Chapter 4. Modified Gravitation.   

We shall now look at how one body of matter modifies the K flux of its surroundings, regardless of what other matter there may be in the neighbourhood. And we shall raise the question whether gravity is proportional to the amount of matter.

We now look at how one body of matter modifies the K flux of its surroundings, regardless of what other matter there may be in the neighbourhood. Looking at the working mechanism in our model, it is evident that when a background flux of Ks hits a body of regular matter, the same K cannot be transformed to a K neutrino twice. As the regular Ks penetrate deeper into matter, more and more Ks will fall victim to K transformation.

Hence we need to look at the survival rate of regular Ks. (See Fig 7). There are a number of Ks available to be transformed which can be represented by the initial K flux multiplied by a negative exponential function, because more and more of the K flux consists of K neutrinos. Therefore, extremely large masses must take into account a reduction factor to correct for a certain amount of already transformed Ks.

  Fig. 7. M  represents a large body of regular matter. The universal background flux of regular Ks (black arrows) hits matter from all direction, but here shown as if they move only from left to right. White arrows represent Ks which are transformed to K neutrinos. When more Ks are transformed to K-neutrinos the remaining Ks will transform less frequently. 

To find the formula for the gravitational potential, let us make a thought experiment. Suppose Ks were to interact with EPs without any gravitational transformation to K neutrinos. Then Ks would scatter in all directions, and it seems evident that there would be an equally strong K flux at the centre of the sphere M as at M’s surface. If so, Ks must interact a number of times which is proportional to the amount of matter.

Since we suppose that the transformation of regular Ks to K neutrinos happens in a fixed fraction of the total number of interactions, we see that K transformation will be proportional to the K flux at any given point inside the sphere M. And the reduction factor in the gravitational constant should then be

G’ = G · e^–aM 

Hence we have that the formula for the gravitational potential must be of the form

U = - G · M · e^–aM / r

Where G is the gravitational constant for smaller masses and “a” is a very minute number, and e^–aM ≈ 1 for most practical purposes, probably even for masses the size of our Earth.

As the regular Ks in Fig. 7 interact with matter time and time again, some fall victim to K transformation, and become K neutrinos. Note that as the flux of regular Ks diminishes due to K transformation, the flux of regular Ks must travel further before another K is transformed to a K neutrino. This is the survival principle, much like the half-life of radioactive decay in matter.

Consequence 8:

The Gravitational Potential, U, is given by the formula:

U = - G · M · e^–aM / r

Where “a” is a very small number, and M is the mass of a body of matter.

Asymmetrical forces of gravity.

The forces that act upon “m” from “M” can be described by the following modified version of Newton’s law:  

F ₁ = G · M ·m · e^–aM / r2

• G = the specific K transformation probability (amplitudes²) of gravitational matter. 
• G · M · e^–aM ~ the deficiency in the flux of regular Ks created by K transformation in the larger mass. 
• m ~ the total target (interaction probability) of the EPs in the smaller mass. 
• 1/r² ~ the space angle factor reducing the effect of the missing regular Ks after transformation to K⁰. 

While the forces that act upon “M” from “m” can be described by

F ₂ = G · M ·m · e^–am / r² 

• G = the specific K transformation probability (amplitudes²) of gravitational matter. 
• G · m · e^–am ~ the deficiency in the flux of regular Ks created by K transformation in the smaller mass. 
• M ~ the total target (interaction probability) of the EPs in the larger mass. 
• 1/r² ~ the space angle factor reducing the effect of the missing regular Ks after transformation to K⁰. 

Since e^–aM ≠ e^–am   the implication is that:

F ₁ ≠ F₂ 

as a general rule for all bodies of matter theoretically, but only noticeable for larger bodies.

It could be that this will effect the orbits of planets, so it should be checked against anomalies in planet orbits. A large planet will typically have more inertia relative to the gravitational field it generates compared to a smaller planet.

For many F₁ ≠ F₂ may seem as the ultimate proof that our equation for the gravitational potential must be false. However, one should note that:

F₁ ≠ F₂ does not mean that a force is not equal to its counterforce, but that F₁ and F₂ does not represent all the forces in play. Only when the whole universe is taken into consideration will the forces in both directions balance out.

So in this respect, Newton is doing fine. 

If the K flux diminishes inside massive bodies, this will also have certain implications for the matter residing inside large bodies. In later chapters, the strong force is shown to be proportional to the K flux, according to our model. Hence a decline in K flux may render less strong force. This may in turn lead to less stable atoms inside large bodies.

The conclusion that there is no attractive gravitational field, only a modification of the universal K-flux, changes the view of how interaction at the elementary particle level with Ks takes place. It seems that in these interactions, the momentum must be conserved at the level of K interaction, while energy is not conserved at the level of the EP. To balance energy, the whole universe must be counted. In the next chapters we shall explore the exact nature of the interaction between Ks and elementary particles (EPs).

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