Chapter 7. The Retention Time.    

We have postulated that Ks give energy to elementary particles (EPs), and shall make a fair assumption about the K interaction frequency with EPs. If we can find the time Ks are kept inside an EP – the retention time of Ks in EPs – then we also have the energy of the Ks.

The law of conservation of a particle’s momentum as a vector requires that Ks have a certain retention time inside the particle. At absorption a K is accelerated to the speed of the particle, and the K will later be emitted with a backward component to give back the momentum it has borrowed from the particle during retention. In a homogenous K flux this ensures conservation of momentum, and this constitutes the mechanism for the conservation of momentum.

Let us revisit the formula for the photon’s energy:

E = hf = mc² 

We suppose that the frequency, f, is correlated to the number of K interactions. Can fermions have a different retention time for Ks than photons? Annihilation of particles and photons producing electron-positron pairs indicate that there must be the same basic mechanism at work. 

To comply with gravity being proportional to mass, we must have the same retention time. If you change the rate of gravitational interaction, you change the rate of net momentum transfer from a given deficiency in the K flux. When gravity is proportional to the energy of the elementary particle, the frequency of interaction must be the same for fermions and bosons, and f is proportional to the energy of the elementary particle.  

If the energy of an EP is proportional to the frequency of K interaction, then we may assume that the retention time of Ks in a fermion is exactly the same as in a photon, and the number of Ks retained simultaneously per unit energy must be the same for both types of elementary particles.

Now we have argued that a fermion at rest also exchanges all its energy at the same rate as a photon. Then we have the same formula regarding K interactions as for a photon:

f₀= m₀c²/h,

And for a fermion in motion, with γ being the Lorentz factor

f = mc²/h = γ m₀c²/h

If the last formula is true, then the frequency of K interaction must increase proportional to the mass, and hence the frequency must increase proportional to γm₀ as the speed increases.

For  2f = f_K we have shown that the frequency of K interaction for the most common fermions is:  

E = hf = mc² = hf_K/2  

f_K (proton) = 2m_proton·c²/h = 4,5·10²³/s ≈ f_K(neutron)

f_K (electron) = 2m_electron·c²/h = 2,5·10²⁰/s

What is the energy and mass of an average K particle?

Let N_K be the number of Ks retained simultaneously in an EP, and let t_R be the retention time for the Ks, then the total energy of the fermion would be N_K·m_K·c², and

N_K = f_K· t_R = 2f · t_R  

E_fermion = hf_fermion = m_fermionc² =N_K·m_K·c ² = f_K· t_R·m_K·c² 

= f_K· t_R·E_K= hf_K(fermion) /2

t_R·m_K = h/2c² = 3,7 ·10^-51 kg·s

t_R ·E_K = h/2

Where  

• N_K = the number of Ks retained simultaneously.   
• E_K = the energy of 1 K.   
• f_K(fermion) = the frequency of K interaction with the fermion.   
• t_R = the retention time of Ks in EPs.   

However, we keep the alternative open where we say that 1 K is emitted per wavelength.

Consequence 18:

The retention time, t_R, of the Ks in an elementary particle times the energy of K, E_K, equals Planck’s constant, h or h/2, depending on our model.

t_R·E_K = h/2 (or h) 

If the average retention time, t_R, for the K is 1 second, then the corresponding energy per K interaction would be E = h·1/s = 6,63·10-34 J and mass of K, m_K, would then be m = (h/s) / c² = 7,37·10^-51 kg. But 1 second is an arbitrarily chosen time which does not relate to the average retention time for a K, t_R. If for instance the average retention time is 10^-12 second, then the energy for a K particle would be: E = h x 10¹²/s = 6,63 x 10^-22 J for an average K particle. Hence we do not know the energy of K, E_K, because we don’t know the retention time tR. We might have to get approximate values for E_K (m_K) by statistical methods on fairly well known quantum mechanical events, like tunnelling. 

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