82944 & THE FOUR FUNDAMENTAL
FORCES & THE GOD PARTICLE
On February 23, 1999, Mr. J. Iuliano
communicated to the writer the fact that after learning of the unique number 82944 on this
web he was led in conjunction with certain regularities noticed by him in his researches
on Fermat's last theorem to the following two formulas for the inverse square root of the
fine structure constant:^{1}
10^{82943.99269/(32×666)}/666 = 11.7062372 . . .,
and
_{e}2π^{-1}(e^{2807.000184[2/1579]})_{
× (1/57+1/37) = 11.7062372 . . . }
In the context of the logical rootedness of 82944, let the first of the formulas above be set out as follows:
_{10}(82944 - [37^{-2}]10)/(37×576)_{/(37×18) = 11.7062372034635. . . }
In this way the simple beauty of the relation between certain logically determined values and the inverse square root of the fine structure constant shows forth. Here the square root of the inverse fine structure constant is transparently a function of certain numbers whose inter-relationship is essentially grounded in the new trinary logic.
This formula shows the fine structure constant as a function of a set of 4 numbers whose inter-relationship is fundamental to the new logic. It is necessary to grasp the full import of this statement. If it were not the case that the basic inter-relationship of the numbers on the left-hand side of this equation had been independently established in a prior logical analysis, then the significance of the result could be justifiably dismissed as pure coincidence. However, anyone examining the logical genesis of the basic inter-relationship of the numbers in question will find that the formula is not simply dismissible. Indeed, the prior logical-numerical analysis is essentially predictive of some relation such as this with the fundamental dimensionless physical number.^{2 }The simplicity & appropriate symmetry of this arrangement of these numbers in this context, adding weight to the argument against arbitrariness, suggests & solicits a serious scrutiny of its logical underpinnings.
The first of the 4 numbers is 82944. It is the unit total area of the two interior and six exterior 'sides' of the dead center cube.^{3} 82944 is also the unique number whose integral product is that number while the integral product of its third part is that part's third part (of all numbers only 82944 and Unity have this double property).^{4}
82944 and the Fundamental Force Constants
As prelude to what immediately follows, the writer notes (September 24, 2003)
that, where the values of the four fundamental force fine structure constants
are α_{w} ~ 3 × 10^{-7 }
(weak force), α_{G }~ 5.9
× 10^{-39 }(gravitation),
α_{s}
~ 1 (strong force), and α_{ }~ 7.297353 × 10^{-3} (electromagnetism),
and the corresponding charge values are, respectively,
g_{w}
~ 1.43 × 10^{-62}, G ~ 6.6739
× 10^{-11}, g_{s} ~ 15,
and e ~ 1.602 × 10^{-19},^{5}
[(g_{w}/G × g_{s}/e)/(α_{w}/α_{G }× α_{s}/α)]^{2} = 8.2944 × 10^{-132},
and, where φ is the golden section, 1.618033989, the ratio of the proofs of these proportions,
[(α_{w } × α)/(α_{G }× α_{s})]/[(g_{w} × e)/(G × g_{s})] = φ × 10^{101}.
On May 22, 1999, in further confirmation of the rootedness of the fine structure constant in the logic of the dead center cube and directly in the number 82944, Mr. Iuliano called the writer’s attention to the fact that 82944^{1/π} = 10^{2} × COS 137.0360009865267 10^{2} ´ COS α^{-1}.^{6}
^{On June 10, 1999, Mr. Iuliano communicated to the writer additional relations he discovered to exist between 82944 and the remaining three of the fundamental physical forces, respectively, the strong, weak, and gravitational forces, so that the four forces are now able to be seen to be functions of 82944 as follows (the writer substitutes the symbol for the Fermi coupling constant, G}F^{, for Mr. Iuliano's g}w^{):}
82944^{1/π} = 10^{2} × COS 7.297352473E-3^{-1} 10^{2} × COS α^{-1},
82944^{10-2/π} = 10^{2} × COS 14.000080571 10^{2} × COS g_{s},
82944^{10}^{-2/π × 1.7} = 10^{2} × COS 1.166390041626E-5^{-1} 10^{2} × COS G_{F}^{-1}, and
82944^{π/8} = 10^{2} × COS 6.672430000986E-8^{-1} 10^{2} × COS G^{-1}.
Here the pattern of the rootedness of the four fundamental physical forces in the unique number 82944 is powerfully evident. Note first that the ratio of the exponents of 82944 which are related, respectively, to the infinite gravitational and electromagnetic forces, (π/8)/(1/π) = π^{2}/8, = the square of the universal geometric ratio of the circumference of the circle to the perimeter of the square, (C_{c}/S_{p})^{2}.^{7} Mr. Iuliano notes that a variant of the exponent of 82944 last listed appears in Einstein's cosmological constant, λ = 8πGρ_{vac}. The writer notes that 8πG = (8^{1/2}/10)^{16}/[1+(829440 × 9)^{-1/2}]. It should further be noted that the product of the four exponents relating the fundamental forces to 82944, 1/π × 10^{-2/}^{π} × (10^{-2/π } × 1.7) × π/8 = .01132711708, ~ .00729735308/.6444762592780, the fine structure constant divided by the sum of the alternating inverse L series. Since the last mentioned sum approximates the observational limit upon the cosmological constant, Ω_{λo} = .64, the product of the exponents of 82944 relating this number to the fundamental forces also ~ α/Ω_{λo}^{8} Note further that the appearance of the factor 10^{2 }at this fundamental level is effectively predicted by the conceptualization of the 'created 100' in the thinking now occurring.^{9} Finally, the exponents of 82944 which relate to the nuclear strong and weak forces employ a specific common factor relating them to each other as nuclear in such a way that they are distinguished only by the factor 1.7, the inverse 16th power of which is the approximate small difference between the exponents of 82944 which are related respectively to the weak and gravitational forces.^{10}
On June 27, 1999, in response to the writer’s observation (above) that the ratio of the exponents of 82944 which relate, respectively, to the gravitational and electromagnetic constants, (π/8)/(1/π), = π^{2}/8, Mr. Iuliano called the writer’s attention to the analogy between the inverse square law operative in both the gravitational and electromagnetic constants and Euler’s infinite series formula for π^{2}/8,
and observed that it follows from this equation that, since π^{2}/8 = (π/8)/(1/π),
The gravitational exponent of 82944 is thus seen to be the latter's electromagnetic exponent divided by the squares of the odd numbers, that is, divided by the squares of the ratio of the distances traversed in successive equal intervals of time in Galileo’s law of universal constant gravitational acceleration. Assuming 82944 as the common coefficient of the fundamental force constants, the gravitational constant is seen to be the electromagnetic constant reduced to the square of the universal constant of acceleration. And since 1/π/(2n-1)^{2} is the equivalent of 1/πr^{2}, the inverse of the area of the circle, the gravitational force exponent of 82944 is seen to be at once the sum of the infinite inverse series of discrete circular areas whose radii are the differences between the squares of the natural numbers. Thus the gravitational force is shown to be inherently the fundamental formative & unifying force of the infinite whole of quantum phenomena. ^{11}
Recurring to the transcription of the first formula originally forwarded by Mr. Iuliano, the second and third numbers under consideration are 18 and 576, which are factors of the area of the side of the dead center cube (18 × 576 = 10368 = the 8th part of 82944).^{12}
The fourth number is 37, the total number of diagonals in the logically outfitted triple dead center cube. And in the formula it agreeably appears three times.^{13}
With respect to the second formula initially forwarded by Mr. Iuliano, it is noted that 2807.000184 approximates 2808, the "dream" number which is approximately 36/100 the inverse square of the fine structure constant divided by the inverse alternating L series sum, that is, 2808 .36(.00729735308/.6444762592780)^{-2}.^{14} 2807 also .36[10^{(82944 - [37}^{]10)/(37×576)}] and .36(11.7062372034635 × 37 ×18), since both enclosed multiplicands the product of the opposed place numbers of the 1-diagonal in the final subsquare of the unum-founded Fibonacci sequence.^{15} The difference between (2/1579)^{-1} and the third and only other number whose integral product is that number, 784, is exactly 5.5, the eighth number in the L series.^{16}
The pairing of 37 and 57 in this second formula appears in the logic as follows: in the infinitely expanding triangle of 0’s, ’s, and 1’s, created directly by infinitely summing the infinitely repeating series of the digits 101010 . . ., beginning with the edge-sharing triangle between the first two discernible edge-sharing triangles, the last two digits of the larger factor producing the numerical value of successive collections of logical digits between the edge-sharing triangles are alternately 37 and (37 + 20 =) 57. 57/37 = 1 + 20/37, where 20/37 is the ratio of the face diagonals to the total number of diagonals in the trinary logically outfitted triple-cube.^{17}
In terms of these numbers fundamental to the mathematics rooted in the
trinary logic, the second formula may be rendered (substituting [37-37^{-1}] for 37):^{18}
_{e}2π^{-1}(e^{[2808-(1-[(37-37}^{)10πδ]}^{)][784+5.5]})_{ × (1/57+1/37) = 11.7062372007985 . . . .}
Also, as communicated by Mr. Iuliano on September 4, 2000, note that 82944^{2}/2808/37/18/10^{4} COS α^{-1}.
82944 and the 'God Particle'
114 GeV/c^{2} 2808^{-2 }× 10 eV m^{-1} s [(82944 - [δ/π]^{8}) × 10^{-5}]^{83} kg.^{19}
As of November 3, 2000, CERN produced the following tentative results: with a current bound on the Higgs boson mass of m_{H} > 113.5 GeV/c^{2} and an expected m_{H} = 115.3 GeV/c^{2},
m_{H} = 115.0 (+1.3, -0.9) GeV/c^{2}.
With respect to the current value, note that
m_{H} = 115 GeV/c^{2} (2808 - 4π)^{-2 }× 10 eV m^{-1} s [(82944 - 10[δ/π]^{2}) × 10^{-5}]^{83} kg.^{20}
With respect to the expected value, note that
m_{H} = 115.3 GeV/c^{2} (2808/.36 - φπ)^{-1 }× 10^{-2} eV m^{-1} s [(82944 - [δ^{2} + (28.08/.36)^{2}/82944]) × 10^{-5}]^{83} kg.
Using the reported results, the possible range of the Higgs boson mass in electron volts is approximately between m_{H} (2808 - 2^{1/2})^{-2 }× 10 eV m^{-1} s and m_{H} (2808 - 2808/10^{2})^{-2 }× 10 eV m^{-1} s, and in kilograms approximately between m_{H} [(82944 - [(δ/π)^{8}-(δ/π)^{8}/10^{2}]) × 10^{-5}]^{83} kg and m_{H} [(82944 - 10[.82944]^{-4}) × 10^{-5}]^{83} kg.^{21}
Finally, where the masses of the weak force carrier bosons, Z and W, are, respectively, m_{Z} = 91.1882 GeV/c^{2} and m_{W} = 80.419 GeV/c^{2}, note that the possible mass of the Higgs boson is
m_{H} ~ π(m_{Z}+m_{W})/δ,^{22}
and, at the high end of the range of the possible Higgs boson mass,
m_{H} + m_{Z} + m_{W} ~ 82944^{1/2} GeV/c^{2} ~ .82944^{3} × 10^{-41} kg.^{23 }
Addenda
On November 24, 1999, Mr. Iuliano forwarded to the writer the following observation (where
m_{p}c^{2} and
m_{e}c^{2}
are the proton and electron mass energy equivalents in MeV):
_{
}_{
}^{24}
On November 27, 1999, Mr. Iuliano called the writer’s attention to the fact that π^{3}/32 = (1/1^{3 }– 1/3^{3} + 1/5^{3} – 1/7^{3} + 1/9^{3 }–^{ }1/11^{3}. . .), and that π/8 can therefore also be expressed in the form, π/8 = 4/π^{2} ´ (1/1^{3 }– 1/3^{3} + 1/5^{3} – 1/7^{3} + 1/9^{3 }–^{ }1/11^{3}. . .). Prompted by Mr. Iuliano’s exposition of certain mathematical relations existing between this form of the gravitational exponent of 82944 and the infinite zero-point energy density formula,^{25}
the writer observed that, where the zero-point energy density at the Planck energy cutoff is ρ_{ZP} = 2π^{2}c^{7}/G^{2},^{26}^{ }the gravitational exponent of 82944 divided by the square of the π-factor identifying zero-point energy density with the maximum sustainable spacetime energy density equals the p-component of the infinite zero-point energy density:
π/8/(2π^{2})^{2} = π/8/4π^{4} = (32π^{3})^{-1 }= E_{o}/L^{3}hk^{4}_{max}.
He also observed that where, as Mr. Iuliano showed, π/8 = 4/π^{2} × π^{3}/32 = 4/π^{2} × (1/1^{3 }– 1/3^{3} + 1/5^{3} – 1/7^{3} + 1/9^{3 }–^{ }1/11^{3}. . .), then, since
infinite zero-point energy density E_{o}/L^{3} = hk^{4}_{max}/32π^{3}, and
zero-point energy at the Planck energy cutoff r_{ZP} = 2π^{2}c^{7}/G^{2} = 4π^{3}c^{7}/G^{2}h, and
π/8, the gravitational exponent of 82944, = 4/π^{2} × π^{3}/32 = 4π^{3}/32p^{2}, and
by transposition, 4π^{3}/32π^{3} = 1/8,
what is made explicit through their relation to the gravitational exponent of 82944 is the conformity of the ratio of the π-components of the zero-point energy finite and infinite density formulas, 4π^{3}/32π^{3}, to the foundational relation ratio, 8^{-1}, whose powers (increasing as the sequential sums of the geometric series where x = 4 and their intermediated doubles) are the denominators of the infinitely alternating sequence of the infinite series of natural numbers and the infinite series of odd numbers which so denominated constitute the series of the differences of the squares of the natural numbers, and the differences of the squares of those differences, and the differences of the squares of those differences, ad infinitum.^{27}
The inverse of this fundamental relation ratio, 8, appears in the "dream" formula for the fine structure constant^{28} as the power of the natural log base, e. Where 8 is the inverse of the relation ratio, and e is the natural log base, and l_{dc} is the length of the edge of the dead center cube (l_{dc} = 10368^{1/2} = 101.8233765 . . . ),^{29} and 10^{-33} is the order of magnitude of the Planck length (l_{P} = 1.6160 × 10^{-33} cm), and 37 & 57 are the alternating final digits of the rational factors of the sums of the mathematical values of the logical digits falling between the edge-sharing triangles of logical 1's in the trinary logic sequential summing triangle (which edge-sharing triangles expand as the geometric series),^{30} and 7.297 352 533 × 10^{-3} (with standard uncertainty of 2.7 × 10^{-8}) is the 1998 recommended value for the fine structure constant, α,^{31} then,
Developments July 2011 - July 4 2012
See, on this web, The Higgs Boson & the Absolute Dead Center Cube: Predictions Within the Probable Range
Also, W Boson Mass & the Mathematics of the Absolute Dead Center Cube
Notes
^{1} For the equivalent formula expressed in terms of the chemical elements, Rubidium
and Lanthanum, see, on this web,
Rubidium (37),
Lanthanum (57) & the Logically Outfitted Cube(s).
For the connection of the trinary logic and Fermat's theorem, cf. D.G. Leahy, Foundation: Matter the Body Itself (Albany,
1996), p. 308, n. 14. For the most recent recommended
values of the fundamental physical constants, cf. P. J. Mohr and B. N. Taylor, "The
1998 CODATA Recommended Values of the Fundamental Physical Constants, Web Version
3.0," available at
http://physics.nist.gov/constants
(National Institute of Standards and Technology, Gaithersburg, MD 20899, 23 July 1999).
^{2} Cf. Leahy, Foundation, Sections III and IV.
^{3} Cf.
ibid., Section III.5, pp. 434ff, for the 'absolute dead center' cube, first constructed by the writer in 1985 in the context of
his elaboration of the logic of the essentially new form of thinking now actually
occurring for the first time in history. As stated
above, the
total area of the two interior and six exterior 'sides' of this dead center cube is 82944. Its surface area is 62208. On January 29, 2001, Mr.
J. DePompeo brought to the writer's attention the fact that the integral product of
Genesis 1:3, ויאמר אלהים יהי־אור ויהי־איר, "And God said 'Let there be light' and there
was light," is 8.2944 × 10^{26}. Upon investigation the writer discovered that the linear
product of this verse is 6.2208 × 10^{22}. For the occurrence of the identical set of base
factors in the structure of the sphere whose radius ~ the equatorial radius of the earth
in miles, see, on this web,
Sorted Diagonals,
Addendum 5. For the definition of the terms 'integral
product' and 'linear product', see, on this web,
Transdecimal Calculation of Number Identity: A
Note
on Integral Product & Related Terms, also, below, n. 12.
^{4}
Ibid., Section III.6-7.
^{5}
Cf. Coupling Constants for
the Fundamental Forces. Online. Department of Physics and Astronomy. Georgia
State University. Available:
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple.html#c1, and P.C.W.
Davies, The Accidental Universe (Cambridge, 1986), p. 39.
^{6} Cf. Toichiro
Kinoshita’s
calculation of the value of the inverse fine structure constant, 137.035999935. For
82944^{1/π}, see also, on this web,
Rubidium
(37), Lanthanum (57) & the Logically Outfitted Cube(s), note 3 and
The v_{maxwell}^{1/16}
× 1 s/m Cube, Human Body Surface & BSA, &
the Infinitely Flat Structure of the Universe.
^{7} Note that 82944^{π2/8}/10^{6}
~ 1.170820393, the locus of the logarithmic spiral (see,
on this web,^{ }
The Golden Bowls & the
Logarithmic Spiral).
Further for 82944^{1/π}, see, on this web,
The Diagonal Logic of the Triple Absolute Dead Center Cube & Certain Fundamental
Mathematical
& Physical Constants. For the new conceptualization of the identity of circle and square, cf.
Leahy, Foundation, Section IV.2, pp. 529ff.
^{
8} For λ, see The Cosmoλogical
Constant. Online. Department of Astrophysical and Planetary Sciences. University of
Colorado, Boulder. Available:
http://super.colorado.edu/~michaele//Lambda/lambda.html.
June 16, 1999. The alternating inverse L series sum .644476259278 (see,
below, n. 16) approximates in general the observational constraints on the value of
l (cf. ibid.,
and, in particular, the calculations of Myungshin et al. (1997) who find for a flat
universe that Ω_{λo} = 0.64 (+0.15,-0.26). For the values of the four fundamental physical
forces, see M. Kaku, Quantum Field Theory : A Modern Introduction (Oxford,
1993). For the latest higher precision measurement of the gravitational constant,
G
= 6.67390 ´ 10^{-11} m^{3}/kg/s^{2}
with an uncertainty of 0.0014%, see Physics News Update Number 482. The American Institute
of Physics Bulletin of Physics News. Online. Available:
http://www.aip.org/enews/physnews/2000/split/pnu482-1.htm.
May 3, 2000. For the transcendental deduction of Einstein's energy-matter
equivalence, cf. Leahy, Foundation, Section II.2.
^{9} Cf. Leahy, Foundation, Section III.5, et passim. For the work of Adelberger et al. in which the force of gravity has been measured over distances
as small as 150 microns, one of the implications of which work is that the unification of
the four physical forces might not need to occur at energies as high as 10^{19}
GeV but rather at energies as low as 10^{4} (= the 'created 100') GeV, an energy
scale within reach of the Large Hadron Collider under construction at CERN, see
Physics
News Update Number 483. The American Institute of Physics Bulletin of Physics News.
Online. Available:
http://www.aip.org/enews/physnews/2000/split/
pnu483-1.htm. May 5, 2000.
^{10} For the logical foundation of the special relationship of the weak and
gravitational forces, see, on this web,
Logical Unity & The
Four Physical Forces. The factor common to the strong and weak force
exponents of 82944, 10^{-2/}^{π}, is the approximate inverse 4th root of the 100th part of the adjusted unit
value of the circumference of the 'missing circle' in the New Jerusalem diagram (see, on
this web, DNA, Apocalypse, & the End of the Mystery).
For the inverse of 10^{-2/}^{π}, 10^{2/}^{π}, see, on this web,
Sorted Diagonals, Addendum 8 (for -2/π,
cf. also, below, n. 18). Note that the product of the ratios of the nuclear and
universal exponents of 82944, 1.7π^{2}/8, factors precisely into the structure of the "dream" formula first
discovered by the writer in 1995 (see, on this web,
Report on a
Dream & Related Matters & the God Particle), as follows: [(1.7π^{2}/8)^{1/16} × 1E33]^{-}^{1/256}/10368^{.5} = α. With
respect to this last, see also, on this web,
Rubidium
(37), Lanthanum (57) & the Logically Outfitted Cube(s), note 3.
^{11}
In this connection, note that
π appears in the inverse form in the case of the electromagnetic, strong, and weak
force exponents of 82944, but in the uninverted form in the case of the gravitational
exponent, further distinguishing the gravitational force as uniquely the universal
unifying force. The appearance of the factor 8^{-}^{1} in the ratio of the gravitational & electromagnetic exponents of 82944 (and
of its inverse in Einstein's cosmological constant) in conjunction with the series of the
squares of the odd numbers is a function of its foundational relational role as the
denominator whose powers increasing as 1, 5, 21, 85, 341, . . . and their intermediated
doubles, are the denominators of the infinitely alternating sequence
of the infinite series of natural numbers and the infinite series of odd numbers
which so denominated constitute the series of the differences of the squares of the
natural numbers, and the differences of the squares of those differences, and the
differences of the squares of those differences, ad infinitum (cf.
Leahy, Foundation, Section IV.2, especially pp. 486ff. and 521ff.; cf. also, in
the text above, Addenda). It is the base series of the squares of the differences of
the squares of the natural numbers which constitutes the denominator of the
electromagnetic exponent of 82944, and, in so doing, constitutes the latter's
gravitational exponent. That the 'integral product' of a number is the product of
the squares of its odd numbered digits (cf., above, n. 3), and that this numerical
operation identifies 82944 as uniquely the equivalent of Unity, is a manifestation of
"the fundamental fact that the constant identity of the system of reference is the
numerator" (cf. Leahy, Foundation, Section IV.2, pp. 486ff.), and is
perfectly consonant with the fundamental principle of order operating in the universal
constant of gravitational acceleration, and most perfectly so with the appearance of the
latter's square in the analysis of the gravitational exponent of 82944, π/8 = 1/π1^{2} + 1/π3^{2} + 1/π5^{2} + . . ..
Cf. also, below, n. 18.
^{12}
Leahy, Foundation, Section III.5.
^{13} For an illustration, see, on this web,
Logically
Outfitted Cube(s); cf., also, Leahy,
Foundation,
p. 524, n. 98. An agreeable number, 37 × 3 also agrees to equal 111. On
March 4, 2001, Mr. Iuliano noted that, where e_{0} is
the value of the electric constant, 8.854187817
× 10^{-12},
c that of the velocity of light, 299792458,
e that of the elementary
charge, 1.602176462
× 10^{-19},
h that of the
Planck constant, 6.62606876
× 10^{-34}, and m_{e}c^{2} the electron mass
energy equivalent in MeV, 37 × 829.44^{.5 }× e_{0} × c^{3} × e^{2} × π^{2}/82944^{3}h ~ m_{e}c^{2}/3.
Equivalently, 111 × 829.44^{.5 }× e_{0} × c^{3} × e^{2} × π^{2}/82944^{3}h ~ m_{e}c^{2}.
For 82944 and m_{e}c^{2},
see below in the text, "Addenda," including n. 24. For .82944^{3},
see below in the text, "82944 and the 'God Particle'," including n. 23.
^{14} See
Report on a Dream & Related Matters & the
God Particle.
^{15} Ibid. Note that the product of the exponents of 82944 (see, above,
in the text, also, n. 8), which ~ .00729735308/.6444762592780, also ~, as here
indicated, 7800^{-1/2}, the
inverse square root of the product of the opposed place numbers of the 1-diagonal in the
final subsquare of the unum-founded Fibonacci sequence (cf. Leahy,
Foundation,
Section III.2, Theorem 4). For a most precise relation between 7800
and the fine structure constant, see also, on this web,
Rubidium (37), Lanthanum (57) & the Logically
Outfitted Cube(s), note 3.
^{16} For the L series, cf. Leahy,
Foundation, pp. 519-29, and,
above, notes 8, 13, and 14. 2807 and 1579 are eigenvalues found in Mr. Iuliano's
researches. 2807.000184249. . . = 2807 + [10(37πδ)]^{-1}, where δ is the Feigenbaum bifurcation constant,
4.669201609102990. . . , which Mr. Iuliano supposes links the double periodic structure of
Fermat's last theorem to the fine structure constant. On May 6, 2001, Mr. Iuliano
noted that, where α_{e}^{-1/2}
is the inverse square root of the fine structure constant,
g_{w} (= the Fermi coupling constant^{ }
G_{F}), the weak force constant,
g_{s} the strong force constant, G the latest higher precision measurement of
the gravitational constant (for this and the other fundamental force values here involved,
cf., above, n. 8), and α the
Feigenbaum constant, 2.502907875, then 10^{35}g_{w}^{9}a_{e}^{-1/2}/(2Gg_{s}) ~
α.
^{17} See above, n. 13. For the full presentation of this array as the logical
foundation of the geometric series of ordinary mathematics, see, on this web,
Real Trinary Logic Geometric Series Infinite Iterative Sequential
Summing. On January 4, 2001, Mr. Iuliano called the writer's attention
to the fact that where the value in kilograms of the Planck mass,
m_{P},
= 2.1767 × 10^{-8}, the four fundamental forces are related
to that mass by the factor 37/57, as follows (where
g_{w} = the Fermi coupling constant^{ }
G_{F}): (37/57)(g_{s}g_{w})/(αG)/10^{16} ~ m_{P}. For 37 and 57, see
also, below, n. 24.
^{18} See above, n. 16. With respect to the fact that 37 appears in several
formulas here presented in significant conjunction with one or another part of itself,
note that it does so in a most fundamentally geometric way in relation to the fundamental
factor, 8^{-}^{1} (cf., above,
n. 11),
viz., where 1 radian = 180°/π =
57.2957795130°, [37 + (37/1 radian/10)]^{1/8}
~, with a difference less than 1 in 100 million, π/2, the central angle of the quadrant of the circle,
or 4 times the gravitational exponent of 82944. It is the negative inverse of the
last, -2/π, which appears as the
power of 10 which is the common factor in the strong and weak force exponents of 82944
(cf., above, the text, also notes 10 and 11).
^{19} For δ/π, see, on this web,
Rubidium (37), Lanthanum
(57) & the Logically Outfitted Cube(s). Note that not only is the
possible mass in kilograms of the Higgs boson a function of 82944, the common coefficient
of the four fundamental forces, as demonstrated in the text above, but that in electron
volts the possible mass of this particle responsible for endowing other particles with
mass is a function of the "dream" number, 2808 (cf., above, n. 14). In the
recent test of QED in the highest possible electric fields at the Experimental Storage
Ring in the GSI lab in Darmstadt, Germany, the measured value of the ground-state Lamb
shift in uranium ions, U91+, is 468 eV = 2808/6 eV, (see Physics News Update, October 10,
2000. Online. Available:
http://www.aip.org/pnu/2000/split/506-2.html.
October 14, 2000).
^{20}
For the ratio, 2808/.36, see, on this web,
Report
on a Dream & Related Matters & the God Particle.
^{21} For the results from CERN, see P. Igo-Kemenes, "Status of
Higgs Boson Searches." Online. LEP Seminar, November 3, 2000, CERN. Available:
http://lephiggs.web.cern.ch/LEPHIGGS/talks/pik_lepc_nov3_2000.pdf.
November 4, 2000.
^{
22}
For the values of Z and
W, cf. D.E. Groom et al.
(Particle Data Group), "Index for Gauge and Higgs Bosons Summary
Table." Online. Eur. Phys. Jour. C15, 1 (2000). Available:
http://pdg.lbl.gov/2000/gxxx_index.pdf.
November 8, 2000. For the ratio π/δ, cf. the text above, including n. 19. Where
m_{H}
is the possible Higgs boson mass, note also that m_{Z}+m_{W}
~ (1+δ/π×10^{-3})(10π^{2}/2)^{2}
GeV/c^{2} ~
m_{H}δ/π.
^{
23}
82944^{3} × 10^{-41} kg ~ (2808/.36)^{-1/16} × 10^{-41} kg ~ δ^{2}/10 × .82944^{83} kg. 82944^{1/2} GeV
= 8.2944 × 10^{221/2} eV. 8.2944 × 10^{22} = the integral
product of
נקדת האפס של תנופה ('point zero of energy'/'dead center'). 8.2944 × 10^{221.5}
= the linear product of Genesis 1:1, בראשית ברא אלהים את השמים
ואת הארץ ('In the beginning God
created the heaven and the earth'). Where 21 and 34 are Fibonacci numbers, and 21 ~
82944^{1/2}/2φ^{4} and 34 ~ 82944^{1/2}/2φ^{3
}and the decimal point ~ the point of division in extreme and mean
ratio, 10^{-21}[10^{-34}(8.2944 × 10^{221.5})] = (.82944^{3}
× 10^{-41})^{1/2}. For 8.2944
× 10^{22} and 8.2944 × 10^{221.5}, cf. Leahy,
Foundation,
pp. 505f., where it says, "Now the mind stands in the center of the absolute circle
of absolute thought." Further, with respect to the possible Higgs boson, the
center of the absolute circle of absolute thought additionally manifests itself - paralleling the procedure equating the linear
product of Genesis 1:1 and the coefficient of mass in the sum of the three bosons - as follows, now
starting with the physical coefficients: where 82944^{1/2}
GeV/c^{2} and .82944^{3} × 10^{-41} kg are
equivalently the mass sum of m_{H} + m_{Z}
+ m_{W}, the coefficients of mass in the equivalent sums,
designated, respectively, x and
y, are related in such a way that - where 42 and 68 are the doubles, respectively, of
the Fibonacci numbers 21 and 34, and where 42 ~ x/φ^{4} and 68 ~ x/φ^{3} and the decimal point ~ the point of division in extreme and mean ratio - 10^{-42}[10^{-68}(10^{9}x)^{6}]
~ y, and in such a way that the integration with
x of the powers of the
rescaling negative exponentials in this last equation yields
x- [x^{2}-(-42
× -68)^{1/2}]^{1/2} ~ 116^{-1/2} ~ the inverse square root of the
coefficient of mass of m_{H} in the original
equation. See, above, n. 3, and, below, n. 28. Note also that .82944^{83} ~ φ^{2} × 10^{-42}. With respect to φ-proportionality - beautifully manifest here in
understanding the possible Higgs boson - in
understanding in general the fundamentals of the physical universe, cf., on this web,
The Golden Bowl Structure: The Platonic
Line, Fibonacci, and Feigenbaum and
The Physical Constants: Functions of the
‘Golden Bowl’ Arrangements on the Φ-Level of Existence Itself.
^{24} In response to a query by the writer, using values approximating the 1998 CODATA
values (see above, n. 1) Mr. Iuliano calculates that 82944 =
9382.716283^{.5109994-1/π}.
He also notes that [m_{e}c^{2}]^{1/π} is related to the Fermat Last Theorem generator
numbers 37 and 57 in their relation as torus volume constructs. Where the loop
radius R = 57.0000000173 and the tube radius
r = 37, the torus volume
f
= 2π^{2}Rr^{2}
= 1540309.680934077064, so that COS f
[m_{e}c^{2}]^{1/π}. Thus
m_{p}c^{2}
82944^{COS
f}/10
and m_{e}c^{2}
[COS
f]^{π}.
See also, on this web,
Rubidium (37), Lanthanum (57)
& the Logically Outfitted Cube(s).
^{25}
Cf. The Cosmoλogical Constant. Online (above, n. 8).
^{26}
Cf. B. Haisch and A. Rueda, "Toward an Interstellar Mission: Zeroing in on the
Zero-Point Field Inertia Resonance." Online. Space Technology and Applications
International Forum-2000, American Institute of Physics Conference Proceedings, Mohammed
S. El-Genk, ed., in press (2000), pp. 3f. Available:
http://xxx.lanl.gov/abs/physics/9909043.
November 28, 1999. The authors estimate
2π^{2}c^{7}/G^{2} to be
"on the order of 10^{116 }ergs cm^{-3} s^{-1}."
The author of The Cosmoλogical Constant
(cf. above, n. 8 and n. 25), who estimates a similar value on the order of 10^{92}
ergs cm^{-3} s^{-1} or W_{lo}
10^{120}, says: "Such a high value for
the cosmological constant is surely absurd. One might argue that we have chosen too
high a value for k_{max}, but in order to satisfy the
observational constraints we would have to use a cutoff energy of ~10^{-2} eV,
which is surely unrealistic." This "unrealistic" value is exactly
what is predicted by the logical analysis of the thinking now occurring (cf. Leahy, Foundation, Section III.5, pp. 368f., et passim), the
inverse square root of the 'created 100', 1E4^{-1/2} (cf., above, n. 9). For
the "observational constraints," cf. the text above and n.8. Mr. Iuliano
notes that 2π^{2} is also the π-component
of the torus volume f = 2π^{2}Rr^{2} (cf., above, n. 24).
^{27}
See, above, n. 11. The relation of 82944 to the mathematics of zero-point energy is
demonstrated in the text above. Note that the integral product (cf., above,
n. 3) of
the Hebrew for 'point zero of energy' or 'dead center', נקרת האפם של תנופה, equals 8.2944 × 10^{22}
(cf., above, n. 23, and Leahy, Foundation, pp. 426ff., et passim.), while the
rational product of the Hebrew for 'relation', יחוס, equals 8^{-1} (cf.
ibid., pp. 521ff.), and its linear product the square root of 82944 × 10^{4},
where 10^{4} is the 'created 100' (cf., above, n. 26).
^{28}
See, above, n. 10.
^{29}
See, above, n. 3.
^{30}
See, above, in the text, passim, and notes 17, 18, and 24. Note that the infinite
iterative sequential summing of the trinary logic geometric series founds the geometric
series which is the numerator in the Maclaurin series for
e^{x},
while the denominator of that series is the factorial of the series of integers
beginning with zero, which is the mathematical equivalent of the infinite sequential
summing of the logical digits, which latter is indifferently sequential
multiplication. In fact, in the infinite sequential summing/multiplication which is
the logical geometric series, numerator and denominator are foundationally
undifferentiated. See (in addition to n.17, above) Leahy,
Foundation,
Section III.1.
^{31}
See, above, n. 1.