Expansion
of the Universe

 W
e are now in a position to examine the apparent expansion of the universe relative to the observer.  There is an expanding sphere radiating from each 'countable' point which encompasses 4 pi R^2 other countable units per unit time. Therefore, the point of origin of that expanding 'field' is itself encompassed 4 pi R^2 times per unit time by other expanding fields, and by the previous discussions, it must 'do something' to embody the fact of its having been counted. It may move, disappear/reappear, expand/contract, or rotate.

Let us consider movement.

It will move in some direction 4 pi R^2 times per unit time. (The fact that there are a few other possibilities does not alter this fact significantly since we will be dealing with orders of magnitude.)
Considering that it might move in any direction, the overall 'path' that the point takes will be 'folded up' 4 pi R^2 times per unit time. We have now a single question which determines whether we are building a possibly valid model of the universe.

What is the reaction velocity of the point? This will determine the size of the point as a finite 'object', i.e. after it is folded up we will obtain some basic unit of length.
Let us propose the following rule, the logical basis of which is given in the next href. Let the time required to traverse the present extent of the positional field (E) at reaction velocity (v) be equal to the time required to traverse the confinement (D) at unit velocity (c).
Here, the positional field is the total space encompassed by the expanding sphere; confinement is the reaction velocity folded up; and unit velocity is set at the obvious (light speed).

Then, E/v = D/c (see Theoretical Equivalence)

Since E = 2R and D = v / (4 pi R^2),

v = 8 pi R^3/2 ul/ut (Unit Lengths per Unit Time) and
D (in terms of R) = 1 / (2 pi R)^1/2 ul.

## This confinement corresponds roughly to the 'size' of the proton

(Compton wavelength) when the baryon number represents the current point count (~10^78), i.e. one baryon represents one integer (countable unit). The universe is then about 10^26 unit lengths in radius and 1 UL is about 1 meter, i.e. there is about 1 hydrogen atom per cubic meter of space on average.

The reaction velocity is then about 10^39 times faster than unit velocity (light speed).

Because confinement shrinks as a function of the R, there is an apparent expansion of the universe when confinement (D) is taken as the standard of measure.
Thus, if we take D, minus some incremental change (iD), as an unchanging standard length we must add a corresponding increment (iR) to R so that,

#1......(D-iD) / R = D / (R+iR)

The instantaneous rate of change of D with respect to R is, #2......d {1 / (2pi R)^1/2} / d R = -1 / (8 pi R^3)^1/2 ul/ut = -iD

Substituting the #2 value into #1, iR (the length apparently added to R, at a distance R, per unit time) is

#3......iR = R / (2R-1) ul/ut .

It can be seen that iR approaches a limit of 1/2 unit velocity. This means that an object seen at the edge of the observable universe, using the Compton wavelength of the proton as a baseline, would be seen to be receeding from the viewer at 1/2 the velocity of light. And this is the apparent limit to be reached by any receeding object, vis. an object receeding from an observer at c would appear to pass a marker one light year distant in two years because of the light travel time back to the observer.

Objects at points between the observer and the most distant object in the universe will show increased velocity in proportion to distance, i.e. from 0 to 1/2 ul/ut (apparent).

This apparent velocity (1/2 at R) is constant throughout the history of the universe except in the most initial stages when the total count is small and the recessional velocity approaches 1/2 ul/ut rapidly.

One empirical observation has its reason here:

### The age of the universe divided by the time required to traverse the confinement at unit velocity always approximates the square root of the baryon number.

```

``` ```
```  