# 基于经典电磁理论的光子质量理论分析Theoretical Analysis of Photon Quality Based on Classical Electromagnetic Theory

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Photon is a gauge particle which has mass, energy and momentum. It has very high research value. Starting from the special theory of relativity, the relationship between mass and velocity, the relationship between mass and energy and the light quantum hypothesis of Einstein, this paper analyzes the concept of photons and the nature of the photon quality, and then finds that the rest mass of photons is zero while the movement quality is non-zero and the nature of the photon quality is the electromagnetic mass movement quality. In addition, this paper also gives two kinds of representation of photon energy and momentum in the vacuum and analyzes the difference and relationship between these two kinds of representation. Finally, this paper uses a new analysis method from the perspective of relationship between energy and momentum to discuss the changes of mass, momentum and energy when photons move from vacuum to the transparent medium, which makes it more comprehensive to discuss the quality of photons.

1. 引言

2. 光子的电磁理论基础

$m=\frac{{m}_{0}}{\sqrt{1-\frac{{V}^{2}}{{c}^{2}}}}$ (1)

$E=\frac{{m}_{0}{c}^{2}}{\sqrt{1-{\left(\frac{V}{c}\right)}^{2}}}={m}_{\gamma }{c}^{2}$ (2)

$E=h\nu$ (3)

3. 讨论

3.1. 光子静止质量为零的理论论证

$P=\frac{{m}_{0}V}{\sqrt{1-{\left(\frac{V}{c}\right)}^{2}}}$ (4)

${V}^{\prime }=\frac{V-U}{1-\frac{UV}{{c}^{2}}}$ (5)

${E}^{\prime }=\frac{{m}_{0}{c}^{2}\left(1-\frac{UV}{{c}^{2}}\right)}{\sqrt{\left(1-\frac{{U}^{2}}{{V}^{2}}\right)\left(1-\frac{{V}^{2}}{{c}^{2}}\right)}}=\frac{E-UP}{\sqrt{1-\frac{{U}^{2}}{{c}^{2}}}}$ (6)

$h{\nu }^{\prime }=\frac{h\nu -UP}{\sqrt{1-\frac{{U}^{2}}{{c}^{2}}}}$ (7)

$h{\nu }^{\prime }=h\nu \sqrt{\frac{c-U}{c+U}}$ (8)

$P=\frac{h\nu }{c}=\frac{E}{c}$ (9)

${E}^{2}={\left(\frac{E}{c}\right)}^{2}{c}^{2}+{m}_{0}^{2}{c}^{4}$ (10)

3.2. 光子运动质量的本质及分析

${m}_{\gamma }=\frac{{m}_{0}}{\sqrt{1-\frac{{V}^{2}}{{c}^{2}}}}$ (11)

${m}_{\gamma }=\frac{h\nu }{{c}^{2}}$ (12)

3.3. 光子在真空中的能量、动量表示方式

3.4. 光子在透明介质中的运动质量、能量和动量

$P=\frac{h}{\lambda }$ (13)

$\lambda =n{\lambda }_{0}$ ；另一种是Minkowski定义的： $\lambda =\frac{{\lambda }_{0}}{n}$ 。最近的研究表明，这两种情况都是正确的，而前者与动

${P}^{\prime }=\frac{h}{{\lambda }^{\prime }}=\frac{h}{n\lambda }$ (14)

${m}^{\prime }=\frac{h\nu }{{c}^{2}}\sqrt{1-\frac{1}{{n}^{2}}}=\frac{h}{\lambda c}\sqrt{1-\frac{1}{{n}^{2}}}$ (15)

3.5. 实验检验光子静止质量的研究进展

${m}_{0}\approx \frac{\hslash }{\Delta t\cdot {c}^{2}}\approx {10}^{-61}\text{\hspace{0.17em}}\text{kg}$ ，上面的估算式中 $\Delta t$ 取宇宙的年龄，即1010年。显然实验探测如此小的质量十分困

3.6. 关于光子静止质量的另一点讨论

Table 1. Representative testing results and methods of photon rest mass experiments

${w}^{2}-{k}^{2}{c}^{2}=0$ (16)

${w}^{2}-{w}_{0}^{2}={k}^{2}{c}^{2}$ (17)

${w}_{0}=\sqrt{\frac{4\text{π}{e}^{2}n}{{m}_{e}}}$ (18)

4. 结论

NOTES

*通讯作者。

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