^{1}

^{*}

^{2}

^{*}

Purpose: To accurately derive
H
_{0} from subatomic constants in abscence of any standard astronomy data. Methods: Recent astronomical data have determined a value of Hubble’s constant to range from 76.9
^{+3.9}
_{-3.4}
^{+10.0}
_{-}
_{8.0}
to 67.80 ± 0.77 (km/s)/Mpc. An innovative prediction of H_{0} is obtained from harmonic properties of the frequency equivalents of neutron, n^{0}, in conjunction with the electron, e; the Bohr radius, α_{0}; and the Rydberg constant, R. These represent integer natural unit sets. The neutron is converted from its frequency equivalent to a dimensionless
constant
,
, where “h” = Planck’s constant, and “s” is measured in seconds. The fundamental frequency, V_{f}
,
is the first integer series set
.
All other atomic data are scaled to V_{f} as elements in a large, but a countable point set. The present value of H_{0} is derived and Ω_{M} assumed to be 0. An accurate derivation of H_{0} is made using a unified power law. The integer set of the first twelve integers N_{12} {1,2,
…
,11,12}, and their harmonic fractions
exponents of V_{f}
represent the
first generation of bosons and particles. Thepartial harmonic fraction, -
3/4, is exponent of V_{f} which represents H_{0}. The partial fraction
3/4 is
associated with a component of neutron beta decay kinetic energy. Results: H_{0}
is
predicted utilizing a previously published line used to derive Planck time, t_{p}. The power law line of the experimental H_{0}
and
t_{p}
conforms to the predicted line. Conclusions: H_{0}
can be predicted from subatomic data related to the neutron and hydrogen.

Hubble’s law refers to the observation that objects at greater than 10 megaparsecs have a Doppler shift interpretable as a relative velocity. The Doppler shift is most commonly quoted as a velocity in (km/s)/Mpc. Galaxies appear to be moving at a rate proportional to their distance from the Earth. This is typically interpreted as evidence of the expansion of the Universe. A high precision Hubble constant H_{0}, is an important physical constant, [_{0} as a proportionality constant with units of s^{−1} times the proper distance, D. The reciprocal of H_{0} is the Hubble time. The reported velocities at one Mpc vary with the model and published values include: 76.9^{+3.9}_{−3.4}^{+10.0}_{−8.0} km・s^{−1}・Mpc^{−1}, 69.32 ± 0.80 km・s^{−1}・Mpc^{−1}, 74.3 ± 2.1 km・s^{−1}・Mpc^{−1}, 67.3 ± 1.2 km・s^{−1}・Mpc^{−1}, _{0} are different. This leads to divergent estimated values based on the methods and model. The methods include the Hubble telescope, Chandra and Sunyaev-Zeldovich Effect data from the Owens Valley Radio Observatory and the Berkeley-Illinois-Maryland Association interferometric arrays, Wilkinson Microwave Anisotropy Probe, and cosmic microwave background, CMB, temperature and lensing-potential power spectra The experimental Hubble rates range from 2.18(4) × 10^{−18} s^{−1} to 2.49(12) × 10^{−18} s^{−1}. The reported Hubble time, ^{17} s or 13.8 byr. The approximate Hubble length equals _{0} is assumed to be present experimental value with an

The goal of this work is to derive a high precision H_{0}, and subsequently a Hubble length, and Hubble time from natural unit frequency equivalents as integer sets of the neutron, _{12} _{12} are referred to as integer fraction exponents,_{0} follow a previously predicted power law relationship used to derive_{0} ratios with

The following is a review and explanation of the harmonic neutron hypothesis. It was initially copyrighted in 2006 and published in 2009, [

s^{2} or s^{−1} | km・s^{−1}・Mpc^{−1} | Exponent | δ | |
---|---|---|---|---|

H_{0k} | 2.49(12) × 10^{−18} s^{−1} | 76.9^{+3.9}_{−3.4}^{+10.0}_{−8.0} | −7.53(12) × 10^{−1} | −3.70(90) × 10^{−3} |

H_{0k} | 2.408(67)×10^{−18} s^{−1} | 74.3 ± 2.1 | −7.543(8) × 10^{−1} | −4.33(50) × 10^{−3} |

H_{0k} | 2.24(2) × 10^{−18} s^{−1} | 69.32 ± 0.80 | −7.556(16) × 10^{−1} | −5.62(20) × 10^{−3} |

H_{0k} | 2.18(4) × 10^{−18} s^{−1} | 67.3 ± 1.2 | −7.562(3) × 10^{−1} | −6.17(32) × 10^{−3} |

H_{0kline fit} | 2.33(11) × 10^{−18} s^{−1} | 71.9(36) | −7.549(11) × 10^{−1} | −4.99(32) × 10^{−3} |

H_{0}_{d} | 2.29726680(12) × 10^{−18} s^{−1} | 70.886246(4) | −7.55202112(1) × 10^{−1} | −5.2021124(11) × 10^{−3} |

1.82611(11) × 10^{−86} s^{2} | −3.670879(12) | −1.37371(1) × 10^{−2} | ||

1.82611(11) × 10^{−86} s^{2} | −3.670879(12) | −1.37371(1) × 10^{−2 } | ||

1.8261712(1) × 10^{−86} s^{ } | −3.670879366(1) | −1.3736509(1) × 10^{−2 } |

system can logically be evaluated as a unified quantum spectrum. The primary natural unit is

tance

The primary hypothesis is that the fundamental constants are inter-related by simple, ubiquitous mathematical and geometric integer patterns. The first twelve integers, N_{12}, and their harmonic fractions,

The Equality Pair Transformations (EPTs) inter―relate matter, electromagnetic energy, and kinetic energy transformations. EPT are common physical phenomena that can be described by Feynman diagrams, but necessitate a definitional approach when utilized in this model. Each EPT is associated with a point transformation from one state to another, or from one force to another, such as, kinetic energy to electromagnetic energy, electromagnetic energy to matter, or vice-versa. This occurs when there is a scale equality of two different states or forces. The pair is identically scaled phenomena, but can represent two different dual (paired) physical manifestations of different forces or states. This is the essence of particle-wave duality paradox. Examples are matter-antimatter pair production or annihilation; or the transformation of electromagnetic energy to kinetic energy as in the photoelectric effect. Not only is there a conservation-equality of total energy-matter, but also a transformation of state or force. These transformations are always associated with symmetric pairs.

Constant unit | n_{ie} or n_{ife} | 1 ± 1/n_{ife}, qf |
---|---|---|

Elemental gravitational kinetic energy of the electron in hydrogen | −1 | −1 |

h, electromagnetic energy, boson | 0 | 0, 1 − 1/1 |

n^{0}, elemental mass, strong force | 1 | 1 |

Beta decay kinetic energy, anti-neutrino mass, cosmic background microwave, CMB, peak spectral radiance | 2 | 1/2, 1 − 1/2 |

Rydberg constant, R, em energy, boson | 3 | 2/3, 1 − 1/3 |

Beta decay kinetic energy, muon anti―neutrino | 4 | 3/4, 1 − 1/4 |

Bohr radius, α_{0}, distance, or beta decay kinetic energy | 5 | 4/5, 1 − 1/5 |

Beta decay kinetic energy, Tau anti―neutrino | 6 | 5/6, 1 − 1/6 |

Electron, e, mass, matter | 7 | 6/7, 1 − 1/7 |

Beta decay kinetic energy | 8 | 7/8, 1 − 1/8 |

Up quark, u, matter | 10 | 9/10, 1 − 1/10 |

Down quark, d, matter | 11 | 10/11,1 − 1/11 |

α^{−1}, reciprocal fine structure constant, coupling constant | 11 | 1/11 |

Higgs boson, H^{0}, boson | 11 | 12/11, 1 + 1/11 |

W, Z, boson | 12 | 13/12, 1 + 1/12 |

The primary fundamental EPT scaling HNH is neutron anti-neutron pair production, and is the scaling factor used to derive further observable phenomena. The fundamental EPT ratio set is composed of a natural physical unit as a consecutive integer series representing the transformation of electromagnetic energy into frequency multiples matter associated with neutron/anti-neutron pair production. The integrally spaced dimensionless elements, v_{f} in V_{f}, are based on the ratio of the respective annihilation frequencies of that physical constant to that of the neutron. At the point where the photon integer frequency series has enough energy to be scaled identically with elemental neutral matter equivalent represents the fundamental EPT. The series restarts again at 1 with each integer representing the number of nucleons in elemental matter or groups of nucleons at the EPT of pair production point. Elements in the set V_{f} scale all of the possible physical phenomena under consideration.

The neutron annihilation frequency, _{f}. We assume that there exists a gravitational binding energy of the electron to the proton in hydrogen, equally as important to the units of gravitational energy, as the ionization energy of hydrogen is to the electromagnetic force. The genesis of this hypothesis was based on the empirical observation that there are integer exponent relationships of

Twice the frequency equivalent of the gravitational binding energy of the electron in hydrogen, 2 × 2.90024(22) × 10^{−24} Hz equals 5.80048(44) × 10^{−24} Hz. We label here the gravitational binding energy of the electron in hydrogen as the elemental graviton. The frequency equivalent of Planck’s constant, h, is 1 Hz. Here,

^{23} Hz. The reciprocal of ^{−24}, and is almost iden-

tical to twice the binding gravitational frequency of the electron in hydrogen.

The factor two in the gravitational binding energy of the electron to the proton arises from the fact that it is a kinetic energy. This “2” has the same origin as the “2” in the Schwarzschild radius equation,

equivalent of the gravitational electron binding energy when multiplied by

malized value of 1 Hz for Planck’s constant h, times

represented by an injective mapping of the sequence: {−1, 0, 1, 2} to exponents of

exponents, are referred to as

Energy multiples of Planck’s constant, h, is also an integer based wavelength or frequency system. This is identical to the resonant modes of a vibrating string. Planck’s constant represents integral units of electromagnetic energy. Though h is quantum by definition, its actual physical manifestation in black body radiation appears to be continuous. When the divisions between the physical values associated with each n unit are smaller than experimental accuracy then the physical system appears to be Almost Everywhere (A.E.) continuous, but is none the less conceptually and mathematically integer-based

If this initial EPT observation is valid, then there logically should be a similarly scaled transformation between the unit values of the gravitational and electromagnetic forces. At

1 Hz. At

quency of

of a black hole, at a frequency of ^{46} Hz. This is an extremely dense from of

matter, and must be the mass of individual unit forming a black hole analogous of neutrons forming elemental matter. This latter mass’s Compton radius is smaller than its Schwarzschild radius, and must represent the matter of a black hole.

In this method all of the physical phenomena are evaluated as exponents of_{k}, of the base

for any physical constant is the natural log

its associated partial fraction represents the δ factor.

Inspection of an integer-based exponent system of the forces/states,

ponential domain Figures 1-4. The only other possible point values are the harmonic fractions, ±1/n_{ife} and harmonic mixed partial fractions, 1 ± 1/n_{ife}. These integer based exponents are associated with the observable fundamental constants. For this paper the only n_{ife}_{ }utilized are points in N_{12}, since they are associated with the first generation of kinetic energies, particles, and bosons of neutron beta decay,

Assignment of the n_{ife} is dependent on that value fulfilling a power law relationship with the natural unit values of the first two natural integer sets. For the simplest situation the fundamental constant is related to the n_{ife}_{ }closest to 1 divided by 1 minus the exponent of the constant. If that value is positive then the partial harmonic fraction is 1 − 1/n_{ife}. If the value is negative then the partial harmonic fraction is 1 + 1/n_{ife}. This is not the greatest integer function. However, the n_{ife} value can be driven far from the closest n_{ife} value by the power law imperative or the fact that some of the constants are divided or multiple by 2. Utilizing these relationships it is possible to logically assign the physical phenomena of the neutron beta decay process to a specific partial harmonic fraction,

The simplest sinusoidal system that is related to a consecutive integer series is the possible wavelengths and frequencies of a vibrating string. This is associated with the harmonic sequence, _{ife} of associated entities and the hierarchy of the physical constants.

Thus, the HNH model hypothesizes that physical constants represent a multi-layered simultaneously linear and exponential inter-locking, transformational integer series, with classic harmonic properties, in both the linear and exponential domains. These types of harmonic/repeating pattern systems are remarkably unified, where if any frequency and its associated integer value are known, then an infinite number of associated possible harmonic fractions and frequencies of the system are defined in Tables 2-4,

Physical constant | Value |
---|---|

2.271859078(50) × 10^{23} | |

53.780055612(22) | |

bwk: y-intercept, weak force, wk line | 3.51638329(18) × 10^{−3} |

awk: slope, weak force, wk line | 3.00036428(15) × 10^{−3} |

bem: y-intercept, electromagnetic, EM line | −3.45168347(17) × 10^{−3} |

aem: slope, electromagnetic, EM line | −3.45168347(17) × 10^{−3} |

Proportionality constant | Known | Derived |
---|---|---|

1.02(15) × 10^{−41} | 1.01118370(17) × 10^{−41} | |

8.03(40) × 10^{−110} | 8.0382241(5) × 10^{−110} | |

1.272(64) × 10^{68} | 1.25796898(7) × 10^{68} |

The Harmonic Neutron Hypothesis was previously used to derive the energy/matter lost in the transformation of a neutron to hydrogen, the masses of the quarks, the Higgs boson, and the Planck time [

The HNH has accurately derived Planck time,

None of the individual elements of the HNH are new or radically depart from standard physics or mathematical methods. The perspective taken, the nomenclature used, and methods are not standard, but are nonetheless logically and mathematically valid. To understand this method, a significant intellectual investment is essential since it is not intuitively obvious. The model is from a global perspective very similar to magnetic resonance imaging. MRI, which was assumed to be impossible at the time of its introduction based on classical physics interpretations of optical imaging criteria, yet disproven [

The standard components of the HNH will be highlighted in italics. The HNH model is not in conflict with the Standard Model or overturns its methods or tenants. The actual physical values used are equivalent to standard unit values, but they are all transformed into frequency; harmonic fraction plus

This model is independent of any specific physical unit system. Converting the standard units to this unit 1 format does not change the absolute

The combined components of the hypothesis are controversial because they are not well understood, are different from standard nomenclature, and novel. The concepts and mathematics are actually not complicated, but require a significantly different conceptual approach. All of the physical relationships are viewed solely as ex-

ponents (integer fractions plus

stants/proportionality constants. One example would be the ratio of the frequency equivalent of the ionization energy of hydrogen divided by the frequency equivalent of the Bohr Radius,

All of the ratios are scaled by _{0},

In this model the identical consecutive integer and harmonic fraction sequences are seen, as exponents of the fundamental frequency, _{12},

The hypothesis is based on classic harmonic fractions, _{0} can be derived with no direct physical measurement. An analogy is Moseley’s law on ion emission spectra.

Another important concept is resonance and products of harmonic numbers. Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies rather than at others. If two systems have common frequency components there will be greater coupling and potential transfer of energy between them. For a musical example, two prime number frequencies can only resonant at the product of the two prime frequencies. This pure number property defines a higher order hierarchy of physically associated entities.

The HNH presents itself as a natural unit system. A natural unit system incorporates known physical units rather than arbitrary units. A natural unit model with all of the other constants driven to 1 greatly simplify the mathematics. This model is based on the annihilation frequency of the neutron, as the fundamental frequency similar to Planck units. In Planck units all of the different fundamental constants are converted into a single common standard unit such as Hz, seconds, kilograms, or meters. The neutron is a logical unified fundamental physical entity that is centered between atomic, subatomic, and cosmic entities.

In the simplest exponential harmonic series, all of the possible frequency values could be defined and related solely to a single fundamental frequency and the harmonic fraction series,

There are four product ratio relationships of these entities associated with the hydrogen atom. For example the

integer fraction associated with 2 must be related to ^{34}, and (2pi) raised to

(1/(39/1155)) is 4.34916 × 10^{23}. There is no common fundamental frequency that can fulfill these conflicting mathematical imperatives. Nature’s solution is to have small δ-values added to the quantum harmonic fractions that “shim” these various values to a common fundamental frequency, in this case

Each physical constant is plotted as a harmonic fraction minus one on the X-axis and the Y-axis is the plot of δ (the exponent minus the harmonic fraction),

The physical datum of each point has the identical value as its standard exponent, and can be translated to its standard routine physical value. The difference between two points on the 2d universal plane represents a proportionally constant, a ratio in the linear domain, a power law. This harmonic plane also has all of the classic mathematical properties of lines. A line connecting any two points can define a proportionality relationship of two or more physical constants. It is possible to derive any harmonic value from the slope and y-intercept of a

δ-line and

or common δ-lines.

In Physics, under most circumstances if one knows a natural unit within a ratio or product relationship that value can be used as a constant, but it does not have inherent predictive value to other multiple other related physical constants. In a harmonic system if the natural unit is known and its associated quantum integer value then an infinite series of other values/constants, can potentially be derived. [

Many of these constants can be derived since the actual δ-values can be derived from the three finite point sets described above sets, provided the harmonic fraction is logically derived. [

the universal harmonic plane. Their slopes and y-intercepts along with

many of the other physical constants in this model. One line is related to the weak kinetic entities, and one related to the electromagnetic entities. The only other possible valid force δ lines are related to sums and differences of the slopes and y-intercepts of those two lines,

The value of the HNH method is that it can derive and predict physical constants beyond what can be experimentally measured [_{0}.

The methodology of HNH derivation generates new insights into connections between the subatomic entities of neutron beta decay, kinetic energy, and the neutrinos, leading to frequency expressions of the neutron, t_{P}, gravity, H_{0}; and the apparent expansion of the universe.

Floating point accuracy is based upon known experimental atomic data, of approximately 5 × 10^{−8}. All of the known fundamental constants are converted to frequency equivalents, _{0}. Equations (1)-(4), ^{2} (speed of light squared) then dividing by h (Planck’s constant). The distances are converted by dividing the wavelength into c. Energies in Joules are converted by dividing by h. The eV value for the neutron is 939.565378(21) × 10^{6}. Its frequency in Hz is converted to eV by multiplying by the constant, 4.13566750(21) × 10^{?15} eV/Hz. The eV was converted to frequency by multiplying by the constant 2.41798930(13) × 10^{14} Hz/eV. N_{A} is Avogadro’s number, 6.02214129(27) × 10^{23} mol^{−1}. Converting the standard units to where they are all 1’s does not change

All of the data for the fundamental constants were obtained from the websites (http://physics.nist.gov/cuu/Constants/ and www.wikipedia.org. The NIST site http://physics.nist.gov/cuu/Constants/energy.html has an online physical unit converter that can be used for these types of conversions.

This model has two parallel domains both describing the identical physical values. One domain is the frequency

equivalent of any physical value. The other domain is the exponent of the base

that exponent equals the frequency equivalent of that specific value. Equation (5). The known exponent, exp_{k}, of

a fundamental constant is the ratio of the log_{e} of the frequency equivalent, n_{k}s, divided by the

subscript d represents a derived value.

Every value in the physical domain is defined completely in terms of its ratio and exponent relationship with

standard physics linear/frequency domain, and the other in the exponential domain which is unique to the HNH model. The value of viewing the fundamental constants in the exponential domain is that their harmonic integer inter-relationships are clearly defined. The other is that any physical relationship can be displayed and calculated across all of the forces, and at any scale in this virtual 2d space. Despite the fact the HNH model utilizes virtual space, that space accurately defines true physical phenomena.

In the Standard Model, only a subset of physical values are quantum by definition or computational in character. In the HNH model every aspect of physical systems is quantized by integral steps. There are regions where the system appears to be experimentally continuous in the Standard Model, but this is not true in the HNH model,

The known exp_{k} minus the harmonic/quantum fraction, qf, equals the known δ_{k}, Equation (6). The known

frequency equivalent of a constant, v_{k}, is calculated by raising _{k} in Equations (6). Equation (7) shows that many of the fundamental constants do not have n_{f} equal to

The n_{ife} (integer-fractional exponents, “ife”) and the associated quantum fractions, qf, the harmonic fractions, and the partial harmonic fractions must fulfill a power law relationship with a natural unit constant. The closest n_{ife} to the experimental value is derived from the exp_{k}, Equations (8), but that value may not be the actual n_{ife} since it may not fulfill a power law relationship [_{ife} assignments from 1 to 12 are listed in

As

Equation (12) calculates the X-axis value for a specific quantum fraction, partial fraction, and n_{ife}.

By definition the exp_{k} of the n^{0} is 1, and the exp_{k} of h is 0. Both have a δ_{k} of 0. All of the electromagnetic spectrum, quantized n-Hz, have an effective ^{18} Hz; where ^{−3}. The exponent ^{−3}, ^{−3}, and ^{23} Hz. The y-intercept of

The frequency equivalent of the electron n_{e}, is 1.23558996(05) × 10^{20} Hz; exp_{e} is 8.6023061(06). The qf is 6/7, X-axis location of −1/7, principal quantum number, 7, and its ^{?3}. The exponent ^{?3}, be 3.60238646(18) × 10^{?3}_{, }of 2.7575290(01) × 10^{23} Hz.

The frequency equivalent of hydrogen ionization energy^{15} Hz; ^{−3}. The exponent ^{−3}, ^{−3}, ^{23} Hz.

The frequency equivalent of ^{2}; ^{−2}. The qf is 1/11, X-axis location of −10/11, principal quantum number 11, and its ^{−4}.

The known and derived exponents of physical constants are plotted/ transformed to the 2d universal harmonic plane. The X-axis is a multi-dimensional physical descriptor, Figures 2-4. The point (0, 0) represents the neutron since that is the exponent of _{ }Hz. The Y-axis is the related to the difference of the known exponent minus its associated qf, Equation (6). The Y-axis is not continuous in terms of the inter-relationships of the fundamental constants either. The slopes and y intercepts of the wk and EM

The points for the e,

The only possible derived exponents are discrete since the only possible qf and ^{−3} and the y-intercept is bwk, 3.51638329(18) × 10^{−3}, Equations (13), (14).

These derived

The EM, line is defined by the points for the Planck constant, (−1, 0) and Rydberg R^{−3}, Equation (15). This line is related to the principal quantum number 3, qf, 2/3. The other potential qf values have also been shown to be related to the quarks and mesons, [

The derived

Many of the fundamental constants are compound product/ratios of other fundamental constants. Therefore

The compound values are plotted at their qf_{d} − 1 X-axis values and their

Equation (21) is the proportionality constant, known or derived

The known experimental h-bar ^{−44} s, relative error 6 × 10^{−5}. The known experimental non h-bar ^{−43} s, ^{2} non h-bar is 1.82611(11) × 10^{−86} s^{2}. The known mean experimental non h-bar exp_{k} is −3.670879(12). The known experimental non h-bar ^{−2}. The qf of

The harmonic neutron hypothesis has derived a high accuracy Planck time^{ }are −1, the gravitation binding energy of the electron −1, negative qf proton, −6/7, negative qf electron; −4/5; negative qf Bohr radius. The sum equals −128/35. This is plotted at the x-value of −163/35, −128/35-1.

The derived ^{−2} and the derive ^{−86} s^{2} relative errors of 5 × 10^{−8}. The derived no h-bar ^{43}. The equivalent ^{−44} s. All these values are within the known experimental values.

The known experimental velocities at Mpc^{−1} are 76.9^{+3.9}_{−3.4}^{+10.0}_{−8.0} km・s^{−1}・Mpc^{−1}, 74.3 ± 2.1 km・s^{−1}・Mpc^{−1}, 69.32 ± 0.80 km・s^{−1}・Mpc^{−1}, 67.3 ± 1.2 km・s^{−1}・Mpc^{−1}, ^{−1} ^{22} meters. These value are 2.49(12) × 10^{−18} s^{−1}, 2.408(67) × 10^{−18} s^{−1}, 2.24(2) × 10^{−18} s^{−1}, and 2.18(4) × 10^{−18} s^{−1}. Their respective exp_{k} are −7.53(12) × 10^{−1}, −7.543(8) × 10^{−1}, −7.556(16) × 10^{−1}, and −7.562(3) × 10^{−1}. The respective ^{−3}, −4.33(50) × 10^{−3}, −5.62(20) × 10^{−3}, and lastly, −6.17(32) × 10^{−3}.

A line fit of the known ^{−86} s^{2} and 2.33(11) × 10^{−18} s^{−1}. The slope is 3.021 × 10^{−3}, and the y-intercept at x = 0 is 3.315 × 10^{−4}. The line fit ^{−2}. This is compared to the derived values in

The generalized

The derived^{−1} calculated values from the ^{−3}, −5.0446820(13) × 10^{−1}, 1.6498650(1) × 10^{−12} s^{−1}, for −3/4: −5.20211263(26) × 10^{−3}, −7.5520211(04) × 10^{−1}, 2.2972668(2) × 10^{−18} s^{−1}, for −5/6: −5.4467515(3) × 10^{−3}, −8.3878008(4) × 10^{−1}, 2.5652661(7) × 10^{−20} s^{−1}, for −7/8: −5.5690708(3) × 10^{−3}, −8.8056907(5) × 10^{−1}, 2.7107717(3) × 10^{−21} s^{−1},

The derived Hubble time is the inverse of^{17} seconds. There are 3.1556926 × 10^{7} seconds per year. The derived Hubble time equals 13.7941161(13) × 10^{9} years. The derived Hubble length is 13.7941161(13) × 10^{9} light years. The reported experimental value is approximately 13.8 × 10^{9} light years.

The known proportionally constant of the ratio of ^{−41}. The derived value is 1.01118370(16) × 10^{−41}, Equation (32),

The known proportionally constant of the ratio from the ^{−110}. The derived value is 8.0382241(5) × 10^{−110}, Equation (33).

The known proportionally constant of the ratio from the ^{68}. The derived ^{68}, Equation (34).

A robust physics model that explains many of the mysteries of today remains elusive [

Many critics of the HNH suspect that these findings are simply coincidence or numerology. The HNH is however a classic dimensionless physical system of the Buckingham Pi theorem type. The speed of light is finite, and constant within any setting. It is logical that the whole system should be based on a finite constant as well. The harmonic neutron hypothesis is highly restricted. Only three starting finite number sets are used. The derivations are not made directly from the original subatomic data, but from the unified scaling of the whole universal harmonic 2d plane, _{0} was derived from a product ratio relationship of the four subatomic constants that would be utilized in a classic physics’ method. It is impossible to manipulate the results since all of the components are fixed previously published natural units, and harmonic integer fractions. It is not possible to derive any value by manipulating the n_{ife} value. An argument by analogy is that it is not possible to derive any wavelength from the Rydberg series by changing the n_{1} and n_{2} values since R is a natural unit

The hypothesis logically states that related physical constants will naturally all fall on a single _{0} from the _{0} are accurately derived. This is viewed as impossible utilizing standard methods.

The typical interpretation of the H_{0} is that it is not felt to be a true constant, but changes with other variables defining the nature of the cosmos. It has been described as the Hubble parameter. It is experimentally impossible to prove that the H_{0} is actually changing from the present value. In the HNH H_{0} is felt to constant, and is analogous to the free space constants of permeability, and permittivity. Interpretation of quantum systems using classical physics concepts is inaccurate and inappropriate. In the HNH the same is true for cosmology phenomena.

It is logical that the H_{0} should be closely related to the gravitational force, and therefore_{0} is related to an expansive kinetic phenomenon, and so is the neutron beta decay process. H_{0} and the beta decay qfs have inverse signs, 3/4 and −3/4, but identical harmonic fractions. The harmonic neutron hypothesis has shown multiple examples of this type of harmonic fraction sign symmetry with inverse sign relationships. The top quark is 1+1/10 and the up quark is 1 − 1/10. The Higgs boson is 1 + 1/11, and the down quark is 1 − 1/11. This is a non-coincidental relationship as seen with the Rydberg series and with Moseley’s law, which in the exponential domain represent inverse exponents.

Perhaps the other qfs −1/2, −5/6, or −7/8 represent the properties of dark matter and energy. It is possible to accurately derive CMB peak spectral radiance from the same ^{2}. The derived

The HNH also explains the precise logical origin of H_{0} and unification with other fundamental constants including the neutron, hydrogen, neutrinos,

H_{0} can be derived from four finite integer natural units and N_{12}. H_{0} is logically related by harmonic fractions to the beta decay kinetic energy based on a common harmonic fraction, 3/4, but with opposite sign. The experimental Planck time and H_{0} data power law data is closely linked to the predicted data. The derived H_{0} can be evaluated in the future to see if this is an accurate prediction. Derivation of accurate coupling constants of the neutron with _{0} has never been achieved before so this is a significant result.

I would like to thank Tom Budinger Ph.D. for his sage advice, and help. I would also like to thank Richard White MD for his support of this work.

Donald WilliamChakeres,RichardVento, (2015) Prediction and Derivation of the Hubble Constant from Subatomic Data Utilizing the Harmonic Neutron Hypothesis. Journal of Modern Physics,06,283-302. doi: 10.4236/jmp.2015.63033