Tuesday, February 3, 2015

Intrinsic Electron Magnetic Moment Derivation

The Bohr magneton μB and hence, the electron intrinic magnetic moment μS, without g-factor or electron rest mass consideration and without anomalous magnetic moment "correction", may be calculated from the fundamental length d and time t constants [1] of binary mechanics (BM) [2]. In this report, μS is computed from d, t, elementary charge e and a classical expression of magnetic dipole moment based on a current around the perimeter of a circular area, marking perhaps the first direct derivation of μS from first principles of a comprehensive physical theory. The more conservative interpretation is that the so-called anomalous magnetic moment represents an experimental artifact with reference to μS measurement.
Fig. 1: Electron Spot Geometry for Magnetic Moment Calculation

Methods and Results
Fig. 1 (from Fig. 1 in [3]) shows the electron spot (yellow), based on a physical interpreation of BM space [4]. By assumption, 1-state mite bits (white circles) are located at the center of their size d cube bit loci within each of the three spot units. With repeated application of the unconditional and strong bit operations [5] [6], a 1-state mite bit will rotate counter-clockwise around the spin axis (grey circle), orthogonal to the plane defined by the mite bit loci (white circles). The spin radius r is sqrt(3)d/2, where d is the bit locus cube size and fundamental length constant, proposed to equal 5.9798551E-16 m [1].

The negatively charged 1-state mite bit centers are assumed to define a circle on their spin plane with area

A = πr2 = π3d2/4 = 8.4254374E-31 m2 (eq. 1)

For the circular current I, we try

I = e/(πt) = 1.602176565E-19 / (π 4.63325E-27) = 11007155.12 amperes (eq. 2)

where e is elementary charge and t is the BM time tick constant in observational space (see [1]).

Combining eqs. 1 and 2, we have

μS = AI = 8.4254374E-31 x 11007155.12 = 9.27401E-24 J/T (eq. 3)

The area A and circular current I components in eq. 3 may be simplied:

μS = π(3/4)d2e/(πt) = 3ed2/4t (eq. 4)

and

μS = 3 x 1.602176565E-19 x (5.9798551E-16)2 / (4 x 4.63325E-27)

= 9.27401E-24 J/T (eq. 5)

This computed, theoretically derived value for μS in eq. 5 is equal to μB within several parts in a billion (eq. 6).

S - μB) / μB = -1.52477E-09 (eq. 6)

Note that none of the computed values above can have a precision greater than the CODATA constants used in this paper or for d and t, in a previous report [1].

Discussion
Look Ma, no g-factor. The present report derives electron magnetic moment μS from elementary charge e, BM fundamental length d and time t, and a classical expression for magnetic moment. A typical expression in physics literature requires electron rest mass me. Not now. Also, conventional conceptions use the Bohr magneton μB and a so-called gyromagnetic- or g-factor. Not any more. Indeed, tick time t may be expressed in terms of length d (eq. 8 in [1]). This reduces required parameters to only two -- elementary charge e and BM length d, to compute μS, where d was independently defined from nucleon scattering results. This work may represent the first accurate derivation of electron magnetic moment from first principles of a comprehensive, fundamental physical theory.

g-factor: the "nail-in-the-coffin" edition. In the present context, the need to invoke a g-factor correction in particle magnetic moment work is clearly an admission of inadequate theory no doubt due to the obsolete assumption of continuous space-time. The electron g-factor of about 2 is typically attributed to the Dirac equation. Perhaps coincidentally, BM was developed from a pair of relativistic Dirac spinor equations of opposite handedness. With this report, μS is obtained directly from elementary charge e and a quantized spatial unit, the BM length constant d, without an intermediate step requiring a g-factor value or indeed, explicit reference to the Bohr magneton μB and intrinsic electron angular momentum. Meanwhile, the experimentalists are stars in the current show, providing precision measurements of magnetic moments for many particles. The current work may suggest to experimentalists that the g-factor nonsense should be dropped by reporting their results directly as, say, J/T.

Anomalous magnetic moment. The present derivation does not account for the anomalous magnetic moment correction based on experimental measurements of μS slightly larger than accepted Bohr magneton μB values. Further analysis might reveal that this correction is due to the potentials which 1-state electron mites and lites represent [6] [7]. First, a 1-state mite is always part of the larger electric potential field. Specifically, in the scalar bit operation, this potential can accelerate a 1-state mite in a concurrent spot unit in a different spot adjacent to the 1-state mite in the electron spot. Second, in the 3T electron bit cycle, 1-state lites occur and can accelerate 1-state mites in adjacent countercurrent spot units during the vector bit operation time tick t. In short, the bit cycling producing μS can and most probably does affect bit motion in neighboring spot units. These sorts of events may account for the small anomalous magnetic moment "correction". If so, it may come down to a matter of judgment in the physics community whether the anomalous magnetic moment should be treated as an unavoidable experimental artifact or in some manner, an integral component of the true μS. Both of these treatments are consistent with BM.

Quantum electrodynamics (QED) with use of Feynman diagrams purports to calculate the electron anomalous magnetic moment with stunning accuracy. It might now seem strange that this considerable effort might have targeted nothing more than an experimental artifact. This is primarily of historical interest since QED has been upgraded to BM as briefly outlined above per relevant underlying anomalous magnetic moment mechanisms.

Why 3 and 4? In eq. 5, notice that 4t = T, the tick cycle in time development (bit operations) of a system state vector (bit function). Specifically, in each cycle T, each of four fundamental bit operations are applied to the system state, each in a time tick t. The electron bit cycle is 3T or 12t, the time required for a 1-state mite bit to return to its original position at t = 0. In this result (eq. 5), 4t is the quantized time required for a 1-state mite to rotate 1/3 of its circular path. Hence, the factor of 3 in eq. 5 may represent the 3T electron bit cycle.

Homework assignment. Consider that the proton has a 21T central bit cycle which accounts for quark (color) confinement in baryons [8]. Calculate the proton magnetic moment directly from this data.

"If I were you" (LuLu). With recent reports of more instances of the success of BM fundamentals in unraveling unsolved problems in physics (see, e.g., [9] [10]), even the present author is beginning to think that BM postulates make sense and are worthy of further study. Finally, LuLu might speak for BM saying "If I were you..."

Editor's note: The reader is invited to post comments in agreement or disagreement with this or other Journal of Binary Mechanics articles at the Binary Mechanics Forum. The Journal also welcomes on-topic articles from other investigators and persons considering serving on the Journal's editorial board.

References
[1] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[2] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[3] Keene, J. J. "Zero electron electric dipole moment" J. Bin. Mech. January, 2015.
[4] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[5] Keene, J. J. "Strong operation disabled by inertia" J. Bin. Mech. March, 2011.
[6] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[7] Keene, J. J. "Electromagnetic bit operations revised" J. Bin. Mech. March, 2011.
[8] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
[9] Keene, J. J. "Physics glossary" J. Bin. Mech. May, 2011.
[10] Keene, J. J. "Solved physics mysteries" J. Bin. Mech. June, 2011.