Unit Measure

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e have then a ray containing 'countable points' with a probability of finding a point in any 'unit' distance fixed at 1/2 (it is or is not there). To embody the act of counting some sort of marker must travel along the ray encompassing point after point

This marker must, by definition, travel at Unit Velocity.

Clearly, without an external absolute standard of measure, there is no way to keep time or measure distance with respect to the marker because increasing speed is equivalent to shortening the unit length. While making a longer unit length would be the same as slowing unit velocity.

Therefore, space and time must be made functions of one another in this manner:
Where space is shorter, the marker slows to maintain a 'spacetime unit' of measure. Where the unit length is longer, unit velocity is faster.

Now, since the countable points are laid out in a probabilistic manner, three concepts will figure into any 'unit' system of measurement: (F) length (F) time (F) probability = 1 unit of measure (to be used in the derivation of Planck's constant).Planck's Constant
Thus, if a countable point is missing by way of probability, in a unit length, it is equivalent to a faster marker speed or longer unit length.

For convenience in what follows, we will consider a double unit length as one unit so that we will have an expectation of 1 countable point per this new unit length.

In section 7 I showed that three dimensions would be required (one for the quantitive aspect of reality and two dimensions for its quality).
The 'marker' in 3D is an expanding sphere which proceeds outward from a point source encompassing (counting) other points in the manifold. By the previous reasoning there will be an expectation of one countable point per unit volume (doubled) in the space through which the marker travels.

Therefore, the marker, travelling outward at unit velocity, will encompass 4 pi R^2 countable points per unit time and will have encompassed 4/3 pi R^3 countable points at any given time (where R is the radius of the present manifold in unit lengths).




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