Derivation of the Ratios of Time Formulas
The derivation of the formulas describing the uniform expansion of spacetime was originally posted in this thread My (Discovered) Unified Field Theory . I have neatened a few things up for repeating them here but I do not wish the comments and analysis of others who have already reviewed the formulas to be ignored since the comments and insight they provided was good and they helped me to improve or make clearer this explanation.

The basic geometry

Nomenclature
Relative measures of time and distance are written with lower case letters. Absolute measures are capitalized. When a letter is followed by a 1 or 2, such as T1 or T2, this establishes which measure is earlier and which is later respectively.

Before delving into the details the result can be simply stated. A volume of spacetime varies to the square of the absolute time elapsed. If you double the age of the universe, the absolute volume enclosed increased 4 times. Simple but tricky. There will be no local indication of the increase in size since all local relative measures of distance have similarly expanded.

The initial idea.
One day I realized that if nothing ever changed, time would not exist. Stated in the positive I thought; “Because space changes, time exists”. This led to the following equations.

S = Volume of Spacetime
T = Absolute time

dS/dT = T, Because space changes, time exits.

Integrating this relationship yields, in its simplest form,

S == T^2

(The == notation can be considered as meaning “proportional to”, but the relationship is more analogous to the relationship described by the speed of light, a relationship between distance and time).

The volume of any object is a distance measure cubed, times some constant,

D^3 x k = S = A Volume of spacetime.

Combining the relationships results in the following

D^3 = k T^2[/b]

Note; this is the exact form of Kepler’s Third Law. This is not a coincidence; the theoretical model truly produces Kepler’s law. It will be shown that this is indeed the relationship predicting the inverse square law required for celestial stability and the principle of conservation of momentum. Kepler’s law, which was experimentally established, is now theoretically predicted from a geometric model. Epistemologically, the relationship proposed, (dS/dT = T ), is as important a relationship as E= mcc, or e = hv

Rewriting the above equation we get

D = k T^(2/3)

Taking the first derivative with respect to absolute time we get how the absolute velocity will vary for two points in spacetime

V = k (2/3) / T^1/3

Similarly for Acceleration we get

A = (-k 2/9)/T^(4/3)

We do not know the value for k but since this is a geometrically described rate of expansion, it is possible to state that at a particular time, T1, points in spacetime are a particular distance D1. Similarly at another later time, T2, the objects are at location D2. Dividing the two relationships by each other eliminates the constants resulting in

D1/D2 = (T1/T2)^(2/3)

Similarly for Velocity and Acceleration we get

V2/V1 =(T1/T2)^(1/3)
A2/A1 = (T1/T2)^(4/3)

These formulas are actually field formulas in that they describe, in absolute measures, the properties of an object when associated with a point in free space. (Free space means that no other unaccounted force is acting.)

The Ratios of Time
(Capitol letters indicate “absolute measures”, 1 and 2 are earlier and later measures respectively)
D1/D2 == (T1/T2)^(2/3)
V2/V1 == (T1/T2)^(1/3)
A2/A1 == (T1/T2)^(4/3)
E2/E1 == (T1/T2)^(2/3)

E = energy, which for now can be considered just the square of the velocity term but this relationship is valid for all forms of energy in which spatial relationships are involved.

(Nuclear energy appears to be a partial exception to these relationships of expansion. It seems that at the nucleus, the expansion of spacetime does stop; nuclear relationships involve measures that are essentially fixed in size. This is discussed in more detail in the paper on Type 1a supernovas).

Physical Explanation
The physical relationships that the Ratios of Time formulas describe need some explanation. The basic derivation of the formulas was based on considering a small discrete volume of spacetime. Within this discrete volume of spacetime physical relationships concerning Absolute measures of Distance, Velocity, Acceleration, and Energy are described.

Consider a Balloon and its enclosed volume to represent the discrete absolute volume of spacetime. If we were to reduce the surface tension in the balloon, the balloon would expand, which is analogous to our expanding spacetime. Molecules of air hitting the retreating walls of the expanding balloon would rebound with less energy and the velocity of the rebounding air molecules would decrease. This slower velocity would eventually be shared with all the molecules in the balloon and the temperature of the air in the balloon would drop. Similarly a discrete or infinitesimal object with its own velocity within a discrete or infinitesimal volume of spacetime will also “lose” velocity as spacetime expands.
(Drawing of expanding balloon with “relaxed” walls used for class).

A mass can be considered a collection of discrete points residing in a collection of discrete absolute volumes of spacetime. Since the collection shares the same physical relationships as its parts, it is possible to generalize the relationship to the entire collection.

If an object has a given absolute velocity, then according to the derived relationships, the absolute velocity of the object should slow with the expansion of spacetime, just as the molecules within an expanding balloon all slow down in an expanded balloon.

Now comes the amazing part , Time
These changes in absolute measures of distance, velocity, acceleration and energy cannot be locally observed using relative measures. It is only from the “Eye of God” perspective that these changes can be described. If an object slows to 1/2 its original absolute velocity, all local measures of time, or all local physical process will also slow to 1/2 their original rate. Just as all relative measures of length maintain their proportional measure in a uniformly expanding spacetime field, all relative measures of time keep their proportional measure.

Continued