The Larson Research Center

Sun wrote:

Hello Doug,
Thank you for your presentation.
Let me use a notation of a-c-b for my own convenient to represent your equation.
Am i correct that you assume everything starts from one net displacement, 1/2 and 2/1? Particles are consequences that combine variable numbers of 1/2 and 2/1 with variable numbers of 1/1? 1/1 represent for unit motion? a, c, b stand for the each dimension of motion?
How did you get 2S|T = 2/4 + 2/1 + 2/1? Why it is not S|T+SUDR=1/2+1/1+2/1+2/1?

The basic S|T equation, S|T = 1/2 + 1/1 + 2/1 = 4|4 num, expresses the total scalar motion of the SUDR (s/ t = 1/2) and TUDR (s/t = 2/1) combination. The middle term (1/1) consists of the inner portion of the SUDR oscillation (the numerator) and the inner portion of the TUDR oscillation (the denominator.) Without it the total of natural units of motion (num), would be incorrect.

The ratio of SUDRs to TUDRs (Ss and Ts) in this equation is 1:1, or balanced. We can unbalance it in two “directions,” by adding an S or a T to the equation. Adding an S, S|T + S, gives us 2S|T. Adding a T, gives us S|2T.

2S|T = (1/2 + 1/2)|2/1 = 2/4|2/1.

In it’s expanded form, this is ((1/2) + (1/2)) + 1/1+ 2/1 = 2/4 + 2/1 + 2/1 = 6|6 num, showing how the additional S unit changes the balanced middle term (1/1) of S|T to the unbalanced middle term (2/1) of 2S|T.

I hope that make more sense now. This new math is a little tricky, because not only do we add numerators to numerators and denominators to denominators, but we CONSTRUCT the middle term from the LH (numerator) and the RH (denominator) terms, after the fact so-to-speak.

Thanks for your question Sun. Sorry it has taken so long to respond. The reversals are definitely a philosophical challenge, but assuming them, we derive the natural numbers from the integers and a whole slew of other things.

Starting with a unit ratio of space/time change (s/t = 1/1), the first possibility is 1/2 and 2/1, depending upon which aspect is reversing. These two ratios equate or resolve to -1 and +1 respectively and the combinations of them can be used to arrive at any natural number.

These fundamental units of motion were called time and space “displacements” in Larson’s works.

At the LRC, we call them SUDRs and TUDRs, denoting them with upper case S and T. A combination of them is denoted S|T.

Combining 1/2 and 2/1 on a calculator generates a sum of 2.5, but this is due to the underlying assumption that reciprocals of positive integers should be treated as fractions of a whole- instead of reciprocal integers.

As far as frequencies go, there is one cycle of reversal per two units of time (space). Summing frequencies, however, is trickier than summing displacements. As you probably know, combining two radio frequencies produces both the sum and difference frequencies, but the frequency of 2/1 is four times the frequency of 1/2.

Moreover, the absolute value of the space over time frequency (1/2) is equal to that of the time over space frequency (2/1). Taking this seeming contradiction into account requires us to think about it a little differently, which I’ll try to explain directly.

Now that our RSt has a basis for calculating the discrete levels of energy transitions observed in Hydrogen, we need a scalar motion model of the atom that serves to explain the changes inducing the transistions, as does the vector motion model of LST theory. For right or wrong, whether it’s the Bohr model of electron particles, orbiting a nucleus, or the Schrödinger model of electron waves, inhabiting shells around a nucleus, the LST’s atomic model provides the LST community with a physical interpretation of the word “transition.” However, this is much more difficult to achieve in a scalar motion model.

In our RSt, where the unit of elementary scalar motion from which higher combinations are derived, the S|T unit, is an oscillating volume of space and time, understanding what accounts for the observed atomic energy transitions in the combinations identified as atoms is not easy.

This is especially challenging given that, in our theory, the electron has no identity and consequently no properties, as an electron, until it is created in the disintegration of the atom, or in the process of its ionization. Fortunately, however, we have the scalar motion equation to help.

Recall, that the basic scalar motion equation is,

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

And our basic energy, or inverse motion equation is,

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

Now, this terminology and notation will be a complete mystery to those who have not read the previous posts, so reading and understanding those posts first is a prerequisite for the study of what follows, and while we are on the subject, let me emphasize the tentative nature of all the conclusions presented thus far. It may be necessary to eat a lot of humble pie from time to time, during the development of our RSt, for several reasons, but if so, it won’t be the first time. It has been said before and bears repeating: It takes courage to develop a physical theory, not to mention a new system of physical theory. Larson was an incredibly courageous man, as well as an intelligent and honest investigator. Perhaps those of us who try to follow his lead appreciate that fact more than most.

With that said, we have taken on the challenge of dealing with units of energy, with dimensions E=t/s, as well as motion, with dimensions v=s/t, and have dared to cross over the line of LST physics, which cannot brook the existence of entities over the speed of light, which are known as “tachyons,” in that system. Nevertheless, the T units in our RSt are just such units, but because the dimensions of these units are actually the inverse of less than unit speed units, no known laws of LST physics are broken.

In retrospect, venturing into this unexplored realm of apparent over-unity, which seems so iconoclastic, appears to be the natural and compelling evolution of physical thought. So much so that one marvels that the world had to wait so long for the Columbus-like pioneer Larson to show science the way. However, incredible as it is, the entire LST community, save just a few, has no idea yet that our understanding of the nature of space and time has been revolutionized. They cannot, as yet, recognize that time is the inverse of space, even though it’s as plain as the nose on your face, as soon as someone points out how it can be.

By the same token, the mathematics of the new system is just as iconoclastic. As we consider the basic scalar motion equation, n(S|T)=n4|n4, and its inverse, n(T|S)=n4|n4, and graph their simple magnitudes, we find that its also possible to formulate a basic scalar energy equation, where

S*T = n².

In the previous posts above, I’ve explained how S|T units combine into entities identified with the observed first family of the LST’s standard model (sm), and these combos combine into entities that are identified as protons and neutrons, which combine into elements of the periodic table, or Wheel of Motion:



The symbolic representation of the S|T units that, as preons, combine to form the fermions and bosons of our RSt, are a reflection of the S|T equation, making it possible to graphically represent them and their combinations as protons and neutrons along with their respective magnitudes of natural units of motion. On this basis, the S|T magnitudes for the proton, neutron and electron combos are:

P = 46|46 num,
N = 44|44 num,
E = 18|18 num

The magnitude of the Hydrogen atom (Deuterium isotope) is then the sum of these three:

H = 46+44+18 = 108|108 num.

At this point, however, representing the constituents of the atom as combos of S|T triplets (see previous posts above), becomes cumbersome and we need to condense the symbols from 20 triangles to 4 triangles, in the form of a tetrahedron, as shown below:



The top triangle of the tetrahedron is the odd man out for the nucleons, so that for the proton this is the down quark, but for the neutron it is the up quark.

The numbers in the four triangles are the net magnitudes of the quarks and the electron. So, the number of the down quark at the top of the proton is -1, because the magnitude of the inner term of its S|T equation is 2/1, (-2+1 = -1), whereas the number of its two up quarks is 2, because the inner terms of their S|T equations are both 3/5, (-3+5=2). For the neutron, the number of the single up quark at the top is 2, while the magnitude of the two down quarks below it is -1, given the inner terms of their S|T equations.

The inner term of the electron’s S|T equation is 6/3, or -3, (-6+3=-3), so that the net motion of the three entities combined as the Deuterium atom balance out at 3-3 = 0, or neutral in terms of charge, as show in the graphic above.

In this way, each element of the Wheel could be represented by the numbers of its tetrahedron symbol, if there were some need to do so, but what is more useful is the S|T equation itself. Expanding the equation for Deuterium:

D = 27/54+27/27+54/27 = 108|108 num,

but factoring out 3³, we get:

D = 3³(1/2+1/1+2/1) = 108|108 num.

To take advantage of this factorization we can represent it by making the S|T symbols of the notation bold:

S|T = 3³(1/2+1/1+2/1) = 108|108 num

Hence,

D = S|T= 108; He = 2(S|T) = 216; Li = 3(S|T) = 324, etc.

This way, we can easily write the S|T equation for any element, X, given its atomic number, Z:

X_Z = z(S|T)

However, while this should prove to be quite helpful as compact notation, there is still more to consider. Recall that the units on the world-line chart actually represent the expanding/contracting radius of an oscillating volume, and as such, its magnitude is the square root of 3, not 1. This factor expands the relative magnitudes involved considerably, which we will investigate more later on.

For now, I want to draw your attention to the scalar energy equation,

S*T = n².

Recall that for the S*T unit,

S*T = 1/(n+1) * (n*n) * (n+1)/1 = n²,.

So when n = 1,

S*T = (1/2)*(1*1)*(2/1) = ((1/2)(2/1)(1*1)) = ((2/2)(1*1)) = 1*1 = 1²,

but, if we invert the multiplication operation, we get:

S/T = (1/2)/(1/1)/(2/1) = ((1/2)(1/1))(1/2) = (1/2)(1/2) = 1/2²,

which we want to do when we wish to view the S&T cycles, in terms of energy, so that:

E = hv —-> T/S = 1/S/T = n²,

where n is the number of cycles in a given S|T unit.

Now, this may seem to be contrived, and perhaps it is, especially when we invert the operation of the inner term of the S*T equation from division (n/n) to multiplication (n*n). However, if we don’t invert it, the equation will always equal 1, while if we do invert it, then dividing ‘T’ cycles, by ‘S’ cycles (T/S) yields the correct answer, T/S = n².

Now, this brings us to something else that needs to be clarified. In the chart showing the correlation between the quadratic equation of the S|T units and the line spectra of Hydrogen, given the Rydberg equation, the frequency of the S|T units is shown as decreasing with increasing energy, rather than increasing as it should. This is problematic to say the least, but I think it can be resolved, when we consider that the “direction” reversals of each S and T unit always remains at the 1/2 and 2/1 ratio, even though their combined magnitude is greater in the absolute sense; that is, while the space/time (time/space) ratio of 1/2, 2/4, 3/6, 4/8, …n/2n, remains constant at n/2n = 1/2, the absolute magnitude of 2n - n increases, as n: 1, 2, 3, 4, …2n-n.

Therefore, the length of the reversing “direction” arrows, shown in the graphic, as increasing in length, as the absolute magnitude increases, is an incorrect representation of the physical picture. The correct representation would show the number of arrows increasing, as S|T units are combined, with their lengths (i.e.their periods) remaining constant, so that, as the quadratic energy increases, the number of 1/2 periods in a given S|T combo increases. The frequency of the unit then is that of a frequency mixer, containing both the sum and difference frequencies of its constituent S|T units..

Of course, this is not exactly what is observed, but upon further investigation, we may be able to resolve the discrepancy. At least it is consistent with our theoretical development.

In the meantime, for the energy conversion of the S|T equation of the Hydrogen atom, where n = 1, with 3³ factored out, we get:

S/T = (1/3³n)² = 1/27², and T/S = (3³n)² = 27² = 729,

when we put the 3³ factor back in, so we get the actual number of 1/2 and 2/1 cycles, or S and T units, contained in the Hydrogen atom.

There are a lot of tantalizing clues to follow in the investigation of these equations and their relation to the conventions of the LST particle physics community, which uses units of electron volts for energy, dividing those units by the speed of light to attain units of momentum, and dividing them by the speed of light squared to attain units of mass. They even divide the reduced Planck’s constant by eV to attain a unit of time, and that result times c to get the unit of space, according to Wikipedia:

Measurement—Unit————-SI value of unit
Energy—————eV———————1.602176565(35)×10−19 J
Mass——————eV/c²—————-1.782662×10−36 kg
Momentum——-eV/c ——————5.344286×10−28 kg⋅m/s
Time——————-ħ/eV——————6.582119×10−16 s
Distance————-ħc/eV—————1.97327×10−7 m

It’ll take a while to untangle these units and see how they correspond to the S|T units of motion, but in the meantime, we can use the progress achieved so far to analyze the periodic table of elements, showing why Larson’s four, 4n², periods define it, using the LRC model of the atom explained so far.

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.