Some consequences of defining the fine structure constant α as the probability of an electromagnetic interaction with a charged particle are explored using the Binary Mechanics Lab Simulator (BMLS) v2.8. An alpha α composite variable was introduced: (S + V) / M0, where S and V are scalar (electrostatic) and vector (magnetic) event counts respectively and M0 is the number of M-type quanta (1-state bits with charge attribute) prior to application of time-development bit operations and eligible to be "source quanta" in the S and V bit operations [1]. In brief, this α definition is simply the observed probability that a M quanta is accelerated by an electrostatic (S) or magnetic (V) potential. The α variable was not constant, but varied as a function of quanta density in the simulated volume (Fig. 1), suggesting that α may have appeared to be constant if previous measurements were conducted at a quanta density of approximately 0.237 of maximum possible density. Proton-electron mass ratio was also found to occur at about the same quanta density suggesting that this density range may approximate laboratory conditions close to "standard temperature and pressure".
Methods and Results
Using the BMLS v2.8, Fig. 1 shows the linear regression of values from seven BMLS runs (Dim = 72, Random Mode) and the estimated quanta density at which reported values of the fine structure constant α were found (red arrow). Each point represents data (N = 900) from Ticks 1201 to 2100.
The first 1200 BMLS Ticks were excluded from this analysis based on plots of variables in the *.csv output file vs BMLS Tick showing that many variables recorded by the BMLS require a large number of Ticks before relatively stable values are obtained. Indeed, considering that about 350 thousand BMLS Ticks represent an elapsed time of only one attosecond (Fig. 2), the 2100 Ticks used in this report might be considered to be much less than appropriate.
The apparent dependence of the fine structure constant α as presently defined on quanta density suggests that α may have appeared to be constant if previous laboratory measurements were conducted at a quanta density of approximately 0.237 of maximum possible density.
Measurements of the proton-electron mass ratio [2] were also found to occur at about the same quanta density (Fig. 3).
The similar values for quanta density for α and proton-electron mass ratio may be pure coincidence or may suggest that this density range may approximate laboratory conditions close to "standard temperature and pressure" where these measurements have been conducted in laboratories in the past.
Discussion
How simple is that? If the present operational definition of the fine structure constant α is correct, the present report may represent a happy ending to a very long story of heroic efforts by many investigators over decades to understand it.
The fine structure constant definition presented is simply a composite variable of three event counts recorded in each BMLS Tick: M quanta prior to application of the time-development bit operations (M0), scalar (electrostatic) events (S) and vector (magnetic) events (V). In brief, α = (S + V) / M0, the proportion of M quanta accelerated by electromagnetic events.
With full quantization in binary mechanics, α appears to have been hiding in plain sight. M0 is part of the system state called the bit function. S and V are events in the time-development laws, called bit operations, which have been precisely defined mathematically [3]. Hence, the α definition qualifies as a derivation from first principles.
And then there was three. The value of α in the present definition varies with quanta density (Fig. 1). That is, strictly speaking, α is not a constant. However, measurements would be expected to produce closely similar values if conducted within a narrow range of quanta densities.
On the other hand, the three primary constants are thought to be invariant along with those secondary constants which depend only on the primary constants and not α (Fig. 4) [4]. In contrast, the values of Planck's constant and the electron magnetic moment depend on α and therefore would be expected to also depend on quanta density, predictions which experimentalists might well follow up. In this context, Elemental action A would be deemed to be more fundamental than Planck's constant h. Likewise, Elementary charge e may be evaluated as more fundamental than intrinsic electron magnetic moment.
To keep physicists busy with additional predictions, α may be plotted over the full range of quanta density from zero to one, as proportion of maximum possible density. This range includes perfect vacuum, the baryogenesis threshold at about 0.07, the observed proton-electron mass ratio at about 0.238, plasma at about 0.60 and lepton-quark soup starting at about 0.75 (which has been wrongly labelled "quark-gluon soup") [5].
References
[1] Keene, J. J. "Binary mechanics" JBinMech July, 2010.
[2] Keene, J. J. "Proton-electron mass ratio derivation" JBinMech April, 2018.
[3] Keene, J. J. "Fundamental forces in physics" JBinMech October, 2014.
[4] Keene, J. J. "Binary mechanics FAQ" JBinMech August, 2018.
[5] Keene, J. J. "Elementary particle energies" JBinMech April, 2015.
© 2020 James J Keene
