[Series #2] A introduction of a Mother function governing all particle’s movements



CAUTION: This series is introducing my a lot of unproved ideas so many mistakes or just ridiculous story you can found. Although I think my view or descriptions correct, I do not guarantee anything written here until precise proofs are ready.

 

This post is continued from my previous article here. Here I will begin with introducing a framework which will explain many weird things happening at subatomic scale level. Initially I will provide a big picture and using that I will try to explain each detail one by one.

 

There is a single mother function Ω which is defined in 11 dimensional vector space and the Ω is the only one rule which determine every bit of time evolution of every state of any subatomic particle in our universe.

Ω( x,y,z,Fx, Fy, Fz, Fr, Fg, Fb,t, R)

Where x, y, z are three Cartesian position vector,

Where Fx, Fy, Fz are three directional forces defined in the position p=(x,y,z),

where Fr, Fg, Fb are three rotational forces along axis x,y,z, defined in the position p=(x,y,z),

Where t is time,

Where R is a scalar value.

 

So let’s assume that the following equation is only one correct root function governing whole future of any subatomic particle from now. It means that for a dynamical system, every state at any instance time t>0 are fully determined completely at t0 using the assumed mother function Ω.

 

Ω( x,y,z,Fx, Fy, Fz, Fr, Fg, Fb,t) = R    ---------- (1)

 

In fact, I assume that Ωshould have a form of several coupled ordinary differential equations similar to the Lorenz equations, a system of deterministic ordinary nonlinear differential equations introduced by Edward N. Lorenz.  [1].

Given the mother function Ω, the trajectory of the dynamical system governed by the equation (1) can be categorized into one of three types. And these types can be interchangeable by varying several parameters such as energy absorption/emission.

 

First type is singularity. The trajectory of the singularity type tends to evolve into a single point defined in the vector space.

Second type is simple periodic system. The trajectory of this second type shows a closed loop or repeated. Quasiperiodic orbits also belong in this type.

These two systems of singularity and simple periodic are related to R of same number category, rational number.

On the other hand, the third type is known as a system with non-periodicity and its trajectory as a strange attractor so far. But my observation is that this third type system seems to be actually a periodic system with irrational numbered period which need to be investigated further. This observation will be discussed more in another article which will follow soon.

 

 

Singularity type

Periodic type

Chaotic type

R

Rational number

Rational number

Irrational number

Periodicity

No period

Rational numbered Period

Looks like non-periodic initially but it has a irrational numbered period. *

Table 1. Symmetry. The relations between the trajectory type and R.

*: The details of the irrational numbered period will be provided in other separate article.

 

The figure 1 is an illustrative example of the force field in space to help readers to feel what I feel too. In every point P, there are 6 forces associated. 3 forces(Fx,Fy,Fz) mean the directional forces and other 3 forces(Fr,Fg,Fb) mean the rotational forces. If we accept the conventional knowledge from the Quantum mechanics, then the minimum distance between two different points in this space would be Plank constant length.

 

Furthermore I have an intuition that what add mass to a massless particle would be some interactions with 3 rotational forces Fr,Fg,Fb.  If a particle moving through this space S have some sort of interaction with one or all of these 3 rotational forces, then it seems to me that the interactions produce a holding effect to it at the position so is the reason why a massless particle gain mass out of the force field. If the particle can have more energy to overcome the holding effect at that position, then it will continue to move further escaping from the region where force affect around the point. This is just my imagination. The 6 forces can be thought as the combinational result of gravity, electromagnetic and strong/weak forces.

 



Figure 1. An illustrative example of the force field filled with 6 forces: Fx,Fy,Fz,Fr,Fg,Fb.

 

To help readers to understand what features the mother function Ω have, instead of using the correct equation form which makes difficult to visualize movements in high dimensional space above 3 dimensional space, it will be much convenient to use the famous Lorenz equations [1] which is believed to have same characteristics with the mother function Ωsuch as sensitivity to the initial condition, etc.

 

Features of the Lorenz equations

The famous Lorenz system is expressed as 3 coupled non-linear differential equations.


 , where σ, r, b are constant parameters.


Regarding equation (2), 3 things can be distinguished.

1.       The equation itself

2.       Initial values of state at t=t0. X0, Y0, Z0.

3.       Parametric coefficients such as σ, r, b. I will call a set of all coefficients as “parameter configuration” for later use.



This system has several characteristics.

1.       Depending on the “parameter configuration”, the system can show one of three different behaviors: Singularity, periodic, and chaotic. If there is a sudden change in the configuration, then there is possibility for trajectory to show a kind of quantum jump to whole different level depending on the amount of changes in the configuration.

2.       In case of chaotic configuration only, the system shows sensitivity to initial values of state. Small changes in the initial values of state can result quite different future of system state.

3.       The trajectory in the state space is bounded. This characteristic is similar to the orbital movement of an electron within a bounded area in atom.

4.       The overall shape (butterfly like) of the trajectory is invariant to the changes in the initial value of state X, Y, Z.

 

The characteristic 1 can be used to explain how an electron can do a quantum jump upon energy absorption or emission.

 

In the next article, I will discuss more about a kind of periodicity of the Lorenz equations which is believed to be found in the mother function Ω.

 

References

[1] Deterministic Non-periodic Flow. Edward N. Lorenz.


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