[Series #3] Energy-Mass relation and black hole
Purpose
I am not proving something here but trying to present a concrete framework and explanations helping readers to understand much intuitively about many weird things found in quantum mechanics such as Wave-Particle duality, measurement problem, and probability density.
This post contains my basic ideas about Energy and Mass relations which are missing in my previous post.
For smooth continuation of discussion, let me restate of the mother function which is introduced in previous post here again:
$$Ω(x,y,z,f_x,f_y,f_z,f_r,f_g,f_b,t)=R$$ |
(1) |
, where R is a dimensionless scalar value.
My fundamental assumption, described in my previous post, is that the dynamical system of every subatomic particle S can be defined as very much like to equation (1). The equation form is assumed to be a set of equations which are several coupled ordinary differential equations similar to the Lorenz equations so it is believed to show very same features which Lorenz equations can show such as deterministic behavior, sensitivity to initial conditions and etcetera.
Due to the lack of knowledge in the true nature, I do not know the exact equations for (1) yet but I believe that the similar behaviors discovered in study of the dynamical system showing strange attractor such as Lorenz attractor can be found too in the dynamical system of every subatomic particle. So I will focus my discussion to ensure people to see the close resemblances in behaviors found in between two different dynamical systems and hope everyone understand many weirdness in Quantum mechanics easily and intuitively with the help of knowledge in Chaos theory.
If we look at the stable trajectory in state space for a dynamical system S, S can be distinguished as one among three types: attractor of singularity, periodic and chaotic. The trajectory of each type will evolve over time and getting close into the fixed position, periodic orbit and strange attractor respectively if there is no change in the equations in the course of evolvement.
With regard to the dynamical system which can be converted into one showing strange attractor, below shows some features what I like to note especially, which are all described in the previous Chaos theory:
1. The trajectory is bounded within finite volume in the state space. It is obvious that not only singularity and periodic attractors are bounded but also strange attractor.
2. The center of bounded area is at one of critical points, normally at origin.
3. The trajectory in form of strange attractor does not repeat itself so it seems to be non-periodic. In fact, it can be thought as a very long string with no intersection in the state space.
4. Sensitivity to the initial condition. The nearby initial conditions in the state space diverge quickly so that predicting the future flow of the other trajectory starting at nearby point impossible.
5. But the trajectories starting at nearby points are getting close to the same overall shape as time flows. For example of Lorenz equation, both trajectories eventually form a so called “butterfly” shape.
6. Upon changes of environment or different configuration (refer to my previous post), the trajectory can be interchangeable between three different types of attractor. For example of Lorenz equations, it is known that the trajectory can have a certain behavior on the r dependence of the attractor. [1]
Fig 1. Various attractor types of Lorenz equation on dependence of r
As can be seen in figure 1, there are 3 types of attractors on dependence of r in the Lorenz equations. In (a) and (b), the trajectory starting at initial point(x0, y0, z0) is attracted to a single position. In (c), two different trajectories starting at different initial points (5, 1, 1) and (-5, 1, 1) occupy almost same region in the state space. It should be noted that each trajectory is actually something like an open ended string and the bounded areas of two which looks like butterfly shape are exact same one. The figure 1-(d) shows a periodic orbit.
Additionally, to fit every weird thing together in consistent manner, my intuition, mostly affected by string theory and chaos theory forces I to make few assumptions as like:
1. From the famous Einstein equation E=MC2, energy and mass can be interchangeable. That being said, a subatomic particle which is a basic building block of everything is assumed initially to be a massless lump of Energy E=hν ( Plank’s equation).
2. In my view, even if a particle is in state of strange attractor (refer Fig 1-c) so its trajectory looks like non-periodic orbits, it is assumed to have a definite frequency. The more details for this will be provided in separate post.
3. For a subatomic particle, the more interactions with the rotational forces within the nearby force field, the much heavier it gets. It means that some partial energy out of total energy turns into mass form. To meet the requirement for energy conservation, the following relation is necessary. Refer to Fig 2:
$$E=hν_1=hν_2+m_1v^2$$ (2)
4. If a particle get mass, then it is slowed down a little bit so its velocity is less than light velocity constant c.
5. If the particle move fairly enough far away out of the field filled with rotational forces and almost no interaction with the rotational forces, then it will restore its massless state with initial frequency ν1.
6. The dynamical system of a subatomic particle can be into a state with singularity attractor which can be seen in Fig 1-(a), (b) under environmental changes.
7. It is also possible that huge number of particle located in a bounded area in space can be resonated to have almost same singularity attractor type with a very same critical equilibrium point. It can be intuitively understood by looking at spin alignment in magnetic fields, although there is no clear evidence that they share a same mechanism. If they put together at a stable equilibrium point in space and grow more and heavier, it is possible for the crowded point like massive thing to become a black hole.
With the assumption above, I will try to explain counterintuitive everything which people are desperate to figure out so that they fit together in consistent way under given the single framework.
Black hole
Figure 2 shows my conceptual view on how
energy of a particle is conserved. All size of rectangle area in different
colors means total energy and is equal. In my view, with hint in Fig 1-a, it
may happen for a subatomic particle to be in a state having singularity
attractor and it eventually be attracted to a critical point of equation (1). For
rectangle 2 colored in orange, it is assumed to be a particle with almost
infinity mass and almost zero velocity. Because the velocity is not zero, so it
is bounded with extremely small area but not zero space.
Fig 2. A conceptual image for how energy conservation works. Rectangle 1 represents a massless particle so it has frequency ν1. Orange colored rectangle 2 means a particle with singularity attractor so it has zero frequency but its energy should be same with hν1. Rectangle 3 has wave and particle like behavior at the same time.
If huge numbers of particles get attracted to a same point and grow bigger and heavier enough to pull nearby particles, it would become a black hole. The black hole can be thought basically as a particle with extreme heavy mass and gradually growing as eating up nearby particles. If there is another growing black hole coming and each is attracted, then it can be thought as a collision of two particles. Furthermore, if the collision of two black holes is so powerful enough to break the binding forces which are the source to keep the singularity attractor of all particles forming the black hole, then it will show super ultra-version far beyond the Large Hadron Collider or even more close to the Big bang.
References
[1] C. Sparrow. The Lorenz equations: bifurcations, chaos, and strange attractors. Applied Mathematical Sciences, 41, 1982.
