Let me start by quoting Mathis' conclusions, regarding time, from that paper (based on his reevaluation of SR and QED):
First off, the Reciprocal System is NOT a branch of the SR/QED tree of physics--the postulates have about as much in common with conventional physics as a tree does with a dog. The premises are totally different--the conventional setting of matter versus a universe of motion. Let me identify some of the key components in Mathis' conclusions, that provide an interpretation in RS2 (projective geometry needed--not as applicable to Larson's RS):As I have shown, time is assumed to be absolute in the sense of being equivalent from one system to another. We must make this assumption in order to calculate velocities, among other things. This does not mean that it is absolute, of course. It means that we must define it as having continuity from our immediate vicinity to any vicinity we want information about. If we do not assume time and space continuity, we cannot hope to build meaningful equations. A universe without continuity is a universe without equations, without mathematics, and without science.
But time is not absolute in the sense of absolutely precise, or absolutely known. It is a concept based on the idea of uniform movement, but the concept allows of only relative measurement. A movement can be known to be more or less uniform, but not absolutely uniform.
Likewise, time is not an absolute in the sense that many "classicists" appear to mean when they mean by it that Special Relativity is wrong. Objects moving at a distance, including of course clocks, look different than objects at hand. And velocity and acceleration influence the appearance of distant objects in quantifiable and dramatic ways. Time dilation is a fact. A poorly interpreted fact—up to now—but a fact nonetheless.
Time is also dependent upon, and therefore relative to, movement. In a sense, time is nothing. Or it is nothing but a second measurement of movement. Displacement is movement. Time is movement. Time is displacement. Time is the displacement of the reference body.
- Mathis' theory, from what I've read so far, is based on the concept of a "universe of velocity", defined by changes in velocity. Larson just calls it "motion" instead of "velocity," having the same relationships of space to time. Twenty years after Larson published his first book, he finally concluded that "we are dealing with nothing but abstract change [of motion] in three dimensions." (See thevideo Q/A on the rstheory site). Same concepts, different words.
- Time as absolute: appears to be a confusion arising from the projective strata. Mathis does not have the same "viewpoint" as Larson (his camera of observation is in the Euclidean stratum, looking up; RS2 is at the projective stratum, looking down). Using projective concepts, RS2 can conclude that "time is absolute" only in the Euclidean stratum of the projection--in other words, it acts as the same velocity in all dimensions (the Euclidean stratum requires scale to be fixed at unity in all dimensions, which is the denominator of velocity--time). So the world in front of our eyes appears to have time as "absolute."
- Time as not absolute: Once you move out of the Euclidean stratum of the projection of scalar motion, there is no requirement that "time" be fixed at any value, and therefore time appears relative to the reference frame. It appears most of Mathis' comments are in the Metric stratum, where time is dimensionally independent. In his Calculus papers, he wants time to be a vector quantity in the denominator, which IS the case with any measurement made above the fixed, Euclidean stratum.
- Time dilation: Does not exist in Larson's Reciprocal System, as Larson only considers the Euclidean projection of scalar motion (as he postulates). What would normally be time dilation in the RS is adjusted by motion in coordinate time (3-dimensional time, clock space), the Cosmic half of the Universe. In RS2, time dilation only occurs in the non-Euclidean geometric strata, again because "time" is not fixed at unity, as it is in the Euclidean. Therefore, time acts as a scale factor in the relations of velocity, appearing to slow things down or speed them up. Relativity, having no analogous concepts to either the Cosmic sector, nor projective geometry, has to adjust the flow of clock time for this scale factor.
- "Displacement is movement. Time is movement. Time is displacement.": Not much to be said on this comment, other than, "Welcome to a universe of motion!"
It all depends on the observer--where the camera is located, and where it is looking. That is why I consider the observer effect to be a key factor in RS2.