Quantum AetherDynamics Institute

BREAKING NEWS: We have successfully developed the electron binding energy equation, which accurately predicts the 1s orbital electron binding energies for all the atomic elements.

As is shown on the Binding Energy page, the internal nuclear length of an atom is proportional to the atom's binding energy per nucleon.  To fully understand the exact nature of the atom it is now necessary to obtain the equation for the internal nuclear length, or the distance between Aether units within the atom.

A short table of all real isotopes up to oxygen is on this web site.  A more complete table for all elements is also on this web site.  Looking at the tables we can deduce several truths about the parameters contributing to the internal nuclear length equation.

The isotope with the shortest average internal nuclear length, and hence the weakest binding energy per nucleon is Hydrogen 5.  The isotopes with the longest internal nuclear lengths are Nickel 62, Iron 56, and Iron 58, and thus have the strongest binding energy per nucleon.  The shells of the nucleus fill according to 2, 8, 20, 28, 50, 84, 126.  Iron 58 appears to be a point where all four inner shells are completely full (2+8+20+28=58).  Iron 56 appears to be a point where the second, third and fourth shells are completely full (8+20+28=56).  Nickel 62 appears to be a situation where all four of the inner shells are full and an alpha particle (helium nucleus) may be formed in the 5th shell. (2+8+20+28+4=62).  From these observations it may be correct to say that the internal nuclear length equation is dependent on the shell structure and fill pattern of the nucleus.

Observing the hydrogen element it is seen that the internal nuclear length for ²H is equal to .187l_C while it is .475l_C for the ³H isotope.  By pairing up the neutrons the binding energy increases by a factor of 2.54.  Add one more neutron to produce ⁴H and the internal nuclear length decreases a factor of 0.49. Add one more neutron and the internal nuclear length decreases again by a factor of 0.39.  With ⁶H the internal nuclear length increases by a factor of 1.76.  

So it is seen that pairing the neutron substantially increases the length the subatomic particles can move within the isotope.  Also, tritium (³H) is radioactive, so an increase in the internal nuclear length does not necessarily mean the isotope is more stable.  In fact, the increased internal length may contribute to radioactivity in some cases.

It is worth noting that ³H and ³He have very similar internal nuclear lengths (.475l_C and .433l_C).  Likewise ⁴H and ⁴Li have internal nuclear lengths of .234 and .194.  These lengths are proportional to the combinations of the particles involved.  In ³H there are two neutrons and one proton.  Neutrons are composite particles containing a proton, an electron plus extra binding energy.  In ³He there are two protons and one neutron.  The slightly lesser internal nuclear length may be due to the lesser total mass of the nucleus.  The lesser internal nuclear length may also be due to the different configurations of particle magnetic moment. The same applies to ⁴H and ⁴Li.

It is also worth noting that elements with even numbers of protons tend to have stronger binding energies and greater internal nuclear lengths than elements with odd numbers of protons.  In even elements with even numbers of protons, the strongest isotope (in the lighter elements) tends to be the isotope with the same number of protons and neutrons.  But because atoms tend to be more stable when protons and neutrons are paired, the elements with an odd number of protons tend to be most stable when the number of neutrons is equal to the number of protons, plus one more neutron.  So that lithium 7 has a stronger binding energy per nucleon and a longer internal nuclear length than does any other lithium isotope.

The above observations indicate, and the nuclear binding energy equation will reflect, that particles like to be paired with their own kind.  

The strong charge of the subatomic particles provides the basis for the strong nuclear force that holds the atom together.  The distance this force moves determines the binding energy of the nucleus.  But for the energy to remain in the nucleus the forces must continue to move a certain length with each quantum moment.  So there must be something that repulses the forces such that they can oscillate.  This repulsion is likely due to the magnetic moment of the subatomic particles. So the internal nuclear length equation most likely involves the magnetic moments of the proton, neutron and possibly the electron.

So there must at least be four factors involved in the equation for internal nuclear length.  The equation must account for the number of each subatomic particle, the odd-even pairing of the subatomic particles, the magnetic moments of the subatomic particles, and the environmental structure that determines how many protons and neutrons can be in a shell with a certain energy state.

Looking at the environment as Aether, and seeing the Aether as having a geometrical constant of 16pi2, the "shape" of spacetime can be determined.

Figure 1.  The "Shape" of Aether

It must be understood that the above image is traced out, not only in space, but also in time.  A more detailed explanation can be found on the Physics of Time page.

Just one fourth of the above geometry pertains to a given subatomic particle.  Even though a subatomic particle looks like a half spin, helical spiral over a sphere when viewed over several moments of time, in our single time frame reference of the present the subatomic particle looks like a toroid, as in figure 2.

Figure 2. A subatomic particle fills one fourth the geometry of a quantum unit of Aether.  The result in a single frame reference of time is that it appears as a toroid.

Due to the logarithmic spiral pattern the toroid makes in spacetime, there is a slight "jitter" imposed on the subatomic particle's strong charge.  This jitter appears to be a function of Phi, which is equal to the Golden Ratio.  As seen on the gfactor page, the gfactor of the electron and proton can easily be expressed as functions of Phi and its inverse, phi.

I have not yet found a true mathematical binding energy equation that would fit for all isotopes.  But I have discovered these amazingly close equations for the hydrogen isotopes.  It might be coincidence, or I might be very close to producing the true binding energy equation.  But here are the five equations I have worked out so far...

For more explanation of the terms in the binding energy equation, check out the binding energy page. 

The measured binding energies for these five isotopes of hydrogen are listed in table 1.

Table 1.

Even if there is yet another parameter that needs to be added, there is mounting evidence that subatomic binding energy may be a function of the Golden Ratio.  The curious observation of the denominators in the internal nuclear length part of the equation involves 1, 5, and 2 raises eyebrows.  The equation for Phi is: