For every process or method, it is wise to set up guidelines—fundamental steps for repeating a process. NUVO is no exception to the rule. A technique arising from exemplar space was implemented. Exemplar space is a boundary in the NUVO theory. It is a boundary for where a clock ticks the fastest in a gravitational potential. No known occurrence exists where time (a clock) ticks faster due to a global (no local) effect. This type of boundary provides a location where all observers can calculate a value without being at the boundary to measure it. In other places in science, this is done; for instance, the speed of light is both the universal speed limit and a constant for all observers. Thus, an observer can extrapolate any other observer measuring light will measure the same in the other observer’s lab as they have in their lab.
This boundary in exemplar space becomes an intermediary for transforming from one observer to another when only one of the observer’s measurements is known. The boundary condition, coupled with the scalar transformation ϕ’s value equaling one, makes exemplar space a mathematically preferred space. It is not, however, a preferred physical space. If such a space existed, it would hold no more physical relevance than any other physical location. Mathematically, one could set any location in space to be the “exemplar” space of their calculations, normalize it so their measurements are transformed as one (as in exemplar space), and perform all the calculations of NUVO. But, as one who has worked with math, the obvious question arises: why? Mainly when the boundary exists, and the measurements have already been normalized.
The first rule of application is that all Newtonian mechanics are accurate in exemplar space, with one major exception: action is not instantaneously propagated. An event at a distant location does not have an instant effect locally; the information about the event must propagate through space-time to interact with the local. Newtonian mechanics are accurate in exemplar space, except that action is not instantaneously propagated throughout space. With this rule, a starting place for calculating equations of motion, forces, energy, etc., is decided. If one wishes to calculate a planetary orbit, one will start with Newtonian mechanics in exemplar space. Apply Newtonian mechanics of the desired action in exemplar space. Once the mathematical process has been worked out for Newtonian mechanics (thankfully, in our day and time, we have the privilege of many great scientists before us who have worked these out), the process must be transformed by the NUVO transformation to the place in privo space the mechanics are physically taking place. Transform the exemplar space Newtonian mechanics to the privo space physical location of the action. This is where the process may grow complex and, in the author’s opinion, frustrating. Suppose the transformation takes the action from a fixed state (as in exemplar space) to a mixed state in privo space. In that case, many of the conveniences of Newtonian mechanics fail due to the loss of symmetry or conservation of quantities.
For example, Newton’s law, starting with the first law: An object at rest will remain at rest, or an object in uniform motion will continue in a straight line until acted upon by an external force This law alone doesn’t provide many (if any) challenges with NUVO, other than the lack of definition for force, rest, and uniform motion (for instance, if the earth is spinning by moving in a straight line, is it uniform motion?). Nonetheless, it was a brilliant observation for his time (as a side note, it may be argued Galileo observed this same law, but in recognition of Newton, Galileo was unable to formulate a full set of laws). Newton’s second law is more challenging when transforming (shown in equation form).F=maWhere F is force, m is mass, and a is the acceleration of the mass. The challenge in transforming this law from one observer to another is force is not invariant (nor part of Group N). So, the changes in a transformation may be subtle and will need to be handled with care. I would like to remind you that each step of the integration must be transformed appropriately. Integrating force dotted with distance and arriving at energy does not guarantee the energy value is invariant. Each step of the force calculation must ensure it was correctly transformed and the distance. Even acceleration in the equation must be dealt with rigorously. As a reminder, two of the three terms in Newton’s second law are derived units. Only mass is a naturally occurring unit. How one derives these quantities may leave the derivation non-invariant.
Newton’s third law is where the transformation challenges blatantly appear.F12=−F21The force of object 1 on 2 is equal in magnitude and opposite in direction to the force of object 2 on 1. All forces appear in pairs and act with equal magnitude and opposite directions. Recalling from previous discussed table wher force transforms by ϕ’s scalar value (or inverse depending on the transformation direction, E→P or P→E). Immediately, this implies Newton’s third law is not invariant in the NUVO transformation. In a sense, it does imply, locally, Newton’s law holds for any observer (where all observer’s ϕ are equal). But, if the laws transform an action (or a force) like gravity across a distance, then the transformation of forces (even as observed by a local observer) may not hold to Newton’s third law.
The implications of following these steps will be discussed as they are applied to cosmic and quantum-level mechanics. The NUVO theory, thus far, by following these steps, has generated many (possibly will prove to be all) General Relativity predictions. Second, following these steps, the theory has discovered that discreteness becomes non-trivial as the system reduces in size (from a massive star down to a hydrogen atom).