[Series #5] How a massless photon gets massive?

This post is continued from the last series #4 to explain more the mechanism how a point like massless particle get massive within the gravitational field conceptually. Again I am neither a mathematician nor a physicist so proving something with precise mathematic equations is beyond my capability. Instead I will try to provide some conceptual ideas such that ordinary people like me can grasp and understand it. Additionally in the end I will propose an experimental way to verify whether my view is correct or wrong. In this series, I will focus to explain the mechanism conceptually on how a massless particle such as a photon moves though the space filled with a rotational force element.

As the string theory suggests that the most fundamental building blocks are all vibrating strings, similarly I assume every subatomic particle should be an oscillating point-like particle whose trajectory in the 11 dimensional space is something like a strange attractor which do not intersect itself such that it looks like an open ended string within a bounded area. My assumption is a possible scenario because there are many examples in various areas as studied in Chaos theory.

My story begins with the conceptual visualization of the internal structure of a massless particle with velocity C such as a photon as can be seen in the Figure 1(a). Basically in my view, a photon is assumed to be in a bounded volume in 3d space such that the probability to find the particle P within the bounded area is 1. Within the bounded area, a point-like particle P is orbiting its trajectory in the 11 dimensional space exactly governed by the rule shown in the series #2 and it means that it is a deterministic system. As a real photon has a definite frequency, the assumed photon-like particle in my model also is assumed to have a sort of frequency. This periodicity sounding crazy to readers will be explained later in detail and for now I will skip it. I believe that the periodicity of light can be understood fully only when considering both time and space simultaneously as Einstein did in the SR.

Figure 1. A conceptual visualization. The mechanism on how the gravitational field changes the movement direction of a massless particle. In (a), a massless particle B moves at constant speed C along x direction. For simplicity it is assumed to have a frequency 10 per a unit time T. In (b), B enters in the region where F is influential enough to attract nearby massive objects to its center like a whirlpool. P which is influenced by F is orbiting the modified route with a less frequency 9 while staying around F at a rate of 1. Here P gets non-zero stickiness or inertial mass.

So under the current scenario my photon is initially assumed to have a frequency 10 per a unit time T in empty space as in Figure 1-(a) and it means that the point-like particle P orbits 10 times around each steady convections per a unit time T. Here the meaning of the unit time T will not be clear to readers but it means the infinity is the unit time and this crazy mind blowing idea will be discussed in other post.

In the figure 1, the photon moves with light speed C from left to right and no mass if it has no interaction with the rotational force element F. If it enters the region in where there exist interactions with the rotational force element F, then it gets massive and its moving direction is curved as in the Figure 1-(b). To sum up, in my model, a massless photon gets massive and bent within the gravitational force field. Let me describe more what happens to a massless particle moving at the speed of light in the gravitational force field.

Again due to my lack of mathematics, it is hard to formulate the exact equation describing correct movement of the photon. Instead I will focus on the concept what a photon will behave. If someone gives me a hint or lesson about the necessary math to precisely calculate values, we can help each other to make some outputs which will be almost impossible solely.

In the region where influenced by F, P travels the modified orbit with a frequency less than one in the Figure 1-(a). It is assumed that P is attracted to F and orbit around F at a rate 1/T and 9/T around each convection points. It means P needs to spend 1/T circulating around F and 9/T orbiting around each convection point. From the view point of two convections, the frequency of P is decreased.

What is important here is that P gets stickier near F in the right of Figure 1. Let us assume the bounded area is a solid body which can be pushed or pulled and trying to move it downward. If we compare the energies needed to move P downward for both cases, then we notice those will be different and the energy used in moving the body downward in the right of figure 1 will be higher than the one in the left. If the power of F is so strong, i.e. a black hole, then P will be attracted to F and will orbit around F all times so that the probability to find P around F would be 1. If P is captured by a black hole and unable to escape out of the event horizon of the black hole, then the mass of the black hole will increase by the photon energy divided by C².

To understand what stickiness or inertial mass means, let us compare two cases. One case is a massless photon moving with light speed and other case is a photon caught by a black hole. The former has the bounded area like in the Figure 1-(a) and the latter is the case that the bounded area of the photon will be the event horizon of black hole. At a time instance t0, lets assume the center of the bounded area is located at a point X0. In the former, the energy needed to move the center of the bounded area out of the point X0 to any direction is guessed to be zero because there is no stickiness at X0. On the other hand, in the latter case, a different story begins. To move the photon bounded within the event horizon of the black hole out of the event horizon some amount of energy is needed and it means the photon has a sort of stickiness or inertial mass. These two cases represent two extreme states; a massless particle with light speed and a massive particle with zero speed. Then what will happen in the intermediate course? I believe it would be natural to think that there is no sudden change in state such as mass, frequency.

I believe if the total energy of the photon must be conserved, the inertial mass can be calculated by the following equation:

$$E=hf_0=hf_1+m_1c^2$$

$$m_1=\frac{h\left(f_0-f_1\right)}{c^2}$$

To verify my model, I would like to propose an experiment as in the Figure 2.

Figure 2. The relation of mass and frequency of a photon. A massive photon bent within the gravitational force field.

I searched many sites to find the relation between mass and frequency of a photon but failed to find the one matched with my view. Anyway, based on my view, I argue that the frequency f2 of a photon at P2 will be higher than f1 at position P1. 

$$f_0>f_2>f_1$$

[Added 2015-08-29]

In my view, the concept of the stickiness or initial mass is closely related with the probability to find a particle within a bounded volume in space as I introduced in the previous post. I guess that it could be a ball shaped volume with a diameter of the plank distance.

If P is interacting with F so that it is forced to orbit around F, then the massless P gets massive. If the rate that P spend orbiting around F is increased, the probability to find P within the unit volume V where F centers is also increase.  So the mass of a photon could be rewritten as probability to find P within the volume V multiplied by photon energy E over c^2 if P is interacting with only a single rotational force element F. It should be noted that in some cases the bounded area of a photon pass through the the unit volume V of F with no interaction with F. In such case, there is no stickiness with F in V so no inertial mass. Even in such cases, if we can make the probability as the function of the interaction with F, then below equation would make sense.

$$m_f=P_f\frac{E}{c^2}$$

,where m_f is a mass in relation with F and P_f is the probability to find it within V in relation with F

If the bounded area of a photon interact with multiple rotational force elements, then the total mass of the particle would be integral of all force interactions.  

[Added 2015-08-29]

Additionally, to support my view, let me describe one more. I believe that the two slit experiment is actually showing the gravitational movement of a particle instead of wave like behavior. We all know that the light is bent near the sun due to the gravitational force. If two suns are located close at a short distance so that a photon pass through the narrow slit between two suns, what do we need to expect from the photon? Will it show the movement of a particle or wave? I think the photon must show a consistent behavior regardless of the scale difference. If it is confirmed that a photon is bent under the influence of gravitational force field, then we can accept that it need to be bent near at the slit wall because the wall also has a mass and the photon can pass at a very short distance from the wall. 

In Newton's law, force is proportional to mass and inverse square of distance. So even though the mass of the wall in ordinary two slit experiment is very small compared to the sun mass, very short distance will compensate the effect of the reduced mass. So in very short distance from the wall, photon will show the very same behavior with the space time curvature in the solar system scale or even larger. I will discuss this more in a separate post later.

[Series #4] What creates mass?

This post contains my personal view on the mechanism on the creation of mass. In my previous posts, I briefly mentioned that three rotational forces Fr,Fg,Fb acting on every location in our 3 dimensional space is the cause to get a massless packet of energy gaining or losing mass. For a particle, the sum of magnitude of active interactions with these three rotation forces is guessed to be proportional to the mass of it. I think this idea is the key to understand the mechanism about what makes mass and what is the gravity working well even in the subatomic scale world. For those who may feel difficult to accept this idea, it is right time to remind us all of Isaac Newton’s original view on inertia.

Classical view on Mass

Inertia is understood as the tendency of an object to resist a change in its state of motion. If an object stays at rest, it has the tendency to keep that position. To make some change in its rest state even if it has non-zero constant velocity, external force should act on it and so energy does. Simply to say, if we want to change the fate of an object into different direction against the path  which is destined to follow initially, with the assumption that we can predict its future motion using well established Newton’s law or whatever suitable, then we need to use some amount of energy. From this point of view, the mass of an object can be measured indirectly by measuring the energy consumed to make the change of the object as Einstein explained in his paper, “Does the inertia of a body depend upon its energy-content?”. The quote taken from it below shows it clearly and could be helpful to accept my idea briefly mentioned above.

“The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 10²⁰, the energy being measured in ergs, and the mass in grammes.” By A. Einstein

My personal view on Mass

The original expression of Energy-Mass relation used in Einstein’s 1905 paper may be written as the equation, “m=L/c²” provides a great insight about the true nature of Mass.

Firgure 1. Higgs mechanism? A mechanism about how a massless oscillating particle moving along x direction with speed of Light c can gain and lose mass depending upon the existence of interactions with the three rotational forces in the space.

To know what mass is and how mass can be measured, consider a scenario that a massless oscillating particle is moving from left to right along x direction with velocity of light c at x=x0 as depicted in Figure 1. At region 1, left side in Figure 1, it is assumed that there is no force at all for a particle to interact with so that the particle moving along x axis will show the translational symmetry which means the invariance of particle’s status such as velocity, periodicity and so on. It will soon move into the region 2 (centered in Fig.1) of which locations are filled with fluctuating forces due to the heavy mass at x=x2. These fluctuating forces which are believed to be created due to the Dark energy residing at the same position in space play key role in putting mass to the particle passing through.

It should be noted that the basic feature of matter is that we can find its location. If a ball is floating around in the ocean and happens to get close to strong swirl pulling anything nearby, it is easy to predict we would see the ball at the center of the swirl. If the ball is moving fast and the pulling energy of swirl is not enough to catch the moving ball, then the ball can escape out of the swirling area.

In my view, there are some sort of swirling forces in region 2 which are trying to hold any particle passing through. If the swirling forces acting on a bounded area is so strong enough to hold nearby particle, that means that there is high probability to find the particle at the position in the statistical point of view. This can lead to the following conclusion that if we want to move the particle to different location opposing the swirling forces sticking the particle to the same location of forces, some amount of energy is required. The necessary amount of energy to pull out the particle can be used to calculate the mass of particle. In this period, the particle is slow down a little bit due to the holding effect so its velocity v1 is less than light speed c.

If the particle is able to move into the region 3, it will lose its mass gained in the region 2 and restore its original masses state and the velocity of Light c.

It is almost impossible to measure the exact mass of a particle at a certain instance since the fluctuating forces are not distributed uniformly over the space and vary over time so the mass itself may vary upon its locations. Instead, it will be our best to get the average of mass over a period. So it will be very important to know what property or state of a particle system is time invariant because the time invariant properties such as energy can be only measured and verified over and over again.

Gravitational force

Newton stated that the force of gravity between two objects is attracting each other and works instantaneously at a distance. In Newton’s universal law of Gravitation, the strength of the force is proportional to the inverse square of distance r between two objects.

$$F=G\left(\frac{Mm}{r^2}\right)$$

In my view, the difference in the strength of swirling forces acting on two points can reason the gravitational forces.

Figure 2. An illustrative image to show how gravitational force work at a distance. The data used here is not correct and this picture is prepared to show the gradual decrements of gravitational force as distance is getting bigger. Blue curve is the sum of the swirling forces power and orange curve is the 2 power of blue curve which is guessed to be the probability to find the particle at distance r.

As shown in figure 2 which is prepared to show just a premature idea, the probability curve in orange color is continuously changing across distance and the gradual difference of the probability curve is guessed to be the cause for gravitational force. I chose this probability curve as a proper candidate to the correct answer with intention to understand the weirdness in dual slit experiment showing the diffraction pattern of particles.

[Added 2015-07-21]

Regarding Figure 2, the true meaning of the blue curve is the strength sum of all rotational forces only interacting with all objects involved in gravitational force. In fact, the strength varies over time because

the "mass" property of a moving particle in the force field full of fluctuating rotational forces is varying too. To get the data in Figure 2 which is time invariant, we need to depend on the statistical analysis which will help us to get such time invariant data. This issue will be discussed further when dealing with the periodicity of "strange attractor" later.

[/Added 2015-07-21]

Here comes my understanding how matters are attracted to each other within the force field. Let's assume that a particle with mass m is placed at distance r=r1 and a heavy mass M at r=0. As shown in Figure 2, the possibility to find a particle tend to increase as distance r is smaller. One additional assumption is that the minimum distance between two neighbor points should be Plank distance. Strong swirling forces at r=0 means there is high probability to find a matter at that point so in my view, the existence of the rotational force ( here I use swirling and rotational both as same) enable the creation of mass.

The probability difference between two neighbor position reasons the attracting force which fits with Newton's law - force proportional to the inverse square of r. This idea helps us to safely ignore the concept of "Spooky action at a distance".

Why gravitational force is the weakest one among all 4 forces?

As can be seen in Figure 2, the probability curve is not always increasing as distance r is getting shorter. Intervals where probability decrease as r goes to zero coexist with the intervals where probability is increasing and this is an interesting property of gravitational force. The existence of decreasing probability intervals makes it weaker than other 3 forces. 

To be continued ...

Reference

[1] DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT? By A. Einstein. 1905.

[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.

 http://kevino.tistory.com/entry/Series-2-A-introduction-of-a-Mother-function-governing-all-particle%E2%80%99s-movements

For smooth continuation of discussion, let me restate of the mother function which is introduced in previous post here again:

, 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.

[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.

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.