Reciprocity XXIV, #2 (Autumn, 1995), p. 13.
Having recently received a copy of PHYSICAL REVIEW, which contains everything known about subatomic particles, I decided to put The Reciprocal System to the test—to see if Larson's original calculations would still hold up under the scrutiny of today's accurate measurement systems. The results, some of which are related here, have been quite interesting.
All observed particle measurements were taken from PHYSICAL REVIEW D, Particles and Fields.1 Values were calculated with "C" language programs, compiled with SAS/C, version 6.51, using standard, double precision floating point with an accuracy of 15 significant digits. The code was executed on an Amiga 3000 computer under AmigaDOS version 2.1.
The calculated values for subatomic particle mass 2, in terms of natural units, are listed in Table 1. In keeping with Larson's original tabular format, not all the significant digits are shown (though they are used in all computations).
|E||electric mass (3 dim.)||0.000868055556|
|e||electric mass (2 dim.)||0.000578703704|
|C||mass of normal charge||0.000044944070|
|c||mass of electron charge||-0.000029962713|
The observed mass values for the various subatomic particles have changed since the publication of Nothing But Motion, and tentative neutrino and "massless neutron" mass now exist.
The observed neutrino mass is taken from the electron neutrino, which is listed with a "formal upper limit" of 5.1 eV, and a "95% certainty level."3 To maintain consistent units in the table, this value was converted to unified atomic mass units (u) with the conversion factor of 931.49432 MeV/u.4
The mass of the "massless neutron" is taken from the muon neutrino, as suggested by Larson: "…and the logical conclusion is that the particle now called the muon neutrino is the particle required by the theory: the massless neutron." 5
The observed proton is included in both the charged and uncharged proton entries, for comparison. (The uncharged proton is listed as "unobserved" in Nothing But Motion.)
Table 2 lists the subatomic mass in natural units, as compared to the unified atomic mass units based on the 12C isotope.
The values calculated for the neutrino and "massless neutron" are considerably out of line with the observed values. Given that the observed values were deduced indirectly from the decay of other particles, there are undoubtedly numerous factors involved that were not taken into account. I have no explanation for the differences. [Note: See Subatomic Mass Recalculated Update for neutrino calculations.]
The calculated values for the charged electron/positron, proton, 1H isotope, and the compound neutron are reasonably close, but not as close as they should be, given the number of significant digits in both the calculations and the observed values. This is due to the measuring system involved, that of the unified atomic mass unit (u). The observed values are based on the 12C isotope. Larson uses observed values in the 16O scale, which are closer to the natural mass units of the Reciprocity system, but still not exact.2
Instead of converting values from the 12C to 16O scales, it may be prudent to avoid both scales, and determine a conversion factor from natural mass units to unified atomic mass units based on an isotope-free, easily measured particle—the charged electron. Of all the particles there are mass values for, the charged electron is, in all probability, the most accurate. Also, the charged electron mass is known more precisely in unified atomic mass units than in any other unit.4
Thus, the conversion factor between natural (n) and 12C (u) mass units can be determined by the ratio between the measured and calculated charged electron:
= 0.99970644 u/n
Applying this factor to Table 1, the mass components in "unified atomic mass units" are obtained:
|E||electric mass (3 dim.)||0.000867800730|
|e||electric mass (2 dim.)||0.000578533820|
|C||mass of normal charge||0.000044930876|
|c||mass of electron charge||-0.000029953917|
With the exception of the neutrinos, the calculated values are now extremely close to the observed values. The error for hydrogen is only 0.011%. The error in the compound neutron is 0.0035%.
Notice, however, the proton. The difference between the calculated and observed mass in the uncharged proton is almost the same as the charged proton, but in the opposite direction. This is rather suspicious, and one could theorize that the observed proton in the laboratory may actually be a 50/50 mix of charged and uncharged protons. Calculating the atomic weight based on a 50/50 mix yields:
|50/50 mixed protons||1.00727614350||1.00727647000||-0.00000032650|
Which is 0.000032% from the observed value (though still outside the stated error of ?0.000000012 u.)
This calculation indicates that there is a high probability that the values obtained for the observed proton are a mix of both the charged and uncharged states, if the Reciprocal System is correct. Back calculating for this set of data, the proton sample would be 50.72668125% charged, and 49.27331875% uncharged (which reproduces the observed value exactly.)
After compensating for differences in measuring systems, the
1959 calculations of mass agree quite closely with the 1993 observed values.
It would be interesting, however, if someone familiar with particle measurement techniques could examine the process of determining proton mass, and propose a method to eliminate either the charged or uncharged protons in the sample. The results should precisely match the values obtained from the Reciprocal System, when corrected for unified atomic mass. This could lead to the acceptance of the charged and uncharged states of subatomic particles (of the proton at least), and maybe even an objective look at Larson's work.