It's certainly understandable, if the ideas presented in the previous post above seem bizarre to the reader. Nevertheless, the development is logical and follows from the system's fundamental postulate. The basic idea follows from the broken symmetry of the quarks, which is quite apparent.

Unlike the leptons and neutrino, which are fully symmetrical, so that rotating their schematic symbols makes no change to their appearance, rotating the symbols of the quarks does change their appearance, due to the broken symmetry of their constituent S|T (T|S) units, and even though this schematic difference is meaningless from a physical standpoint, it does illustrate that there exists a lack of symmetry in the analogous physical attributes of the particles.

What I am asserting is that the broken symmetry in the physical attributes of the quarks may be due to the combinations of different unit sizes. It seems clear that a given LC can be based on any of the three units, √1, √2 or √3. Regardless of which unit size is considered, there are always the three radii associated with it, the radius of the inner, the middle and the outer balls, defined by the LC based on that unit size.

Each of the three sets of dimensional magnitudes, or values generated by these three possible LCs, contains one integer magnitude: √1, √4, √9, as shown below

For unit size = √1:

1) √((√1)2+(√1)2+(√1)2) = √(1+1+1) = √3;

2) √((√1)2+(√1)2+(√0)2) = √(1+1+0) = √2;

3) √((√1)2+(√0)2+(√0)2) = √(1+0+0) = √1;

For unit size = √2:

1) √((√2)2+(√2)2+(√2)2) = √(2+2+2) = √6;

2) √((√2)2+(√2)2+(√0)2) = √(2+2+0) = √4;

3) √((√2)2+(√0)2+(√0)2) = √(2+0+0) = √2;

For unit size = √3:

1) √((√3)2+(√3)2+(√3)2) = √(3+3+3) = √9;

2) √((√3)2+(√3)2+(√0)2) = √(3+3+0) = √6;

3) √((√3)2+(√0)2+(√0)2) = √(3+0+0) = √3;

The conjecture is that if one quark of a nucleon's three quarks, whose constituent S|T units are combos of LCs that are based on a √3 unit size, then the S|T units of the other two quarks would necessarily have to consist of √1 and √2 based LCs, in order to dimensionally balance the opposing scalar motions, and when a neutron under goes beta decay, the unit size of the transformed down quark's LCs would have to change size accordingly, forcing the others to change as well, in order to maintain dimensional balance.

While this may seem bizarre, I would submit that it's no more so than the observed physical properties and behavior of the nucleons themselves.

## Meeting a Terrific Challenge

**Moderator:** dbundy

### Re: Meeting a Terrific Challenge

In the previous post above, I referred to the quarks in a nucleon as dimensionally balanced "color" charges, but I think the phrase is mis-leading, since their constituent Ss and Ts are all 3D. What we are comparing to color in them is the unique integer value of one of their three radii. The color red is assigned to the √1 based LC, the color blue to the √2 based LC and the color green to the √3 based LC.

On this basis, we can identify each of the three LCs by the color assigned to their integer-valued radius, so that a √1 size LC is red, √2 blue and √3 green, where a red LC is characterized by its 1d integer radius (1), a blue LC by its 2d integer radius (2) and a green LC by its 3d integer radius (3).

Of course, we are still handicapped by not knowing what the traditional equivalent of the natural unit is, since we've yet to determine, whether it is Larson's value, or Borg's value, or some other value.

Recently, the work of Brian Nelson has come to our attention, which pins down the mass of the nucleons' constituent quarks by numerical means, but to do so, he first derives a unit wavelength from Einstein's and Planck's equations, by recognizing the Pythagorean theorem relationship between rest mass and momentum and quantizing it (see here).

Interestingly enough, his conclusion is that mass and momentum are related, through the Pythagorean theorem, to a helical pattern of vector motion, a la Hestenes, although he doesn't mention him or the hypothetical zitterbewegung motion of the electron that Hestenes works with.

What he does do is combine the two energy equations into one equation by quantizing the energy of a unit wavelength.

His work is based on the full Einstein equation which includes both the rest mast (mc

These two energy components are summed as two integers of mass energy and kinetic energy in the hypotenuse, which integers are derived by assuming that we can start with a unit wavelength and divide it into smaller and smaller lengths, representing the harmonics of a fundamental frequency, as the energy increases. Plugging the total energy, as a sum of these two energy components, into the Pythagorean theorem, gives us a way to combine Planck's energy equation (E=hf) with Einstein's energy equation (E= mc

Nelson writes: "The hypothesis states that elementary particles absorb precise quantities of kinetic energy in order to form integer multiples of their total energy wavelength in addition to their deBroglie wavelengths. This means that particles that bond, like the electron and proton with their respective rest masses (n

In addition to his papers on this, available on his website, he explains it in a YouTube video here, and, in another video, he describes how the hypothesis, that "elementary particles share force carrier particles with precise quantities of energy in order to bond using integer multiples of their [total energy]," not only leads to a precise calculation of quark masses, but also explains how their total energy is not the same in the neutron and proton.

Based on Nelson's hypothesis, the total energy of the quarks actually changes, according to their number in the nucleons, because, the common kinetic energy, which they must share in order to bond, changes, depending on whether there are two of them or one of them in a given nucleon. In other words, in terms of the LST's standard model, the "gluon" energy binding the quarks, which constitutes most of the "mass" of the nucleon, is not the same in a proton as it is in a neutron, as shown in the graphic below:

Of course, in our RSt, we don't have "gluons," but we do have the 1, 2 and 3 "colored" LCs described above, each able to contribute its unique integral value to the combo's dimensional requirements. Whether this will work or not, I don't know yet, but I'm happy that it comes out of the logical development of the system.

On this basis, we can identify each of the three LCs by the color assigned to their integer-valued radius, so that a √1 size LC is red, √2 blue and √3 green, where a red LC is characterized by its 1d integer radius (1), a blue LC by its 2d integer radius (2) and a green LC by its 3d integer radius (3).

Of course, we are still handicapped by not knowing what the traditional equivalent of the natural unit is, since we've yet to determine, whether it is Larson's value, or Borg's value, or some other value.

Recently, the work of Brian Nelson has come to our attention, which pins down the mass of the nucleons' constituent quarks by numerical means, but to do so, he first derives a unit wavelength from Einstein's and Planck's equations, by recognizing the Pythagorean theorem relationship between rest mass and momentum and quantizing it (see here).

Interestingly enough, his conclusion is that mass and momentum are related, through the Pythagorean theorem, to a helical pattern of vector motion, a la Hestenes, although he doesn't mention him or the hypothetical zitterbewegung motion of the electron that Hestenes works with.

What he does do is combine the two energy equations into one equation by quantizing the energy of a unit wavelength.

His work is based on the full Einstein equation which includes both the rest mast (mc

^{2}) and the momentum term (pc^{2}) of the equation, or what we would call the scalar motion term (n_{m}) and the vector motion term (n_{v}).These two energy components are summed as two integers of mass energy and kinetic energy in the hypotenuse, which integers are derived by assuming that we can start with a unit wavelength and divide it into smaller and smaller lengths, representing the harmonics of a fundamental frequency, as the energy increases. Plugging the total energy, as a sum of these two energy components, into the Pythagorean theorem, gives us a way to combine Planck's energy equation (E=hf) with Einstein's energy equation (E= mc

^{2}+ pc^{2}).Nelson writes: "The hypothesis states that elementary particles absorb precise quantities of kinetic energy in order to form integer multiples of their total energy wavelength in addition to their deBroglie wavelengths. This means that particles that bond, like the electron and proton with their respective rest masses (n

_{me}and n_{mp}), share the same quantity of kinetic energy (𝑛_{𝑣}) in order for their total energy wavelengths to share common factors."In addition to his papers on this, available on his website, he explains it in a YouTube video here, and, in another video, he describes how the hypothesis, that "elementary particles share force carrier particles with precise quantities of energy in order to bond using integer multiples of their [total energy]," not only leads to a precise calculation of quark masses, but also explains how their total energy is not the same in the neutron and proton.

Based on Nelson's hypothesis, the total energy of the quarks actually changes, according to their number in the nucleons, because, the common kinetic energy, which they must share in order to bond, changes, depending on whether there are two of them or one of them in a given nucleon. In other words, in terms of the LST's standard model, the "gluon" energy binding the quarks, which constitutes most of the "mass" of the nucleon, is not the same in a proton as it is in a neutron, as shown in the graphic below:

Of course, in our RSt, we don't have "gluons," but we do have the 1, 2 and 3 "colored" LCs described above, each able to contribute its unique integral value to the combo's dimensional requirements. Whether this will work or not, I don't know yet, but I'm happy that it comes out of the logical development of the system.

### Re: Meeting a Terrific Challenge

In order for the idea of "colored" LCs to work as described in the previous entry, I think we must assume that a given S|T unit is comprised of one color of LC, not a mix. If this is correct, then it forces us to assume that, since a nucleon has to consist of all three colors, then the neutrinos of all three families (electron, muon and tau) are contributing to the quarks.

This condition would not need to hold for the electrons, since they need only consist of three one-dimensional S|T (T|S) units.

Yet, this line of reasoning leads to further consideration of the LC and its three radii. Recall that the LC is a mathematical object in three dimensions. It would be wonderful if nature worked in the same way; that is, expanding (contracting) in two "directions" of each dimension, resulting in a 2x2x2 stack of 8 unit cubes, in one unit of time.

However, this is not the case, but the 3d stack does define the radii of three balls, the inside, the middle and the outside balls, which radii happen to be √1, √2, and √3, and so we can identify what we are want to call three unit magnitudes of nature.

As everything in a universe of motion is either a motion, a combination of motions, or some relation between them, having these three unit motions to work with is perhaps the key to exploring the various configurations that appear possible.

If we change the unit in the stack from the first magnitude of √1, to √2, we get three magnitudes that are double the first, in terms of the new unit (√2):

That is to say, √2 * √1 = √2; √2 * √2 = √4; √2 * √3 = √6. We can also see this in terms of the √3 unit LC:

Now, we have √3 * √1 = √3; √3 * √2 = √6 and √3 * √3 = √9.

As noted previously, one member in each of these three sets, which is a multiple of the original set, turns out to be an integer-valued radius, the one, two or three-dimensional ball of their respective LC. They are denoted in the slides above.

Clearly, while the LCs mathematics has defined the geometry of the balls, it does not follow that they are dependent in anyway on an expanding/contracting stack. The significance of this observation is that the three radii, and multiples of them, can form S|T (T|S) units as discrete combinations of space and time (time and space) oscillations, just as we have combined them in our version of the standard model.

In a discrete universe, integer magnitudes are paramount, and as Brian Nelson has shown, things work out marvelously when we look for them. Maybe we are on the right track.

This condition would not need to hold for the electrons, since they need only consist of three one-dimensional S|T (T|S) units.

Yet, this line of reasoning leads to further consideration of the LC and its three radii. Recall that the LC is a mathematical object in three dimensions. It would be wonderful if nature worked in the same way; that is, expanding (contracting) in two "directions" of each dimension, resulting in a 2x2x2 stack of 8 unit cubes, in one unit of time.

However, this is not the case, but the 3d stack does define the radii of three balls, the inside, the middle and the outside balls, which radii happen to be √1, √2, and √3, and so we can identify what we are want to call three unit magnitudes of nature.

As everything in a universe of motion is either a motion, a combination of motions, or some relation between them, having these three unit motions to work with is perhaps the key to exploring the various configurations that appear possible.

If we change the unit in the stack from the first magnitude of √1, to √2, we get three magnitudes that are double the first, in terms of the new unit (√2):

That is to say, √2 * √1 = √2; √2 * √2 = √4; √2 * √3 = √6. We can also see this in terms of the √3 unit LC:

Now, we have √3 * √1 = √3; √3 * √2 = √6 and √3 * √3 = √9.

As noted previously, one member in each of these three sets, which is a multiple of the original set, turns out to be an integer-valued radius, the one, two or three-dimensional ball of their respective LC. They are denoted in the slides above.

Clearly, while the LCs mathematics has defined the geometry of the balls, it does not follow that they are dependent in anyway on an expanding/contracting stack. The significance of this observation is that the three radii, and multiples of them, can form S|T (T|S) units as discrete combinations of space and time (time and space) oscillations, just as we have combined them in our version of the standard model.

In a discrete universe, integer magnitudes are paramount, and as Brian Nelson has shown, things work out marvelously when we look for them. Maybe we are on the right track.