Absolutely. One of the major differences between string theory and reciprocal system theory, is that reciprocal system theory is quantified and makes predictions in terms of physically measurable quantities. I have already mentioned the atomic number and isotopic mass, which QM cannot predict. However, there is more, much more. Nevertheless, so far, what we have in the way of calculations is the work of a few men, applying the system, whereas, in contrast, the Newtonian system has been applied for generations by armies of highly trained people.

One of the areas in which QM excels is in predicting the atomic spectra with the nuclear model, but we have so far been unable to complete these calculations with the RST model. We're working on it, though, and have every expectation of success.

This guy is not a member of our Society and never has been as far as I know. He makes no attempt to communicate with us, but has been trying to promote Larson's ideas for years from his own perspective. Not that there's anything wrong with that, there isn't, but I think people's impressions are sometimes less than what they might be, if they don't get their information from members of our Society. ISUS was formed in the mid seventies, and was specifically organized to promote Larson's work. We are not perfect either, by any meams, but we are determined to present Larson's work as honestly and straightforwardly as possible, having associated with him for many years before his decease in the early nineties.

While he was alive, there was an active interest in his work as indicated by his frequent invitations to address university audiences, NASA personnel, and other interested groups. After he passed away, things died down quite a bit until after the turn of the century. Today, as should be evident from my postings in this forum, theoretical physicists are more prepared than ever to seriously consider his work.

Brilliant Excal, very fine exposition of the possible upcoming change in the fundamental background of physics, as force a function of motion, where space/time is a reciprocal function of motion. In your RST part III, you write: This can be understood, I think, in the sense that even when a reference frame is at rest, say at v=0, the motion continues to exist as "space moving" so that any material quantity at "rest" is in fact already in motion. This is supported by the first and second postulates:

"The first fundamental postulate posits the existence of motion, as the sole constituent of the universe; ...the second postulate, that posits 'motion expressed in space' presents a conundrum, similar to the one we see arising from the conflict of GR and QFT: how do we describe motion in space, when space is defined as an aspect of motion?"

One way out of this conundrum was to simply make space's "motion" (which must have some vectorial direction) as a directionless scalar. At least, this is how I understand it so far. Time as a reciprocal of motion can then be defined as dt = ds/v, which is the same as ds = v*dt; however what is unclear to me, is time now a fixed unit of measure, or can it be a variable as per SR? The choice of "time" units of measure may then affect how we see symmetries in physics, since using time as a unit of measure in space and scalar motion would change the symmetries, I should think.

This problem of symmetries derived from "time as a reciprocal of space/motion" may also have its equivalence in the "conservation law of energy". This is how I see it, and perhaps this could be understood as radiation electromagnetic energy conserved within parameters of its scalar motion of space. In effect, if the Energy Conservation Law is incomplete, meaning it is missing some component to make it whole and totally symmetrical, then there may be a reciprocal form of energy that is (perhaps) gravitational in nature, which is also part of the conserved total. This would mean total Energy is both as an electromagnetic wave and something in gravity (of which we are still ignorant) to give us the fully conserved value. We know both are responsible for motion, both act as a force, and yet in today's fundamental background of physics they are essentially divorced from each other. At present, this is the reason we had not reconciled the two to date. Yet, if Larson's system could show that motion resulting from gravitational force is related to scalar "motion" of moving space, then we should be one step closer towards a system where radiant energy and gravitational energy are two aspects of the same motion. Is this sensible, or am I simply saying it all wrong?

Thanks for bringing up Larson's alternative Reciprocal System of Physical Theory, Excal. I just hope I didn't botch it up (am assuming I did!) too much, trying to explain what I may not yet really understand. I'll read the math next... Still reading...

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Well, the important thing to try to grasp is that space and time don't have any existence apart from motion. What often happens when we first start thinking this new way is that we try to visualize space as something that exists apart from motion in some way. However, just as the left and right ends of a rod can be described as two reciprocal aspects of the rod, which couldn't exist without them, and because we could describe them independently in terms of their different positions, the direction they face, etc, and could treat them in the abstract as if they actually had an existence in their own right, we might begin to forget that they are only aspects of the rod, that the rod is the only thing that actually exists, we would eventually run into trouble.

So it is with scalar motion. Motion is what actually exists. Space and time are only its two reciprocal aspects. No matter how hard you try, you can never have one without the other, just as you can never have a left end of a rod without a right end.


Actually, to be clear, time is an aspect of motion that is the reciprocal of the other aspect of motion, space. In SR, the measure of space and time change to acommodate the speed of light, which must remain constant relative to any inertial frame of reference, but, in the RST, the measures of space and time are discrete values that are absolute, and the constant speed of light in relatively moving inertial frames is accounted for by motion in time, dt/ds, the effect of which is noticable only at relativistic speeds. Therefore, there is no need for adjusting the length of measuring rods, and the rate of clocks to maintain the constancy of the speed of light. See K.V.K Nehru's paper on this entitled "Precession of the Planetary Perihelia Due to Co-ordinate Time," at http://www.reciprocalsystem.com/rs/c...planetperi.htm

I think I understand what you are getting at, and it's an astute observation. However, the details differ somewhat, but that's to be expected. In the RST, the second law of thermodynamics becomes a relatively minor player, since the major cycle of nature is a process whereby matter is transformed over time through the action of gravity. It cycles, over billions of years, between two reciprocal sectors of the universe, which Larson named the material and cosmic sectors. In the material sector, in which we live, the equation of motion is defined on the "low speed" side of unity where ds/dt = 1/(1+n). However, in the cosmic sector of the universe, motion is defined on the flip side of unity, the "high speed" side, where dt/ds = 1/(1+n) as well, but from our perspective it is ds/dt = (1+n)/1. Thus, the perfect symmetry of space/time, provides two sectors of motion relative to the unit datum, or natural reference system of uinversal progression. Gravity is the driver of the evolutionary process in one sector, while inverse gravity is the driver of the process in the reciprocal sector. Thus, as you suspect, total energy is conserved in the symmetry of the system.

However, in the LST, because the definition of motion is limited to an object's change of locations over time, ds/dt, the magnitude of its velocity is limited to 1/1, or c. Nevertheless, dt/ds, is also motion in the RST, therefore matter can move at speeds higher than c, but the motion is not space motion, it is time motion. This gives rise to bizarre astronomical phenomena from the "low speed" perspective, because it's not recognized for what it is.

No problem. In the next post, part VI, we'll be looking at the contrast between the application of mathematics in the LST, based on PDEs, and the application of mathematics in the RST, based on the rational number system as a mathematical group. I think you will find it most interesting.

Regards,

Doug

In the Newtonian system of physical theory, which I'm going to presumptiously refer to as the legacy system of physical theory (LST), for brevity's sake, everything is based on the function x(t), given Newton's laws of vectorial motion, while in the Reciprocal System of Physical Theory (RST), everything is based on the function x(t), and a new function, t(x), given the new interpretation of the nature of space/time, as the two reciprocal aspects of scalar motion.

In the LST, the focus on forces to describe and explain the relationships between the properties of mass, magnetic moment, and electrical charge, necessarily involves understanding the coordinate path of an entity, because changes in the coordinate path, or location, of a physical entity constitutes the condition which gives rise to force, given Newtons laws. However, the science of dimensional analysis, initially employed in the investigation of forces, quickly becomes tedious and unwieldy in this respect.

Fortunately, however, it was discovered that such studies could be simplified to a great extent by expressing these relationships in terms of energy, instead of force. Thus, the total energy of a system, in terms of its kinetic and potential energy, can be formulated as Legrangian equations of motion, leading to Hamiltonian mechanics, taking advantage of the principle of least action to simplify the study of forces.

Consequently, the Legrangian and Hamiltonian fomalisms of mechanics have led the way to understanding how the properties of physical entities are related, including easing the transition from the concept of force associated with a coordinate path, an x(t) function, to the concept of force associated with a coordinate field, written as a q(x) function, where x represents both space and time coordinates. This mathematical reinterpretation of the x(t) function, enabled the reformulation of Newton's universal law of gravity into a function of a field, the G field, the gravitational field, and eventually, it enabled Maxwell's formulation of the magnetic and electric equations of motion as fields as well, the E and B fields, and their unification in the electromagnetic field theory.

The dramatic success of these and subsequent developments have led to unimaginable advances in engineering and technology that have harnessed this knowledge for the material benefit of mankind, and led to the enshrining of theoretical physics as the foundation of modern civilization and enlightenment. Interestingly enough, it has also led to the conviction among physicists that the "unreasonable effectiveness of mathematics in physics" is the hallmark of modern theoretical physics.

However, it should be clear that removing the requirement that we need a background of space and time coordinates in order to define motion, and moving up to a more fundamental understanding of the nature of space and time, as the reciprocal aspects of a universal motion, existing in three dimensions, and in discrete units, is going to have an enormous impact on the need for these complex mathematical formulations, used so effectively in the LST research program, namely the ubiquitous use of partial differential equations.

Moreover, since the primary aim of the RST program is not to determine how the given properties of physical entities relate to one another, as it is in the LST program, but rather to determine how the observed properties of physical entities originate from more fundamental entities, namely the discrete units of space/time, the mathematics of the RST most likely will be dramatically simplified, at least initially, but, by the same token also, it will likely exhibit another surprising and enlightening aspect of the "unreasonable effectiveness of mathematics in [theoretical] physics."

In the RST definition of motion, the postulate of the reciprocal relation of space and time, and discrete units of motion, constitute a major move of physics into the rational number system that is closed under non-zero division. Since the progression ratio of space and time can never be zero (time and space never stop progressing), this means that the system itself is indeed closed, containing its own boundary. More importantly, this means that the mathematics of the RST is a group, the ultimate closure structure.

The significance of this is that the Reciprocal System mathematics can be encapsulated in one sentence: the RST mathematics is the set of all properties that can be conserved by the rational number system group. So, just as special relativity is the study of all properties conserved under the Lorentz group of transformations, the RST is the study of all properties conserved under the rational number system group of transformations. The basic concept of group is symmetry, and, as mentioned in previous posts in this series, Emmy Noether proved that symmetry is the conservation law of nature. This is why mathematical groups have such predictive power and have assumed such a prominent role in modern theoretical physics, starting with Murray Gell-Mann's prediction of the omega minus particle on the basis of completing the symmetry of a group. [6]

With the progression ratio ds/dt defining the mathematics of RST motion, the group structure implies that the inverse ratio, dt/ds, is also closed. Thus, the symmetry of the RST is the perfect symmetry of the group, which is ds/dt = dt/ds = 1/1. With the possibility of zero eliminated, the datum of the system becomes this operational definition of unit magnitude, and any displacement of the progression rate of space or time, relative to its reciprocal aspect, "breaks" the fundamental symmetry of the unit ratio, but conserves it in the symmetry of the group. In other words, |1/n| is equal to |n/1|, because there is no way to distinguish the two magnitudes from the point of view of the datum of the system, 1/1.

This is interesting, because it sheds new light on the meaning of the natural and integer number systems as well as the meaning of Euclidean geometry, which is assumed to be a property of the universe of motion, in the second fundamental postulate of the system. The difference between the natural number system and the integer number system is found in the negative numbers of the integer system that don't exist in the natural number system. Both the natural number system and the integer number system start with the number zero, an enigmatic concept to say the least, but one we have come to take for granted.

However, because the negative numbers are the mirror image of the positive numbers in the integer system, zero stands between -1 and 1 in that system. Yet, while zero quantity makes some sense in the natural number system, it is completely out of place in the integer system, since, strictly speaking, zero is not actually a number and therefore cannot be an integer. The Merriam-Webster dictionary definition of the word integer reveals the subtlty involved. It defines an integer as, first, "any of the natural numbers, the negatives of these numbers, or zero," which explicity excludes zero as a natural number, and, secondly, as "a complete entity," something, by definition, zero is not.

Hence, something is obviously askew in our need for the quasi-number zero, but it's difficult to define exactly what it is. Obviously, we can't manage without it, yet we can't strictly define it as a number either. As it turns out, in the RST definition of motion, the quasi-number zero doesn't exist. In listing the integers of the integer system defined by the operational definition of an integer, zero disappears. This is because, operationally, the definition of the zero datum, the system's point of reference, is 1 = 1/1; that is, the difference between negative 1 and positive 1 is the operationally defined difference between 1/2 and 2/1, and the operational magnitude that stands between these two magnitudes is 1/1, not zero. Hence the integer number system is the set of integers operationally defined by the ratio of natural numbers, which excludes zero, because it is not a natural number. It is true that it is included in the mainstream list of integers, but including it in the list of integers is misleading, if the difference between an operationally defined magnitude and a quantitatively defined magnitude is not understood.

(See continuation in following post)

There is another important aspect to this number system as well. Not only can integer magnitudes be interpreted operationally, or quantitatively, but also the difference can go the other way, wherein the ratio of two integers may be understood operationally or quantitatively as well. Thus, in the quantitative interpretation, the ratio of 1/2 = .5 is not a magnitude equal to 2/1 = 2. However, in the operational interpretation, the magnitude of the ratio 1/2 = 1 is a magnitude equal to the ratio 2/1 = 1, just as the unequal magnitude on one side of a pan balance is no different than the same imbalance, if it were to be placed on the other side of the balance. The only difference is which side of the balance the magnitude happens to be found. We can distinguish this in the number system by the use of the "direction" concept of positive and negative, and so we do in the integer number system, but there is no difference in the magnitudes themselves. Hence, it makes no sense to write operationally defined magnitudes as ratios of signed integers. Operationally defined integers are all simply magnitudes. The "direction" we use to distinguish them is only an indication of which "direction" in the ratio, relative to the unit ratio, the magnitude lies. We can say one is "above" unity, while the other is "below" unity, or we can say that one is "positive" and the other "negative," but relative to the datum of the system, 1/1, there is no material difference in the magnitudes themselves.

One method that has been found to encapsulate the nature of this relationship of the integer number system to the rational number system is an adaptation of a cellular automata (CA) rule, designated rule 254, by Steven Wolfram. [7] This automaton is, to Wolfram, one of the most uninteresting of all automata generated by CA rules: a perfectly symmetrical triangle as shown in figure 1. However, by slightly modifying the meaning of the output of rule 254, we obtain an operational definition of integer magnitudes; that is, if we define the center column of rule 254, as the demarcation between the reciprocal integers, the operation indicator served by the '/' symbol in mathematical notation of rational numbers, and then define the total number of units to the left of the center column as one integer and the total number of units to the right of center as the corresponding reciprocal integer, then as the rule proceeds and adds one unit on each side of center to the accumulated total number of units on either side, as each successive row is generated by the rule, the result is a visual graph of the 1/1 reference datum of the rational number system expressed as a progression of reciprocal integers, the ratio of which is constant at 1/1.



Figure 1. Wolfram's CA Rule 254.

Thus, we start with row 1, which contains one black cell, then row 2 has two black cells on either side of the operation symbol, or 1/1. When row 3 appears, there are 2 black cells on either side, or 2/2, which is also a 1/1 ratio, and so on, ad infinitum. Therefore, the output of CA rule 254 is the integer 1, operationally defined as 1 = 1/1, which is actually the reference datum of the rational number system, sometimes mistakenly denoted as zero, as explained above.

To generate the integer commonly designated 1, or -1, which is really 1 = 1/2, or 1 = 2/1, as also explained above, we need to change the rule. Now, I don't know if there is a CA rule that will do this, although there may be one, but, nevertheless, I do know there is an algorithm, that I have dubbed the progression algorithm (PA), that will reproduce the pattern of CA rule 254 and also a deviation from this pattern, which will produce the 1/2 ratio, or the 2/1 ratio.

The PA adopts the operationally interpreted rational output of CA rule 254, and designates the left side integer as the space progression, and the reciprocal, or right side integer, as the time progression. Thus, the PA corresponding to CA rule 254 is a representation of the RST's natural reference system as defined by Larson, as shown in figure 2.



Figure 2. The Natural Reference System PA.

Obviously, we can use this to study the properties of the system. For instance, the sides of the triangle represent the unit ratio boundary, since any change in the ratio from 1/1, would immediately change the location of the sides, breaking the symmetry of the system in the process. Also, we can visually see the meaning of "direction" in our system, as the left unit boundary is distinct from the right unit boundary relative to the center column, but at the same time they are one and the same boundary, viewed from different points of view, giving us at once a clear understanding of the meaning of the concept of reciprocity, as the symmetrical growth of one entity with two reciprocal aspects.

We also clearly see the concept of discrete units of space and time in the PA, but only as the reciprocal aspects of the units of progression, or the rows. Without the reciprocal integers, we would lose the definition of the row, without the row, we don't have a progression. Therefore, one cannot exist without the other. There are other properties of the PA, which give us great insight into the RST, but we will have to wait to consider these until we can take up the subject again in the next post.

I hope that I have been able to show in this post, that, while the mathematics of the RST are based on the deceptively simple set of rational numbers, there is a lot here that we are not used to perceiving in connection with this number system, and also, that the fundamental symmetry of the system portends great things to come, for as some great philosophers have noted in the past, many times, out of that which is small, proceedeth that which is great.

References:

6) Jon Hays, "Arithmetic Redux", http://members.fortunecity.com/jonhays/redux.htm

7) Steven Wolfram, Mathworld at Wolfram Research, http://mathworld.wolfram.com/Element...Automaton.html

Are you talking about predicting the mass defect, or the most stable isotope?
Is there a page that would show me how to do the calculation that I mentioned earlier (how long it would take for a mass to fall a certain distance in a 1g gravitational field.)? As I said, I'm may seem a bit impatient, but it's the maths that would give me the warm fuzzy feeling about the approach.

I hope you don't get too impatient with me, Fortis, but you have to understand that once you have the mass, magnetic quantity or electric charge, the standard LST equations apply in calculating the interaction of that mass, magnetic quantity, or charge with another. The thing that the RST provides is the calculation of the mass, magnetic quantity, or charge, given only the unit of space (4.558816 x 10^-6 cm), and the unit of time (1.520655 x 10^-16) of the system. This is something that no LST theory can do, so it's big news.

However, in order to carry out the calculations of mass, say, of the electron, proton, neutron, or the atom of a given element, or the magnetic moment or charge of an electron, proton, etc, you first have to learn how to do it. To learn to do it, you have to understand the concepts I'm introducing in my posts, because it's a whole new ball game, if you know what I mean.

Now, I understand that the explanations are a little verbose, but I find it necessary to motivate the conclusions involved, as well as expound them, so this is why I'm taking it so painstakingly slow. However, we will get to the calculation part in due course, if you can stick with me.

As far as the mass defect goes, in the RST model of the atom, protons and neutrons don't exist as such within a "nucleus" surrounded by electrons. So the missing mass, called mass defect, cannot be attributed to the "binding" energy between these particles, as it is in the LST model. In the RST model, it is due to secondary mass effects, which will be explained eventually. The average isotopic mass calculations for a given element have to do with an isotopic build up process involving a magnetic "charge" and interactions with neutrinos, so it's quite involved. The only way to understand it, is to understand how the model is constructed from discrete units of motion.

It looks like a "double helix" to me, where the positive electron values are one strand, and negative ones are the other. Otherwise, it is a more intuitive illustration than the standard box format.

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somehow I am getting the suspition that in the end all physical calculations are going to be the same, except that the philosophical background is going to be different. But we will never be able to observe this background.
Just my 2 eurocents at this point

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Martin ( http://www.geocities.com/DrMartinV )

That's an interesting observation!

The assumption of the Newtonian system is that matter consists of a composite of particles. The fundamental particles form atoms and atoms form matter. The aim of the system is to classify these constituent particles according to how they interact. This means finding the way to calculate (predict) these interactions given the properties of the particles. Thus, the standard model, which represents the "final answer," the best answer we can come up with so far, identifies three families of particles classified according to a set of interactions that we have been able to identify.

However, the model must be given the properties of these particles before these calculations can be carried out. I think it's something like 19 to 24 parameters that must be obtained from observation, before the model can be constructed. This is not what we want for a final answer. We want to be able to explain the properties of radiation, matter, and energy in terms of fundamental entities, but it appears that the Newtonian research program isn't going to get us there. We are stuck. We are stuck with the standard model of matter, and we are stuck with a separate model of gravity. It's an awful, and unsatisfactory (ugly and adhoc in the words of Hawking) result of the program.

Now, having said that, we also have to recognize that the Newtonian program was never intended to do what we are now demanding of it; that is, its aim was to classify a few particles according to a few interactions, and, for the most part, it has done that, and it has done it extremely well. But now, we want to go beyond that, and the program simply is not up to it. We need a new research program to go beyond the standard model.

I'm suggesting that the Reciprocal System is just the research program to do what we want. So, we are not talking about a specific theory here, but a new research program that will enable us to construct physical theory on a completely different basis. One that will not need observed properties, and a myriad of "constants," to describe and explain all the physical properties of all physical entities. The system to do this is based on a new type of motion, a motion that is posited to be the intrinsic motion of matter, never understood before.

However, the thing I must try to make clear is that, if this is true, the dynamics of the new, intrinsic, motion of matter, does not replace the motion of matter, nor the principles that we have learned, and the methods we have devised that enable us to describe how the properties of matter relate to one another. In other words, all that has been accomplished by the Newtonian system is not invalidated and replaced by the Reciprocal System, it is simply expanded into a new realm that only a new interpretation of the nature of space and time could achieve.

But please understand, though philosophy necessarily must be a big part of the description of the new research program, the theory developed to date under the new system has achieved a great deal. It has calculated properties of matter, it has eliminated "constants" of nature, it has resolved many conflicts of current models of electrical and magnetic phenomena, it has predicted major astronomical events before they have been observed, it has unified the known forces into one primary force equation, and, much, much more. It's not just philosophy.

However, what it has not done is provide a new way to calculate the interactions of matter. We already know how to do that.

Would it not be simpler to say that n/1 integer times its inverse 1/n is always equal to 1 = 1/1 ? In this way, the (non) integer zero makes sense: as n increases to infinity, 1/n decreases to zero. So what you get is n/1 * 1/n = 1, of necessity always, and zero is retained. Therefore, if it can be used this way, ds/dt = 1/1 = 1, so that the reciprocallity of space/time symmetry is conserved. Would this explanation alter the balance of what "integer" based RST math represents? Taking it to any integer, say 3, then 3 * 1/3 = 1, etc., just reciprocal values of ds and dt, but always within the symmetry of unity. At n = ds = 'space to infinity', then dt = 1/n = 'time to zero', for example, yet symmetrical.

This would also work, I think, for x^2 + y^2 + z^2 = c^2*t^2, as per your earlier illustration: x^2 + y^2 + z^2 - c^2*t^2 = 0. The conclusion drawn would be that at t=0, space is contained on a point in motion. Would this be right, or am I off on an imaginary tangent here?

Is this definition of unit magnitude within the parameters of math you are presenting?

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This is a good point. However, defining zero as an integer = 1/infinity just shows the inverse compliance of the group, it doesn't enable us to place zero between the negative and positive integers in the integer number system, as if it were the datum of the system. We start with the natural numbers, which does not include zero. Then we operationally define the integer number sytem from the natural number system, which generates the positive and negative integers, as described. These extend from 1 to infinity, because the natural numbers extend from one to infinity, but, in a sense as you point out, the inverse of infinity is zero, so it could be understod as infinity/1 * 1/infinity = infinity/0 at the far end of range. Fortunately, however,the discrete unit postulate rescues us from the logical impasse this presents, as I hope to show eventually.

I wrote

That was blatant error, as obviously infinity/1 * 1/infinity does not equal infinity/0. I was too tired when I was writing the above post. Obviously, the above equation would actually equal infinity * 0 = infinity, not infinity/0. However, infinity times its inverse, 1/infinity, is actually equal to infinity/infinity, which is equal to 1/1. We must remember that 1/infinity is NOT actually, zero, although it's conveniently regarded as such many times. In fact, given Zeno's paradox, zero is not any more attainable than infinity, so the most acurrate position to take operationally is that infinity times inverse infinity = 1/1, or 1, as you say. Whether it means that "at t=0, space is contained on a point in motion," I don't know.