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The Reciprocal System of Theory (RS) is a Theory of everything devised by Dewey Larson postulating that the origin of all physical activity in the universe is motion which exists in three dimensions and conforms to the laws of commutative mathematics and Euclidian geometry.

The theory’s postulates are tested by hypothesizing the existence of motions, and combinations of motions, which are logically permitted by the postulates. These hypothetical motions are then compared with known physical phenomenon. If the comparison of the properties and behavior of the hypothetical motion resembles that of known facts, it is counted as evidence that the postulates of the theory may be valid. Such evidence cannot prove that the postulates are valid because there is always the possibility that future findings will fatally contradict the postulated conditions. Therefore, if the investigation produces positive evidence for the validity of the postulates, the probability of finding fatal negative evidence that invalidates (falsifies) the postulates is somewhat reduced, but it is never eliminated.

Some members of the scientific community ignore the Reciprocal System of Theory because, in their view, its postulates are neither verifiable nor falsifiable. Thus, they conclude that the theory is not truly science, subject to the Scientific method, but rather is an example of Pseudoscience. They further contend that 'RS theory does not contain any mathematical properties'.

These arguments are easily refuted. If I say, for instance, that the universe is made of chocolate and conforms to a certain recipe of chocolate, such an assertion is easily disproved. Then why, if it is hypothesized that the universe is made of motion, would anyone protest on the grounds that such an assertion is not disprovable? Such allegations are themselves unfounded - where is the conclusive argument for this claim to be found?

On the other hand, why can't the hypothesis be verified? If it is shown for instance that a hypothetical combination of motions can be derived, consistently and logically from the postulates, which then has the theoretical properties of mass, the behavior of gravity, and systematically compounds in a precise manner that conforms to the pattern of the periodic table of elements, does that not constitute evidence in favor of the postulates, and thus verifies the theory to some extent? No one claims that the theory is proven. That verdict is not in yet, the jury is still considering the evidence, but some want to claim that the order of the court is unjust and call off the trial - clearly a bogus and unfounded assertion.

The claim that RS doesn't contain 'any mathematical properties' reveals more about those making the claim than it does about RS. Mathematics is a tool not a theory. If an investigator is attempting to see how the unit charge calculated for a hypothetical RS 'electron' compares to the known experimentally measured charge of an actual electron, does he have to have special 'RS mathematics' to do it? That's just absurd. He uses the already established mathematics that all physicists use, no special mathematics are required. The motions of his hypothetical electron have the quantities and dimensions of discrete units of space and time and he uses the principles of ordinary commutative mathematics and Euclidian geometry (the postulates exclude the use of non-commutative mathematics and non-Euclidian geometry) and the established equations of physics to make his calculations.

It's so straight forward, why all this to do? Maybe it's because it's just so much easier to go on repeating baseless allegations for the support of which not a shred of evidence has been produced, than to spend the time and effort necessary to get the truth of the matter.

The claim that RS has no mathematics is based on the fact that it has no defining equations - I checked the text - but rather is simply based on fiddling around with dimensional symbols. Such manipulations are generally not coherent. See below about the invalidity of s/t as a general form unless s and t are associated with something. I'll disagree, though, that it is inherently unfalsifiable, because it seems to make predictions - for instance, it seems to predict that there are only three phases of matter, which is incidentally false.

In 'fiddling around' with dimensional symbols, Larson managed to do what no one else before him did; he was able to generalize from observations that time is the reciprocal of space and that both time and space are aspects of motion. That motion, in effect, (this is pure Bundy expression) produces the notion of what we call space and what we call time, but neither space nor time enjoy an independent existence apart from motion. That the existence of this motion in three dimensions is solely responsible for the expanding universe, the propagation of radiation, the existence of matter and gravitation can be logically derived from that fact. One can use any mathematical tool that helps in the analysis of theoretical relationships that are based on this generalization. However, it generally does not take multiple pages of advanced equations with many variables to calculate these, because they are so simplified in the context of RS theory.

What this means is that everything physical is a derivative of motion, or, stated in another but equivalent way, is determined by its constituent space and time units. Thus, the physical constants, the so-called 'fundamental constants' of physics such as the velocity of light, Planck’s constant, electron charge and mass, etc. can all be expressed in terms of the quantities of their space and time units when those quantities are derived mathematically and consistently within RS theory. Quoting Larson:

'There has been a great deal of speculation as to the nature and origin of the "fundamental constants" of present-day physics. An article in the Sept. 4, 1976 issue of Science News, for example, contends that we are confronted with a dilemma, inasmuch as there are only two ways of looking at these constants, neither of which is really acceptable. We must either, the article says, "swallow them ad hoc" without justification for "their necessity, their constancy, or their values," or we must accept the Machian hypothesis that they are, in some unknown way, determined by the contents of the universe as a whole. The development of the Reciprocal System of theory has now resolved this dilemma … by exposing it as fictitious. When all quantities are expressed in the proper units--the natural units of which the universe of motion is constructed--the "fundamental constants" reduce to unity and vanish.

... [The results are then:]

Natural Units of Primary Quantities
 Space-time UnitsConventional Units
s space 4.558816 x 10-6 cm 4.558816 x 10-6 cm
t time 1.520655 x 10-16 sec 1.520655 x 10-16 sec
s/t speed 2.997930 x 1010 cm/sec 2.997930 x 1010 cm/sec
s/t² acceleration 1.971473 x 1026 cm/sec² 1.971473 x 1026 cm/sec²
t/s energy 3.335635 x 10-11 sec/cm 1.49175 x 10-3 ergs
t/s² force 7.316889 x 10-6 sec/cm² 3.27223 x 10² dynes
t/s4pressure 3.520646 x 105 sec/cm41.57449 x 1013 dynes/cm²
t²/s² momentum 1.112646 x 10-21 sec²/cm² 4.97593 x 10-14 g-cm/sec
t/s inertial mass 3.711381 x 10-32 sec/cm 1.65979 x 10-24 g

Units of space are so big? -Juuitchan

The values given in the first column of this tabulation are those derived by applying the natural units of space and time to the space-time expressions for each physical quantity. In the case of the quantities of the speed or velocity type, these are also the values applicable in the conventional systems of measurement. However, mass is regarded as an independent fundamental variable in the conventional systems, and a mass term is introduced into each of the quantities of the energy type. Momentum, for example, is not treated as t²/s², but as the product of mass and velocity, which, in space-time terms, is t/s x s/t. The use of an arbitrary unit of mass then introduces a numerical factor. Thus, in order to arrive at the values of the natural units in terms of the cgs system of measurement, each of the values given for the energy group in the first column of the tabulation must be divided by this factor: 2.236055 x 10-8.' [Larson NBM Chap 13]

As far as the magnitude of the units of time and space that enter into these relationships goes, see my comments with yours below.

Larson continues with the theoretical derivation of mass and charge with results as follows (The empirical values cited are from the 1957 compilation by Cohen, Crowe and Du Mond):

e - c charged electron 0.00054874 0.00054876
e - c charged positron 0.00054874 0.00054876
e electron 0.00057870*massless
e positron 0.00057870*massless
e neutrino 0.00057870*massless
p + m + e massless neutron 1.00697075*massless
p + m + 2e proton 1.00754945 unobserved
p + m + 2e + C charged proton 1.00759439 1.007593
p + m + 3e hydrogen (H1)1.008l28l5 1.008142
p + m + 3e + E compound neutron 1.00899621 1.008982
* potential mass

I think you are used to an old manual typewriter.

I think a careful review of these results will show that what we are dealing with is at least 'coherent,' even if you disagree that it is valid.

Questions and comments from Josh:

The Reciprocal System of Theory (RS) is the work of the late Dewey B. Larson of Portland, Oregon. RS theory is an unusual and unfamiliar approach to most scientists because Larson incorporates deductive logic in developing his theory as opposed to the more familiar inductive logic used by most scientists. [Scientists use deductive logic all the time - consider the predictions of radio waves, positrons, etc.]

Answer: Actually I believe those are examples of a hypothesis posited to explain the cause of unknown phenomenon – an inductive process. But all I’m saying here is that deductive logic is much less common than inductive, and certainly less used in Cosmology!

No. Electromagnetic waves were predicted within the framework of Maxwell's electromagnetics and discovered later, and positrons were predicted by Dirac in his attempts to create a relativistic model for the electron. Both were discovered experimentally somewhat later. _______

It's important to understand that while mistakes often occur in developing the logical consequences of a deductive theory, these wrong deductions can be indicated and eliminated or revised as needed to clarify the situation, without jeopardizing the entire theory. [This statement says that any deductive theory can be bent into fitting observations, and thus denies the possibility of falsification, but very few real theories I have seen do this.]

Answer: No, this statement points out an obstacle to using deductive logic. The logical developments can be erroneous, which is a problem arising when the developer incorrectly applies the premise, not a problem with the premise itself. The remedy therefore is to correct the incorrect logic of the developer, if possible, and move on. This does not mean that the premise is not falsifiable, it only means that the argument that proposes to invalidate the premise cannot be illogical.


Conflicts that are proven to be incompatible with the postulates themselves on the other hand, are completely without remedy. Ad hoc assumptions, often seen, even in many "accepted" scientific investigations, are totally excluded, except as they might be used in a consistent manner that temporarily facilitates the course of the investigation. [I can't see any use for the quotation marks except as an insult.]

Answer: I didn’t mean it as an insult. I only meant to indicate that the meaning of “accepted” scientific investigations is a slippery term, depending upon who gets to guard the portal. But I will remove the quotes no problem.


Second, the concept of motion itself is not clearly understood. By definition, motion is strictly the reciprocal relationship of space and time, unit space per unit time or s/t. [Unit space per unit time is the unit of velocity, velocity is measured as space per time.]

Answer: You are 100% correct. The postulates of RS theory posit that space and time are discrete units, so given the size of unit space and the size of unit time, the velocity is the speed of light.

Then s/t is the definition of the basic unit in which velocity is measured, not a definition for motion. A quantity and its units are completely different things, and you should either edit the main page to distinguish them or mention that the theory is somehow conflating them. I can't comment further on most of the below until this is sorted out, because none of it makes any sense as a result.

No, s/t is a definition of motion. The definition of the motion’s dimensions (meters/second for instance) defines the units. The quantity, of course, is the numeric ratio of the dimensions, which itself is dimensionless. I'll edit the page.

You can't divide space by time. You can divide a measure of space, say the distance of something away from me, by a measure of time to get a new measure, say the velocity of recession, but it has to be made clear how we are measuring them, because you can only divide numbers, not things. So for instance the text below, about the datum, means absolutely nothing because you have not specified which measure of space and which measure of time are in a 1:1 ratio.

No one is saying that it is possible to somehow divide space by time (dimensions) without specifying a quantity of each dimension. The assertion is that space and time are not independent entities that are associated arbitrarily. They are postulated to be reciprocal aspects of motion necessarily. That is, an increase in time units relative to the quantity of space units, for example, reduces motion from its unit value to a lesser value, and conversely, a decrease in time units relative to a quantity of space units increases motion from its unit value and vice versa. So, on this basis, one discrete unit of space associated with one discrete unit of time is the natural datum of the universe of motion. The measure of that unit motion, the velocity, is 299,793,000 m/sec. Larson uses the reciprocal of the Rydberg frequency to obtain the natural unit of time by multiplying it (1.520655 x 10-16 seconds) by c to obtain the natural unit of space (4.558816 x 10-6 cm). These two discrete units are then used in a multitude of equations to calculate various theoretical physical entities for comparison to actual physical data in the course of the investigation.


Notice that nothing else is required for a complete definition. In other words, it is not required that an object is moving, only that a certain quantity of space is associated with a given quantity of time. [Motion doesn't require anything to be moving - something is funny about your definition here, and it needs to be clarified.]

Answer: This is a difficulty we all have at first, because we are accustomed to dealing exclusively with the motions of mass and radiation. However, strictly speaking we can see that the definition of motion is space per unit time, s/t, period. When space and time are associated in this manner motion is defined, it exists. Velocity is a measure of the ratio of the space and time aspects of the motion. When that ratio is 1:1, the natural datum of motion, the velocity is determined by the size of the discrete space unit and the size of the discrete time unit. This motion is not the motion of any “thing,” it is actually a mathematical progression of space and time: 1,2,3,4,5,..n. Evidence that both space increases and time increases is evidence that motion exists by definition because neither an increase in space, nor an increase in time can occur without motion. Does that help? Let me know. ___________

This motion is not vectorial, but scalar. A scalar motion, unlike a vectorial motion, has no direction in space that can be described by a vector. It has only magnitude, which can either increase or decrease. This increase or decrease in scalar value can be described in terms of direction, but in this case the word direction is used in a scalar sense, like saying the stocks in the stock market are going `up' in value or `down' in value. The clearest examples of scalar motion, identified by Larson, are the universal expansion of space (as evidenced by the galactic recession), which is an outward scalar motion, and the local contraction of space (as evidenced by the effects of gravity), which is an inward scalar motion. [Galactic recessions and gravity both have directions, and they are well-documented, which would mean that this sort of motion being ignored by science is not true.]

Answer: This is a good observation Josh, the galaxies do have directions, but not vectorial directions in the usual sense. The vectors that you refer to result from the coupling of the scalar motion to a fixed reference system. Let me try to elaborate. Say I were on galaxy A and you were on galaxy B and Larry was on galaxy C, all lying in a straight line. A funny thing happens as result of the scalar expansion of space. Since a scalar has no direction in space, space is expanding in all directions, that is every point is moving away from every other point in space. Therefore, if you were to observe me, I would appear to moving away from you along the line and Larry would also be moving away form you on the line. You could measure the velocity, you could measure the acceleration, etc. Larry could take the same measurements and they would show you moving towards me with a velocity x and an acceleration y and me moving away from both of you at certain values. No, I would exclaim, that’s impossible Larry (assuming we could all communicate), because my data shows Josh moving in your direction, not mine! But Larry would protest that his data is indisputable. Who is correct? The answer is they both are correct because the vectors they are plotting are generated by the reference system they occupy. So all galaxies are moving away from our galaxy, and unless we think that our galaxy is special (who knows, maybe it is) we are also moving away from them. That is scalar motion. _________

The third observation is the recognition that the natural datum or reference point of motion is unity not zero as we are accustomed to think. [Objects move zero space in unit time relative to themselves; I have no clue what you mean by a datum, but if it is to be non-zero it must mean something other than this, and so ought to be thoroughly explained.]

Answer: This point in the article needs to be clarified. What this should say is that we need to recognize that the proper reference for scalar motion (not the vectorial motion of our common experience – you can’t talk a Cop out of a ticket with this) is unity, not zero. In our normal experience, the motion of an object is measured relative to some fixed point considered to be at rest. We measure the time it takes the object to move a given distance and then we can state its velocity as s/t. But this is dealing with the object’s motion, not motion proper. When we speak concerning establishing a reference point for s/t itself for measurement purposes, we must measure s/t in terms of the magnitude that the ratio of space to time varies from 1. __________

Finally, it is recognized that since space and time are reciprocal aspects of motion, [We divide the two to get the velocity, sure, but what are reciprocal aspects?] the principle of symmetry implies that the property of one is also the property of the other. [What is this principle, and where did it come from?] For instance, since the space aspect of motion is a discrete or quantum unit, the time aspect must be also, and since space is three dimensional, time must be also. [How did we decide space is quantized, and how does a three-dimensional time relate to the single number that is measured by our clocks?]

Answer: The first two questions can best be answered by consulting Wikipedia or another reliable source. The answer to the first part of the last question is that it is assumed in the postulates. The answer to the second part is very interesting, but it’s a little beyond what I can do here. Suffice it to say that the clock time is a well known scalar value and that we need the Special theory of Relativity to mathematically compensate for the effects of three-dimensional time at relativistic speeds without RS. But within RS theory, we don’t need Special Relativity to understand its effects at these speeds.

I have read hundreds of reliable sources and never run into the concept of reciprocal aspects, and I'm afraid that without an explanation as to what happened to the extra dimensions of time, the theory is talking about something that has no relationship to observed reality whatsoever.


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

Answer: Please consult normal sources for these answers.

I am in a pure mathematics department, for heaven's sakes. Neither term has ever been used, so they are at the very least extremely non-standard. Please define them.

LOL - I stand to be corrected by math whizes, but I always assumed these terms referd to the normal sense of the words. Commutative mathematics means the product or sum of terms is the same regardless of the order of operation and absolute magnitude means |s| and |t|. We cannot use an expression such as -s/t or s/-t, the 2 postulate excludes it. I'm guess I'm assuming too much here - so sorry. ___________

An important aspect of the theoretical existence of the progression is the recognition that an arbitrarily chosen reference frame of fixed spatial coordinates, within which we are accustomed to considering and experiencing physical phenomena, is necessarily limited in its capability to correctly represent all the motion present in the natural reference frame. [People using moving reference frames all the time, and our theoretical framework does not actually need reference frames at all, any more than Euclidean geometry needs a coordinate system - they just come in handy.]

Answer: It is difficult to understand the limitations of the conventional reference frame without understanding the natural reference frame first. The natural frame of reference in RS is a moving reference system; therefore, there is relative motion between it and a gravitationally bound conventional fixed reference system. A location that is stationary in the moving system, actually moves at maximum velocity (c) with respect to a fixed system, and a location moving with respect to the moving system is actually moving slower relative to the fixed system. It is helpful to master the concept of the moving system first, here is a helpful quote from Larson:

“Cosmologists often begin their analyses of large-scale physical processes with a consideration of a hypothetical ‘empty’ universe, one in which no matter exists in the postulated space-time setting. But an empty universe of motion is an impossibility. Without motion there would be no universe. The most primitive condition, the situation which prevails when the universe of motion exists, but nothing at all is happening in that universe, is a condition in which units of motion exist independently, with no interaction. In this condition all speed is unity, one unit of space per unit of time, and since all units of motion are alike--they have no property but speed, and that is unity for all--the entire universe is a featureless uniformity. In order that there may be physical phenomena that can be observed or measured there must be some deviation from this one-to-one relation, and since it is the deviation that is observable, the amount of the deviation is a measure of the magnitude of the phenomenon. Thus all physical activity, all change that occurs in the system of motions that constitutes the universe, extends from unity, not from zero.” ___________

When motion is considered in the natural frame of reference however, such confusion, and the need for complex mathematics to deal with it, are eliminated. For instance, viewed from an arbitrary fixed coordinate system, photon emission is puzzling because photons are somehow able to travel from any point, in any direction at constant speed, c, forever (the speed of light is usually denoted by the letter c), unless intercepted by an intervening object. But when this same physical phenomenon is viewed within the natural reference system, it is easy to see that a motion such as a photon must progress with the natural reference system in at least one dimension at unit velocity (s/t or c) from whatever point it originates. It's as if the photon becomes a marker, making a given location in space visible, and thus revealing the preexistent motion of the Progression from that particular point in the fixed reference system. [I honestly don't understand this at all, but hopefully clarification of the above terms will fix this.]

Answer: The vibrational motion of a photon is measured by its frequency, but its translational motion is always c with respect to a conventional reference frame. This motion of propagation, as we’ve come to call it, is a result of the fact that when the motion of at least one dimension of the photon in the moving system is unity, meaning, remember, that it is “at rest” in that dimension of the system, the location of the photon is carried by the moving system’s motion (c) relative to the fixed system, from whatever point it originates.


In fact, some of these properties can now be calculated from theory for the first time in the history of science, the charge of an electron for example. [2] [How can things be calculated when no mathematical framework has been set up?]

Answer: Exactly! This allegation can only come form those who know next to nothing about RS. That’s why it is hopeless to try to refute it. I hope you can begin to see now that RS is a new conceptual view of the origin of all physical activity. Changing a conceptual view of the origin of mass and energy does not require a new mathematical treatment of these entities! We use the same math that has always been used in physics. Some clarifications have been accomplished because the RS view has cleared up some confusion in ascribing correct dimensions to equations, but there is no need for a new convoluted mathematical treatment of physical relationships because the new concept clarifies those relationships to well known and relatively easily expressed relationships already firmly established by science. What RS has done, which is a monumental achievement, is to demonstrate that all quantities and values of physical entities, whether mechanical, electrical or magnetic, can be reduced to equivalent space and time dimensions!

'It hasn't demonstrated anything until you accept the postulates, there is no reason to accept the postulates until it has been shown they conform to physical reality, and it hasn't been shown to conform to physical reality until a coherent mathematical framework has been presented. If one hasn't, you should mention this as a critical weakness in the theory.


Again, these theoretical properties of the theoretical combos are not only easily identified with the actual properties measured by experimental techniques, but give additional insight for the first time. It explains for instance, for the first time ever in the history of science, why the force of gravity between mass aggregates is proportional to the square of the distance between them. It also explains, again for the first time ever, why magnetic force ?induces? electrical force and vice versa. [So you don't like our explanations. Well, some people do, believe it or not.]

Answer: As far as I know, there are no answers outside RS to these questions Josh.

The inverse square nature of gravitation comes about naturally from its consideration as a field, and is a theorem based on the fairly simple postulates of general relativity, so I would consider it explained. Electromagnetic induction is somewhat inherent to the structure of Maxwell's electromagnetism, but at the very least is a derived property in the Kaluza-Klein theory, so has to count as being explained in some models as well. ________

In RS, atomic combos theoretically bind together to form theoretical molecules when their relative motions bring them to within one unit of space of each other. At this point, a theoretical reversal takes place in the effective scalar direction of their motions such that the natural progression acts to draw them closer while their less-than-unit motion acts to push them apart, thus establishing a stable point of equilibrium known as the inter-atomic distance. If this equilibrium exists between all three dimensions of motion, the combos form a theoretical solid molecule. If two of the dimensions are in equilibrium, the combos form a theoretical liquid molecule, and if only one dimension is in equilibrium, the combos form a theoretical gas molecule. [4] [Do we have any explanation of other phases, or of chemistry? If not, this should be noted.]

Answer: This is a huge question and I don’t mind telling you that I’m getting in over my head here. But at least one short answer is that RS theory can account for chemical bonds that are formed, not by electron valences, not by covalent bonds, not by ionic bonds, not by any of the other concepts that chemistry and physics employ to account for them. In RS theory, the answers to atomic and molecular cohesion in solids, liquids and gases has nothing to do with the nuclear and electronic concepts of the atom. In RS theory, all these bonds are the result of the interactions of the constituent motions of the combos involved and the fact that when only one unit of space remains between combos, the scalar direction (inward/outward) of the motion due to the progression and the motion due to gravity reverses at the unit space boundary and enables the combos to take up equilibrium positions in space relative to one another. When theoretical calculations of these distances are made and compared to actual empirical data, the match is impressive.

So, you manage to explain why we observe structures like H2O and H2O2 but not HO or H3O? CO but not CH2? XeF4? You still haven't explained, though, how RS handles other phases like liquid crystals and superfluids, or handles allotropic materials like carbon. Since the solid-liquid-gas trichotomy is inherent to the theory, I would doubt it can. __________

Once again, these theoretical entities are easily identified with actual physical atoms and molecules according to physical data obtained by experiment. Not only can many of their properties be calculated theoretically and closely correlated with experimental data, but many, heretofore unexplainable behaviors are now easily explained as well. For instance, the inter-atomic distances in compounds and the binding energy involved, the ionization potential of matter, thermal expansion and specific heat properties, electrical properties of electrical conductors and the behavior of electrical current, and many others are theoretically consistent and quantifiably predictable within RS and highly correlate with actual empirical results obtainable from experiment. [Again, conventional physics does a great job with these, and it is questionable if RS has a math framework strong enough to give any results without having the results in mind from the outset.]

Answer: The point is not that conventional physics doesn’t arrive at precise values for electrical properties and behavior characteristics, but that it can’t do so from first principles. RS researchers are so rare and so new at it, that in many, many cases solutions are much more readily obtained by conventional means and of course RS researchers depend upon the empirical data obtained by conventional science for testing and verifying RS ideas.

Depends on what part of physics you look at. _________

Well, I hope this helps. I just want to say in closing, that these are good questions, and that my feeble attempts at answers do not do justice to RS. Hopefully though, the result of this attempt will be that at least some of you will go to the source to learn more, and that we can get past this fake science issue eventually.

Thanks for your efforts Josh.


Saa.... if space is discrete, objects cannot rotate except through either 60-degree or 90-degree angles, can they?