1 Introduction

Photons (Solar) are the main source of energy available on Earth and provide hope of clean energy in the future [1, 2]. Optical fiber communication and photolithography have made today’s great information age [3, 4], and photons are still the most used tools for human observation of nature [5]. The human body is an energy utilization and information processing system, and photosynthesis is a key link in life activities. There is no doubt that photons will bring more human needs, and the propagation of energy by photons at the speed of light is the basis of all photon applications; therefore, a deep understanding of the characteristics of photon energy and its source, as well as photon behavior is important. Human exploration of light has never stopped and will inevitably continue [6,7,8,9,10,11].

Photons and waves are important controversial topics. The quantum theory of “wave-particle duality” is difficult to understand; it conflicts with common-sense notions derived from observations of the everyday world. Waves are a form of matter movement, and photons are matter (particles) that can travel through a vacuum. Photons behave like particles, and like waves, but are they both? Though we know what photons seem like, we want to know what they are. Therefore, understanding the fluctuations of photons in terms of particle behavior will help to enhance the understanding of photon properties. There are some important questions to consider, for example, why do photons have such a high speed? Is this the limit? Why is the speed of conduction the same as the speed of light? Where does the energy of the electromagnetic waves emitted by electrons come from? How can we understand the relationship between mass and energy?

Nearly 100% of the substances discovered so far comprise electrons and protons (neutrons are a combination of electrons and protons). Hence, there is reason to believe that they are unique and fundamental particles in the material world. There is huge potential energy between electrons and protons (the calculated value of the electron surface potential is greater than 500 kV, and that of the proton surface potential is greater than 1,700 kV) that can result in serious consequences, i.e., an electron–proton explosion, which has exhibited the maximum intensity–volume ratio known to date. This follows the law of Coulomb, Newton’s law of motion, and the law of conservation of energy.

It is empirically believed that this intense explosion will produce some smaller broken particles, which are positively or negatively charged, and have the same charge–mass ratio as the parent. Owing to the repelling effect of electricity, these particles can obtain a high speed (kinetic energy). In fact, photons are very important energy carriers. This study assumes that the particles produced by these explosions are photons, including negatively charged negative photons and positively charged positive photons. Negative photons are fragments derived from electrons that are negatively charged. Photons of different sizes have different masses and spin magnetic moments, and the charge-to-mass ratio is the same as that of electrons. Positive photons are fragments derived from protons that are positively charged. Photons of different sizes have different masses and spin magnetic moments, and the charge-to-mass ratio is the same as that of protons. Based on these assumptions, calculation of the photon speed and photon energy are discussed herein.

2 Photon Speed Calculation

The conversion between potential energy and kinetic energy is a common phenomenon. A negative photon leaves the surface of an electron, which is a process of converting potential energy into kinetic energy. Assuming that negative photons are projected from the surface of the electron to the area where the potential is zero, the speed of the negative photons can be calculated according to the conservation of energy.

The potential energy of a system of charges, which is the total work required to assemble the system [12], is given by \({U}_{\mathrm{ext}}\) (40.1). The photon is a tiny part of the charge system, and the assembly of photons and the projection of photons are two reciprocal processes. The kinetic energy \({m}_{\mathrm{o}}{{c}_{-}}^{2}/2\) of the photon obtained by projection is equal to the potential energy required to assemble the photon, and can be calculated using (40.2). \({c}_{-}\) is the speed at which negative photons leave the surface of the electron to the zero-potential zone (equivalent to in vacuum), \({q}_{\mathrm{o}}\) is the photon charge, \({m}_{\mathrm{o}}\) is the photon mass, \(e\) is the electron charge, \({m}_{\mathrm{e}}\) is the electron mass, \({r}_{\mathrm{e}}\) is the electron radius, and \({q}_{\mathrm{o}}/{m}_{\mathrm{o}}=e/{m}_{\mathrm{e}}\).

$${U}_{\mathrm{ext}}=\frac{{\varepsilon }_{0}}{2}\int\limits_{R}^{\infty }{\left(\frac{Q}{4\pi {\varepsilon }_{0}{r}^{2}}\right)}^{2}4\pi {r}^{2}\text{d}r=\frac{{Q}^{2}}{8\pi {\varepsilon }_{0}}\int\limits_{R}^{\infty }\frac{\text{d}r}{{r}^{2}}=\frac{{Q}^{2}}{8\pi {\varepsilon }_{0}R}.$$
(40.1)
$$\frac{1}{2}{m}_{\mathrm{o}}{{c}_{-}}^{2}=\frac{e{q}_{\mathrm{o}}}{8\pi {\varepsilon }_{0}{r}_{\mathrm{e}}}$$
(40.2)

In another photon velocity calculation method, the electric potential on the surface of the electron is \({U}_{\mathrm{e}}=e/4\pi {\varepsilon }_{0}{r}_{\mathrm{e}}\) [12], and the internal force performs the same work on the photon and the electron as the photon leaves the electron. The photon and the electron each gain half of the potential energy \({U}_{\mathrm{e}}{q}_{\mathrm{o}}/2\), and the negative photon velocity calculation result is the same as (40.2); thus, the following is obtained (40.3).

$${c}_{-}={\left(\frac{e{q}_{\mathrm{o}}}{4\uppi {\upvarepsilon }_{0}{r}_{\mathrm{e}}{m}_{\mathrm{o}}}\right)}^{1/2}= {\left(\frac{ee}{4\uppi {\varepsilon }_{0}{r}_{\mathrm{e}}{m}_{\mathrm{e}}}\right)}^{1/2}.$$
(40.3)

Therefore, the fragmentation of charged particles produces new photons with a certain mass \({m}_{\mathrm{o}}\) (speed of light \({c}\)), which increases the kinetic energy of the particle system \({\Delta E}_{\mathrm{k}}\), \({\Delta E}_{\mathrm{k}}={m}_{\mathrm{o}}{c}^{2}\). This is an understanding of the relationship between mass and energy. Nuclear energy can be understood as part of the potential energy of the particles converted into kinetic energy and released. The photoelectric effect is another case in which the kinetic energy of photons is converted into potential energy.

2.1 Negative Photon Velocity

Substituting \(e\) and \({m}_{\mathrm{e}}\) [13], respectively, then \({c}_{-}=2.99792457973037\mathrm{E}+8\). Substituting \(e/{m}_{\mathrm{e}}\) [13] into (40.3) as a whole, then \({c}_{-}=2.99792458025253\mathrm{E}+8\).

According to the CODATA recommended values of the fundamental constants of physics and chemistry based on the 2014 adjustment [13], the relative standard uncertainty values of \(e\), \({m}_{\mathrm{e}}\), and \(e/{m}_{\mathrm{e}}\) are 6.1E−9, 1.2E−8, and 6.2E−9, respectively. The speed of the negative photon was chosen as \({c}_{-}=2.99792458025253\mathrm{E}+8\), and the relative error was 8.42E−11, compared with the constant of light speed \({c}=2.99792458\mathrm{E}+8\). Thus, the calculated negative photon speed has a very good accuracy.

2.2 Positive Photon Velocity

The principle of a positive photon obtaining speed \({c}_{+}\) is the same as that of negative photons, (40.4), except that the radius of a proton \({r}_{\mathrm{p}}\) is smaller, the mass of a proton \({m}_{\mathrm{p}}\) is larger, and the charge-to-mass ratio is much smaller, taking \({r}_{\mathrm{p}}=8.33\mathrm{E}-16\) [14].

$${c}_{+}={\left(\frac{ee}{4\pi {\varepsilon }_{0}{r}_{\mathrm{p}}{m}_{\mathrm{p}}}\right)}^{1/2}.$$
(40.4)

Substituting \(e\) and \({m}_{\mathrm{p}}\) into (40.4), respectively, then \({c}_{+}=1.286796\mathrm{E}+7\). Substituting \(e/{m}_{\mathrm{p}}\) into (40.4) as a whole, then \({c}_{+}=1.286796\mathrm{E}+7\), and \({c}_{-}/{c}_{+} \approx 23.\)

It can be seen that the calculated speed of the positive photons is significantly smaller than the light speed constant \(c\). Because existing knowledge does not consider photon charging, the speed of positive photons has not been verified, but X-rays exhibit certain properties of positive photons.

The calculation of the speed of photons shows that the speed of light is a normal phenomenon of the strong interaction of charged particles and is the result of the conversion of potential energy into kinetic energy. The calculation model of light speed is not perfect, but it shows that it is possible for photons to achieve such a huge speed. The speed of light particles is related to the electric potential field and can be larger or smaller, but remains fixed in the region where the potential is zero. At this time, the negative photon speed is equal to the light speed constant \(c\), and there is a huge difference between the positive photon velocity and the light velocity constant.

As a charged particle, photons should theoretically participate in the macroscopic conduction process, and responding to changes in the electric field is an inherent property of photons. They silently contribute to the conduction of current, but have not been found, which is consistent with the conduction velocity constant. The photon itself has energy and transfers energy at the speed of light, and hence functions as an energy propagation medium.

Electromagnetic waves also have a speed of light and can propagate in a vacuum. Their electrical properties are remarkable and exhibit all the properties of light. It is reasonable to consider electromagnetic waves as a group of smaller negative photons. Because the photon volume, mass, electricity, and magnetic moment are very small, they have not been detected by current measurement methods.

2.3 Compton Effect and Derivation of the Compton Shift

X-ray refraction exhibits positive photon properties (see Sect. 40.3.2 for detailed analysis), so understanding the Compton effect regarding the interaction between positive photons and atoms has certain significance. The Compton effect is the action of X-rays (positive photons) in the electron gravitational field and the nuclear repulsion field. The scattered light can be divided into two parts: One is the scattering (including reflection) of positive photons by the nucleus, with a wavelength shift; the other part is that positive photons escape after accelerating in the gravitational field of electrons, and there is no wavelength shift.

The scattering of positive photons by the nucleus has the same physical mechanism as that of common light reflection. The kinetic energy of the photon enables it to approach the center of the repulsive field very close, so the repulsive force is very large; therefore, the repulsive work is also significant. Photons in the repulsive field continue to lose kinetic energy owing to external work, resulting in a wavelength shift (decline in kinetic energy). Because of the large mass of the nucleus, and the nucleus is not a rigid body, the wavelength shift \(\Delta \lambda ={\lambda -\lambda }_{0}\) is not significantly affected by the change in the incident wavelength and atomic number, but is greatly influenced by the scattering angle. This is why the Compton shift of an X-ray seems to be independent of the target material. Positive photons escape from the gravitational field of electrons and are regarded as scattered. In fact, they are irregular refractions caused by scattered distribution electrons, and there is no wavelength shift. Compared with scattered photons, the distance between the escaped photons and the center of the gravitational field is much larger. Therefore, the gravitational work is small compared to the repulsive work, and the kinetic energy of refracted (considered as scattered) photons hardly changes.

The absorption, collision, and escape of positive photons coexist in the gravitational field of the electrons. When the atomic number increases, more outer electrons of the atom enhance absorption and refraction, reducing the probability of nuclear scattering, and the intensity of the scattering (with wavelength shift) decreases.

According to the explanation of quantum mechanics, the relation between the shift in wavelength \(\Delta \lambda\) and the scattering angle \(\theta\) is found to be [15]:

$$\Delta \lambda =\frac{h}{{m}_{\mathrm{e}}c}\left(1-\mathrm{cos}\theta \right)={\lambda }_{\mathrm{c}}\left(1-\mathrm{cos}\theta \right),$$
(40.5)

where \({m}_{\mathrm{e}}\) is electronic mass, c is the light speed constant, and \({\lambda }_{\mathrm{c}}=h/{m}_{\mathrm{e}}c\) is the Compton wavelength.

The derivation of the Compton shift is different from the perspective of positive photons. When positive photons hit the nucleus, they are scattered by repulsive fields. Consider the Compton effect as an elastic collision between a photon \(h\nu\) and an atomic nucleus \({m}_{\mathrm{p}}\), ignoring the influence of the Lorenz force and angular momentum. In the collision, the photon transfers energy and momentum to the nucleus; the scattered X-ray photon thus has a reduced energy \(h\nu ^{\prime}\) and a reduced momentum \(2h\nu ^{\prime}/c\) (\(m{c}^{2}/2=h\nu ^{\prime}\), \(c\) should be \({c}_{+}\), use \(c\) as usual) (see Fig. 40.1a).

Fig. 40.1
figure 1

Explanation of the Compton effect. The influence of Lorenz force and angular momentum is not considered. a Incident X-ray (positive photons) with energy \(E =h{\nu }\) and momentum \(p=2h{\nu }^{ }/c\) collides with a nucleus. In the collision, positive photons do work on atomic nuclei with repulsive force and lose kinetic energy. b Elastic scattering of positive photons and nuclei in the repulsive field

Full size image

Energy before and after the collision is conserved, so (40.6):

$$h\upnu -h{\nu }^{\mathrm{^{\prime}}}=\frac{1}{2}{m}_{\mathrm{p}}{{V}_{\mathrm{p}}}^{2}.$$
(40.6)

For the momentum in the y-direction before and after the collision, we have (40.7):

$$\frac{2h{\nu }^{^{\prime}}}{c}\mathrm{sin}\theta -{m}_{\mathrm{p}}{V}_{\mathrm{p}}\mathrm{sin}\phi =0.$$
(40.7)

And for the momentum in the x-direction, we have (40.8):

$$\frac{2h\nu }{c}=\frac{2h{\nu }^{\prime}}{c}\mathrm{cos}\theta +{m}_{\mathrm{p}}{V}_{\mathrm{p}}\mathrm{cos}\phi .$$
(40.8)

Substituting \({\mathrm{sin}}^{2}\phi +{\mathrm{cos}}^{2}\phi =1\), \(\nu \nu ^{\prime}=-c\Delta \nu /\Delta \lambda\), and solving (40.6), (40.7), and (40.8) simultaneously, where \(\Delta \nu =\nu -\nu ^{\prime}\) and \(\Delta \lambda ={\lambda -\lambda }_{0}\), we obtain (40.9):

$$\Delta \lambda =\frac{4hc}{{m}_{\mathrm{p}}{c}^{2}-2h\Delta \nu }\left(1-\mathrm{cos}\theta \right)\approx \frac{4h}{{m}_{\mathrm{p}}c}\left(1-\mathrm{cos}\theta \right).$$
(40.9)

This is different from formula (40.5), \({\lambda }_{\mathrm{c}}=4hc/\left({m}_{\mathrm{p}}{c}^{2}-2h\Delta \nu \right)\), and requires explanation.

\(h\Delta \nu\) is the kinetic energy loss of positive photon scattering, and its value is related to the photon mass and \(\theta\), which is the inevitable result of scattering. Figure 40.1b provides a more intuitive explanation. In the figure, the nonlinear trajectory of the photon is simplified as a straight line. When \(\theta =0^\circ\), \(h\Delta \nu =\mathrm{min}=0\), and when \(\theta =180^\circ\), \(h\Delta \nu =\mathrm{max}\), hence, it is reasonable to obtain different values of \(h\Delta \nu\) with different \(\theta\). When the photon mass changes, the same \(\theta =180^\circ\), and \(h\Delta \nu =\mathrm{max}\) will have a different magnitude, so \({\lambda }_{c}\) should not be a fixed wavelength shift. The extreme case of elastic collision is the loss of all kinetic energies, which also shows that the wavelength shift is not a fixed value.

The cause of the wavelength shift is the nucleus, which has a large mass, not an electron.

\({m}_{\mathrm{p}}{c}^{2}\gg 2h\Delta \nu\), \(\Delta \lambda \approx 4h\left(1-\mathrm{cos}\theta \right)/{m}_{\mathrm{p}}c\), and \({\lambda }_{\mathrm{c}}=4hc/({m}_{\mathrm{p}}{c}^{2}-2h\Delta \nu )\) is not a constant, but it does not change much.

The kinetic energy of photons decreases due to scattering. Therefore, the essence of the wavelength shift \(\Delta \lambda ={\lambda -\lambda }_{0}\) is the shift of light speed \(\Delta c={c}_{0}-c\), which corresponds to a reduction in photon kinetic energy \(\Delta E={E}_{0}-E\). By transforming (40.9), we can obtain the formula of light speed shift (40.10), where \(m\) is the photon mass.

$$\Delta c=\frac{2m{c}_{0}\left(1-\mathrm{cos}\theta \right)+m\Delta c\left({{c}_{0}}^{2}-{c}^{2}\right)/{{c}_{0}}^{2}}{{m}_{\mathrm{p}}+2m\left(1-\mathrm{cos}\theta \right)}\approx \frac{2m{c}_{0}}{{m}_{\mathrm{p}}}\left(1-\mathrm{cos}\theta \right)$$
(40.10)

When \(\theta =180^\circ\), \(\Delta c=4m{c}_{0}/{m}_{\mathrm{p}}\), and the incident photon of 1,000 eV can be calculated as

$$\frac{\Delta E}{{E}_{0}}=\frac{{{c}_{0}}^{2}-{c}^{2}}{{{c}_{0}}^{2}}=\frac{\Delta c}{{c}_{0}}\left(2+\frac{\Delta c}{{c}_{0}}\right)=\frac{9.29 \,\mathrm{eV}}{1000\, \mathrm{eV}}.$$

This result deviates significantly from the experimental results in [15]. In the magnetic field outside the nucleus, the Lorenz force enhances the photon scattering and reduces the photon repulsion work to the outside, resulting in a wavelength shift of less than 2.9.

The scattering mass of the nucleus is taken as \({m}_{p}\), because the repulsive force of the photon and the nucleus directly acts on the proton, and it is difficult to determine whether the entire nucleus can be regarded as a rigid body. When the scattering mass of the nucleus is \(2.32{m}_{\mathrm{p}}\), then \(\Delta E/{E}_{0}=4\mathrm{ eV}/1{,}000\,\mathrm{ eV}\). This result is consistent with the Compton experiment [15], and the value of \(2.32{m}_{\mathrm{p}}\) is reasonable to a certain extent.

When the incident photon energy is 1 meV, the calculated photon mass is greater than the proton mass, which is difficult to explain and verify.

Three points are added to the physical meaning of the Compton effect from the perspective of photon charging:

  1. (1)

    X-rays are positive photons, as they are significantly repulsed by the nucleus. High-speed positive photons with a mass close to or greater than an electron are impossible to be reflected at \(\theta =180^\circ\) by the electron;

  2. (2)

    The wavelength shift \(\Delta\uplambda\) is evidence that the photon loses kinetic energy and the photon velocity changes. The speed shift of light is the result of photons doing work externally, and the scattering angle significantly affects the speed shift of light;

  3. (3)

    \({\uplambda }_{\mathrm{c}}\) (corresponding to the speed shift of light) is approximately constant and exhibits a small change with the incident wavelength \({\uplambda }_{0}\).

Inertially confined fusion is an important physical experiment, and the role of X-rays is an important link [16]. If calculated according to the actual wavelength, the X-ray (positive photon) energy is only about 1/23 of the conventional calculation value, and X-rays cannot easily get close to the nucleus. Further, the electrons around the nucleus have an absorption effect on X-rays. These disadvantages clearly increase the difficulty of laser-driven nuclear fusion.

The abilities of positive and negative photons to pass through the Earth’s atmosphere are significantly different. The total amount of photon electricity that reaches the earth is not zero, so sunlight may be an influencing factor on the Earth’s electromagnetic environment.

2.4 Scattering and Speed Shift of Negative Photons

Negative photons also exhibit a similar repulsive field scattering (reflection). When a negative photon moves to an electron, the photon continues to work externally with a repulsive force, resulting in a shift in the speed of light. Equation (40.11) is thus obtained, where \(m\) is the mass of the photon and \({m}_{\mathrm{e}}\) is the mass of the electron.

$$\Delta c=\frac{2m{c}_{0}\left(1-\mathrm{cos}\theta \right)+m\Delta c\left({{c}_{0}}^{2}-{c}^{2}\right)/{{c}_{0}}^{2}}{{m}_{\mathrm{e}}+2m\left(1-\mathrm{cos}\theta \right)}\approx \frac{2m{c}_{0}}{{m}_{\mathrm{e}}}\left(1-\mathrm{cos}\theta \right).$$
(40.11)

Comparing the speed shifts of negative and positive photons, taking \({\lambda }_{+}=\) 0.1 nm and \({\lambda }_{-}=\) 500 nm photons as an example, the relative speed shift of negative photons is slightly smaller. Negative photons have greater speed, the electron magnetic moment is greater, and the Lorenz force is much larger than for a positive photon. The particularity of the Lorenz force is that it changes the photon momentum (direction) but does not work, and the speed drift of negative photons is small. Equation (40.11) is used only for discussion and comparison with positive photons and has no precise meaning. However, the speed drift of negative photons should exist.

The light velocity shift of negative photons can also be observed, and the magnitude of the light velocity shift is estimated from the experimental data of the beat frequency given in [17]. The two stabilized lasers \({\lambda }_{1}\) and \({\lambda }_{2}\) participate in the beat frequency, where \({\lambda }_{1}=632.991 212 57\,\mathrm{ nm}\) (6.3E−11) and \({\lambda }_{2}=632.991 354\,\mathrm{ nm}\) (approximately 1E−9); \({\lambda }_{1}\) undergoes two 90° reflections, and \({\lambda }_{2}\) undergoes three 90° reflections. Owing to the shift in the speed of light, \({\lambda }_{2}\) decreases further, resulting in an increase in the beat frequency. Taking the difference between the measured beat frequency and the calculated beat frequency between \({\lambda }_{1}\) and \({\lambda }_{2}\) as the contribution of one (3 – 2 = 1) 90° reflection to the light velocity shift, the calculated relative value of the light velocity shift is 0.0295 ppm (see Table 40.1). The extended uncertainty is less than 0.02 ppm, according to the accuracy of the interferometer. 0.0295 ppm is three orders of magnitude smaller than formula (40.11), so it is believed that the Lorenz force considerably influences the reflection of negative photons.

Table 40.1 Calculation of light velocity shift of negative photons
Full size table

3 Photon Reflection and Refraction

Under the effect of the gravitational and repulsive fields in an atom, the movement direction of the photon changes.

Matter is composed of atoms. The potential distribution inside an atom is extremely uneven, and the potential distributions on the surface and inside a substance are extremely uneven at the subatomic scale. The reason why both reflection and transmission coexist is precisely due to the uneven distribution of the electric potential of the material (subatomic scale), the area with gravitational field, and the area with repulsive field, as shown in Fig. 40.3, \({U}_{2}>0\) or \({U}_{2}<0\). Negative photons are transmitted (refracted) in the region of positive potential near the center of the atom and reflected (scattered) in the region where the negative potential is large enough around the electron.

The reflection and refraction of positive photons are different. The Compton effect occurs when the angle of incidence is zero. Electrons can cause refraction of positive photons. Because the potential field of electrons in atoms is scattered, the regular refraction pattern is not strong. The nucleus can reflect positive photons, but it is surrounded by electrons, and the reflection phenomenon is not significant.

3.1 Photon Reflection

When a negative photon enters a region of negative potential energy equal to its kinetic energy, its velocity drops to zero, and then it is emitted back by the potential energy. This is a negative photon reflection. Positive photons can be reflected by protons, involving complex atomic structures, and electrons are located on the periphery of the atoms, resulting in different reflections of positive photons.

The reflection behavior of the negative photons is the result of their interaction with electrons. Regardless of the influences of magnetic force and Lorentz force, the electric force does work and obeys the law of conservation of energy. Photons are reflected by the conversion of kinetic energy, potential energy, and kinetic energy. Figure 40.3 shows that due to the incident angle \({\theta }_{\mathrm{i}}\), the kinetic energy movement to the surface of the medium (electrons) is only a component of the total kinetic energy of the photon \({m}_{\mathrm{o}}{{c}_{-}}^{2}/2\). This component \({m}_{\mathrm{o}}{{c}_{-}}^{2}{\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}/2\) reduces to make the reflection easier, which is equivalent to the increase in the reflection cross-sectional area of electrons. The coefficient corresponding to the increase in the radius \(R\left({\theta }_{\mathrm{i}}\right)\) of the reflecting circle is \(1/{\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}\) (40.13), the coefficient of increasing the reflection area is \(1/{\mathrm{cos}}^{4}{\theta }_{\mathrm{i}}\), and the reflectivity \(r\left({\theta }_{\mathrm{i}}\right)\) has a definite relationship with the incident angle \({\theta }_{\mathrm{i}}\), which is derived as follows.

The speed of light \({c}_{-}\) in the zero-potential region is constant (40.12).

$$\frac{1}{2}{m}_{\mathrm{o}}{{c}_{-}}^{2}=\frac{e{q}_{\mathrm{o}}}{8\pi {\epsilon }_{0}{r}_{\mathrm{e}}}.$$
(40.12)

The change in the incidence angle \({\theta }_{\mathrm{i}}\) is related to the electron reflection radius \(R\left({\theta }_{\mathrm{i}}\right)\) (40.13).

$$\frac{1}{2}{m}_{\mathrm{o}}{{c}_{-}}^{2}{\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}=\frac{e{q}_{\mathrm{o}}}{8\pi {\epsilon }_{0}R\left({\theta }_{\mathrm{i}}\right)}.$$
(40.13)

The photon’s magnetic attraction and kinetic energy (corresponding to the potential-related refractive index) jointly affect the reflection. Let the magnetic influence coefficient equivalent to \({\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}\) be \({R}_{\mathrm{m}}\), \(R\left({\theta }_{\mathrm{i}}\right)\sim 1/({\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}+{R}_{\mathrm{m}})\), and \(r\left({\theta }_{\mathrm{i}}\right)\sim 1/{\left({\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}+{R}_{\mathrm{m}}\right)}^{2}\).

Substituting \(r\left(0\right)={\left({n}_{2}-{n}_{1}\right)}^{2}/{\left({n}_{2}+{n}_{1}\right)}^{2}\), we obtained:

$$r\left({\theta }_{\mathrm{i}}\right)=\frac{{\left(1+{R}_{\mathrm{m}}\right)}^{2}{\left({n}_{2}-{n}_{1}\right)}^{2}}{{\left({\mathrm{cos}}^{2}{\theta }_{\mathrm{i}}+{R}_{\mathrm{m}}\right)}^{2}{\left({n}_{2}+{n}_{1}\right)}^{2}}.$$
(40.14)

To compare with the existing physical laws, the two reflection coefficients related to the refractive index and incidence angle are given in Fig. 40.2, taking the experience value \({R}_{\mathrm{m}}=0.265\) (according to the reflectivity of 632 nm laser at the air–water interface).

Fig. 40.2
figure 2

Relationship between reflection coefficient and refractive index and incident angle

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Figure 40.2 shows that the effects of the refractive index and incident angle on the reflection coefficient are significantly different. Combined with the results of existing physical experiments, it can be considered that the reflectance of S-light is mainly affected by the incident angle and fixed refractive index, while the reflectance of P-light is affected by the incident angle and changing refractive index. When the photon in a medium of higher index of refraction approaches the other medium, the normal velocity component of the refracted photon will decelerate. As the angle of incidence increases, when the normal velocity tends to zero, the photon flies to the negative potential area, resulting in total reflection. The refracted photon is transformed into a reflected photon, and the photon trajectory has a particularity; total reflection occurs.

The reflection angle \({\theta }_{\mathrm{r}}\) is determined by the ratio of the photon velocity components in the two directions. When the photon enters the repulsive field and returns to the original potential area, regardless of the light speed shift, the velocity component amplitude in both directions remains almost unchanged. The reflection angle is equal to the incident angle (40.15).

$${\theta }_{\mathrm{r}}={\theta }_{\mathrm{i}}.$$
(40.15)

Negative photons use electrons as reflection targets, while positive photons use atomic nuclei as reflection targets. The electron and nucleus have different peripheral potential fields, motion modes, and spatial distributions. Therefore, the reflection characteristics of the positive and negative photons are different. As a reflective target, compared with electrons, atomic nuclei have smaller linear velocity and smaller position change; thus, positive photon reflection optical imaging has advantages.

3.2 Photon Refraction

When photons enter the electromagnetic gravitational field and escape, their direction of movement changes with strong consistency, that is, photon refraction. Edge diffraction also occurs due to the change of photon direction, which is clearly affected by the gravitational field, and can be regarded as a special refraction.

Refractive index convention: when a photon passes from one medium into another, if \({\theta }_{\mathrm{i}}\) is the angle of incidence of photons in vacuum and \({\theta }_{\mathrm{t}}\) is the angle of refraction, the refractive index \(n\) is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction, specifically, n = sin \({\theta }_{\mathrm{i}}\)/sin \({\theta }_{\mathrm{t}}\). The refractive index is also equal to the velocity \(v\) of a photon of a given wavelength in a substance divided by its velocity \(c\) in empty space, \(n=v/c\) (not \(n=c/v\), due to \(v>c\)), (40.16).

The forces that cause a change in the direction (momentum) of the photon include the electric and magnetic forces. After the photon enters the equipotential field before the incident, although the overall work of the electric force and magnetic force is close to zero, the flight trajectory of the photon changes. Because the photon wavelength determines its magnetic moment, its refraction also changes with the wavelength. The electric force contributes to refraction, without considering the influence of the magnetic force, and the formula for the refractive index of the electric force can be derived.

In the positive electric field near the nucleus, \({U}_{2}\)>0, photon refraction occurs, and positive and negative photons behave differently. In Fig. 40.3, the relative refractive index of the material is \(\mathrm{n}\), the corresponding negative photons and positive photons are \({\mathrm{n}}_{-}\) and \({\mathrm{n}}_{+}\), the negative photon incidence speed is \({\mathrm{c}}_{-}\), the transmission negative photon speed is \({\mathrm{c}}_{-\mathrm{t}}\), the positive photon incidence speed is \({\mathrm{c}}_{+}\), the velocity of the transmitted positive photon is \({\mathrm{c}}_{+\mathrm{t}}\) (it is not true refraction for positive photons, but conventional understanding is still used here), the charge of the photon is \({\mathrm{q}}_{\mathrm{o}}\), the mass is \({\mathrm{m}}_{\mathrm{o}}\), the electron mass is \({\mathrm{m}}_{\mathrm{e}}\), the proton mass is \({\mathrm{m}}_{\mathrm{p}}\), and the positive potential in the transmission area is \(\mathrm{U}\) (\({\mathrm{U}}_{2}\) in Fig. 40.3); thus, \({\mathrm{c}}_{-\mathrm{t}}>{\mathrm{c}}_{-}\) and \({\mathrm{c}}_{+\mathrm{t}}<{\mathrm{c}}_{+}\).

$$n=\frac{\mathrm{sin}{\theta }_{\mathrm{i}}}{\mathrm{sin}{\theta }_{\mathrm{t}}}=\frac{v}{c},$$
(40.16)
$${c}_{-\mathrm{t}}={n}_{-}{c}_{-}, {c}_{+\mathrm{t}}={n}_{+}{c}_{+}.$$
(40.17)
Fig. 40.3
figure 3

Coexistence of reflection and refraction: reflection of negative photons in repulsive field (left), negative photon refraction in gravitational field, positive photon refraction (actually scattering) in repulsion field (right)

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Upon entering the region of positive potential, the kinetic energy of the negative photons increases (40.18).

$$\frac{1}{2}{m}_{\mathrm{o}}\left({{c}_{-\mathrm{t}}}^{2}-{{c}_{-}}^{2}\right)=U{q}_{\mathrm{o}.}$$
(40.18)

When entering the positive potential region, the positive photon kinetic energy decreases (40.19).

$$\frac{1}{2}{m}_{\mathrm{o}}\left({{{c}_{+}}^{2}-{c}_{+\mathrm{t}}}^{2}\right)=U{q}_{\mathrm{o}}.$$
(40.19)

The electrical refractive indexes of negative photons and positive photons can be obtained as follows, respectively:

$${{n}_{-}}^{2}=1+\frac{2U{q}_{\mathrm{o}}}{{m}_{\mathrm{o}}{{c}_{-}}^{2}}=1+\frac{2Ue}{{m}_{\mathrm{e}}{{c}_{-}}^{2}},$$
(40.20)
$${{n}_{+}}^{2}=1-\frac{2U{q}_{\mathrm{o}}}{{m}_{\mathrm{o}}{{c}_{+}}^{2}}=1-\frac{2Ue}{{m}_{\mathrm{p}}{{c}_{+}}^{2}}.$$
(40.21)

The electrical refractive index curves of the positive and negative photons were calculated using (40.20) and (40.21), and are shown in Fig. 40.4. Using 0–360 kV as the hypothetical potential, which is lower than the proton surface potential, the calculated value of the proton surface potential is 1,728.649 kV.

Fig. 40.4
figure 4

Calculated negative and positive photon electrical refraction indexes under the condition of 0–360 kV potential

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The refractive index of X-rays is slightly less than 1.0, due to \({c}_{+\mathrm{t}}<{c}_{+}\). The equation \(n=v/c\) in this case indicates that the velocity of X-rays is smaller than its velocity in empty space.

The above calculation shows that the electrical refractive indexes of negative and positive photons are very different, and the refractive index of positive photons \({n}_{+}<1\), which is consistent with the experimental results. This extreme refractive index contrast of positive and negative photons indicates that the photon momentum changes in the opposite direction; therefore, X-rays are positive photons. For the same reason, the total reflection of positive and negative photons appears as distinct external reflection and internal reflection, respectively.

The refractive index of the positive photon and the negative photon will be larger considering the influence of the photon magnetic moment (corresponding to the polarization) force, and negatively relate to the wavelength. Besides refraction, photons can also orbit (photon absorption) in the gravitational field, negative photons fly around the nucleus, and positive photons fly around electrons; the photon orbital radius is positively related to the wavelength. Photon orbital flight is closely related to blackbody radiation and atomic spectrum (Note: Related research content omitted).

4 Photon Wave Phenomenon

A nucleus comprises protons and electrons. The density difference between them is approximately 70,000 times. They are combined together, and the center of mass and the center of the overall charge may not coincide. The nucleus has spin motion. In theory, the spin axis passes through the center of mass. When the charge center and spin axis are eccentric, the charge distribution center fluctuates sinusoidally with the spin of the nucleus, resulting in periodic fluctuation of the potential field in the atom.

In addition to the nuclear rotation \({\omega }_{\mathrm{n}}\), the electric field fluctuation of electrons inside the atom also has a similar effect. Because the orbital electrons rotate relative to the atomic nucleus, as shown in Fig. 40.5, the electromagnetic field caused by the electrons changes with the angular position of the electron rotation \({\omega }_{\mathrm{e}}\), so the electromagnetic field fluctuates periodically. In general, the periodic fluctuating electromagnetic potential field inside the atom persists over a wide range, and the superposition of various factors produces a fluctuating influence, which is the internal reason for photon wave performance. The influence of the fluctuating electromagnetic field on the reflection and refraction of photons is different, and it is related to optical imaging, hence is worthy of in-depth study.

Fig. 40.5
figure 5

a Wave electromagnetic field inside the atom; b calculated three-dimensional electric equipotential line

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The wave electromagnetic potential field \(U\) inside the atom can be expressed as (40.22), where \(\omega\) is the angular velocity of the wave potential field.

$$U=\mathrm{sin}\omega t.$$
(40.22)

As a charged particle, the photon’s movement trajectory (refraction) will be affected by this wave potential field \(U\), resulting in a corresponding change in the direction and position \(y\left(U\right)=y\left(\mathrm{sin}\omega t\right)\). To simplify the description, consider \(y\left(U\right)\) as a simple linear relationship, \(y\left(U\right)\propto U=\mathrm{sin}\omega t\), which yields (40.23). The time integral \(I\left(y\right)\) of \(y\left(U\right)\) is the geometric distribution of a large number of photons, as shown in Fig. 40.6. The light intensity \(\mathrm{I}\left(\mathrm{y}\right)\) is a simple fringe distribution that represents the formation mechanism of the photon interference fringes.

Fig. 40.6
figure 6

Time-integrated distribution of photons across the wave potential field forms diffraction spot

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$$I\left(y\right)\propto {\int }\mathrm{sin}\omega t d\omega t=2{\mathrm{sin}}^{2}\frac{\omega t}{2}.$$
(40.23)

The diffraction spot width is unrelated to the fluctuation period of the potential field, but is affected by the fluctuation amplitude of the electromagnetic potential field. If the orbiting electron is the main factor in the amplitude fluctuation of the potential field, the diffraction spot of the photons near the electron orbit are wider. For large-wavelength negative photons, the refractive index is lower and the electron orbit is closer (farther from the nucleus), so the diffraction spot width is larger; for the same reason, the short-wavelength photons have narrower diffraction spot.

The formation of the abovementioned particle diffraction spot is the result of the merging time integral of the influence of the periodic wave potential field on the trajectory of the photon flow. This constitutes the basis of all light diffraction. The superposition of existing diffraction spots on each other to generate new diffraction spot is a general phenomenon of light diffraction. Therefore, it is not surprising that single-photon interference forms fringes, and there is no need for some nonexistent agreement between photons. The single-photon interference phenomenon also proves that the photon wave originates from the electromagnetic field fluctuation in the optical path. The photon is not a wave, but it shows the characteristics of a wave under the influence of the wave potential field.

The photon (particle) behavior exhibits a wave phenomenon in a statistical sense, which can produce interference fringes, or it can be manifested as wave propagation, which is consistent with the existing wave theory. The photons arranged along the flight direction are like waves propagating in space, exhibiting periodic fluctuations in amplitude and specific wavelengths.

An explanation of the beating phenomenon of dual-frequency lasers is shown in Fig. 40.7, where photons (particles) are represented by the round spots, and light waves are represented by the harmonic curves. Photons are periodically arranged in the flight direction, similar to the propagation of light waves. Different wavelengths \({\lambda }_{1}\) and \({\lambda }_{2}\) are mixed together, causing the photon number distribution period (beat frequency) to change. This beat frequency period is much larger than the period of a single wavelength, so that photocells with insufficient time and space resolution can detect it. The beat frequency travels at the speed of light and has a time period and space period. This is the basis for the use of the Doppler effect in integrating the movement speed to measure the change in length.

Fig. 40.7
figure 7

Comparison of light intensity distribution between two-wavelength photon flight and dual-frequency light wave beat frequency

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For two beams of photons with the same wavelength, the interference fringes are easier to be observed, because their locations do not change over time.

5 Conclusion

Considering the widespread existence and interaction of electrons and protons, as well as Coulomb’s law, Newton’s law of motion, and the law of conservation of energy, the hypothesis that electrons and protons act strongly to generate photons is proposed, and the following conclusions were drawn.

In the zero-potential (equivalent to in vacuum) region, the negative photon velocity is equal to the optical constant \(\mathrm{c}\), and there is a huge difference between the positive photon velocity and the light velocity constant. Photons have energy and are also media that transfer energy at the speed of light. Charged photons participate in the macroscopic conduction process, which is why the conduction speed is a constant of the light speed. Electromagnetic waves have the same physical properties as photons and are a group of negative photons with a smaller volume.

The effect of the charged spin photon and the uneven and fluctuating potential field of the atom are the internal mechanisms of all optical phenomena. The main factors affecting these macroscopic optical phenomena include

  1. (1)

    Positive or negative photons. The behavior of positive and negative photons varies greatly. X-ray is a positive photon;

  2. (2)

    Gravitational field or repulsion field: scattering (reflection) occurs only in the repulsion field, and refraction, collision, and absorption only occur in the gravitational field. Scattering of the repulsion field causes the photon speed shift;

  3. (3)

    Nonuniform field and structural characteristics within the atom: electrons are located at the periphery of the atom, with strong reflection laws for the negative photon. The central location of the nucleus increases the significance of the refraction phenomena, and the mechanism of refraction for positive and negative photons remains the same. The scattered electrons in the atoms make the refraction of positive photons less obvious;

  4. (4)

    Periodic fluctuation of the internal potential field of the atom, which is the internal cause of various diffraction phenomena;

  5. (5)

    Incident angle of the photons, which significantly affects the reflectivity and photon speed shift.

Very different electrons and protons form atoms, and the microscopic potential field of the material is not uniform at the subatomic scale, resulting in the coexistence of photon reflection and refraction in transparent materials and the Compton effect. The scattering or reflection in the repulsive field causes the loss of photon kinetic energy (light speed shift), and the reflection and refraction behaviors of negative and positive photons are very different. Edge diffraction is a special case of refraction.

Photons are the key carrier and transmission tools of energy. They have kinetic energy that originates from the potential energy of the electrons or protons. It is believed that the charged spin of light particles conforms to the existing physical laws. Understanding the nature of photons will help new developments in energy utilization and measurement technologies.