Introduction

The Gravitational Interaction Force

2.Observation of the Gravitational Force

In the physics textbook, there is a description of the early discovery of electric charge and the attractive and repulsive forces between two charges [1]. As early as 600 BC, the ancient Greeks discovered that if amber was rubbed, it would attract light objects, such as wool. Today we know that the amber acquired net electric charges, or became “charged.” The net charges on the amber would attract the wool.

When you rub a plastic rod with fur and a glass rod with silk, both become “charged” and can attract other light objects. If you perform experiments by rubbing a plastic rod with fur and a glass rod with silk, you will find the plastic rod can be attracted by the glass rod. However, two plastic rods rubbed with fur or two glass rods rubbed with silk repel each other. Today we know there are two kinds of electric charges: negative and positive, produced by rubbing a plastic rod with fur and a glass rod with silk, respectively. The rubbed fur and silk also become “charged”. When the signs of the charges on two rods are the same, they repel each other. When the signs on two rods are opposite, they attract each other. The rubbed plastic rod and silk become negatively charged, while the rubbed glass rod and fur become positively charged.

When wool is attracted by “charged” amber, you need to consider this: the wool is not rubbed with any material and has not acquired any net charge. It is neither negatively nor positively charged. An “uncharged” object should be electrically neutral and, in theory, should not be attracted to or repelled by a “charged” object, regardless of whether the charge is negative or positive. So why does the “charged” amber attract the “uncharged” wool?

Here, the generation and influence of induced electric charges are involved. In an object, there are free electric charges that can move easily from one region to another. If an external electric field exerts force on an object, the free charges will move, changing the distribution of total charges. This change affects the electric fields in and out of the object, as the electric field generated by the charges within the object can exert force externally. Thus, the regional distribution of electric charges and the spatial distribution of the electric field influence each other, and the equilibrium of charge and field distributions is determined by both.

Free electric charges in an object arise because some atoms have weaker attractions to their electrons, allowing them to escape more easily. Additionally, many objects contain polar molecules. These molecules have equal amounts of positive and negative charges but an uneven distribution, forming an electric dipole. The dipole moment direction of a polar molecule may change with the external electric field. Furthermore, non-polar molecules can become polarized under an external field, with positive and negative charge centers shifting from concentric to non-concentric status. Similarly, electrically neutral atoms can undergo atomic polarization, altering their positive and negative charge centers shifting from concentric to non-concentric status too.

The movements of free charges, changes in dipole moment directions of polar molecules, and emergences of polarized non-polar molecules and atoms form induced electric charges. These induced charges alter the distribution of electric charges and the spatial distribution of electric fields inside and outside the object. The amount of induced electric charges depends on the number of molecules and atoms within the object; generally, the greater the mass of the object, the more induced electric charges it has.

Under an external electric field, the change in the distribution of free and induced charges is the key reason why "charged" amber can attract "uncharged" wool. Whether an object is electrically neutral or has net positive or negative charges, the external electric field will change the charge distribution within that object.

Suppose that the "charged" amber is close to the "uncharged" wool. If the amber has net positive charges, it will exert a positive electric field on the wool, attracting the free negative charges in the wool to the amber side, keeping them close. Since the amounts of positive and negative charges in the electrically neutral wool are equal due to conservation of electric charge, the amount of net negative charges increased in the region close to the amber will equal the amount of net positive charges increased in the region farther from the amber. Because the net negative charges are closer to the amber than the net positive charges, the amber's attractive force on the net negative charges is slightly greater than its repulsive force on the net positive charges. Thus, the net force exerted by the amber on the wool is attractive. This net force is much smaller than the real attractive or repulsive force of the amber on the wool, but it is enough to pick up a light object such as the wool as shown in Figure 1.

At the same time, the polar molecules and polarized non-polar molecules and atoms in the wool will produce two kinds of induced net charges. Under the positive electric field of the amber, the center of all induced net negative charges will be closer to the amber, and the center of all induced net positive charges will be farther from the amber. The location difference between the two charge centers will make the amber's attractive force slightly larger than its repulsive force on the wool, which helps to pick up the wool.

The produced attractive force between the amber and wool is a synthetic electric interaction force produced by a huge number of electric charges in both the amber and wool. Though the wool is small, it may contain a huge number of molecules and atoms, and thus a huge number of electric charges.

If the amber is replaced by a negatively "charged" plastic rod, the plastic rod can also pick up the "uncharged" wool. In this case, the plastic rod will exert a negative electric field on the wool. The negative field will attract net free positive charges close to the rod and push net free negative charges far from the rod. Because the amounts of the two kinds of net free charges in their respective regions in the wool are equal, but the region distances from the rod are different, the net force of the plastic rod on the wool will be a small attraction force, sufficient to pick up the light wool. The two kinds of induced net electric charges in the wool will produce a similar small attractive force between the plastic rod and the wool, helping to pick up the wool too. Thus, whether an object has net positive charges or net negative charges, the "uncharged" wool will always be attracted by the "charged" object.

The author answered why a small "uncharged" piece of paper can be attracted by a "charged" object in an electromagnetism examination at the university with such a detailed explanation when young but did not think further at that time, and was unaware that understanding such a phenomenon approached realizing the origin of the gravitational force.

2.Calculation of the Gravitational Force

As described above, the gravitational force is generated by non-uniform distribution of electric charges in an object. The non-uniform distribution of charges may be very complicated, which makes the analysis and calculation of the resulting electric fields difficult. To simplify this analysis and calculation, the concept of the "mass center" used in mechanics is employed.

Every object is composed of many small regions, and each region experiences a gravitational force. If all the gravitational forces exerted on these small regions are synthesized into a single gravitational force, then the point where this synthetic gravitational force is exerted at is the "mass center" of the object. Similarly, two net "charge centers" can be defined to describe the distribution of net electric charges in an object.

In an object, regardless of the complexity of the distributions of the net positive and net negative charges, all electric forces generated by the net positive charges can be synthesized into a synthetic net positive electric force. The point at which this synthetic net positive electric force is exerted on another object is the net positive "charge center" of that object. In the same way, the net negative "charge center" of the object is defined.

With this simplification, any object with non-uniform charge distribution can be regarded as having a net "positive charge center" and a net "negative charge center." All net positive charges in the object are considered concentrated at its "positive charge center," and all net negative charges are considered concentrated at its "negative charge center." As emphasized above, because these two charge centers are almost impossibly at the same point exactly, nearly any object with non-uniform charge distribution can be regarded as an electric dipole, as shown in Figure 2.

The theoretical electric dipole is a pair of two point electric charges with equal magnitude and opposite signs (a positive charge $q$ and a negative charge $–q$). A small distance $\mathit{l}$ is between two point charges. The electric dipole moment $\overrightarrow{\mathit{p}}$ is the product of the distance $\mathit{l}$ and the charge $q$.

$$\overrightarrow{\mathit{p}}=q\overrightarrow{\mathit{l}}.$$

(2)

Where $\overrightarrow{\mathit{P}}$ and $\overrightarrow{\mathit{l}}$ are vectors. The direction of the electric dipole moment $\overrightarrow{\mathit{P}}$ is from the negative point charge to the positive point charge.

When an object with a non-uniform charge distribution is regarded as an electric dipole, $q$ is the absolute value of the total net positive charges or the total net negative charges in the object. Additionally, in the object, the distance between the net “positive charge center” and the net “negative charge center” may not be small. However, if the size of the object is much smaller than the scale related to the considered problem, such as considering the attraction between a planet and a star in the universe, the size and shape of the object are less important. Thus, the distance between the net positive and net negative “charge centers” in an object may be treated as small, so the object with a non-uniform charge distribution may reasonably be regarded as an electric dipole.

The electrical field strength $\overrightarrow{\mathit{E}}$of the electric dipole at the distance of R is [2]

$$\overrightarrow{\mathit{E}}={\displaystyle \frac{1}{4\pi {ϵ}_0{R}^3}}[3\left(\overrightarrow{\mathit{P}}·\overrightarrow{\mathit{R}}\right)\overrightarrow{\mathit{R}}-\overrightarrow{\mathit{P}}]$$

(3)

In Eq. (3), $\overrightarrow{\mathit{R}}$ is unit distance vector along R direction. From Eq. (3), we know that when the direction of the vector $\overrightarrow{\mathit{R}}$ changes, the electric field strength $\overrightarrow{\mathit{E}}$ changes too. When the direction of $\overrightarrow{\mathit{P}}$ is the same as or opposite to the direction of $\overrightarrow{\mathit{R}}$, the electric field strength $\overrightarrow{\mathit{E}}$ becomes $E_S$ or $E_O$,

$$E_S={\displaystyle \frac{2P}{4\pi {\epsilon }_0{R}^3}}$$

(4)

$$E_O={\displaystyle \frac{-2P}{4\pi {\epsilon }_0{R}^3}}$$

(5)

The $E_S$ in Eq. (4) is positive, which expresses a repulsive force away from the dipole to a positive point charge. The $E_O$ in Eq. (5) is negative, which expresses an attractive force towards the dipole to a positive point charge. And when the direction of the dipole moment is perpendicular to the direction of $\overrightarrow{\mathit{R}}$, the electric field strength $\overrightarrow{\mathit{E}}$ becomes $E_P$.

$$E_P={\displaystyle \frac{-P}{4\pi {\epsilon }_0{R}^3}},$$

(6)

the $E_P$ in Eq. (6) is negative. Please note that $E_P$ is a deflective force.

Then, a puzzle arises: if the electric field strength of an object with a non-uniform electric charge distribution is not isotropic, why haven't we observed obvious changes in the gravitational force with the relative direction between two attractive objects? For example, many planets orbit stars in circular paths in the universe.

The reason is that, although the electric field of an electric dipole may exert repulsive, attractive, or deflective forces on another electric dipole, in most cases, the repulsive and deflective forces will ultimately change to an attractive force. This occurs because, when the interaction force between two electric dipoles is repulsive, both electric dipoles are in states of highest electric potential energy. Such states are unstable. Any change in the electric charge distribution in one of the two objects will produce a deflective force between these two electric dipoles. This deflective force will rotate the two electric dipoles.

Supposing there are two objects, that is, two electric dipoles. The first electric dipole moment is ${\overrightarrow{\mathit{P}}}_1$, and the second electric dipole moment is ${\overrightarrow{\mathit{P}}}_2$. Two electric dipoles will produce a rotating torque $\overrightarrow{\mathit{\tau }}$ to each other [3]

$$\overrightarrow{\mathit{\tau }}={\displaystyle \frac{-1}{4\pi {\epsilon }_0{R}^3}}[3\left({\overrightarrow{\mathit{P}}}_1\bullet \overrightarrow{\mathit{R}}\right)\left({\overrightarrow{\mathit{P}}}_2\bullet \overrightarrow{\mathit{R}}\right)-{\overrightarrow{\mathit{P}}}_1\bullet {\overrightarrow{\mathit{P}}}_2].$$

(7)

In Eq. (7), R is connecting distance between two electric dipole centers, and $\overrightarrow{\mathit{R}}$ is unit distance vector of R. Because of the rotating torque, two electric dipoles rotate until the two dipole moments have the same directions. When two electric dipoles have the same directions, the rotating torque $\overrightarrow{\mathit{\tau }}$ has its minimum value ${\tau }_{MIN}$

$${\tau }_{MIN}={\displaystyle \frac{-2{P_{1}P}_2}{4\pi {\epsilon }_0{R}^3}}.$$

(8)

Please note that, ${\tau }_{MIN}$ becomes a pure attractive force between two electric dipoles.

Of course, in some cases, the gravitational force between two attractive objects still changes with their relative direction, which is one of the reasons that some planet orbits around the stars are elliptic.

Below, the interaction forces between two electric dipoles are calculated further. First, supposing the directions of two electric dipole moments are the same as shown in Figure In Figure 3, the first electric dipole moment ${\overrightarrow{\mathit{P}}}_1$ consists of positive pinot charge $q_{1+}$ and negative point charge $q_{1-}$. The second electric dipole moment ${\overrightarrow{\mathit{P}}}_2$ consists of positive pinot charge $q_{2+}$ and negative point charge $q_{2-}$. The distance between the positive and negative point charges of the first dipole moment ${\overrightarrow{\mathit{P}}}_1$ is $r_1$. The distance between the positive and negative point charges of the second dipole moment ${\overrightarrow{\mathit{P}}}_2$ is $r_2$. The distance between the centers of two electric dipoles is R.

From Eq. (3), the first electric dipole will produce the electrical field ${\overrightarrow{\mathit{E}}}_1$ at the distance R from its center

$${\overrightarrow{\mathit{E}}}_1={\displaystyle \frac{1}{4\pi {\epsilon }_0{R}^3}}\left[3\left({\overrightarrow{\mathit{P}}}_1\bullet \overrightarrow{\mathit{R}}\right)\overrightarrow{\mathit{R}}-{\overrightarrow{\mathit{P}}}_1\right],$$

(9)

In Eq. (9), $\overrightarrow{\mathit{R}}$ is unit distance vector along R direction. In the electrical field ${\overrightarrow{\mathit{E}}}_1$, the positive point charge $q_{2+}$ of the second electric dipole will feel a force ${\overrightarrow{\mathit{F}}}_{\mathit{q}2+}$ as

$${\overrightarrow{\mathit{F}}}_{\mathit{q}2+}=q_{2+}{\overrightarrow{\mathit{E}}}_1={\displaystyle \frac{2q_{2+}{\overrightarrow{\mathit{P}}}_1}{4\pi {\epsilon }_0{(R-0.5r_2)}^3}}$$

(10)

the direction of force ${\overrightarrow{\mathit{F}}}_{\mathit{q}2+}$ is along the direction of $\overrightarrow{\mathit{R}}$. The negative point charge $q_{2-}$ of the second electric dipole will feel a force ${\overrightarrow{\mathit{F}}}_{\mathit{q}2-}$ as

$${\overrightarrow{\mathit{F}}}_{\mathit{q}2-}=q_{2-}{\overrightarrow{\mathit{E}}}_1={\displaystyle \frac{2q_{2-}{\overrightarrow{\mathit{P}}}_1}{4\pi {\epsilon }_0{(R+0.5r_2)}^3}}.$$

(11)

The direction of force ${\overrightarrow{\mathit{F}}}_{\mathit{q}2-}$ is also along the direction of $\overrightarrow{\mathit{R}}$. Because the absolute values of $q_{1+}$ and $q_{1-}$ are equal, and the absolute values of $q_{2+}$ and $q_{2-}$ are also equal, when $R\gg r_1$ and ${R\gg r}_2$, the total force felt by the second electric dipole in the electric field ${\overrightarrow{\mathit{E}}}_1$ is ${\overrightarrow{\mathit{F}}}_{\mathit{T}}$ approximately

$${{\overrightarrow{\mathit{F}}}_{\mathit{T}}=\overrightarrow{\mathit{F}}}_{\mathit{q}2+}+{\overrightarrow{\mathit{F}}}_{\mathit{q}2-}\doteq {\displaystyle \frac{{6r}_1{r}_2}{R^2}}{\displaystyle \frac{1}{4\pi {\epsilon }_0}}{\displaystyle \frac{{q_{1}q}_2}{R^2}}\overrightarrow{\mathit{R}},$$

(12)

where $\overrightarrow{\mathit{R}}$ is unit distance vector along R direction.

In Eq. (12), if ${\displaystyle \frac{{6r}_1{r}_2{q}_1}{R^2}}$ is replaced by $m_1$, ${\displaystyle \frac{{6r}_1{r}_2{q}_2}{R^2}}$ is replaced by $m_2$，and ${\displaystyle \frac{1}{4\pi {\epsilon }_0}}$ is replaced by gravitational constant G, then Eq. (12) becomes Newton’s gravitational law

$${\overrightarrow{\mathit{F}}}_{\mathit{G}}=G{\displaystyle \frac{{m_{1}m}_2}{R^2}}\overrightarrow{\mathit{R}}.$$

(13)

We can see that the physical essence of the mysterious mass is just the electric charges. In other words, the mass is another expression of the amount of the electric charges.

In fact, the electromagnetic theory, and especially the modern electromagnetic theory developed over more than two hundred years since Coulomb, has strongly hinted that the gravitational force is the electric force. Compare the famous Newton's law of gravitational force $F_G$:

$$F_G=G{\displaystyle \frac{m_1{m}_2}{R^2}},$$

(14)

and the famous Coulomb’s law of the electric force $F_E$:

$$F_E=K{\displaystyle \frac{q_1{q}_2}{R^2}}.$$

(15)

We can see that their expressions are very similar. Eq. (14) expresses the attractive gravitational force generated by two point-like objects with masses of $m_1$ and $m_2$. Eq. (15) expresses the attractive electric force generated by two point electric charges of $q_1$ and $q_2$. G and K are proportionality constants whose numerical values depend on the system of units used. R is the distance between two mass centers or two charge centers. If two masses in Eq. (14) are replaced by two charges in Eq. (15) without considering the difference of the dimensions of two constants G and K, then Eq. (14) becomes Eq. (15). Because $m_1$ and $m_2$ are mass, and $q_1$ and $q_2$ are electric charges, the dimensions of the constants G and K are different naturally. Considering that the gravitational force is generated by a huge number of electric charges, and that the most of the electric forces produced by the electric charges with opposite signs have been cancelled, the values of the constants G and K have large difference naturally.

The striking similarity between Eq. (14) and Eq. (15) strongly hints that the gravitational force is the electric force. If the natures of two physical forces are different, their expressions should be significantly different. Where else can we find such similarity between the expressions of two different physical forces?

Another hint indicating that the gravitational force is the electric force is that the gravitational wave propagation speed equals to electromagnetic wave propagation speed. Since the gravitational force is the electric force, the gravitational wave propagation speed is equal to the electromagnetic wave propagation speed naturally.

Eq. (12) expresses the interaction force between two electric dipoles when two dipoles have the same directions. This interaction electric force is just the gravitational force between two objects. According to Eq. (12), the gravitational force has the following properties:

First, since the gravitational force is produced by electric charges$q_1$ and $q_2$, the gravitational field is the electric field.

Second, the gravitational force strength depends on the force direction, meaning that the gravitational force is anisotropic.

Third, replacing ${\displaystyle \frac{{6r}_1{r}_2{q}_1}{R^2}}$ with $m_1$ and replacing ${\displaystyle \frac{{6r}_1{r}_2{q}_2}{R^2}}$ with $m_2$, because in most cases, $R\gg r_1$ and $R\gg r_2$, so the magnitudes of $m_1$ and $m_2$ are much smaller than the magnitudes of $q_1$ and $q_2$. This is why, although the gravitational force is electric force, the strength of the gravitational force is much smaller than the strength of the electric force.

Fourth, the values of $r_1$, $r_2$, $q_1$ and $q_2$ in Eq. (12) are not fixed because they are determined by electric charge distributions in two objects. Since variations of charge distributions in two objects can change the values of $r_1$, $r_2$, $q_1$ and $q_2$, the gravitational force between two objects is not fixed even their so-called masses don’t change.

These characteristics make the gravitational force exhibit strange and mysterious behaviors, causing confusing phenomena observed in the universe. Some of these phenomena have puzzled humans for a long time. However, by using new understandings of the gravitational force, these confusing phenomena can be explained simply and effectively. On the other hand, these phenomena may be regarded as indirect evidences of the correctness of the introduced understanding.

Even though the difference between Eq. (12) and Newton’s law is not significant for applications on the Earth, this discrepancy has still caused inaccuracies in advanced engineering calculations, such as for spacecraft flight. Furthermore, Newton’s laws have been unable to explain some astronomical observations.

Below, the forces between two electric dipoles with different moment directions are analyzed. As shown in Figure 4, the case where the directions of two electric dipoles are perpendicular to each other is considered. In Figure 4, the first electric dipole moment ${\overrightarrow{\mathit{P}}}_1$ consists of positive and negative point charges $q_{1+}$ and $q_{1-}$, and the second electric dipole moment ${\overrightarrow{\mathit{P}}}_2$ consists of positive and negative point charge $q_{2+}$ and $q_{2-}$. The distances between the positive point charge $q_{2+}$ and the positive and negative point charges $q_{1+}$ and $q_{1-}$ are $R^{\text{'}}$. The distances between the negative point charge $q_{2-}$ and the positive and negative point charges $q_{1+}$ and $q_{1-}$ are $R^{\text{'}}+r^{\text{'}}$ approximately.

The positive point charge $q_{1+}$ and negative point charge $q_{1-}$ produce repulsive force $\overrightarrow{a}$and attractive force $\overrightarrow{b}$ to the positive point charge $q_{2+}$. The synthesized force of $\overrightarrow{a}$and $\overrightarrow{b}$ is $\overrightarrow{c}$. The positive point charge $q_{1+}$ and negative point charge $q_{1-}$ produce attractive force $\overrightarrow{a^{\text{'}}}$ and repulsive force $\overrightarrow{b^{\text{'}}}$ to the negative point charge $q_{2-}$. The synthesized force of $\overrightarrow{a^{\text{'}}}$ and $\overrightarrow{b^{\text{'}}}$ is $\overrightarrow{c^{\text{'}}}$. Note that $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$, $\overrightarrow{a^{\text{'}}}$, $\overrightarrow{b^{\text{'}}}$ and $\overrightarrow{c^{\text{'}}}$ all are vectors. The components along the x-axis of two synthesized forces $\overrightarrow{c}$ and $\overrightarrow{c^{\text{'}}}$ are $x_{+}$ and $x_{-}$, and the components along the y-axis of two synthesized forces $\overrightarrow{c}$ and $\overrightarrow{c^{\text{'}}}$ are $y_{+}$ and $y_{-}$. Since two components $y_{+}$ and $y_{-}$ have equal magnitudes with opposite directions, they are cancelled. Two components $x_{+}$ and $x_{-}$ are added to each other since they have equal magnitudes and same directions. Therefore, the electric field of the first electric dipole ${\overrightarrow{\mathit{P}}}_1$ exerts a net deflective force on the second electric dipole ${\overrightarrow{\mathit{P}}}_2$. Under this deflective force, the electric dipole ${\overrightarrow{\mathit{P}}}_1$ and electric dipole ${\overrightarrow{\mathit{P}}}_2$ will rotate to have the same directions.

The directions of two interacting electric dipoles cannot remain perpendicular to each other for long. As long as an electric dipole is affected by a deflective force, its dipole moment direction will rotate. The rotation of the electric dipole does not require the rotation of the actual physical body. It only requires changes in the distribution of the net electric charges, including free and induced charges in the object. Such changes occur very quickly and are not visible. Therefore, when considering only the gravitational force between two objects, because the directions of two electric dipoles are almost always the same, the gravitational force between the two objects can be expressed only by Eq. (12).

When three objects interact with each other, the free and induced charges in each object are redistributed in response to the electric fields generated by the other two objects. If each object is simplified as an electric dipole, each object will interact with two external electric dipoles. Thus, the redistribution of the free and induced charges in each object may be regarded as forming two electric dipoles. Each of these electric dipoles in one object responds to an external electric dipole in another object, making the problem an analysis of the interactions among six electric dipoles. When more objects interact, the gravitational force analysis becomes more complex. However, the redistribution of electric charges in each object may still be regarded as forming multiple electric dipoles in principle, with each electric dipole responding to an external electric dipole in another object.

Nature of the Magnetic Force

Origin of the Strong Interaction Force

4.Possible Structure of the Nucleus

It is known that any nuclear reaction, whether it is nuclear fission or nuclear fusion, will produce an extremely strong gamma-ray burst. The gamma-ray consists of high-energy photons. These phenomena strongly suggest that a lot of high-energy photons are stored in the nucleus.

The author should emphasize that the gamma-ray burst is not transferred from the mass of the nucleus. The abstract concept of "mass-energy transfer" is not true, although many people are familiar with it and believe it. Here, we must clarify that mass is mass, and energy is energy; they are different things and cannot change into each other. In familiar natural phenomena, such as the burning of an object or the fission and fusion of nuclei, the substance, that is, the mass, does not disappear, although the mass becomes light including x-ray, visible light, infrared light, microwaves, and so on. This is because light are photons and the photons even with extremely low frequencies are still the substances.

In the following, we will explain that the photon is the real substance. In other words, before burning, fission, or fusion, the photons are bound together as a bulky substance with easily detectable weight and electromagnetic field. After burning, fission, or fusion, the photons are separated individually as light without easily detectable weight and electromagnetic field. However, the photons still exist there as the substance. The concept of the mass-energy transfer is completely wrong. Light is the substance, not the energy, or light is the substance with energy, not the pure energy.

Thus, the gamma-ray burst is just the release of real substance from the nuclei directly, because every nucleus inherently consists of a lot of photons.

Another piece of evidence proving that the photons are the most basic building blocks of any substance is that almost all black holes in the universe emit extremely strong gamma-rays. This means that under the most ultimate conditions, including extremely high pressures and temperatures, any substance will be broken into its basic units, that is, the photons.

Any substance consists of atoms, and every atom consists of protons, neutrons, and electrons. Therefore, it is a reasonable deduction that the neutron consists of multiple photons, and the proton consists of multiple photons but lacks an electron, which leaves the proton and still stays in the atom.

The author has inferred that the photon is an extremely tiny electric dipole consisting of an electron and a positron pair. This inference is based on the following well-known observed phenomena: The photon appearing after electron-positron annihilation; The photon splitting into an electron and positron in high-energy collisions. More explanations of this inference are provided in the paper titled “Origin of the Light” [10].

As an electric dipole, even though it is extremely tiny, the net electric field of the photon is not zero within very close area around the photon. However, because the sizes of the electron and positron are extremely small, and the distance τ between them is very short since they are bound tightly due to their strong electric fields with opposite signs. According to Eqs. (3), (4), (5), and (6), the net electric field of the photon is only effective in the small range around the photon because the net electric field strength of the photon drops quickly with the distance $R$ at a rate of ${\displaystyle \frac{\tau }{R^3}}$. For a distant observer, the photon is almost electrically neutral, meaning there is almost no net electric field for the photon, as shown in Figure In Figure 5, the positive and negative electric fields of the positron and electron are represented by the red dotted line and the blue solid line, respectively. We can see that these two fields almost completely overlap for a distant observer, so the net field strength is almost zero for a distant observer.

But, for a nearby observer, the net electric field of the photon is not zero. In other words, every photon has its electric field within very short distance $R$ as shown in Figure In Figure 6, the positron and electron are represented by a red circle and a blue circle, respectively. We can see that if near the positron, the net field is positive, and if near the electron, the net field is negative. Thus, multiple photons can be combined together within a tiny volume in the way that the positive end of each photon attracts the negative end of its adjacent photon in series or in parallel.

The calculations of the electric field strengths of the photon are described in detail in the paper titled “Origin of Light” [10]. The calculation results show that at the site with the distance of $R=1fm$ from the photon center, the electric field strength is from $2.9⨉{10}^{16}{\displaystyle \frac{V}{m}}$ to $2.9⨉{10}^{19}{\displaystyle \frac{V}{m}}$ $({\displaystyle \frac{V}{m}}={\displaystyle \frac{Volt}{meter}})$ for photons with dipole moment lengths of $10zm$ ($1zm=1\times {10}^{-21}m$) to $10am$ ($1am=1\times {10}^{-18}m$). Please note that taking the photon dipole moment length with such a large range (from $10zm$ to $10am$) is due to the fact that the photon size cannot be estimated accurately at present. Such a large electric field can certainly bind multiple photons tightly within a small range.

However, as the distance $R$ increases, the electric field strength of the photon decreases rapidly. For example, at the site with the distance of $R=1\mu m$ from the photon center, the electric field strength drops to from $2.9⨉{10}^{-11}{\displaystyle \frac{V}{m}}$ to $2.9⨉{10}^{-8}{\displaystyle \frac{V}{m}}$ for photons with dipole moment lengths of $10zm$ to $10am$. Therefore, measuring the electric field strength of a photon is very difficult. This is why a photon is regarded as having no electric field.

These calculation results show that the author's inference of the nuclear structure is reasonable because the results are consistent with observational data. This explains why the effective interaction distance of the so-called strong force is about $1fm=1\times {10}^{-15}m$ (Please note that when multiple photons are bound together, their synthesized net electric strength has a shorter effective distance too), and why the strength of the strong force drops more quickly than expected rate of ${\displaystyle \frac{1}{R^2}}$.

The neutron and proton might consist of a photon shell or several photon shells. The photon shell consists of multiple photons in such a way that the positive end of each photon attracts the negative end of its adjacent photon in series, as shown in Figure 7.

In Figure 7, each photon is represented by an electric dipole consisting of a positron (small red circle) and an electron (small blue circle). In this section, the dipole moment directions of the photons are parallel to the shell surface. Supposing the spherical shell has a radius of $r_p$. The full structures of the proton and neutron, which describe the entire distribution of the photons in the proton and neutron, are not provided now due to the need for more nuclear information and analysis.

Since each neutron consists of multiple electric dipoles, although the sum of all electric dipole fields of the neutron is zero, in the vicinity very close to the neutron, the net electric field is not zero. For example, in the regions near the positrons, the net fields are positive, and in the regions near the electrons, the net fields are negative. Thus, binding multiple neutrons one by one in the nucleus is possible and only requires the electric force. It should be mentioned that, according to current theory, there is no explanation for how multiple neutrons are kept in the nucleus since the neutrons are electrically neutral.

Compared with the neutron, each proton just loses an electron. Because the mass of a proton is 1836.5 times the mass of an electron, there should be several hundred photons, that is, several hundred positrons and electrons in each proton. Therefore, in each proton, the sum of the positive electric fields of all positrons is only slightly larger (being over 1 in several hundreds)than the sum of the negative electric fields of all electrons. Such a small difference between the positive and negative net electric fields in each proton cannot create a force to strongly repel another nearby proton. The net positive electric force of each proton in the nucleus can only make the nucleus unstable when the number of the protons is large, which helps to cause emissions of radioactive decay rays.

Furthermore, in a similar way as the neutron, because in the vicinity very close to the proton, the net electric field is not zero, the multiple protons can be bound with or without the neutrons in the nucleus. Therefore, the forces binding multiple protons with or without the neutrons in the nucleus can be only electric forces. It is not required to introduce the idea of a special strong interaction force for binding the multiple protons in the nucleus.

Due to unavoidable thermal vibrations, the photons in neutrons and protons continuously fluctuate around their average positions. These fluctuations, coupled with the attractive and repulsive forces received from adjacent photons, may cause the photons to rotate on their own, resulting in the photons having angular momentum and magnetic moment as well. This maybe is another reason causing photonon’s rotation (detailed explanations about photon rotational angular momentum and magnetic moment are given in the paper titled “Origin of the Light” [10]).

4.Origin of the Electron Spin Angular Momentum and Magnetic Moment

When a proton and an electron meet, they attract each other because they have electric charges with opposite signs. For some currently unknown reasons, the electron cannot combine with the proton to become a neutron. Since they are close enough, the electron, having a much smaller mass than the proton, is usually bound to the proton and stays close to it. Thus, one proton and one electron compose the simplest atom, with an atomic number of 1.

When such an atom is formed, the charge center of the electron does not coincide with the charge center of the proton. Therefore, the negative electric field of the electron cannot cancel the net positive field of the proton uniformly and completely. This results in a non-uniform distribution of the synthetic electric field in the vicinity of the proton, i.e., near the nucleus.

However, for the electron and proton, the effective interaction distances of their net electric fields are much larger than their physical sizes (the proton diameter is about $1\times {10}^{-15}m$, and the diameter of the electron is smaller further). Thus, even if the charge centers of the electron and proton don’t coincide with each other, since the distance between charge centers of the electron and proton is small (the atom diameter is about $1\times {10}^{-10}m)$, for a distant observer, the negative electric field of the electron can still almost completely cancel the net positive electric field of the proton. Therefore, the distant synthetic electric field strength of the atom is almost zero, and such an atom can be considered electrically neutral.

In the proton, the electric charge cannot be stored within a point-like volume. Furthermore, the positive electric field distribution of the proton is non-uniform. For example, the proton has a magnetic moment, which means that the proton's electric field distribution has a centrally symmetric axis. Thus, the electron may stay in a small area near the proton where the proton's net positive electric field is relatively high, and so the electron doesn’t rotate around the proton. Of course, the electron cannot remain still in that small area and cling to the proton. The inevitable thermal motion will make the electron move restlessly in that small area and keep a small distance from the proton.

For an atom consisting of a proton and an electron (hydrogen), its distant electric field strength is zero. But the electric field distribution in or near the atom is non-uniform. If close to the electron, the net electric field is negative, and if close to the nucleus (proton), the net electric field is positive. It is very important that the electron can stay near the nucleus and doesn’t need to rotate rapidly around it. Thus, some confusions can be eliminated:

Since the electron doesn’t rotate around the nucleus, no continuous electromagnetic radiation is emitted from the atom.

The electron is close to the nucleus and the electron's electric field is around the nucleus, because the effective length of the electron’s electric field is much larger than the nucleus size, the electron seems to exist at any position around the nucleus at any time. Thus, the seemingly strange behaviors of the electron, such as its exact position, don’t require using wave functions and probabilities to describe. Here, it should be emphasized that in many cases, the detected thing is the electric field of the electron, not the electron (core) itself.

As described above, when a proton meets another proton, including the proton attached to an electron, because the electric field distribution on each proton's surface is not uniform since each proton consists of multiple photons, the surface region of one proton with a net positive electric field will attract the surface region of another proton with a net negative electric field. In this way, two protons may bind each other with or without neutrons to compose a nucleus of two protons. Such a nucleus will bind two external electrons to form an atom with an atomic number of 2.

Because the net electric forces between the nucleus and the two external electrons are attractive, two external electrons are drawn as close to the nucleus as possible. Meanwhile, since two external electrons repel each other due to their negative charges, they attempt to push apart. As a result, the electrons are positioned on opposite sides of the nucleus at a suitable distance where the attractive and repulsive forces are balanced as shown in Figure 8.

In Figure 8, the electric charge centers of two external electrons are located on the x-axis with a distance of Ʌ. The diameter of the nucleus is η. The centers of the spherical electric fields of two electrons are not concentric, so the distribution of the combined negative electric field of the two electrons is ellipsoidal (drawn by solid line in Figure 8), with a central symmetric axis along the x-axis. Although this field distribution is ellipsoidal, it can approximately cover the spherical field distribution of the nucleus (drawn by dot-dash line in Figure 8). The two electrons outside the nucleus form an electron shell.

The two electrons located on both sides of the nucleus, with a short distance between them, cause a very important result. Each electron will exert a strongly repulsive force on the other electron, and the direction of this repulsive force will continuously change with the fluctuations of the two electrons. During these complex movements, an equivalent tangential repulsive force will be generated on both electrons, causing them to rotate on their own quickly. Thus, the two electrons rotate fast and in opposite directions. This is the physical origin of the electrons' rotational angular momentum and magnetic moment. The rotation directions of the two electrons are opposite, so their angular momenta and magnetic moments have opposite signs. The electron angular momentum and magnetic moment are extremely important. They are fundamental sources for creating the rotational angular momenta and magnetic moments of protons, neutrons, and atoms.

The structures of atomic electron shells with more electrons are not discussed further. Here, the author indicates some properties of the atomic electron shells as follows:

Each electron in the shell stays within a certain area close to the nucleus with unavoidable thermal vibrations but does not rotate around the nucleus.

In each shell, mutual electrical repulsive forces with unavoidable thermal vibrations generate equivalent tangential forces exerting on all electrons, which make all electrons rotate on their own and thus have spin angular momenta and magnetic moments with different values.

In a fully occupied shell, the repulsive forces between every two adjacent electrons should be as equal as possible.

The synthetic electric field generated by all electrons in the fully occupied shell should be symmetrical around a central axis because the nuclear net positive electric field is symmetrical around a central axis due to the net magnetic moment of the nucleus.

With increase of electrons in each shell, the synthetic net electrical field distribution of the electrons in each shell gradually becomes closer to a sphere.

Origin of the Weak Interaction Force

Conclusions

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