Harmonic Theory: Atoms and ParticlesIndexNext Reference: RT109 Date: Date: 1-Dec-94 Author: Ray Tomes Email: rtomes@kcbbs.gen.nz Tomes Harmonic Theory is applied to the abundance of the isotopes of the elements and the masses of the sub-atomic particles. It is found that there are patterns in both that are consistent with the theory and that these should help in predictions of stability of new isotopes, and in predictions of new particles. Keywords: Harmonics, Isotope Abundances, Sub-Atomic Particle Masses In other papers the author has shown that a pattern of harmonics can explain all observed phenomena. This pattern can be compared to the pattern of particle masses because masses in the subatomic realm are a substitute for frequencies. It is highly desirable before trying to fully understand this paper to first read:- RT103 Harmonic Theory Overview. The theory of harmonics predicts that around the atomic scale will occur the first occurrence of the ratios 17 and 19 in the mainline of harmonics (See earlier papers for definition of mainline). Also, this should occur near the second occurrence of a ratio 11. This means that most particle masses should be expected to have ratios that have powers of 2 and 3 in them, but that there should be ratios including 11, 17, 19, and that 17 should occur before (at a lower frequency than) 19. To get an impartial view of the actual ratios found in the masses of particles, the following method is used to search for masses which harmonically fit the masses concerned. Take a prospective mass, say m, and then divide this into every different particle mass and see how near to an integer the answer comes out. Add up the differences from integers (the errors if you like) and keep changing m until the best fit is found. Actually we also allow masses to be a fraction of m as well as a multiple. I found this method in an article on quantisation in the solar system concerning the 160 minute period, and have lost the reference, so if anyone knows of the authors, I would like to give credit as it is a very useful technique. When the above procedure is used, the best fit answer is one of a little under 70 Mev. I have found one reference in the literature to this figure by a Japanese researcher who also found this value independently. I prefer the second best solution of 34.76 Mev, simply because it divides into a proton 27 times, while 70 Mev goes 13.5 times which is not an integer. The following table shows the masses of the particles compared to multiples of 34.76 Mev, and the resulting factorisations of that multiple. Particle Actual Theoretical Multiple Factorisation Name Mass(Mev) Mass(Mev) of 34.76 of the multiple e +- .5110 .5112 1/68 1/2.2.17 Mu +- 105.6 104.3 3 3 Tau +- 1784 1773 51 3.17 Pi 0 135.0 \ Pi +- 139.6 / 139.0 4 2.2 K 0 497.7 \ K +- 493.6 / 486.6 14 2.7 Eta 0 548.8 556.2 16 2.2.2.2 D 0 1865 \ D +- 1869 / 1877 54 2.3.3.3 D +-s 1969 1981 57 3.19 B +- 5278 \ B 0 5279 / 5284 152 2.2.2.19 W +- 79310 79250 2280 2.2.2.3.5.19 Z 0 91175 91140 2622 2.3.19.23 p +- 938.3 \ 938.5 27 3.3.3 n 0 939.6 / lambda 0 1116 1112 32 2.2.2.2.2 sigma + 1189 \ sigma 0 1192 ) 1182 34 2.17 *** sigma - 1197 / Xi 0 1315 \ Xi - 1321 / 1321 38 2.19 Omega - 1672 1668 48 2.2.2.2.3 Lambda+c 2281 2294 66 2.3.11 J/psi 3094 3094 89 89 *** B * 5330 5318 153 3.3.17 *** Upsilon 9463 9455 272 2.2.2.2.17 *** Rho 770 \ 765 22 2.11 omega 782 / K * 892 904 26 2.13 *** Phi 1019 1008 29 29 *** D * 2010 1981 57 3.19 D * s 2113 2086 60 2.2.3.5 *** means that the author considers the multiple to be mis-identified because it probably also has a divisor. more on this later. The above data may also be arranged to show the relationships in a diagram that represents the harmonic structure: - e+- \ 2 \ 2 17 / 34.76 Mev 3 / / \ \ 2 mu+- \ \ \ 2 3 / / \ pi+-0 3 / / \ \ 2 p+-n0 / / \ 2 \ 2 / / eta0 D+-0 / / 3 / \ 2 / / omega- lambda0 17 / \ *** / \ 3 /\ 2 \ 19 tau sigma+-0 \ 3 / \ 2 3 /\ 2 B* \ 2 D+-s xi0- \ 2 \2 \ 2 upsilon /\2 \ 2 23/ \2 B+-0 / 5/ Z0 W+- *** The branch which is at a multiple of 17 from 34.76 Mev is probably mis-connected. The reason is that the 17 ratio has just occurred to get to 34.76 Mev (from the electron). For this reason, the whole branch labelled is considered to be correctly placed at 17.1 which is 19x9/10. That is, we must divide by 10 and then multiply by 9 and 19. This also makes the masses nearer to the estimates. The diagram can then be reconstructed as: e+- \ 2 \ 2 17 / 34.76 Mev 3 / \ \ 2 mu+- \ \ 2 3 / \ pi+-0 3 / \ \ 2 p+-n0 _ / \ 2 \ 2 / \5 / eta0 D+-0 / \2 / 3 / \ 2 / \/ omega- lambda0 3 / \ 3 / \ 3 /\ 2 \ 19 tau sigma+-0 \ 3 / \ 2 3 /\ 2 B* \ 2 D+-s xi0- \ 2 \2 \ 2 upsilon /\2 \ 2 23/ \2 B+-0 / 5/ Z0 W+- The above diagram is very consistent with the predictions of the harmonic theory in having mainly ratios of 2 and 3, with just a few other ratios. It also introduces the primes 17, 19 and 23 in the correct order. I had constructed this diagram before I knew of the Z0 and W+- masses. The fact that the Z0 fits with a further 23 multiple is an excellent confirmation of the theory. It would require enormous energy to reach the next prime, 29, because it is well above 23, and would have some ratios of 2 and 3 first. The most puzzling thing about the diagram is the three successive ratios of 3 before reaching the proton/neutron. Although it is possible to arrange things so that there are only two ratios of 3 here, the theory predicts at least two ratios of 2 between every 3. There are frequent other locations with three successive multiples the same. It seems that something extra is going on, possibly to do with the three spacial dimensions. The above table hints at many energies which are possible candidates for resonances (other particles). At the very low masses which might be investigated by electron/positron collisions, the prediction of possible resonances at: electron X 2 4 17 34 68 6 12 Mev 1.022 2.044 8.69 17.37 34.75 3.066 6.132 At some of the branch points not occupied by particles other possible resonances are possible: 34.76 Mev X 11 19 19x9/10 6x19 Mev 382.4 660.4 594.4 3963 There are in fact many other masses which could be put in the diagram, but these are recognised as compound particles. The deuteron and alpha particle for example are as fundamental under the harmonic theory as the proton or the mu. A tentative identification of the exact harmonic numbers of the particles has been made. This connection should be regarded with caution, but is a working hypothesis. The values agree within 0.2% with values obtained by working backwards from cycles and distances in the years and light years range. The harmonic numbers for the electron and proton and deduced value for the number one harmonic period are: Prime 2 3 5 7 11 13 17 19 number one power to raise prime to cycle (secs) Electron 50 21 9 5 1 1 0 0 4.4743x10^17 Proton 52 24 9 5 1 1 1 0 4.4740x10^17 4.444yr 19 5 2 0 0 0 0 0 4.466 x10^17 These values (4.474x10^17 s ) are consistent with a Hubble constant of 47.8 km/s/Mpc. The details of this connection are dealt with in another paper. Abundance of Nuclei with various masses. As yet, I have not identified any reason for charge within my theory. This, together with the fact that the proton and neutron have the same harmonic number in the above analysis has lead me to consider on the number of baryons in each nuclei. The following analysis is therefore based on only atomic weight, and the abundance of all isotopes (of different elements) with the same mass have been combined. The following diagram shows the abundance (log scale) vs the atomic weight. 6 I 1 I 4 5 I 16 I 2 1214 20 4 I 28 56 I 2224 32 3 I 19 26 29 40 I 1315 18 21232527 30 54 58 2 I 7 17 31 34 52 5557 60 I 3 911 33353739 48 59 1 I 6 10 36 44 50 53 I 42 46 4951 0 I 38 4143 47 - I 5 8 45 -------------------------------------------------------------- Log Atomic Mass (unit=1 baryon) Abundance Masses 5 and 8 abundance are zero. You need to do a sort of connect the dots to get the graph, but I have tried to make it easier by plotting the numbers. Existing theory says that even numbers and even multiples of 4 should be more common because they are more stable. It also has the concept of shells, although this is fairly mystical, using the term "magic numbers" which are not explained. My theory says that masses higher than the proton should favour certain values (depending on their factorisation) for the following reasons. 1. Because the proton is a multiple of 3 smaller parts, it should want to go in multiples of 2 then 2 then 3 next. This predicts that 3 should be rare (which it is) and 2, 4, 12 should be common (which they are) and that 8 should be rarer (although the extent of this is a surprise). 2. Because a factor of 7 is almost due, 7, 14, 28, 56 should be common. They are, and particularly 56 and 28. This is the multiple 7 really coming into its own. 3. Because the factor 11 is near due, (11), 22, 44, 88 should be abundant (and they are). 4. Because the factor 3 has just occurred, numbers with high powers of 3 in their factorisation should be rare. This includes 3, 9, 18, 27, 36, 45, 54, 63. Most of these range from rare to very rare (45 is the least common existing number in the 10 to 60 range). 18 and 36 are noticeably low. 54 is the only one not depressed. 5. The factor 5 is not due, so 5 and 10 are low abundance, but after two powers of 2 it begins to reappear and 20, 40, 80 are common. Note that 40 is the peak. This is because there are 5 or 6 powers of 2 for every power of 5 in the harmonics. The common atomic numbers may be shown more clearly in the same sort of diagram as the particles are shown above. (1) / \2 / (2) / / \2 / / (4) / / 3/ \ 7/ 11/ (12) \ / / \2 \ / (22) (24)\ (7) \2 \2 \ \2 (44) (48)\5 (14) \2 \ / \2 (88) (20) 19/ (28) \2 / \2 (40) (266) (56) Just for fun, The atomic number 266 is shown. We know that the factor 19 is due to occur just above a proton, and so it is no surprise that 266 is vastly more stable than surrounding isotopes. Ultimately, it should be possible to formulate this to give some indication of the abundance of each atomic-mass just from the factors in its makeup. This could be done know on an empirical basis, but should at some stage be done on almost purely theoretical grounds. What can be predicted about undiscovered isotopes? The answer to this is that any of the above abundant numbers when multiplied by:- 12 or 7 (when not already a multiple of 7) or 11 (when not already a multiple of 11) or 19 (yes you've got the idea) should be generally more stable than other numbers. Particularly unstable ones should be multiples like 9, 27 and 25 of the above numbers. To see this from a harmonics perspective, it is necessary to not see a nucleus as made of baryons, but to see it as a frequency which is so many times a baryon. It is also some number of times a variety of other particles, including an electron. These relationships are important, and if it were not for the existence of charge, I would say that some nuclei are as fundamental as a proton. I am trying to have people see that all these things are oscillations, and that a small number of sub-atomic particles are NOT the building blocks of the universe. The relationship electron x 68 = 34.76 Mev x 27 = proton indicates the possible existence of a particle of mass 34.76 Mev. No such particle has ever been detected to my knowledge. It would be interesting to know if electron/positron collisions showed a resonance here. There are two other ways that these numbers (68 and 27) seem to be important, and indicate that 34.76 Mev is important. Firstly, if a proton is assumed to be made of n smaller particles and then the "magic numbers" are worked out (that is the number of baryons which make a closed shell) then the existing magic numbers are very well explained when n=27. This confirms that the proton could be made of 27 smaller parts. Secondly, the fine structure constant (which relates to the interaction of the proton and electron) has an inverse of 1/alpha = 137.035989 about. There is an expression which gives very close to this number, namely 137/(1-1/136/28) which is 137.035986341. This would be entirely numerology except for the above facts. Note that 136 = 68 x 2 and that 137=136+1 while 28=27+1. So what you might say? Well, if a proton and a 34.76Mev particle were to orbit each other, they would have a centre of gravity that was 1/28 of the way from the proton to the 34.76Mev particle. Likewise, with an electron and 2x34.76Mev giving 1/137. Therefore the expression above is almost intelligible in terms of a structure containing the three particles in some way. This will be unconvincing to many. However as 1/alpha is determined more accurately, if it continues to confirm this, what then? Next Email: Ray Tomes