Planck's constant h was derived for the first time from first principles, based on the intrinsic proton spin in the proton bit cycle, confirming the derivation based on the electron bit cycle (Fig. 1 from [1]) [2]. A new method to derive h and the intrinsic electron spin based on summation of 1-state bit motion components of the total angular momentum was applied to the proton bit cycle to sum its angular momentum components. Results confirm (1) binary mechanics (BM) [3] postulates including the physical interpretation of BM space [4] and the time-development bit operations underlying the fundamental forces [5] which create the proton and electron bit cycles themselves and (2) the victory of Binary Mechanics Lab (BML) in the century-long physics grand championship race to derive constants from first principles of a coherent, comprehensive physical theory (BM) [6].
Legend: Six 1-state bit positions in electron cycle (yellow). 42 1-state bit positions in proton cycle. Matter d quarks (dark red, green, blue); anti-matter d quarks (light red, green, blue). Positron positions (gray). Arrows (purple) indicate bit motion direction and results of the strong bit operation. The unconditional bit operation (black) accounts for all motion between color-coded spot types. XYZ positions shown without commas: e.g., 013 is {0,1,3}.
Background
A bit cycle is a path in BM space where an energy quanta (1-state bit) returns or "cycles back" to its initial position if no particle motion occurs [7] [8]. There are two and only two bit cycles: electron and proton (Fig. 1). It is easy to visualize that all quanta circulate in one direction around a central axis in the simpler electron cycle: counter-clockwise in the perspective shown in Fig. 2.
The spin axis is orthogonal to two planes, one defined by the three M bit loci and the other by the three L bit loci. Spin axis vector A in Table 1 lists the axis-plane intersection points.
On the other hand, the proton bit cycle -- the basis for color confinement -- is more complicated: (1) quanta motion occurs in every direction, (2) its duration is 7x the electron cycle duration, (3) the proton cycle has 7x more bit loci positions and (4) quanta loci radius from the spin axis is constant for loci in the electron cycle, but varies considerably in the proton cycle.
The research objective is to derive the intrinsic proton spin in two steps. First, Planck's constant h, and hence, intrinsic electron spin, will be expressed as a sum of the angular momentum of each 1-state bit in the electron bit cycle. Then, the formalism used for the electron bit cycle will be applied to the proton cycle. The research question is simply whether the intrinsic spins in the electron and proton bit cycles, based on BM postulates, are equal, just as the absolute values of intrinsic spins of the electron and proton (nucleon) particles are thought to be equal, namely 1/2 of h/2π.
Electron Angular Momentum Components
Previous Derivation. The first derivation of Planck's constant h from first principles took advantage of the unidirectional quanta motion in the electron spot around an axis. Hence, the absolute value of intrinsic electron spin was set equal to classical angular momentum (from eq. 5 in [2]):
(1/2)(h/2π) = mer2/t (eq. 1)
where me is electron rest mass, r is radius of the quanta from the spin axis (approx. 0.816 in primary length constant L units) and t is primary time constant T times fine structure constant α in seconds (t = Tα). Duration T is a quantized time interval called a tick. Eq. 1 was rearranged to solve for the Planck constant,
h = 4πmer2/t = 6.62606957E-34 Js (eq. 2)
Present Derivation by Components. To represent the six 1-state bit movements in the electron bit cycle, let
me = 3M (eq. 3)
where M is the quantized primary energy constant expressed in kg (convertible to the customary electron volts ev). Second, let
r2 = L2 ∑Ri˙Pi; i = 1 to 6 (eq. 4)
where L is the quantized primary length constant and R for "radius" and P for "motion" are vectors (Table 1). R is orthogonal to the spin axis unit vector A = {1/sqr(3), 1/sqr(3), 1/sqr(3)}. R length is distance between a 1-state bit (point) and the spin axis A (line). P is a unit length vector, with components in L units, expressing quanta motion along one of the x, y or z coordinates (Fig. 1). Finally, let
t = nTα (eq. 5)
where n is the number of 12 tick durations in the bit cycle. n = 1 for the electron cycle and n = 7 for the proton cycle.
Using values in eq. 3 to 5, eq. 2 becomes,
h = -4πML2(∑Ri˙Pi)/nTα = 6.62606957E-34 Js; i = 1 to 6n (eq. 6)
where M and L2 are constants removed from the summation of the Ri and Pi dot products. The negative sign in eq. 6 may pertain to spin sign and this addition of a -1 factor to eq. 2 will be discussed below.
Fig. 3 shows the values of primary constants M, L and T.
Table 1 lists the numeric data for the six Ri and Pi dot products and their sum = -2.
Legend: Bit type: M, mite; L, lite; P, photonic L. Spot: particle label, electron (e-L where L denotes left-handed). Vectors: X, bit locus position; A, position on spin axis vector intersecting orthogonal radius vector R; R = X - A, i = 1, 2, 3; P, next position change. radius: R length in L units. RiPi, dot product.
Proton Angular Momentum Components
Table 2 lists proton spin components with the same Tick labels used in the original report on the proton bit cycle [9]. The position X and subsequent motion P vectors are visualized in Fig. 1.
Legend: Tick: Sequence number of a cycle of 4 bit operations over 4T; u, unconditional bit operation; s, strong bit operation. Bit type: M, mite; L, lite; P, photonic L; G, gluonic L. Spot: particle label, e.g., Right-handed red d quark (drR). Vectors: X, bit locus position; A, position on spin axis vector intersecting orthogonal "radius" vector R; R = X - A, i = 1, 2, 3; P, next position change. radius: R length in L units. RiPi, dot product.
The sum of the 42 Ri and Pi dot products (i = 1 to 6n in eq. 6) is -14. Note that -14 / n = -2, the same dot product sum found for the electron bit cycle components (Table 1).
Thus, for n = 1 (electron) and n = 7 (proton), eq. 6 derives Planck's constant h from the electron and proton bit cycles respectively.
Elemental Action A
In a previous report [6], elemental action A was defined as a more microscopic action constant (Fig. 3):
h = A / α (eq. 7)
where α is the fine structure constant. Thus, removing α from eq. 6,
A = -4πML2(∑Ri˙Pi)/nT = 4.83527658E-36 Js; i = 1 to 6n (eq. 8)
Discussion
Mystery Negative. In eq. 1, electron spin was expressed as a scalar classical angular momentum. Without explicit definition of spin direction, Planck constant h could only be positive -- the accepted value. In this context, what is the physical significance of ad-hoc addition of the negative sign in eqs. 6 and 8? Given the geometry presented, this -1 factor may simply represent an arbitrary convention for intrinsic spin sign for both electron and proton: namely 1/2 of the reduced constant h.
The present analysis does not support the notion that intrinsic electron and proton spin can be positive or negative quantum values ("up" and "down"), as many in particle physics believe based in part on beam splitting in Stern-Gerlack experiments. A previous article [10] analyzed the role of quantized time phase in "mysterious" beam splitting phenomena consistent with the 1/2 spin above. That is, events previously thought to define an up or down particle spin property are now accounted for with a time phase quantum number ±1.
Elemental Action A. The empirical value of Planck's constant h based on the photoelectric effect is much greater than elemental action A (eq. 7). At the level of fineness in BM, elemental action A might imply that sequences of numerous more microscopic events occur when photon arrival causes electron emission, events completely hidden in a simplistic Feynman-type diagram vertex.
Century-Long Race Finish Confirmed. What are the odds that analysis of the more complicated proton bit cycle (Fig. 1) would yield a Planck constant h derivation and consequent particle spin by "accident" or chance alone? Probably winning a mega-lottery is more likely. Hence, present results again confirm (1) binary mechanics (BM) [3] postulates including the physical interpretation of BM space [4] and the time-development bit operations underlying the fundamental forces [5] which create the proton and electron bit cycles themselves and the non-spherical proton shape [11] and (2) the victory of Binary Mechanics Lab (BML) in the century-long physics grand championship race to derive constants from first principles of a coherent, comprehensive physical theory (BM) [6] (Fig. 4).
References
[1] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[2] Keene, J. J. "Intrinsic electron spin and fundamental constants" J. Bin. Mech. January, 2015.
[3] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[4] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[5] Keene, J. J. "Fundamental forces in physics" J. Bin. Mech. October, 2014.
[6] Keene, J. J. "Binary mechanics FAQ" J. Bin. Mech. August, 2018.
[7] Keene, J. J. "Particle flux and motion" J. Bin. Mech. May, 2018.
[8] Keene, J. J. "Zero Kelvin particle states" J. Bin. Mech. May, 2018.
[9] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
[10] Keene, J. J. "Particle up-down spin and quantized time parity" J. Bin. Mech. January, 2015.
[11] Keene, J. J. "Non-spherical proton shape" J. Bin. Mech. February, 2015.
© 2018 James J Keene
