Larson takes a completely different approach to the problem. Instead of seeking a background independent theory directly, as Smolin et al do, that is motivated by modern theoretical perplexities, he concludes that the definition of motion not only does not require a background of space and time, but he also realizes that it does not even require a separate entity in its definition; that is, in the equation of motion, v = ds/dt, the only requirement is a change of two reciprocal magnitudes, space and time. In retrospect, we might imagine him thinking that since the universal "march of time" is observed locally, and the universal "march of space," is observed globally, in the recession of the distant galaxies, that one approach might be to assume that these observed phenomena are the reciprocal aspects of a universal motion.

However, this was not the avenue by which he arrived at the conclusion. Rather, he arrived at it because he noticed that the data from his studies of inter-atomic distances in solids made more sense, if he assumed a reciprocal relation between space and time. Of course, if we think of space and time as a background, then the idea of space being the reciprocal of time seems absurd, but in considering the equation of motion, the reciprocal relationship of these two enigmatic concepts makes perfect sense.

Recognizing that this approach to the nature of space and time would work if space and time were quantized, he soon arrived at the basis for a new system of physical theory: if somehow the progression of space/time formed discrete units of motion, they could provide the basis for physical entities consisting of nothing but space/time.

Of course, Larson knew nothing of Smolin's work in the decades before he published a preliminary edition of his work in 1959. In fact, Smolin wasn't even alive at that time. More importantly, the perplexities that dog background dependent physical theories had not yet emerged, and physicists were fascinated with QFT and fixating on gauge symmetries, and applying group theory to quantum mechanics. Nevertheless, a comparison of the RST with Smolin et al's concept of relational space and time, is very revealing:

1) There is no background.
Larson's concept of space and time as nothing more than the reciprocal aspects of a universal motion eliminates entirely the concept of a space and time background as the initial condition of the theory. It thus complies perfectly with Leibniz's principle of sufficient reason in this regard. In fact, it will be shown later that the degrees of freedom associated with space and time in modern theories are actually more properly attributed to motion, and that exactly three degrees of freedom are sufficient for all geometries, including non-Euclidean geometries such as elliptical and hyperbolic geometries.

2) The fundamental properties of the elementary entities consist entirely in relationships between those elementary entities.
Again, in Larson's RST, the elementary entities of the theoretical universe are not pre-existing particles of matter. They are discrete units of the universal motion, which Larson called scalar motion, because it consists of a scalar increase of space and time, reciprocally related. The initial state of this scalar motion is altered when a continuous reversal in the scalar "direction" of the progression of one or the other of the reciprocal aspects occurs at a given point in the progression. A more detailed explanation of this change in state will be provided later, but the result is that emerging degrees of freedom produce various properties in these entities due to the relationships between them.

3) The relationships are not fixed, but evolve according to law. Time is nothing but changes in the relationships, and consists of nothing but their ordering.
Larson's universe of motion consists entirely of units of motion, combinations of units of motion, and relations between units of motion. These entities emerge and evolve soley as a result of, and as the necessary consequences of, the two fundamental assumptions of the system that Larson called the Fundamental Postulates. Time, in this system, is on an equal footing with space. However, all the dynamics of the system stem from the initial dynamic relationship of space and time. Therefore, while time is the change in the relationships, it does not exist apart from space in the equation of motion. Neither space nor time can exist as separate entities apart from motion. In the RST, space is ordered by time, and time is ordered by space. Hence, the spatial position of physical entites cannot change without time, neither can the temporal position of physical entities change without space.

Clearly, Larson's Reciprocal System anticipated the requirements of a background independent theory. Meeting the need for a modern theory that can explain how the physical entities that populate the universe as constituents of radiation, matter, and energy, can acquire the observed properties they have without invoking a background of space and time, is exactly what it claims it can do. I hope to be able to present, and sucessfully defend, the bonafides of that claim in the ensuing discussion that I anticipate will take place here. Let me close this post by providing you with the formal expression of the basis of the Reciprocal System, composed by Larson, the two Fundamental Postulates from which the entire universe of motion is deduced:

First Fundamental Postulate: The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

Second Fundamental Postulate: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.

References:

1) Lee Smolin, The Case for Background Independence, hep-th/0507235, 25 July 2005