Positional Field

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he positional field is that field which measures the distance and direction to any other distinct unit or position, vis. you point to an object and say "It is one mile away to the east". Such a field is no more nor less "real" than any other logical construct in accordance with the fundamental postulate of this work, i.e. that the universe is the geometric embodiment of logic ... the thing itself.

Here is the positional field and its action.
(please excuse minor drawing errors)

As you can see the outside circle, representing the positional field at some distance, is initially unmoved when the field center changes position. This is required if the transmission velocity of the "notice of movement" is less than instantaneous. Clearly parts of the field more distant must wait to be notified of movement at center for a longer time than parts of the field which are closer to the center.

The field is then stretched and compressed into ellipsoidal shapes during the time of acceleration.

After acceleration, the field catches up to the center and everything proceeds as the former spherical unit (with the understanding that the field may be of any finite size).


The center of the positional field is the existential unit (the thing counted). It is active in that it responds to notification of the existence of other units by moving, rotating, etc.

The locus of its activity remains near the center of its own field because that field determines the definition of a straight line. If the positional field becomes warped (as in acceleration) the locus of action will also be warped in like manner. Thus, if the field is bent to one side, the center (particle) will move in that direction following its own general field lines. Or more exactly,

The central unit "self-interacts" with its own field.

The field center, moving in response to some as yet to be determined influence, is accelerated in a specific direction. It compresses (warps) its own field and in the process sets up a "self-resistance" to further motion which we call inertia.


The positional also rotates as the embodiment of absolute time (just as the isotropic field embodies absolute space by means of the unit length).

It does so as a unit to avoid being "wound up" like a spring. This requires that the direction of rotation be sent through the positional field at a velocity (presently) about 1039 times greater than light velocity, i.e. the notification of rotation reaches the Hubble radius in about 10-23 seconds.

The direction of rotation is at right angles to the direction of motion when the central unit moves in response to the "appearance" of another unit (presently about 1065 new units per second.


The rotation is at right angles to the direction of motion such that a "handedness" is displayed when the object is in motion relative to an 'observer'. Thus, each time that a new unit comes into existence relative to another, that other moves and the motion is concurrent with a rotation. Since the "reaction motion" may be in any direction, there is not net rotation observed. Rather, net motion in some direction relative to an observer allows that observer to detect the "extra" motions which allowed the observed unit to change position, vis. if there were equal motions in every direction (as a response to the appearance of new units) there would be no net relative movement.


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