IV  Are the “Laws” of physics preserved?   The Ratios of Time formulas pertain to measurements based from the Absolute Reference frame.  In order for the proposed model to be correct, and allow the “rules” of physics to be consistent, then the “rules” of motion should conform to observation for both reference frames.  A stable orbiting object in a relative reference frame must also be stable in the Absolute reference frame. Newton’s Laws of gravity must be conformal to both the Absolute field description and the Relative field description.    Figure 13 shows a relative reference frame  (or space time field) expanding, relative to the vertically oriented Absolute reference frame, or field of points.  The “rules” that define dynamic structure, such as the perseverance of a stable orbit, must be compatible both for the Absolute field of points and the relative field of points associated with the orbiting objects.  Stability must be preserved in our local observation of the orbiting masses, and stability must be preserved in the absolute observation of the orbiting masses.   Preserving Celestial Stability   The first real test of the proposed model will be to determine if Celestial Stability is preserved based upon relationships defined by the absolute reference frame. There are specific changes in velocity and acceleration imparted to an object in an expanding space-time field that are based upon an “absolute” reference frame. If these changes imparted to orbiting objects do not maintain celestial stability, the model fails since congruence is not preserved.  Stable orbits are observed in a relative reference frame, so stable orbits should be preserved in an absolute reference frame.   Figure 4 shows two equally sized objects, gravitationally bound, rotating around each other in a stable orbit.  Given that the orbit is stable at T1, would the necessary celestial stability be preserved at T2?   Centrifugal force must equal Gravitational force   The centrifugal force on a mass is described by                            Centrifugal Force = M V^2/R,                      Eq IV-1                         (m= mass of object, V= velocity, and R = radius that the moving mass is “forced” to conform to. = D/2)   The gravitational force between the masses is described by                           F = g M^2/ D^2                                              Eq IV-2                                                 g= Gravitational “constant”   Equating the relationships of Gravitational forces, Eq 10,  and  Centrifugal forces, Eq 13, for two points in time (1) and (2) as a proportion yields   Centrifugal Force1/Centrifugal Force2  = Gravitational Force1/Gravitational Force2  Eq IV-3                                                                                              (V1/V2)^2/(D1/D2) = (D2/D1)^2                 Eq IV-4   The centrifugal force must equal the gravitational force for both points in absolute time.  If the centrifugal force is decreased by a half with a given expansion, the force of gravity must also be reduced by a half.  The proportional reduction must be the same between the centrifugal force and gravitational force.  Is the proper balance preserved for all choices for T1 and T2?    Substituting the temporal relationship of Eq 9 for the velocity ratios, and similarly Eq 8 for the Distance ratios into equation 14  yields           (V1/V2)^2/(D1/D2) = (D2/D1)^2                                                       Eq IV-5 ((T2/T1)^(1/3))^2 / (T1/T2)^(2/3) = ((T2/T1)^(2/3))^2                        Eq IV-6 (T2/T1)^(4/3) = (T2/T1)^(4/3)                             Eq IV-7   The two masses maintain their balance between centrifugal and gravitational forces in an expanding space-time field.  As the distance between objects increase, the velocity of the objects also decreases in the correct proportion to maintain the balance between centrifugal and gravitational forces. This means that the expansion of space is conformant to Newtonian Gravitational Relationships.  This idea is further supported by the following example.   Orthogonal Velocity   Note that since there was a direct mapping of a relative distance to an absolute distance, (the distance between the two objects), when the change in velocity is determined by absolute time, the direction of the change in velocity is perpendicular to the distance between the two points.  The velocity change can also be associated with a loss of intrinsic properties.     Parallel Velocity?   Since there is also a change in the distance between the two orbiting bodies due to expansion, it initially seams that there should also be a change in absolute velocity directly between the two orbiting objects.  This is not observed locally based upon local measures since the measured relative distance remains the same.  Also, as will be shown in section V on time, the measure of time between the two points remains the same. It is only in the perpendicular direction to the line between two points that any change in the velocity between the two points is noticed.   Predicting Newton’s Laws of Gravity   Newton's Laws of Gravity can be used to describe the relationship of two independent points in space in that the mass of a object can be generally be assigned to being located at the objects centroid. If the hypothetical uniform expansion of space-time predicts that the acceleration between two points varies the same as the acceleration associated with gravity, then the theory becomes a theoretical model that conforms to Newton’s experimentally derived Laws of gravity.  The theory must result in producing a dynamic structure to space-time that results in the inverse square law observed within atomic and orbiting celestial structures.   Newton's Law of Gravity, is   F = g M1M2/ D^2                  Eq IV-2 , 8   Newton’s Law of gravity expressed as a ratio between two objects separated at two distances, D1 and D2 becomes the following expression.   F2/F1 = (D1/D2)^2.              Eq IV-9   F2/ F1 can be reduced to A2/A1 since the masses involved are the same.   A2/A1 =  (D1/D2)^2.             Eq. IV-10   The acceleration a body experiences at two different locations varies to the inverse square of the distances.  This relationship is based only on Newton’s experimentally derived Law of Gravity.   Does the uniform expansion of space-time predict the same inverse square relationship expressed by Equation IV-10?    The Absolute distance between the two points is expressed by the following relationship, as described by the uniform expansion of space-time.   D1/D2 =   (T1 /T2) ^ (2/3)     Eq III- 8 Eq. IV-11   Squaring equation 8 results in               (D1/D2)^2 = (T1/T2) ^(4/3)   Eq IV-12   The acceleration experienced for two points in absolute time are, according to the relationships established by the uniform expansion of space-time, is expressed by the following expression.   A2/A1  =  (T1/T2) ^(4/3)   Eq III-10 Eq IV-13   This is exactly the same inverse square law expressed by Newton’s Law of gravity               A2/A1 =  (D1/D2)^2.             Eq. IV-14   The theoretically derived expression describing the acceleration at a point exactly corresponds to Newton’s experimentally derived law of Gravity.   (Note:  since the relationship between the electron and nucleus of an atom also follows the same inverse square law, the same preservation of atomic stability would be maintained.  While the dimensional relationships are preserved by the proposed model in terms of adherence to the inverse square laws, the specific numeric or scalar value for g and coulombs constant are not derived by this model.  This will be a topic of another paper.)   Special Relativity issues   Those who are familiar with special relativity know that as the velocity increases, the effective relative mass increases.  This initially may seem to imply that the above relationships are only valid at non-relativistic speeds, which would tend to reduce the overall completeness of the theory.  This concern will be addressed later, but for now it will be stated that the effects predicted by special relativity are described by relative measures, and since relative measures remain constant, there would be no change in locally observed relativistic effects. Conservation of Energy and Momentum Another important prediction of the proposed model is that based upon relative measures of realty, there is conservation of energy and momentum. The relative velocities and relative distance is maintained locally.   It is only from the Absolute reference frame that the loss of energy and momentum is observed.  Also, while from the absolute reference frame there is a loss of energy and momentum, celestial and atomic structures are maintained. These are fundamental physical constraints on any theoretical model proposing to describe the dynamic dimensional structure of our Universe. General Relativity and Conservation of Newton’s Laws Newton’s laws do not completely describe celestial motion. One example of this shortfall is the precession of the orbit of mercury.  If Newton’s laws were only involved, the location of where Mercury’s closest approach to the sun in it’s elliptical orbit would remain the same. (Ignoring for now the advance of the perihelion due to the gravitational interaction with the orbiting planets).  General relativity does a good job of explaining the advance of the perihelion.  The proposed theory seems to base it’s validity in predicting Newton’s laws, not the more encompassing relationships of general relativity.  For many, this may appear to be signs of the invalidity of the theory.  This is not the case.  The same advance in the perihelion for the orbit of mercury can be predicted using a uniform expansion to space-time.  The advance of the perihelion is observed over historical measures, which are associated with absolute measures of time.  In the application phase of this work, the advance of the perihelion of mercury will be shown, but a far more convincing validation of the proposed theory will be the perseverance of stable orbits of galaxies without resorting to non-baryonic matter, something that is required if one adheres to General relativity alone.  Again, the proposed theory does not negate the relationships of general relativity, an expanding space-time field that varies in the rate of expansion results in a curvature to space-time.   This curvature and it’s interaction and association with matter results in the same observed relationships associated with general relativity. The main difference is that the dynamic effect imposed on general relativity is not determined by gravity in this model, it is the expansion of space-time itself that determines the effect of gravity and the curvature to space-time.    The motivation for developing this theory in the first place was based upon dimensional analysis.  This is illustrated in Figure 15.  The dimensional expression describing an inertially applied force is not the same as a force applied gravitationally.  The gravitational constant “g” is a “fudge factor” used to balance the expression that is determined by experimental means; “g” is not found in inertial expressions of force.    Dimensional Analysis and Equivalence Since both situations have the same one Newton force applied, the expression that quantifies the force must also be the same. One expression has no “g” the other does.  There is also no theoretical model predicting the value of g and the Inertially applied force does not require it.  If there was some way to equate the two forces without resorting to a “fudge factor” then a common theoretical basis for the two identical forces could be expressed.  If g could be eliminated and the expression could be balanced dimensionally with out a fudge factor, fundamental dimensional relationships could be established.   Newton = 1 Newton                             Eq. IV-15 M1*(A )  =   M1*(gM2/ (D*D))               Eq. IV-16          A  =         M2/(D*D)                                Eq. IV-17     D/T/T = M/D/D                                      Eq. IV-18                        Dimensions do not "Balance"   For years I played with various dimensional transformations that would allow the balancing of the dimensional relationships without resorting to a “fudge factor”.  There had to be some basic mathematical relationship that is characteristic of space-time and matter that would allow these two equivalent forces to be dimensional equivalent.   Those who object to the loss of the gravitational constant g to balance the equation must remember that g is not a just a number, it carries with it dimensional relationships imposed to make the experimentally determined relationships work.  The goal is to express all relationships as functions of distance and time alone, based on a theoretical model of the universe.     Equation Eq. IV-18 (D/T/T = M/D/D) has dimensions of distance and time and mass.  Distance and time are real dimensions in that they can be plotted, and special relativity allows an equating of these two dimensional measures.  Mass is a bit nebulas, just what makes mass have the properties of mass? Intuitively it seems that distance and time are the real measures of mass. Expressing Mass as a function of distance and time from the above relationship results in the following.   M = D^3/T^2              Eq. IV-19   The use of the equal symbol rather than proportional symbol to is to emphasize the dimensional relationship. How does such relationships of space and time conform to those describing matter?  It is my contention that matter is of the same dimensional structure as is the space-time structure that describes the universe itself.  If the entire universe is described by specific dimensional relationships, then all the parts of the universe must also conform to the whole.  Matter becomes more than a structure made of different quarks, (which are "pieces" of space and time), but a structure based on a dynamic relationships of space and time that are consistent from the smallest to the largest scale of observation.   If the equivalence principle gives us a relationship in which mass is defined by a specific relationship between space and time, and if the idea that all parts of the universe must conform to the whole, or the same set of “rules”, then there must be a dynamical expression of the universe that corresponds to that found in matter. From the Uniform Expansion theory we have the following dimensional relationships describing the expansion of a volume of space-time or an object.   dS/dt = T                                Eq. III-1 (IV-20) S = T2                                     Eq. III-2 (IV-21) S = D3                                     Eq. III-3 (IV-22) D3 = k T2                                 Eq. III-4 (IV-23)   k is added in equation 4 to allow a scalar number to describe a measure of a volume of space time. Doubling the age of the universe T results in a 4-times increase in the volume of space described by the scalar number k.  The larger k is, the larger the volume of space.   k = D^3/T^2                Eq. III-4  (IV-24)   Note that Eq. III-4 and Eq. IV-19 are dimensionally equivalent. A theoretical model describing a relationship between distance and time associated with properties of space-time corresponds dimensional to that of matter. Matter and space-time are now dimensionally equivalent.  A mass represents a volume of space-time; the only difference between space-time and matter is the associated scalar number, k.   Dimensional Simplification   Having confirmed a theoretical dimensional basis for matter, some interesting relationships can be established and confirmed. The dimensional relationships for force becomes:     Inertial Force = F = M*(A)  =  D^3/T^2  *(D/T^2)   = D^4/T^4      Eq. IV- 25   Gravitational Force = F =(M1*M2)/D^2 =((D^3/T^2*D^3/T^2)/D^2 =D^4/T^4      Eq . IV-26   F =  D^4/T^4                        Equation IV-27   The dimensional relationships for energy also match for Newtonian and Einstein's relativistic energy equation.               Energy = F*D = D^4/T^4 *D =         D^5/T^4          Eq. IV-28 E = mc*c = D^3/T^2 * D^2/T^2 =     D^5/T^4          Eq. IV-29 Energy = D^5/T^4                                                    Equation IV-30   The fact that Newton's and Einstein's dimensions for energy now match is another validation of the Uniform Expansion Theory.  The dimensional expression for matter results in the same dimensional balance when applied in Einstein’s theoretically derived relationship between mass and energy and the classic Newtonian expression for the energy associated with work.   Matter is not so much an entity of itself, but a property of space and time.  It’s units of measure should conform to the dimensional structure proposed.  This will be discussed in more detail later regarding the dimensional make up of Quarks.