## Introduction to Doug's RSt

Discussion of Larson Research Center work.

Moderator: dbundy

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Introduction to Doug's RSt

Ok, this is good. I appreciate Bruce's generosity in providing this space for discussing my work at the Larson Research Center, http://www.lrcphysics.com

It should be understood that, just as the Newtonian program of research is a system of theory, under which many physical theories are developed to explain nature in terms of the fewest number of interactions among the fewest number of particles, so too Larson's Reciprocal System of physical theory accommodates various theoretical approaches to explain nature in terms of scalar motion.

So far, there are three different approaches. One is the approach of Ronald Satz, who continues to develop Larson's original work. Another is the RS2, which is pursued by Bruce Peret and Gopi, and then there is my approach, being developed at the LRC.

To keep this understanding as clear as possible, I refer to Larson's SYSTEM as the Reciprocal System of Physical Theory (RST), and a given RST-based theory as a Reciprocal System theory or RSt.

The fundamental differences between these three RSt approaches is found in the way they treat the uniform progression of space and time, the scalar motion posited by the fundamental postulates of the RST, the foundation of the new system.

In my RSt, the deviation from the uniform progression that creates physical entities is a 3D oscillation, which replaces Larson's 1D oscillation leading to the photon. In my RSt, the photon is created when a 3D space oscillation combines with a 3D time oscillation. These entities are named, but I will refer to them here as the S and T entities.

Because of the reciprocal nature of space and time that the RST posits, The Ss progress in time only, while the Ts progress in space only, making it possible for them to collide and combine, forming an S|T combo that progresses both in space and time.

When these S|T units combine in two or more, as parallel combos. like sticks in a bundle, they form bosons, and when they combine in three or more, as triplets in a triangle, they form fermions. These are identified with the bosons and fermions of the first family of the legacy system of theory (LST) community's standard model of particle physics (SM), with the exception of the HIggs boson. To read more on this, please see:

http://dbundy.squarespace.com/scalar-ph ... odels.html

The major advantages of this approach are that it is consonant with the postulates of the RST, and it is formulated mathematically, something for which students of Larson often longed to see in closed form.

As requested earlier in the General Discussion topic "Dimensions in the Reciprocal System," I will explain the mathematical formalism of the S|T units, or preons, in a subsequent post.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

To teach the algebra being used in the RST-based research of the LRC, we start with the chart showing that the one-to-one numerical ratio of increasing space and time of its 3D uniform motion, the fundamental motion of the system, is changed to a one-to-two ratio by the introduction of the continuous oscillations in one aspect or the other (Please ignore the two PA charts in the upper right corner for now):

No oscillation: s/t = 1/1
Space oscillation: s/t = 1/2
Time oscillation: s/t = 2/1

Since the increasing space and time of the system are reciprocal quantities, this implies that any given instance of these oscillating entities is subject to encountering the space or time location of another, reciprocal, instance. When that event occurs, we assume the possibility of their combining into one compound entity, which we designate as an S|T unit.

The algebraic operation of adding the space/time ratios of these two entities adds like terms together; that is, it adds numerator to numerator and denominator to denominator:

1/2 + 2/1 = 1+2/2+1 = 3/3

However, this operation is incomplete in that it does not take into account that the two RATIOS are actually reciprocals. As reciprocals, they are equally distant, or "displaced, "we might say, from the unit ratio, 1/1, but in opposite "directions." In fact, each ratio is unit distant, or displaced one unit from the unit ratio, in opposite "directions."

Normally, we designate these two opposite "directions," as opposite "+" and "-" poles, and our algebra gives us "0" when -1 is added to +1. However, in our case, the reference (or datum) from which the ratios 1/2 (-1) and 2/1 (+1) are measured is 1/1 (0), and we want to include it in our sum of ratios, in order to account for the changing delta inherent in the oscillations of the two entities. Hence, in this algebra, the sum of the two, reciprocal entities is not zero, but four:

S|T = 1/2 + 1/1 + 2/1 = 4/4

This result is intuitive, when we consider that only the "direction" of the oscillating aspect of the displaced entity is changing. The actual quantity of space (time) changed per cycle is always two units. So, the progression of the entity is really s/t = 2/2 in absolute terms, and 2/2 + 2/2 = 4/4.

(More later)

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

Given the scalar motion algebra of our RST-based research, introduced in the previous post, the fact that everything in the development of our RSt is either a motion, a combination of motions or relation between them, makes such an algebra very useful, even though we don't have a scalar motion calculus, as yet.

The clearest example of this is the first and most fundamental algebraic operation of summing scalar motions. It enables us to quantify the scalar motion of the S|T unit:

S|T = 1/2 + 1/1 + 2/1 = 4/4

Identifying this unit with the photon is straightforward, since it is an oscillating entity, or quantum, of space and time, the translational scalar motion of which is unit speed, relative to the uncombined S and T oscillations (Please refer to the chart in the previous post.)

So the question naturally arises regarding other operations of the scalar motion algebra: Can we subtract, multiply and divide with it as well? Happily the answer is an unqualified yes, we can!

This mathematical development actually entails a great clarification of fundamental algebra and geometry, which has been explored in detail at the LRC website, for those interested.

Briefly, though, the development focuses on the fundamental relation of the mathematics of the binomial expansion to the geometry of what we have dubbed "Larson's Cube." As it turns out, we are able to show that the first four levels of the expansion, dubbed the "Tetraktys" in our RSt, constitute a mathematical equivalent to the 3D geometry of Larson's Cube, in terms of the dimensions and the binary "directions" of its magnitudes.

Indeed, one of the conclusions that we draw from this exciting discovery is that those three properties are the fundamental properties of numbers: A number in the tetraktys has an associated dimension, magnitude and "direction," which corresponds to those same properties in the stack of 2x2x2 = 8 unit cubes of Larson's cube.

This is vitally important to understand in our RSt, because the geometry of scalar expansion in three dimensions is the geometry of the S|T unit, identified as the photon in our theoretical development. As such, it is the preon, or pre-cursor, to the bosons and fermions of the theory.

The tetraktys has the same magnitudes, dimensions and "directions." To wit:
• 20 = 1 = 0D unit expansion of LC (point)
21 = 2 = 1D unit expansion of LC (Line)
22 = 4 = 2D unit expansion of LC (Area)
23 = 8 = 3D unit expansion of LC (Volume)

With this much understood, we can move on to explain how the S|T preons form bosons and fermions, next time.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

Identifying the numbers of the binomially expanded tetraktys, with the geometry of 2x2x2 = 8 unit stack of cubes known as Larson's cube, discussed in the previous post, is an exciting breakthrough in RST-based theoretical research, because it helps us to quantify the unit space and time oscillations of the system in closed form expressions that enable us to combine them, mathematically, in various ways, and explore how these motions and combinations of motions relate to one another.

Recall that we start with the 3D space/time (time/space) unit progression and then posit that oscillations, or simple harmonic motion, exists in the system, as well as the uniform linear progression. Here is the basic 2D illustration of the concept:

Here, the square root of 3 is the magnitude of the radius of the 3D space and time oscillations, while the dimension of their respective, non-oscillating aspect is 0, or scalar. Now, it's important to understand that the chart illustrates the two possibilities being posited, it should not be inferred that the two occur together as shown, but only that at some space location, or moment of time, in the unit progression, it is possible that instances of these oscillations may exist.

When they do exist, the further possibility exists that a time oscillation may be in the future of a space oscillation and vice-versa. If they do come into contact we can also assume that they, being reciprocal in nature, would combine into a compound unit of space and time oscillations. This being the case, our understanding of the properties of the tetraktys and Larson's cube, leads us to the following equation of motion:

S|T = 1/2 + 1/1 + 2/1 = 4|4,

where the pipe "|" symbol indicates the joining together of the less-than-unit magnitude of the space oscillation with the greater-than-unit magnitude of the time oscillation. Since these two oscillations are quantified as ratios of space and time, which are changed from the unit value of 2/2 to 1/2 and 2/1, by the changing "direction" of the oscillating aspect, it's necessary to include a separate third term into the equation that quantifies the "missing" half of the cycle, its inward half, we might say.

Now, for simplicity's sake, the three-dimensional character of the actual space and time oscillations is not indicated in the S|T unit equation, but it can be easily inserted, as I explain in more detail on the LRC website.

Using the S|T unit equation, it's possible to combine additional space and/or time oscillations with the 4|4 S|T unit, as shown in the chart below:

In the upper left of this chart, we see the 4|4 S|T unit formed by the initial combination of a space oscillation (SUDR, or S) and a time oscillation (TUDR, or T). Then, to the right of this S|T, we see a depiction of a 4|4 S|T encountering another T oscillation, and below that a depiction of one encountering another S oscillation.

Notice how the ratio of the resultant space/time progression of these entities is altered by these combinations. We can quantify them as follows:

S|T = 1/2 + 1/1 + 2/1 = 4|4,

2S|T = 2/4 + 2/1 + 2/1 = 6|6

S|2T = 1/2 + 1/2 + 4/2 = 6|6

It's important to note that the S|T = 4|4 unit is identified with the photon in the LRC's RSt, and that it is a balanced (1:1) unit, progressing equally in both space and time, whereas the 2S|T and the S|2T units are not balanced, but are unbalanced to either side of the balanced S|T unit. The 2S|T unit progresses at less-than unit speed, while the S|2T unit progresses at greater-than unit speed.

The importance of the consequences of this trichotomy of fundamental magnitudes (-1,0,+1) cannot be over emphasized, as it leads to the observed physical particles of the first family of the LST community's standard model, as we will explain in the next post.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

Understanding the three equations of scalar motion combinations, 2S|T, S|T and S|2T, as explained previously, we are ready to use them to quantify more complex combinations, a set of which will be identified with the first family of the observed standard model (SM), which is divided into the two categories of bosons and fermions.

There are fourteen fermion and four boson particles in all identified, excluding the Higgs boson. Each particle consists of three preons, or combinations of the S|T units, which are symbolized as previously explained and shown in the figure below:

In this figure, the symbol on the left, with three red preons, is identified with the electron particle. The symbol on the right, with three blue preons, is identified with the positron particle. The symbol that is not shown is the all green combination, identified as the neutrino particle.

Particles identified with this triangle symbol are all fermions. The remaining fermions consist of combinations of red, blue or green preons. Each fermion has a separate particle that is known as its anti-particle and both of them come in left and right, or chiral versions.

The four bosons also consist of three preons, but they not combined as triangles. Rather, they are combined as parallel stacks, as shown below:

The associated S|T equations of each particle can be written as shown in the first figure above. For instance, the equation of the electron, consisting of three red preons, or three 2S|T units, may be written as:

3(2S|T) = 6S|3T = 3(2/4+2/1+2/1) = 6/12+6/3+6/3 = 18|18 num,

where num = natural units of motion.

The inner term, 6/3, shows the scalar motion imbalance created by the greater number of negative S units (6), compared to the number of positive T units (3), so the sum of these is -3, which quantifies the electron's electrical charge.

In the case of the electron's anti-particle, the positron, which consists of three blue preons, the equation may be written as:

3(S|2T) = 3S|6T = 3(1/2+1/2+4/2) = 3/6+3/6+12/6 = 18|18 num,

where the middle term, 3/6, shows an imbalance in the opposite "direction" of that of the electron, quantifying the positron charge as +3, on the same basis.

The scalar motion equations for the two quarks, the up and down quarks, and their anti-particles, may be written in the same manner, or in a shorter manner, counting only the S & T units, with the underlying equations of motion implied, as follows:

Up Quark = (S|T + 2(S|2T)) = (S|T + 2S|4T) = 3S|5T = 2

Down Quark = ((2(S|T)) + (2S|T)) = (2S|2T + 2S|T) = 4S|3T = -1

Hence, combining two up quarks with one down quark, in a proton, we get:

Proton = (2(3S|5T) + (4S|3T)) = ((6S|10T) + (4S|3T)) = 10S|13T = 3,

in which the inner term of the full equation will be 10/13 = +3.

Therefore, combining the proton with the electron, in the Hydrogen atom, the short form S|T equation may be written as,

H = E + P = ((6S|3T) + (10S|13T)) = 16S|16T = 0,

which is, of course, a balanced combination, or neutral in charge, we might say.

Adding a neutron's combination of scalar motion to the Hydrogen atom's combination, we get the Deuterium atom's combination:

D = H + N = ((16S|16T) + (11S|11T)) = 27S|27T = 0,

an electrically neutral result, as observed,

In the next post, we will see how these same scalar motion equations can be used to calculate beta decay processes and the observed products of those processes, which involve both fermions and bosons.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

In the previous post, it was shown how the three S|T units, 2S|T, S|T, S|2T, like the numbers, -1,0,1, can be combined as preons to form combos that can be identified with the fermions and bosons of the LST community's standard model (SM) of particle physics.

The scalar motion properties of the preons are such that those combinations identified as fermions, like quarks and electrons and positrons, have values that correspond to those observed in their physical counterparts, at least to the extent the investigation has been carried out.

This enables us to identify these values with the magnitudes of electrical charge, which constitutes evidence further validating the LRC's theoretical development, which has previously led to the remarkable set of combinations that have been identified with these particles.

However, as remarkable and outstanding as this achievement is, there is yet more evidence to come. This time it involves preon combinations identified as bosons as well as fermions. Recall that, in the universe of nothing but motion, everything is either a motion, a combination of motions or relations between them. The preons and their combinations as SM particles are examples of motions and combinations of motions, while the correspondence of the values of their properties with observed values is an example of relations between them.

Another example of relations between these combinations of scalar motion is much more complex than the previous case. It is called "beta decay," and there are two types of beta decay, positive and negative. In order for our preon combinations to exhibit the two types of beta decay observed in nature, not only do we need to have specific combinations with the properties of fermions, such as quarks, electrons and positrons, with the correct magnitudes and polarity, but also neutrinos and anti-neutrinos.

Yet, this is not all. The beta decay process requires these fermions to have the correct chiral instances as well, and, to add further to the demanding requirements, bosons, with the correct magnitudes and polarity, are also required. Anyone with a sufficient grasp of the remote possibility that all of these requirements could be met by chance, should be able to appreciate the significance of the following results.

For convenience of reference, the fermion and boson chart previously shown above is shown again here:

As shown in the chart above, the combos to the right of the neutrinos are a mirror image of those on the left. This is due to what the LST community calls chirality, or handedness in nature. In the LRC's RSt, the observed chirality of these combos identified with SM particles is due to the positive and negative nature of the universe of motion, where the left side is the below-unit-speed side of the unit progression, the Material Sector (MS), and the right side is the above-unit-speed side, the Cosmic Sector (CS), where the MS S is the CS T, and vice-versa, the CS S is the MS T.

Though not explicitly indicated in the chart above, recall that the total natural units of motion of the S|T, or green preon, is 4|4, while it is 6|6 for the red and blue preons. The neutrino and anti-neutrino consist of three green preons, so their total units of natural motion is 3 x (4|4), or 12|12.

Hence, in-as-much as the magnitude of the neutrinos is balanced at unity (green), the net magnitudes of the scalar motion combos to the right of the neutrinos (i.e. the right-handed ones) are positive, or above-unit magnitudes, whereas those to the left (i.e. the left-handed ones) are negative, or below-unit magnitudes.

Now, in the observed beta minus decay process, one of the neutron's two down quarks is transformed into an up quark, changing the neutron into a proton, The transformation takes place when the down quark emits a W- boson, which quickly transforms into an electron and an anti-neutrino. The loss of the W- boson's energy transforms the down quark into an up quark.

However, viewing this same process from the perspective of scalar motion combos, the conservation of total units of natural motion is used to account for the changes in the transformations, as follows:

Given that the total motion of the proton's three quarks is 46|46, while that for the neutron is 44|44, the next graphic shows the chirality of their respective quarks:

In this graphic, the constituent quarks are labeled with abbreviations for left and right up and down quarks, and the respective values of their total motion magnitudes are indicated as positive (blue) and negative (red), depending on their chirality.

As shown, the motion difference between the right down (Rd) quark of the neutron (14) and the left up quark (Lu) of the proton (-16) is -30, indicating that a change from the neutron's Rd quark to the proton's Lu quark, requires a change of 30 units from positive 14 to negative 16. Reversing the process requires a change of 30 units from negative 16 to positive 14.

The details of the beta minus decay are shown in the graphic below:

The total units of natural motion of each preon in the W- boson in the graphic is 4S|T = (4(1/2)+1/1+2/1) = (4/8+4/1+2/1) = 10|10 num, for a total of 3 x (10|10) = 30|30 num.

This is a highly non-symmetrical and thus unstable magnitude that quickly decays as shown. The nu symbol on the anti-neutrino should have a bar over it, which was inadvertently omitted.

For the beta plus decay, the process is reversed. The left-handed up quark goes to the right-handed down quark, by emitting a W+ boson, which changes to a positron and neutrino, shortly after. The change from negative 16 to positive 14 units of scalar motion, a total of 30 units, changes the up to a down quark, conserving the scalar motion quantities as before, as shown on the graphic below.

This time, the total units of natural motion of each preon in the W+ boson in the graphic is S|4T = ((1/2)+1/1+4(2/1)) = (1/2+1/4+8/4) = 10|10 num, for a total of 3 x (10|10) = 30|30 num.

The fact that the magnitudes of the required polarities are found just where they have to be in order for these two observed physical processes to work out like this cannot be attributed to chance. Therefore we conclude that is is strong evidence that we are on the right track.

Yet, we are not done. There is more to come, including the formation of the elements of the periodic table and their atomic spectra.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

As we proceed with the development of the LRC's RSt, with the help of the new math of scalar motion, we come next to the fundamental relation between energy and mass.

In the physics of the LST community, all motion is the motion of something, while the inverse of motion is not. For that community, inverse motion, where E = $\Delta$t/$\Delta$s, does not require an object's change of location to define the delta of space, as it does in v = $\Delta$s/$\Delta$t, at least in any direct fashion.

However, in our RST community, neither equation requires a change in the location of an object to define the respective deltas. It's as if a space clock existed in conjunction with the familiar time clock, endlessly counting off the locations of space, as it were.

Things get complicated very quickly, however, given that the magnitudes of motion, like the values of numbers, have three properties: Three dimensions, two "directions" in each dimension, and degree, we might say, or the value of the magnitude itself, the absolute magnitude denoted by a number.

In the LST community, the vital concepts of numbers, algebras and geometries, developed slowly, over centuries. However, these same concepts have to be redeveloped, in a manner of speaking, in the RST community, due to the change in the fundamental concept of motion and the introduction of the space clock, which the act of developing theory under the new system of theory demands.

This is one of the reasons, I believe, that what K.V.K. Nehru called the "great lacuna" in Larson's RSt, emerged to confound developers. He called the inability of the RST community to calculate the observed atomic spectra a “great lacuna” in the theoretical development of Reciprocal System theory. In his 2002 paper, “Quantum Mechanical Approach Inevitable?” he suggested that the only course open to us was to use the vector motion wave equation after all. Unfortunately, nothing ever came of that idea.

The reasons for this are many and varied, but the failure points to the fact that the developers of RST-based theory have not had a foundation of scalar mathematics to build upon. Now that this deficiency has been eliminated by the scalar math that has been introduced here, namely the math based on the LRC's equation of scalar motion,

S|T = 1/2 + 1/1 + 2/1 = 4|4 num (natural units of motion),

perhaps the "great lacuna" of RST-based theoretical development can finally be filled.

Nevertheless, while this equation of scalar motion has helped us with the investigation of discrete motions and combinations thereof, its form is not able to help us with the energy aspect of those investigations, which is at the very heart of the LST theories of physics, which have been so central to understanding the periodic table of elements and their unique atomic spectra.

The study of the atomic spectra by LST scientists led to Balmer's line spectra equation, then to Rydberg's refinement of it and the exciting fit of that to Bohr's model of the atom, leading to what has since become known as the "old" quantum mechanics, which evolved into today's quantum mechanics, based on energy transitions in a quantum system, where the energy to be calculated depends on Planck's constant times the frequency of the radiation emitted or absorbed: E=hv.

However, the most interesting part of the story of the LST community's development of quantum mechanics is the transition, or integration, that it required the scientists and mathematicians to make between classical, or continuous physics and quantum or discrete physics. The former had been reformulated into Hamiltonian mechanics, and when it was applied to the study of atomic spectra, "the interaction between the atom's charged particles and the electromagnetic field shows up as a term in the Hamiltonian (the energy operator, which governs the time evolution of the system)," as one author puts it.

In essence, Bohr led out by applying the well known vector motion energy formula to his model of orbiting electrons, where the kinetic and potential energy trade off over time, and Heisenberg, Dirac and other quantum theorists translated that into the operators and eigenvalues of the Hamiltonian, which allowed them to account for spectral changes induced by electric and magnetic field effects.

The full story is as complex and fascinating as any mystery novel ever written, but the bottom line of the plot is the wedding of the discreet and continuous concepts implicit in Einstein's equation, E= hv. Einstein and Planck were investigating the interaction of light and matter. Scientists at the time thought they understood light, given Maxwell's stunning equations, but though they had no way of knowing if Newton's laws of motion held true for atoms and electrons, they assumed that they did.

However, Einstein's postulate, E=hv, threw a monkey wrench into the works: The question "How can a particle also be a wave?" has driven scientists mad ever since. They eventually accommodated the seeming impossibility of this duality of nature with the ad hoc invention of the "quantum field" concept, which plagues them to this day, in their efforts to integrate the discrete equations of quantum mechanics with the continuous equations of gravity, in Einstein's theory of general relativity.

The quest to understand the discrete science of quantum mechanics in light of its incompatibility with the continuous science of general relativity is the modern equivalent of the ancient challenge of pulling the sword from the stone, where the brute force of words alone are not enough. The future king of the realm can only triumph by demonstrable reason; i.e. by employing the concepts of discrete numbers and continuous geometry and an appropriate algebra to integrate the two - in other words, a new mathematics - to pull the sword out of the stone.

Our efforts at the LRC are an attempt to do this, as I will begin to explain in the next post.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

In analyzing the relations between scalar motion combinations, we need to understand them in terms of energy as well as motion. In the RST, the dimensions of scalar energy, t/s, are the inverse of the dimensions of scalar motion, s/t, so the energy relationship we are looking for, is, in some sense the inverse of our fundamental S|T equation, or a T|S unit.

Recall that the fundamental S|T equation is,

S|T = 1/2+1/1+2/1 = 4|4 num (natural units of motion).

On the world line chart, the LH term of this equation is s/t = 1/2, because space is oscillating, while the RH term is s/t = 2/1, because time is oscillating.

Therefore, in the fundamental T|S equation, the space and time dimensions are inverted, so the LH term becomes t/s = 1/2, and the RH term becomes t/s = 2/1:

T|S = 1/2+1/1+2/1 = 4|4 num.

We can plot these two equations as world line charts, as shown below:

The Cosmic Sector (CS) Chart is the inverse of the Material Sector (MS) Chart, where the MS under unity, oscillating space unit (S: s/t=1/2), becomes the CS over-unity, oscillating space unit (S: t/s=2/1)), and the MS over-unity, oscillating time unit (T: s/t=2/1) becomes the CS under-unity, oscillating time unit (T: t/s=1/2).

In other words, S|T --> T|S, when we invert the "direction" of the unit progression plot. Of course, we haven't actually reversed the "direction" of the progression, but only changed our view of it.

When our point of view is from the material sector, then the 'S' unit is under-unity, while the 'T' unit is over-unity, but if we change our point of view to the cosmic sector, then it's the 'T' unit that is under-unity, while the 'S' unit is over-unity.

However, it's one thing to invert our MS world line chart to obtain the CS world line chart, and it's another to find the mathematical operation that will transform S|T combos into T|S combos!

Recall that the boson combo, identified with photons in our preon chart in the previous post, consists of all green preons:

The green color symbolizes a balanced S|T unit; that is, S|T = 1/2+1/1+2/1, and, because it's balanced, the S|T unit is almost indistinguishable from the balanced T|S unit; i.e. S|T = T|S = 4|4. The only difference is one of perspective, just as a balanced teeter-totter, with a boy on one end and a girl on the other, looks the same when viewed from its left side as it does when viewed from its right side, except the two left and right genders are swapped. From one side the girl is on the left, and from the other side the girl is on the right.

So, the question is, how do we change our perspective of the gamma boson from the MS perspective of scalar motion (i.e. magnitudes of s/t) to the CS perspective of scalar energy (i.e. magnitudes of t/s)? In other words, how do we transform MS motion into CS energy?

Well, one approach is to use the concept of linear algebra where a rotation matrix can be used to perform a rotation in Euclidean space, which is what we need in order to rotate the MS world line chart 180 degrees out of the plane of the paper and back into the plane on the opposite side, so that the rotation transforms the MS chart into the CS chart.

Of course, we don't need to transform the actual chart, but we do need to find an equivalent multiplication operation that will transform the S|T unit into its inverse T|S unit, and, as it turns out, we can do that by analyzing the world line chart in light of the LST community's energy equation, E = hv.

Larson pointed out that the dimensions of their equation, t/s = t2/s x 1/t, are incorrect, because the expression of frequencies by counting the number of times a unit of space or time completes one unit or cycle of rotation is actually an ad hoc convention that is misleading, and it comes at a cost of confusing our un-examined understanding of the true space/time dimensions of the equation.

The frequency term, 1/t, when properly understood, is actually a velocity, as far as space/time dimensions are concerned, because the uniform change of "direction," the oscillation, doesn't change the dimensions of the physical entity. Therefore, the dimensions of the energy of the equation are correctly understood as momentum times velocity:

t/s = t2/s2 x s/t.

However, the frequency measure, 1/t, is necessary to get the correct energy, so, while we know the time velocity of the S units and the space velocity of the T units, we need to calculate the energy of the S|T units in terms of cycles. Please refer to the graphic below:

We can see here that both the S unit and the T unit can be expressed in terms of frequency. For the S unit, we count the units of time per cycle (nt/1), and for the T unit, we count the units of space per cycle (ns/1).

Placing these on a number line, with the magnitude of the S units extending to the left and the inverse T units to the right, we can see how dividing T cycles by S cycles yields a very interesting result:

The next image shows graphically how the number of cycles increases with the increase of S and T units:

With this result, the inverse wavelength, known as the wave number, 1/λ, for the line spectra of Hydrogen, falls out from Rydberg's formula,

1/λ = RH(1 – 1/n2)

The interesting thing that students of the LRC's RSt should note is the mysterious role that the number 4, or 2 squared, plays in the work of Balmer and Rydberg, as summarized in the following image:

Of course, this just catches us up to the two-body solution of the "old" quantum mechanics, before the work of Heisenberg, Dirac et. al., but it's much more than we have ever accomplished before, so it's very encouraging and adds to the growing number of achievements being racked up by the LRC's RSt.

dbundy
Posts: 93
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Introduction to Doug's RSt

As we proceed with the development of the LRC's RSt, with the help of the new math of scalar motion, we come next to the fundamental relation between energy and mass.

In the physics of the LST community, all motion is the motion of something, while the inverse of motion is not. For that community, inverse motion, where E = $\Delta$t/$\Delta$s, does not require an object's change of location to define the delta of space, as it does in v = $\Delta$s/$\Delta$t.

However, in the RST community, neither equation requires a change in the location of an object to define the respective changes. It's as if a space clock existed in conjunction with the familiar time clock, endlessly counting off the locations of space, as it were.

Things get complicated very quickly, however, given that the magnitudes of motion, like the values of numbers, have three properties: Three dimensions, two "directions" in each dimension, and degree, we might say, or the magnitude itself, the absolute magnitude denoted by a number.

In the LST community, the vital concepts of numbers, algebras and geometries, developed slowly, over centuries, while these same concepts have to be redeveloped, in a manner of speaking, in the RST community, due to the change in the fundamental concept of motion and the introduction of the space clock, which developing theory under the new system of theory demands.

This is one of the reasons, I believe, that what K.V.K. Nehru called the "great lacuna" in Larson's RSt, emerged to confound developers. He called the inability of the RST community to calculate the observed atomic spectra a “great lacuna” in the theoretical development of the Reciprocal System. In his 2002 paper, “Quantum Mechanical Approach Inevitable?” he suggested that the only course open to us was to use the vector motion wave equation after all. Nothing ever came of it however.

The reasons for this are many and varied, but the failure points to the fact that the developers of RST-based theory, have not had the foundation of the scalar mathematics that's been introduced here, Namely, the LRC's equation of scalar motion:

S|T = 1/2 + 1/1 + 2/1 = 4|4 num (natural units of motion).

Nevertheless, while this equation of scalar motion might help us with the investigation of discrete motions and combinations thereof, it doesn't help with the energy aspect of those investigations, which is at the heart of the LST theories of physics, which have been so central to understanding the periodic table of elements and their unique atomic spectra. We have made some progress lately, as explained in the previous post, but we really need a model of the atom to go along with that progress, if we are going to finish the work and fill the "great lacuna."

Bohr's model of the atom worked well for two body atoms, and though the LST community had to move beyond it, when it came to three or more body atoms, like two or more electrons and a nucleus, or two nuclei and an electron, their solution was to turn to the Hamiltonian, where the interaction between the atom's charged particles and the electromagnetic field shows up as a term (the energy operator, which governs the time evolution of the system).

The LST's new quantum theory, which replaced Bohr's model of spinning electrons in stationary orbits, with clouds of orbiting electrons that have no definite locations, still has problems, but the scientists of the LST community simply accept the rationalization that it succeeds in principle, an approach Larson almost railed against. However, given that we don't have a scalar motion model of the atom that we can use to calculate the atomic spectra, it's hard to rail against the LST's vector motion model, even though it's problematic.

Of course, in the scalar motion model of our RSt, there are no orbiting electrons, popping in and out of clouds in a likely or unlikely fashion, as it were, but the atom consists of a composite of scalar motion combinations, based on the S|T equation of motion, as explained above in previous posts. In the LST's new quantum mechanics, clouds of calculated probabilities are called orbitals today, and they are based on squaring the net-zero magnitudes of a wave, which is symmetrically oscillating above and below zero. By squaring the magnitudes of the wave, all its values are translated to lie above the zero line, so that they range from zero to some positive magnitude, varying with time.

In order to understand our approach to constructing a scalar motion model of the atom, it's best to have some understanding of the LST's model. Basically, the wave equation magnitudes that are squared exist in three dimensions, and they arise from the harmonics on the surface of a sphere, or what is called spherical harmonics.

Once the model was in place, certain selection rules were invented as a procedure for filling the orbitals with electrons in order to obtain the observed energy levels and line spectra, corresponding to transitions between the orbitals.

The numbers used in the QM equation are called “q-numbers” and are shown in the graphic below, with a general notion of what their individual roles are, as understood by chemists.

The first number, n, is the distance of the electron from the nucleus. The next number, l, determines the number of the orbitals, the ml number specifies the shape and the s number, the only non-integer of the four numbers, provides a unique magnitude to each set of four.

Here is a summary of the first three sets of the numbers and the orbitals corresponding to them, the so-called s, p and d orbitals. They are numbered according to the principle quantum number, n, to which they correspond.

The orbitals for n = 1, 2 and 3 are shown here. Notice that, for n = 1 there is only 1 spherical orbital, for n = 2 there are 1 spherical and 3 double oblong orbitals, and for n = 3 there are 1 spherical, 3 double oblong, 4 quadruple oblong and 1 double oblong orbitals.

When n = 4, the number of orbitals calculated by the wave equation's four q numbers expands to seven, as shown below:

Notice that there are 8 lobes for each of 4 of these orbitals, while 3 are double oblong orbitals. It’s easy to see how all of these orbitals are visualized as corresponding to the one, two and three dimensions of a three-dimensional coordinate system, which the wave equation captures in terms of spherical harmonics.

Now, our challenge is to see if we can find the same sets of three dimensional magnitudes that QM uses, but in terms of the 3-D scalar motion of our RSt quantum theory, rather than the 1-D vector motion of the LST quantum theory.

As a summary of the steps in our theory that have lead us to the elements of the periodic table, we recall the motion equation of the S|T combinations, and the corresponding energy equation, which enabled us to calculate the line spectra of Hydrogen, following the LST’s Bohr model of the atom.

We also showed how the scalar motion totals of our equivalents of the proton, neutron and electron fit together naturally, forming hydrogen (S|T = 64 num) and deuterium atoms (S|T = 108 num), as summed up in the graphic below:

The periodic table, in the form of the wheel of motion, then follows, in multiples of deuterium, on up the concentric circles of elements.The key chart, showing how the levels of atomic spectra emerge from the S|T transitions of Hydrogen, is shown in the previous post, In the next post. I will explain the tentative atomic model of the LRC's RSt.

rossum
Posts: 28
Joined: Thu Jan 17, 2013 1:36 am

### Spectroscopy

Hello Doug,

I have seen your presentation of reproduction of Rydberg formula. It is very nice to see, that someone is taking the effort to incorporate spectroscopy into RS. However I'm not sure whether you can get any more complex results than you already have (the Balmer/Rydberg formula) without going through acoustics: all the results of quantum mechanics are results of acoustics in various conditions (a.k.a. potentials) with the moment of inertia limited to natural multiplies of the Planck's constant $J=n\hbar$.

In LST we use basically three types of these wave equations (in an unusual formalism) which represent three types of approximations to the full physical situation:
• The Schrodinger equation:
$\frac{\hbar^2}{2m}\nabla^2\Psi+V\Psi=\frac{d}{dt}\Psi$
It is based on the original Jacobi-Hamilton equation describing waves where the speed of the wave can be ignored or is to high
• The Klein-Gordon equation:
$\hbar c^2\nabla^2 \Psi + \frac{m^2c^4}{\hbar}\Psi+V\Psi=\hbar\frac{d}{dt^2}\Psi$.
It is based on the classical Laplace's acoustic equation. Here the approximation is only in potential which is taken directly from classical electromagnetism (or in case of other interactions potentials like the Yukawa potential are used). Dirac equation $\Big(\beta mc^2 + c\big(\sum^3_{n=1}\alpha_n\hbar\nabla\big)\Big)\Psi+V\Psi=i\hbar\frac{\partial}{ \partial t}\Psi$
where $\alpha$ and $\beta$ are the label matrices, is used in most cases, however it's practically only a reformulation (square root) of the K-G eq. (I will not go in to details now.)
• The most precise option is the QED/QFT equation that is basically the the same equation as above reformulated in the form of Lagrangian but the potential is replaced with the 'quantum field' which is a wave equation itself.
$\mathcal{L} = \bar\psi(i\hbar c \, \gamma^\alpha D_\alpha - mc^2)\psi -\frac{1}{4\mu_0} F_{\alpha\beta} F^{\alpha\beta}$
Here the $\Psi$ represents an analogy to the optical path. As you know, these equations have certain type of problem in that in one way or another they diverge and this is only 'dug under the rug' by renormalization. In the first and the second case it is connected with the electromagnetic potential $\frac{q^2}{4\Pi\epsilon_0r}$, in the last case with the diverging sum in the electromagnetic tensor $\frac{1}{4\mu_0} F_{\alpha\beta} F^{\alpha\beta}$
Without going into the details I think that here is the place where RS could help the most. I have some ideas how this can be done but so far only preliminary.

Following Nehru's approach, the Schrodinger equation was assimilated into RS and spectroscopic calculations are possible right now without changes to the methods used today. To my opinion however, to fully merge RS with QM or to develop RS's own methods to calculate spectroscopy the connection between wave-function and the Larson's triplets has to be understood first. Have you dig into this so far?

Best wishes
Jan