For all intents and purposes, the electron is a perfect particle. It can’t be broken down into other components like the proton and other heavier particles. It has two siblings that are exactly like it only heavier, the muon and the tau particles. The three of them constitute what is known as a family of leptons. It is clear that they are alike by their similar magnetic moment anomalies. As far as I know, no one has figured out exactly why the magnetic moment anomalies of the muon and tau particles do not match that of the electron's. I intend not only to show why their values are different from that of the electron, but also that other spin-1/2 particle families have hitherto unknown family members. These other families are related by their masses and magnetic moments in the same manner as the electron and its siblings.
Magneton values are the presumed ideal magnetic moments for spin-1/2 particles. They are easily calculated for any mass, regardless of whether that mass is a known particle. Magnetic moments of particles have been plotted in many ways throughout the 20th century. One of the most telling ways is through plotting them as points on a power curve. To see a power curve plot effectively, one must convert the values to natural logs, which allows the plots to be straight lines. When plotted this way, all potential particle masses fall onto a single straight line with a -45° slope—a diagonal line running from upper left to lower right—when plotting magneton vertically versus mass horizontally. Figure 1A shows a magneton graph with slope equation for the lepton family.
Figure 1A
If the lepton family is plotted on this same type of graph using actual magnetic moments, the resulting curve is still a straight line, but the slope is slightly less than -45°. Figure 2A shows this curve with slope equation.
Figure 2A
To verify the two graphs, the values used are as follows:
Electron Mass: – 9.10938214505E-31 kg Muon Mass: – 1.8835313E-28 kg Tau Mass: – 3.1677788E-27 kg
Electron Magneton: – 9.274009147055E-24 J/T Muon Magneton: – 4.485218447775E-26 J/T Tau Magneton: – 2.666868406461E-27 J/T
Electron Magnetic Moment: – 9.284763771983E-24 J/T Muon Magnetic Moment: – 4.4904478564E-26 J/T Tau Magnetic Moment: – 2.6700027726E-27 J/T
There are only a few spin-1/2 particles that have magnetic moments that fall below the magneton curve, most are above it. There shouldn’t be anything below the line, as that would make them more than perfect. The SM cannot answer the question of why magnetic moments fall where they do on this or any type of plot. More importantly, what is it that makes the magneton curve a power curve? The only relationship in particle physics that is a power relationship is c and c-squared. This is only supposed to apply to energy and mass equivalence, so how do magnetic moments fit in this scheme? There is no answer for that in the SM either.
When all of the known spin-1/2 particles with published magnetic moments are plotted onto a power curve graph, no other complete family can be found. Although there is no reason to do it in the SM, since the magnetic moments of atomic nuclei are supposed be created by unpaired protons and neutrons, spin-1/2 nuclei can be plotted this way too—see Figure 3A. When looking at the results of adding the nuclei to the particle graph, what stands out is the fact that two of the nuclei fit with the proton, neutron, sigma +, and sigma 0, as if they are the largest particles in a family of three. The two nuclei that make these sets complete are the carbon 13 nucleus and the nitrogen 13 nucleus. Out of all the possible nuclei, these two are close together in mass just like the proton and neutron, or for that matter the sigma + and sigma 0. These two sets combining particles and nuclei are just as convincing as the particle-only lepton family when looking at the mass and magnetic moments.
Figure 3A — all curves project forward to show slope direction
(A large portion of the graph is missing between the electron, which is not shown, and the muon, which is the first point shown on the upper left, as the graph size would have been too small to see the necessary detail.)
With a little massaging, it is possible to fit all of the spin-1/2 nuclei, along with other particles or other nuclei, into families of three. There are some that can be put into families of four, but that causes problems for curve fits with other families of three. It appears that three-member families are sacred for some as yet unknown reason. To create a fit, the mass or magnetic moment changes were held below a combined 1% threshold, and in most cases it was one or two orders of magnitude less than 1%.
The most interesting fact about this graph is that out of the 80 spin-1/2 particles and nuclei shown there are at least 65 curves to which the data points are able to be perfectly tuned. Many of the curves intersect through certain data points, providing evidence that a particular pattern may exist to explain the phenomenon. This pattern may reveal why the mass values exist at the points they do, and even why some particles or nuclei are stable while others are not.
It is not difficult to determine if a particle falls onto a power curve, as long as its mass and magnetic moment are know, and if all possible power curves are also known. Each particular curve can consist of either stable or unstable particles or nuclei. Curve slopes begin to increase as mass increases, but there are a few examples of steeply negative slopes. At high mass values the curves become nearly vertical, which is just as much an indicator to a mass limit for matter as are the known elements.
An interesting aspect of the positive and neutral group’s magnetic moment power curves is that they cross the magneton curve at a point close to the muon magneton location when the curves are extended in that direction. It is unclear if this is significant, but the fact that similar events occur at all three lepton magneton locations, as well as at other spin-1/2 particle-occupied locations along the curve, suggests that it is. Not all spin-1/2 particles have published magnetic moments, so these particles were not plotted. It would be interesting to see how many curves intersected near these unplotted magneton values, and if this fit any type of recognizable pattern. Seven curves came extremely close to projecting to the same location near the muon, which seemed more than just coincidental.
One glaring omission in the list of nuclei as potential particles is that of neutral nuclei; they just can't be presented in the appropriate manner. It doesn’t mean that they don’t exist, it is just that as neutral atoms they are considered to be different from charged nuclei. In essence, when an atom is neutral it can be equated with a neutron, but when it loses a certain amount of mass it can become charged and can be equated with a proton, or anti-proton if negative. At least from looking at power curve plots, it sure seems that spin-1/2 nuclei are actually particles, and that the atoms they come from are not constructed as described by the SM.
Supplement: If you are interested in creating your own graph, which will give you even greater access to the fine details, Table A gives the adjusted natural log values for each particle and atomic nucleus in order of increasing mass. If you desire, the natural log values can be converted back to their original values, which will show any deviation from the WebElements listings, or those from other sources where no information existed on Webelements.com in 2002. There have been some changes to the accuracy of the measurements of the nuclei values, but the difficulty in making all the changes is great. A program needs to be designed to do all of the calculations automatically by adjusting the values of the particles and nuclei to keep the R-squared values at unity. (That type of work is beyond my knowledge base. I most likely won't be doing any corrections by hand, as they are too time consuming.)
(In the book, the radioactive elements were highlighted in Magenta. I did not notice that the colors did not transfer to this site. I appologize for any inconvenience this may have caused to earlier visitors to this site.)
The nuclei names in Bold letters in Table A are radioactive and show their distribution as compared to the stable nuclei. Since there are many stable and radioactive spin-1/2 nuclei with no widely published magnetic moments, this list is far from complete. All listed particles are very unstable except for the electron and proton, and of course the neutron, which lasts about 15 minutes as a free particle. Everything else is presumed to be stable, unless new data shows otherwise. Because many of the spin-1/2 nuclei are radioactive, it appears that magnetic moments are not influenced by the radioactive nature of the nuclei, but are merely a function of the mass. The fact that radioactivity occurs in isotopes all along the periodic table indicates that stable nuclei are surrounded by ones that cannot become stable.
