A Geometry for Outer Space

From Newton’s Principia, page 77 (pdf 83)

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, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes ; at another time it will be another part of the same, and so, absolutely understood, it will be perpetually mutable.

Newton made the assumption that space is immovable. But space is absence of matter, and it cannot be assigned such a characteristic as immovability. So there are no positions in space that are automatically fixed. The only thing fixed in space is a theoretical object of infinite mass. The fixity of the location of any other object shall be proportional to its mass (see Motion & Force).

So earth, moon and sun have locations in space with uncertainties attached to them according to their fixity. We may project abstract positions using these locations, such as, a position half-way between the earth and the moon. A projected position shall have uncertainty depending on the actual reference locations.

The location of an abstract position far from any mass shall be totally uncertain. This gives us a new non-Euclidean geometry.

This subject may be called “space geometry”. The uniform absolute speed of a body shall determine the uncertainty associated with its location in space geometry. The distance between two locations shall be determined by the difference in the uncertainties of those locations. Two locations with similar uncertainties shall be at equal distance from the location to no uncertainty.

The gravitational field around a body shall be defined by increasing uncertainties of positions around it.

This geometry shall be based on a universal constant that establishes the absolute motion of a body and the uncertainty of its location. The absolute velocity and mass of a body, or a system, may change but the absolute motion of the body, or the system, shall remain constant.

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