are (the ship); absolute spaces are not. Relative spaces appear to us;
absolute spaces are the reality behind the appearances. Newton emphasizes that his science cannot be limited to what is directly observable because that would exclude absolute space. Readers of Kant will recognize his distinction between phenomena and noumena: between appearances and things-in-themselves. Early in his career, Kant was a vigorous Newtonian and defender of absolute space, as we shall see.

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