Professor, The Ohio State University
Empiric initial observation leading to the harmonic neutron hypothesis
The harmonic neutron hypothesis was initially based on the empiric observation that the strong, electromagnetic, and gravitational force units were all ratio scaled by integer exponent multiples of the annihilation frequency of the neutron, vn, times one second, vns. The frequency equivalent of the neutron is 2.2718591 x 1023 Hz. The frequency equivalent is the mass of the neutron times c2 divided by h. The neutron is the unit associated with the strong force, and the elements. The frequency equivalent of Planck’s constant is 1 Hz, and is the unit of the electromagnetic force. Two times the gravitational binding energy frequency equivalent of the electron in hydrogen is 2 x 2.900 x 10-24 Hz or 5.800 x 10-24 Hz. This is the unit of the graviational force, or hydrogen’s graviton. The reciprocal of the annhilation frequency of the neutron is 4.4016815 x 10-24 which is nearly identical to hydrogen’s graviton value. The 2 arises from gravity being a kinetic force. Therefore, these three frequency equivalent force unit values are all ratio spaced by the annihilation frequency of the neutron times one second.
The gravitational binding energy of the electron in hydrogen, the hydrogen graviton, is assumed to be as important to the gravitational force as the ionization energy of hydrogen is for the electromagnetic force. It is identical in concept to the Rydberg series. Two times the gravitational binding energy of the electron in hydrogen as a frequency equivalent times vns is almost identical to a frequency of 1Hz. In this crude calculation it is 1.318. 1 Hz is associated with the frequency equivalent of Planck’s constant. 1Hz times the annihilation frequency of the neutron equals the frequency equivalent of the neutron. This pattern is similar to classic harmonic music systems where the scaling factor, fundamental frequency times a consecutive integer series defines each next octave. In the physical domain, the annihilation frequency of the neutron times one second exponents -1, 0, 1 are related to the unit values for the gravitational, electromagnetic, and strong forces. This integer exponent series spans a 1046 range. If this is true then the harmonic fraction exponents, (n±1)/n, or 1±1/n should also represent other unit physical values, which have been shown to be true. This pattern is the classic harmonic series of 1/n for n equals 1 to ∞. For example, the exponents of the annihilation frequency of the neutron are almost equal to the following prime number harmonic integer fractions: electron, exponent 0.86023062, harmonic fraction 6/7 (.857142857); the Bohr radius, exponent 0.80291631, harmonic fraction 4/5 (.8); and the ionization energy of hydrogen, exponent 0.66436554 , harmonic fraction 2/3 (.6666). This pattern is seen with all studied fundamental constants.
This is observation is further supported since the annihilation frequency of the neutron is associated with Planck time squared, tP2, no hbar. Planck time squared is identical to the Newtonian gravitational constant, G, in the frequency domain. Planck time squared equals the frequency equivalent of the energy between two masses each equivalent to a frequency of 1 Hz separated by the distance light travels in one second. G times two masses with of each 1 kg separated by 1 m equals the gravitational energy of this system in Joules. Multiplying G by h/c5 converts the two masses from 1 kg to 1 Hz. This is associated with factor h/c4. The final c is related to converting the distance from 1 m to c times one second. Planck time squared times the frequency equivalents of vmass1, vmass2, and their separation distance vλ equals the
gravitational energy of that system in units of Hz. This is the identical result as the standard gravitational equation, but in Hz not Joules.
tP2 is logically related to the annihilation frequency of the neutron. Analyzing the system based on the hydrogen graviton is the annihilation frequency of the neutron raised to the exponent of -1-1-6/7-4/5 divided by two. These are the integer fractions associated with the proton (1), electron (6/7), Bohr radius (4/5), and the binding energy of the electron in hydrogen (-1). That derived gross predicted tP2 value is 1.9114 x 10-86 Hz. The known value is tP2 is 1.8261 x 10-86 Hz. This is a relative error of 4.669 % from a predictive ratio spread of 10109 digits. Therefore Planck time squared, and G are intimately associated by integers, and integer fraction exponents of the annihilation frequency of the neutron.