## The photon and the constant of Planck mathematically

**When you are interested in physics you must read “Unbelievable“!**

A photon, with enough energy, can transform, split up into a positron and an electron. The assumption that a photon can be described as two charges in oscillation seems acceptable. The Coulomb-force between the two charges is:

If we try to calculate the energy of the oscillation with *F* we have to solve a few problems first. Unknown are the size of the charges *Q**f*, the distance *R**f* at the beginning of the oscillation and at what distance *F* becomes inactive (so the singularity is avoided).

We assume the maximum distance between the two charges *R**f* is ¼* **λ**.* The force is then:

This is the total force between both charges. When +*Q**f* moves *R* to –*Q**f*, then –*Q**f* also moves *R* to +*Q**f*. The force while both particles moved *R* will be:

When we integrate *F* to a distance *R=0* a singularity arises. Both the force and energy become infinite. This problem was not solvable before. Now we have an indication for the distance to which *F* is active: the radius of the neutron *Rn* or the radius of the proton *Rp*.

The diameter, the distance between +*Q**f* and –*Q**f* when *F=*0, when both charges penetrate the point-volume, is twice the radius of the point-volume and therefore approx. twice the calculated radius (*2Rn*) of the neutron or proton. The energy of the oscillation *Wψ* will be:

The last formula demonstrates that the arbitrary distance *Rf=1/4*λ , the maximum distance between the two opposite charges, is of no influence for the energy Wψ of the oscillation because 8Rn<<λ. The oscillation energy will be:

The only unknown factor is *Qf*. We assume that *Qf=Qe/n *where n is an arbitrary number:

The charge *Q**f* is replaced *Qe/n*. The unknown factor is now *n*. The most straightforward assumption is that , because the radius of the electron with charge –*Qe* is *Re* and the wavelength λ has to be proportional with . Substitution gives:

Like electron, proton and neutron the photon has two degrees of freedom to store energy: oscillation and movement. So the total energy of the photon *W**f* will be equal to *2Wψ**.*

while the energy of the photon is:

*W**f **= hν*

with *H* the derived constant and *h* the constant of Planck. The deviation between *h* and *H* is 6%, so the relation is not exact, but fair enough when one considers the radius of the neutron is playing a crucial part. The coincidence that the constant of Planck will derived within a 6% accuracy, when the ether is no more than a wild fantasy, is very unlikely. There are many possible causes to explain the difference, like:

- The mathematical constant
*π*and the natural logarithm*e*have to arise somewhere. Maybe they arise in the point-volume? - The electric field of the with speed
*c*moving charges of the photon is forced in a two dimensional circle. Is the three dimensional equation for the electrostatic attraction still completely valid? - Can the point-volume be transformed in some way when it becomes a neutron?

The picture the ether showed us so far is that the point-volume is not rigid.

We assume that the constant of Planck (*h*) determines the radius of the point-volume rather than the calculated, and probably deformed, radius of the proton or neutron.

When we use the above derived formula and replace *H* with the experimental derived value for Planck’s constant *h* we can calculate *Rplanck*; the radius of the point-volume according to the experimental value of *h*:

The calculated radius of the point-volume; the Planck-radius (*Rplanck*), considering that

and , becomes:

**Next chapter: QM and the Ether: The Derivation of Planck’s Constant**