The Impact of Inverses
Doug
23 Comments
At the end of the previous entry, I promised to show how the neutron is the inverse of the proton. Actually, the LST community’s abstract concept of quantum “isospin” treats them as inverses, even though they differ by charge and by a very small difference in mass.
Also, the LST’s concept of quarks provides a sense of the inverse composition of proton and neutron, since the proton consists of two up quarks and a down quark, while the neutron consists of two down quarks and an up quark.
In our case, since the difference between the quarks consists of differences between their three sets of discrete, inverse, oscillations, the preons forming them, we can quantify this net inverse relation by employing a schematic diagram to represent the combinations.
The up quark has two sets of 3D oscillations with one more TUDR (2) than SUDR (1), together with one balanced set consisting of one SUDR and one TUDR. Hence, we can replace it with the number 2, because 1+1+0 = 2.
The down quark consists of two balanced sets and one unbalanced set with two SUDRs and one TUDR. We can therefore replace it with the number -1, because -1+0+0 = -1. Consequently, representing the proton with two 2s, for its two up quarks, and one -1, for its one down quark, placed at the three vertices of a triangle, we get 2, 2, -1, while doing the same thing for the three quarks of the neutron will give us a -1, -1, 2 pattern, which is the inverse pattern of the proton.
Using the same procedure with the electron, which has three unbalanced sets of 3D oscillations, all unbalanced to the SUDR (red) side, we get -1 + -1 + -1 = -3. Thus, the electron “neutralizes” the excess positive sum of the proton’s quark numbers ((2+2+(-1)) + ((-1)+(-1)+(-1)) = 0), while, of course, the sum of the neutron’s quark numbers is already 0.
Thus, it all comes together nicely in the schematic of triangles, which represents the net oscillations, after a fashion, as shown graphically here.
This development was so encouraging when it first emerged two and half years ago, that I was sure we would be able to continue it and reach our goal of tying our preon version of the standard model of particle physics, with our 4n2 version of the periodic table, the Wheel of Motion.
This would be an important achievement, since it would be the first time in history that an alternative to the LST community’s quantum mechanics and its wave equation, based on the concept of rotation, would have emerged.
Alas, however, crossing the bridge between the preon model and the Wheel of Motion has been more difficult than imagined. As described here, it appears that we have to follow Hamilton’s work with rotation and accept the fact that the number four plays an essential role in the combining of our preons to form the correct series of elements in the Wheel of Motion.
While it’s true that the inverse numbers in the schematics of the proton and neutron work nicely to combine them into combos that have interesting properties, including spin, the Pauli Exclusion principle and the concentration of numbers at the center of the combo, with numbers spread out at the periphery, the fact is, there is no mechanism for limiting the preon numbers, in the same way that the correspondence with vectorial motion in rotations limits the quantum numbers. It’s the limit that we are lacking. The question boils down to this: “What is the ‘n’ in the “4n2” relationship of the Wheel of Motion?
Schematically, we can build an atom by placing the proton and neutron together as shown for deuterium, helium and lithium in figure 1, below:
Figure 1. Building Atoms from Preons
As can be seen from figure 1, when represented with the three vertices of a triangle, schematically, the up and down quark and electron preons, form combinations that we can identify as hydrogen (the proton and electron combo without a neutron (not shown separately)), as deuterium (one hydrogen and one neutron), as helium (two hydrogen and two neutrons) and as lithium (three hydrogen and three neutrons). The electron is shown schematically in two states: The black letter “e” represents one state (on top of the proton triangle), while the white letter “e” represents the other state (on the bottom of the proton triangle).
While this enables us to find parallels with the four quantum numbers schematically, if not physically, the problem is there is no variable ‘n’ that can be identified that corresponds to the radius of an electron shell in the quantum mechanical model of the LST, the primary quantum number ‘n’ in the 2n2 relations of the periodic table.
This has driven me back to the beginning, to take another look at the fundamental 3D oscillations, the SUDRs and TUDRs. While we have only considered one family of the standard model’s quarks and leptons, it has always been evident that we could probably derive the second and third families by adding to the number of SUDRs and TUDRs in the preons, while maintaining their ratios. It was left at that, because it was assumed that connecting the Wheel to the preons was not related to the other families, and that part of the development could therefore be delayed, until later.
However, this appears to have been an error. I’ll explain why next time.
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Reader Comments (23)
Hi Doug,
I haven't commented here in awhile. Good to see you're still at it!
Regarding quarks, I got a nice mention on Tommaso Dorigo's blog concerning a
a relation I found between the lepton and quark masses. Go to...
http://www.science20.com/quantum_diaries_survivor/blog/whats_going_around_0
...then click where it says...
Marni Dee Sheppeard puts forth a remarkably simple diagram to compute quark masses.
Cheers,
Dave
Hi Dave,
It's good to hear from you again. I have always thought Carl's stuff was on to something, but I can't understand it. From reading all your comments on his site, looks like you really got into it last year.
I am still reeling from the Le Cornec data you turned me on to years ago. Now, you turn up with information on triplets that intrigues me, even if I don't quite get it yet.
I sure appreciate your intensity. I wish I had half the energy you have! lol.
Hi Doug,
The other night I came across the Le Cornec paper, googled to see if any further research had been done, and your site came up near the top of the search results.
Anyway, about a year ago I redid Le Cornec's chart with the latest data from NIST. I'll send you the spreadsheet if you want, cause it's fun to chase hypotheses around creating different charts & such.
Since your research is focused on geometric relations, I thought I'd re-mention the interesting finding of Hans de Vries, that the fine structure constant is exp(-pi^2/2) (plus the radiative corrections), at
http://physics-quest.org/fine_structure_constant.pdf
Since alpha might be a geometric relation, it's interesting to recall the relation I found between the unit charge and the lepton unit mass (5.594997565E-028 kg * c = p).
Starting with the standard definition of alpha:
e^2 / (E*hbar*c) = 4pi*a (E is vac. permittivity)
We can set P=hbar=c=1 to give charge^2 in Heaviside-Lorentz natural units, e^2=4pi*a
Then we get the following relation...
(exp(-4pi*a))^.5 = 0.9551846
e/p = 0.95518996
...which I think reveals an amazing connection between a fundamental mass unit and elementary charge.
This would mean charge is momentum, which it is when voltage is equated with velocity (see chart at end of http://www.dartmouth.edu/~sullivan/22files/System_analogy_all.pdf)
Best Regards,
Dave
Sorry Doug, just noticed a typo...
We can set P=hbar=c=1 to give...
should read...
We can set E=hbar=c=1 to give...
Hi Dave,
It is interesting. Does the fact that the dimensions of e/p, s^4/t^3, are the dimensions of fluidity, F = s^4/t^2, times frequency, 1/t, mean anything to you?
I realize that you are only interested in the ratio here, but I thought I would ask.
since e and p are both momentum, it's dimensionless.
I'm thinking "charge" represents the momentum of the virtual photon flux.
Like heat, we normally see it as scalar, until another charge is around to bias the momentum into a particular direction, then it becomes a vector.
Well, from what I remembered from our conversations long ago, I thought you were taking the LST point of view, which doesn't differentiate e from electrical quantity s, and electrical charge t/s.
Larson's view was that charge has dimensions t/s, in which case the ratio e/p would be dimensionless.
But if the dimensions of e are s, then the ratio wouldn't be dimensionless, it would have dimensions s^4/t^2, which are the dimensions of fluidity (I don't know how I got s^4/t^3, sorry).
You're right, I don't differentiate charge that way.
All the LST papers that come up with analogies between electrical and mechanical quantities come to the conclusion that you can equate voltage with velocity, or voltage with force. Interestingly, it is the Voltage=velocity analogy which allows you to keep the topology of the circuit the same, ie, you don't have to reconfigure a mechanical series-circuit as an electrical parallel-circuit to keep the energy equations valid. Refer to the Dartmouth paper above to see why.
So while it is perfectly VALID to have charge as "s", it's even better to have charge as momentum, and let flux be "space". Keep in mind that h=charge * flux.
I no longer go by the assumption that mass=t^3/s^3 (and all that follows), because I believe the quarks are more fundamental that the atomic mass unit. I don't yet have a way to equate mass with time & space, unfortunately. Although I suspect mass is closest to time.
However, I believe a huge step has been taken in simplifying the units if charge is tied to the lepton unit momentum.
Lepton unit mass= 5.594997565E-028 kg (LM)
Lepton unit momentum= (LM)*c = 1.677338073E-019 kg*m/s = (p)
Lepton unit charge = 1.602176462E-019 = (e)
p/e = 1.046912193
exp(2*pi*a) = 1.046918009
I already glanced at the paper. I'll have to read it more carefully, I guess. Presumably it will explain how, if voltage is equated to mechanical velocity and electrical flux to s/1, which is normally t/s, what is current, which is normally equated to velocity, s/t?
Sorry, by flux I meant "magnetic" flux. "Electric flux" reduces to s^2/t, and current becomes force.
Hi Doug,
I've made a lot of progress in reducing the arbitrary parameters of the diagram for computing the Lepton and Quark masses. I created an interactive java applet where you can control the angle and see how the masses "lock on" to the correct value at 2/9 rad...
http://home.comcast.net/~davelook/Quark%20Files/LeptoQuark_slider.html
Enjoy!
Dave
Hi Dave,
Thanks for your hard work on this. I'm still struggling to get a handle on it. Any help you can offer in the way of clarifying the picture for me will be greatly appreciated.
Hi Doug,
I hope I haven't the impression that I have a clue as to WHY this diagram is able to generate the fermion masses. I was just trying to expand Brannen's work to the quarks.
So far, this work is in a similar stage as when Rydberg discovered the constant that governs atomic spectra, but before Bohr came along with an explanation in terms of other constants.
If you're unclear of the mechanics of the diagram, I can definitely help with that if I know where you're having trouble.
Dave
Well, I've been able to work out the charges of quarks and leptons and the baryons through the four lambdas, based on the mathematics of the tetraktys and the geometry of Larson's cube, but the masses throw me somewhat, because I suspect they are related to the harmonics of the oscillations more than the volumes involved.
However, everything that I've been able to do is based on the LRC's new number system, where the unit value is not one, but the inverse of the square root of 2, in which there is a one octave difference between the inverses, instead of the four octaves in 1/2, 1/1, 2/1. Thus, the Le Cornec data and the Koide formula intrigue me, because there seems to be a connection, but I can't understand the diagram of the triangles.
I would like to know what the angle means. Of course, I am cognizant of the meaning of 2/9 in the context of Larson's work, but I don't understand what is happening when we change the angle with the slider in the app. I've tried to read Carl's stuff, but I just get lost in the talk about "circulants" and the matrices.
I also don't understand how you were able to find that the lepton mass values were nested in the quark mass values like that. I think there's a lot there for me, if I could just understand what's happening.
Hi Doug,
Brannen found the 2/9 empirically, through his investigation of the Koide relation. I don't think anybody has an understanding of it's physical significance yet, although Brannen thinks it has to do with fermions being composites of more fundamental particles (snark, as he calls them).
When you use the slider, you are allowing the 2/9 to vary, while keeping the other relationships, or constraints, intact. For the Lepton, this means keeping the radius at sqrt2, so that the equation for lepton masses becomes: (1+sqrt2*cos(2*pi*g/3+V))^2, where "g" is the generation, and "V" is now the variable angle.
The way I found the nesting was by laying out geometrically the suggestion by Kea that the up-quarks ratios fit the lepton formula, if, instead, you used an angle of 2/27, and a radius of ~1.76 (vs sqrt2):
(1+1.76*cos(2*pi*g/3 + 2/27))^2. This was curious, but rather arbitrary. Excitement came when I pointed out 1.76 is the required radius, if the lines connecting the up-quarks "nest" the lepton triangle. This would've been nearly impossible to find using the equation alone. It takes VISUALIZATION for some relationships to become apparent. This was the main motivation for adding the slider, to see what pops out as you vary 2/9 rad.
This slider paid huge dividends when it allowed me to realized that the down-quarks, with mass ratios governed by: (1+1.76*cos(2*pi*g/3 + 4/27))^2, simply have a different rotation basis than the leptons, (with a circle centered at Q). So the quark-lepton connection isn't due to the weird nesting, it's due to a different rotation basis, as only the slider could reveal.
I hope that helps! Let me know if I can help further.
Dave
I think I understand it now. Thanks so much. I am always amazed at how people can come up with formulas like this. I wonder how Koide found the relation in the first place and how Carl and Marni were able to extend it.
When I read their writings, I get so lost, but then, when you make it plain like this, it's so simple. How can something so simple and straight forward come out of all that gobbledygook is beyond me.
But I'm really glad that you shared it with me. It came at the perfect time. I've run across the 2/9 value myself in a very significant way. It turns out that the volume of the inverse ball of the outer ball that just contains Larson's cube (LC is the geometrical manifestation of the mathematical tetraktys), is exactly 1/8 the volume of the outer ball, just as the volume of each of the inner 8 cubes of the 2x2x2 stack of the LC is 1/8 the volume of the stack.
The volume of the inverse ball (radius 1/2^.5) turns out to be the inverse of the square root of 4.5 times pi, which of course is the inverse of 2/9 times pi. Taking this value as the volume of the SUDR and 8 times this value as the volume of the TUDR (radius 2^.5), the charges of the quarks and leptons, calculated from these volumes, come out perfectly, magnitude and sign wise, when plugged into our preon model, which, not coincidentally, is inspired by Bilson-Thompson's ribbons (see here.)
What I'm really interested in finding out now is how the masses can be related to these volumes, or the frequencies of their oscillations. Since the inverses of 2/27 (13.5) and 4/27 (6.75) are 3 and 1.5 times the inverse of the inverse of 2/9, respectively, I can probably find them in terms of combinations of S|T units (SUDRs and TUDRs).
This is exciting, because it enables us to move into the "relations between motions and combinations of motions." What encourages me the most is that, even though we have moved completely away from the concept of 2D rotation, as a basis for describing nature, we continue to find powerful, yet simple, analogs in the geometry and mathematics of 3D oscillations.
Dave,
Maybe I spoke too soon. I can't make the calculations come out right. Evidently, I'm still missing something. Does the equation work as a standalone equation, or is there something else that I need to include?
Well, first, I highly recommend a cool little program called "allercalc". You can copy and paste my equation into it.
Anyway, don't forget to include the conversion constants: 313.856 MeV for the 3 charged leptons, .00965 eV for the 6 neutrinos, 22989 MeV for the 3 up-type quarks, and 557.7 Mev for the 3 down-type quarks.
So for the electron, the equation is: (1 + sqrt2*cos(2*pi*1/3 + 2/9))^2 = 0.001628115, then
0.001628115 * 313.856 MeV = 0.51099 MeV = Electron Mass
... and don't forget to switch to radians!
Dave
Ok, now it works. Thanks. I missed the conversion constants. Where did you get them? I will download the Allercalc program - it's got to be better than the Windows calculator!
The constants are just back-calculated from the results of the equation(s). For the charged leptons, see previous post how Lepton unit mass is directed related to the elementary charge. For the Up-type quarks, it's derived from the Z boson mass. The rest are still just derived by back-calculating.