Abstract and Introduction
Breaking news: elementary charge e has been calculated for the first time from first principles of the leading comprehensive, fundamental quantum theory known as binary mechanics (BM) [1]. A quantized Coulomb force was defined (eq. 1). Based only on the time-development scalar bit operation [2] [3] and the three quantized units of measurement -- M, L and T (Fig. 1) [4], calculated electrostatic force (eq. 2) accounted for 97.6% of the quantized Coulomb force. Elementary charge e may be derived from three primary physics constants based on energy-space-time quantization (eqs. 3 and 4).
Quantized Coulomb Force
Primary length constant L (Fig. 1) and Coulomb's law may be used to express quantized electrostatic force F in newtons:
F = k0e2/L2 = 509.77178 newtons (eq. 1)
where k0 is Coulomb's constant, e is elementary charge of q and Q in the customary expressions and L is the BM length constant. Note that this quantized Coulomb force F at intercharge distance L (Fig. 2) avoids infinity issues if the r2 value in eq. 1 could be less than L2. However, in the time-evolution scalar bit operation, intercharge distance is always L. Hence, eq. 1 quantizes all electrostatic force events along each spatial dimension. In this text, numeric values are written with eight significant digits, which should not be confused with the appropriate number of significant figures based on CODATA values (www.usnist.gov).
Coulomb Force From Primary Constants
Fig. 2 shows two 1-state M bits (black circles) at initial t = 0 in a pair of concurrent spot units [5], separated by distance L (vertical line in red triangle). The charge sign in this M bit pair is the same (eqs. 5, 9 and 10 in [1]). In Fig. 2 upper, the scalar bit operation moves a M bit to the L bit locus at final t = 1 (black arrow), a displacement of distance L (horizontal side of red triangle). In L units at t = 1, the distance between the two energy quanta is sqr(2) (diagonal line in red triangle). Hence, the displacement due to the electrostatic potential from t = 0 to t = 1 is {sqr(2) - 1} = 0.41421356.
Force F in eq. 1 may be written without reference to elementary charge e, by using all three BM primary constants (Fig. 1) to express mass and acceleration over the distance {sqr(2) - 1} specified by Coulomb's law:
F = me{sqr(2) - 1}L/T2 = 497.52080 newtons (eq. 2)
Eq. 2 accounts for about 97.6% of the quantized Coulomb force (eq. 1). The missing 2.4% may be attributable to some degree of same-charge separation due to the other permutations of M and L bit states in concurrent spot units (e.g., Fig. 2 lower) [2].
Fig. 2 lower shows the case where the scalar bit operation (S) moves both M bits to the L bit loci in their respective spot units. In this event, same-sign charge separation might be deemed to be zero. Alternatively, one might say that the separation is 100%, since L bits have no charge property. However, in the SUVF bit operation sequence [1], in the very next tick t, the unconditional bit operation (U) moves these quanta in L loci to M loci (with same-charge properties) in the next spot units in the L bit direction.
In summary, some combination of two possibilities require consideration:
1) eq. 1 may overestimate Coulomb force in the L meter range. This possibility may be another failure of continuous space-time theory used in legacy quantum mechanics (e.g., Standard Model math) at more microscopic distances.
2) eq. 2 may need modification, such as a second term added, to equal eq. 1 at a satisfactory level of precision. E.g., the initial states shown in Fig.2 (upper and lower) might be both used weighted by their probabilities of occurrence for a given overall bit density. In this case, note that Fig. 2 upper shows one of two permutations if the illustration is flipped vertically.
Elementary Charge From Primary Constants
Setting eq. 1 equal to eq. 2 and solving for e2:
e2 = ameL3/T2 (eq. 3)
where a is {sqr(2) - 1} / k0. Eq. 4 substitutes bit velocity V (Fig. 1) in eq. 3:
e2 = ameV2L (eq. 4).
The derived elementary charge e is simply the square root of eqs. 3 or 4.
Fractional Charge
Since the term "fractional charge" is used in different contexts in physics literature, Fig. 1 lists fractional charge as "elemental charge" C. Fig. 2 shows motion of a single 1-state M bit with mass M in the scalar bit operation and its charge is e/3 = C. If quantized mass M is used in eq. 2 instead of me, the calculated force is reduced by a factor of 3:
F = M{sqr(2) - 1}L/T2 = 165.84027 newtons (eq. 5)
Using C in eq. 1 reduces quantized Coulomb force by a factor of 9. Thus, at the single M bit level, the applicable Coulomb constant becomes 3k0:
F = 3k0C2/L2 = 169.92393 newtons (eq. 6)
If both M and C are used in eqs. 3 and 4, the a constant needs division by 3 to maintain the correct force comparison between eqs. 5 and 6. These fractional charge expressions may be more appropriate in further quantitative work.
Discussion
Death by 1,000 Knives. The quantization of Coulomb force and calculation of elementary charge e from space-time-energy quantization in this report is yet another blow to legacy quantum mechanics and another credibility boost for BM postulates. Fig. 1 is a working hypothesis that all so-called physics constants are really secondary values which can be derived from three, or perhaps four, primary constants. Given the full integration of quantum and gravitational phenomena in BM, the gravitational constants are on the roster for derivation from BM postulates and primary constants.
Ironically, BM is more "quantum" than legacy quantum mechanics. As summarized in Fig. 1, each paper that derives a secondary constant from the BM primary constants is, alas, another of the "1,000 knives". At present, one must wonder why publications like Wikipedia and others would even bother to present Standard Model math, given its basis in discredited continuous space-time theory. In other words, legacy quantum physics has not even bothered to reverse-engineer the universe to the point of defining primary physics constants for the units of measurement. To go full quantum, look for Binary Mechanics Lab on your GPS.
Polymers, Cakes and LHC Resonances. A chemist cooking up a new polymer may hope it has useful physical properties and would not usually expect that the effort would result in a fundamental breakthrough in chemistry knowledge. Likewise, a chef cooking up a new cake recipe may be aiming at a desirable taste rather than a fundamental chemistry advance. Strangely, workers at CERN's LHC appear to be seeking a basic physics breakthough by increasing beam intensity and improving event detection. But similar to the polymer chemist and cake chef, the outcome will most likely be similar, namely more complex assemblies of the eight truly elementary particles [1] clearly within known predictions of binary mechanics. In short, nothing new whatsoever.
As described previously [6], a research frontier bulging with questions of high scientific merit is exploration of the smallest object known in physics -- the spot unit. Please keep in mind that convincing probes below the femtometer range may reveal features of internal spot unit structure, regardless of the theoretical orientation in particular labs. That is, the data and methods are important, while theories of the principal investigators might be relevant or irrelevant (example: LIGO). Keep your eyes open.
Sound Effect Insert.
Don't think I can't hear you from the grave, Jim. You're talking about action at a distance.
Sports Broadcaster
Yes, Albert, in the leading quantum theory of binary mechanics, action at a distance is a postulate. But rest in peace, because it's a rather small distance, less than a femtometer, OK?
References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Electromagnetic bit operations revised" J. Bin. Mech. March, 2011.
[3] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[4] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[5] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[6] Keene, J. J. "Elementary particle energies" J. Bin. Mech. April, 2015.
© 2018 James J Keene
