The Reciprocal System of Theory (RST) is held by advocates to be a theoretical framework capable of comprehensively explaining all physical phenomena from subatomic particles to galactic clusters. The framework, based on the work of Dewey B. Larson, an American engineer and author, was originally described in his book The Structure of the Physical Universe in 1959 and has more recently been published in three revised and enlarged volumes. The ideas are promoted by the members of 'The International Society of Unified Science, Inc.' (ISUS) whose only stated objective is to "advance in all ways deemed feasible the Reciprocal System of physical theory as proposed by Dewey B. Larson".

The RST and the work of Larson assumes that the basic constituent of the universe is motion (i.e. space & time), not matter. Thus, it is a unique approach in the science of physics. However, so far, it has remained essentially unknown or ignored in the mainstream physics community, since it is completely at odds with current theories such as relativity, quantum mechanics and the Big Bang and many other modern theories. Although it is generally dismissed by those physicists who are aware of it, proponents claim that it rests on solid philosophical grounds, and that it is the first general theory of physics ever developed. Unlike conventional theory, they point out, the RST has no empirical content, but rather all its conclusions are based solely on its initial assumptions. These initial assumptions are contained in only two brief statements that Larson designated the "Fundamental Postulates" of the system, namely:

1) 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.

2) The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.

From the first postulate, Larson concludes that while both space and time are three dimensional, or, in other words that it takes three magnitudes to completely specify them, they can have no physical significance other than what they have in the equation of motion. Therefore, it follows that space is not an independent entity that can be affected by matter in any respect. Considered apart from motion, space is only a concept, or mental construct, which can be utilized to devise a convenient system of reference for measurement purposes. Likewise, time is not an independent physical entity that can be considered apart from motion. Space and time only have meaning as reciprocal aspects of motion.

Larson further concludes from the first postulate that, since the postulated three-dimensionional motion is assumed to exist in discrete units, the dimensions of motion are therefore independent. This means that independent two-dimensional and one-dimensional motion are also possible. In fact, in the due course of the theory's development, Larson shows that quantities of one-dimensional motion correspond to electric potential, quantities of two-dimensional motion correspond to magnetic potential, and quantities of three-dimensional motion correspond to gravitational potential. Larson argues that this is the basis for explaining many otherwise unexplainable electrical and magnetic phenomena such as induction (in general, 2D motion (magnetic motion) cancels a portion of 3D motion (matter) leaving a 1D motion residue (electric motion), or, alternately, 1D motion (electric motion) cancels a portion of 3D motion (matter) leaving a 2D motion residue (magnetic motion)).

New Paradigm Emerges

Of course, this theoretical approach of a universe consisting of nothing but motion (space and time) constitutes a completely new paradigm that departs radically from the current paradigm of a universe consisting of matter contained in space and time. This is most simply illustrated in the difference between Einstein's conclusion, called the Equivalence Principle, that the force of gravity is equivalent to an acceleration, and Larson's conclusion that the force of gravity is an acceleration. Another example is Einstein's conclusion that matter and energy are equivalent. Larson asserts that this leads to a contradiction at high speeds, which is resolved by the conclusion that matter and energy are not equivalent, but interconvertable, meaning matter can be converted to energy and vice-versa, but the two are distinct degrees of motion (matter is 3D motion, while energy is 1D motion.) These are just two of the many cases where the concepts of the different paradigms lead to conflicting conclusions; there are many others.

No Gravitational Waves

For instance, the RST concludes unequivocally that gravitational radiation, a requirement of general relativity, cannot exist, and that gravity operates without any medium or continuum such as the four-dimensional (4D), curved-space of relativity, or any process of transmission between gravitating bodies. Although this is in accord with current observations, it is at odds with existing indirect evidence for the existence of gravitational radiation, from binary neutron star measurements. While General relativity (GR) predicts that, due to gravitational radiation, the orbit of such systems will decay at a specific rate, the RST attributes the force of gravity to the inherent 3D inward motion of the mass of gravitating bodies. In this way the same motion that constitutes the mass of a body also produces the force of gravity associated with that mass. No energy transmission process is involved in this phenomenon, and, thus, no orbital decay should result from its operation.

However, an orbital decay is observed in these binary star systems, and the rate of decay is as predicted by general relativity, to an accuracy of 0.5%. On the other hand, it must be conceded that these systems are not well understood, and definite conclusions are premature at this point. For instance, at least one system (PSR B1744-24A,) is exhibiting an orbital decay of five times the rate attainable through gravitational radiation. Fortunately, new gravitational wave detectors, such as LIGO, VIRGO, LISA and others, are soon expected to detect gravitational radiation directly, which promises to settle the matter definitively.

Euclidian Geometry of the Universe

Meanwhile, RST proponents claim that the theory is also consistent with recent observations that the geometry of the universe is flat (from the CMB data), and that the cosmological parameter, Omega, is precisely equal to one. These data are in conflict with traditional big bang cosmology, where Euclidean geometry would appear to be highly unlikely. While the theory of cosmic inflation is the method accepted by most physicists for overcoming this apparent contradiction, the fact that such ad hoc theories are necessary at all, is prima facia evidence, say RST proponents, of the problems experienced in current physical theories, which they complain are, as Richard Feynman said, "a multitude of different parts and pieces that do not fit together very well."

Integrated Dark Energy

The most embarrassing example of this predicament, advocates say, is the consternation caused by the recent discovery of the accelerating expansion of the universe. The observed acceleration is thought to be produced by a gravity-like repulsive force. Some think that this force, dubbed "dark energy," by Michael Turner of the University of Chicago, might be vacuum energy, represented by the "cosmological constant" (λ) in general relativity or possibly something called "Quintessence."

Quintessence (φ) is a hypothetical "scalar field" that cosmologists can use to explain the values of certain cosmological parameters such as the flat geometry of the universe and its current proportions of energy and matter. However, the problem is that the use of scalar fields, a wide spread practice in the construction of modern physical theory based on quantum physics, exacerbates the growing conflict between quantum physics and general relativity. This happens because, if scalar fields, such as φ are coupled to gravity in the equations of general relativity, they cause what physicists call violations of "energy conditions."

Indeed, Carlos Barcelo, of the University of Portsmouth's Institute of Cosmology and Gravitation in Great Britain, has concluded that, because of these violations of the energy conditions, caused in general by the coupling of scalar fields to gravity, "the conflict between quantum physics and gravity is now becoming acute," and he suggests that physicists "banish scalar fields from [their] theories" altogether, as the simplest solution to the problem, though he admits that it would not be the easiest way out due to the crucial role scalar fields play in many important physical theories today.

In contrast to the turmoil that the evidence of dark energy has induced in the state of affairs in mainstream physics, a similar outward, gravity-like motion has always been an integral part of the RST from the beginning, and is a major component in the RST's calculations and explanations of both the large-scale structure of the universe and its atomic and molecular scale structure. It plays a fundamental role in the RST's explanation of the recession of galaxies, star formation, galaxy formation and the explosions of stars, without the need for scalar fields, the big bang, cosmic inflation, or black holes.

Of course, the RST is not necessary to explain this outward motion--Einstein himself proposed the expedient of inserting the cosmological constant into his equations soon after he proposed the theory of relativity, and mainstream scientists, with new ad hoc theories of expansion such as Quintessence to address the problem, may succeed in explaining the observations without the need for the RST. Nevertheless, the proponents emphasize, it's important to note that these theoretical adjustments, that add ad hoc elements to physical theory in order to account for new observations, cannot be made in the RST, because everything in this system of theory must follow from the consequences of its fundamental postulates. Needless to say, such a claim of logical rigidity and inevitability sets the RST apart as very unusual and extremely unorthodox.

No Atomic Nucleus

Other examples of unusual and unorthodox theoretical conclusions reached in the RST include the derivation of a non-nuclear model of the atom in Nothing But Motion, which leads directly to the periodic order of the elements. Larson claims that his theory accurately derives the elements in correct order without employing the nuclear concept of electrons orbiting an atomic nucleus, and predicts that the maximum number of elements in the periodic table is 117. However, his theory has not yet accounted for the atomic spectra of the elements. In contrast, the extremely accurate results obtained by quantum mechanics and the nuclear model of the atom are well known.

Calculating Basic Chemical Properties

On the other hand, in Basic Properties of Matter, Larson makes theoretical predictions for a large number of properties of a range of chemical species, including atomic mass, interatomic distance, compressibility and heat capacity. It appears that he calculates these values from simple closed-form analytic formulas. If accurate, this would be a vast improvement on the complex calculations required to make theoretical predictions under quantum mechanics. For instance, using the RST non-nuclear model of the atom, Larson begins with calculations of inter-atomic distances of the elements. These distances, which in the RST are a result of an equilibrium reached between two opposing, non-electronic forces, are calculated by an equation derived from the "specific" motion of the atom's combination of motions in several dimensions. In it's simplest form, applicable to the noble elements, where there are only two such specific motions involved, the equation is:

so = 2.914 ln t angstroms

where so is the center-to-center distance in angstrom units and t is the specific motions of the elements. Where these two specific motions are equal, only 1 of them enters into the calculation. However, if they are unequal, a single value is obtained by squaring the first and taking the cube root of its product with the second:

t = (t2 t)1/3

On this basis, the result for Neon, with its two specific rotations of 3 and 3 is exceedingly simple to calculate:

so = 2.914 * ln t = 2.914 * ln 3 = 2.914 * 1.098612 = 3.201355 angstroms

This value compares with an observed value of 3.17 angstroms for Neon (see The calculated values of the other noble elements for which data is available are also quite comparable. For instance, the calculation of Argon is 3.76 angstroms, which compares to an observed value of 3.72 angstroms; the value for Krypton is 4.04, compared to 4.04 observed; and 4.38 for Xenon, compared to 4.39 observed.

However, in many cases Larson must modify the equations to be used, changing them from species to species on grounds difficult for non-initiates to easily follow without further study. For example, Larson lists characteristic values for the various species which are specific to the RST, such as "specific electric rotation". Because the basis for the procedure for calculating these values is explained in an earlier volume of the work, it is necessary to devote a great deal of time to the study of the RST to rule out the allegation that they were selected arbitrarily to make the predictions fit the data. Nevertheless, it's interesting to note that Larson's calculations of the values shown above, except for Neon, are closer to the accepted values today than when he published them in the early 1980s.

Calculating Relativistic Speeds

According to its proponents, the RST can also be used to solve the famous problem of the precession of the perihelion of the planet Mercury. This problem was first solved using Einstein's equations of general relativity, which assumes relative values of space-time in the equations of motion, as opposed to Newton's assumption that space and time should be treated as absolute concepts in the equations of motion. Larson, in the RST, also assumes absolute values of space and time, but goes beyond Newton in the definition of these crucial concepts. Using these definitions, K.V.K. Nehru produced a paper describing the orbital motion of high-speed planets. The result he found from the RST was precisely the same as that from relativity. Hence, like general relativity, the RST is fully in agreement with accurate measurements of Mercury's orbit.

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