# Newton's Space

### Peter Oye Sagay

The great Isaac Newton (A.D. 1642-1727. Born in Woolsthorpe, England) gave the world some of the most productive and foundational concepts in mathematics and science: the laws of gravitation and motion, the establishment of modern optics, calculus, the concept of field, etc. Newton's philosophical thought on Space and Time as he presented them in his great treatise, The Principia is our focus here. In particular, his notion of absolute motion and absolute rest.

How can Space and Time be absolute amidst modern relativism? To answer this question we must first acquaint ourselves with the following commentary on Space and Time as presented by Newton in his " Principia":

I. "Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year."
II. "Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneous, an aereal, a celestial space, determined by its position in respect of the earth."

Next we note the following definitions by Newton:
Place: a part of space which a body takes up.
Absolute Motion: the translation of a body from one absolute space into another.
Relative Motion : the translation of a body from one relative place into another.
Absolute Rest : the continuance of a body in a part of immovable space.

The conceptualization of Newton's absolute space in a dynamic Universe requires a fundamental understanding of the residency property of matter. In other words, matter always resides in a container. This requirement of matter is the reason for the containership property of space. The physical Universe is a collective of matter, consequently, it resides in a container. This container may not be the Ultimate Container. In other words, the container that contains the Universe may itself reside in another container and so on.

Whatever the case, It is reasonable to conjecture that an Ultimate Container with infinite non-expandable boundaries exists. It is the space inside this Ultimate Container that is Absolute Space and which Newton defined as "always similar and immovable." Relative space is the space inside any container that is contained in Absolute Space. This implies that for any relative space, there is an equivalent absolute space and to the extent that motion is the translation of a body from one place to another, a relative motion has associated with it an absolute motion.

Imagine a swimming pool with water in it. Suppose at time t1 a ball is set in motion from position p1 and at time t2, the ball is at p2. Definitely a relative motion has occurred in the water. Relative motions have also occurred in the swimming pool that contains the water, the ground that contains the swimming pool, the Earth that contains the ground and so on. If it were possible to exhaustively enumerate these relative motions, we would eventually expose the absolute places p1a and p2a in absolute space that correspond to the positions p1 and p2 respectively, in the water in the swimming pool. Unfortunately, it is not yet possible for humans to actually carry out this type of enumeration. Nonetheless, we can intuitively, philosophically and deductively assert that relative places are ultimately contained in absolute spaces. As a result, every relative motion has associated with it, an absolute motion.

Neither absolute space nor the motions in it are self-evident. Newton was aware of this difficulty when he wrote: "But because the parts of space can not be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them... 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 themselves, distinct from what are only sensible measures of them ."

Newton explained absolute rest as follows:
"In a ship under sail, the relative space of a body is that part of the ship which the body possesses; or that part of its cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved ."
This absolute rest in Newton's explanation, I call Transient Absolute Rest (TAR). It is transient because of the continual motion of the Earth.

It is the containership property of Absolute Space that makes Absolute Time, all relative spaces and the motions in them, possible.

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