[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 mf is a mass in relation with F and Pf 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.
