📚 Michelson-Morley Experiment and the Constancy of Light | 迈克耳孙-莫雷实验与光速不变
The speed of light in vacuum, c, is one of the most fundamental constants in physics. In the late nineteenth century, physicists believed that light waves needed a medium to travel through, just as sound needs air. This hypothetical medium was called the luminiferous aether, and the Michelson-Morley experiment was designed to detect it. Its famous null result forced scientists to rethink the nature of light and motion, ultimately leading to Einstein’s postulate that the speed of light is constant.
真空中的光速 c 是物理学中最基本的常量之一。十九世纪末，物理学家认为光波与声波一样，需要某种介质才能传播，这种假想介质被称为“以太”。迈克耳孙-莫雷实验正是为了探测以太而设计。该实验著名的“零结果”迫使科学家重新审视光与运动的本质，最终推动了爱因斯坦提出光速不变原理。
1. The Luminiferous Aether Hypothesis | 以太假说
James Clerk Maxwell’s equations showed that light travels at speed c = 1/√(ε₀μ₀), where ε₀ is the vacuum permittivity and μ₀ is the vacuum permeability. However, since all known mechanical waves had a medium, physicists assumed that light must also require one. This medium, named the luminiferous aether, was thought to fill all of space and provide a fixed reference frame for light propagation.
麦克斯韦方程组表明，光速满足 c = 1/√(ε₀μ₀)，其中 ε₀ 是真空介电常数，μ₀ 是真空磁导率。然而，当时已知的一切机械波都需要介质，因此物理学家假设光也必须依赖某种介质。这种被称为“以太”的假想介质被认为充满整个宇宙，并构成光传播的绝对参考系。
If the Earth moves through this aether, then an observer on Earth should detect an “aether wind” caused by the Earth’s orbital motion around the Sun, about 30 km/s. Michelson and Morley designed a sensitive optical experiment to measure this aether wind.
如果地球在以太中运动，那么地球上的观察者应当能探测到“以太风”，其来源是地球绕太阳的公转，速度约为 30 km/s。迈克耳孙和莫雷设计了一个灵敏的光学实验，试图测量这种以太风。
2. The Goal of the Experiment | 实验目标
The experiment aimed to compare the speed of light in two perpendicular directions. Imagine light travelling along the direction of the Earth’s motion through the aether. If the aether hypothesis were correct, the light’s speed relative to the apparatus would be c − v on the outward journey and c + v on the return journey. In the perpendicular direction, the speed would be √(c² − v²). This difference should produce a measurable shift in interference fringes.
该实验的目标是比较光沿两个互相垂直方向的传播速度。假设光沿地球穿过以太的运动方向传播。如果以太假说成立，那么光相对于仪器的速度应为：去程 c − v，回程 c + v；而在垂直方向，速度应为 √(c² − v²)。这种速度差异应当产生可测量的干涉条纹移动。
3. The Interferometer Setup | 干涉仪装置
Michelson and Morley used an interferometer consisting of a light source, a half-silvered mirror called a beam splitter, two perpendicular mirrors, and an observing screen. A single light beam was split into two beams: one travelling parallel to the expected aether wind and one travelling perpendicular to it. The two beams were then reflected back and recombined, producing interference fringes.
迈克耳孙和莫雷使用了一台干涉仪，其组成部分包括光源、半镀银分束镜、两个互相垂直的反射镜以及观测屏幕。一束光被分为两束：一束沿预期以太风方向传播，另一束沿垂直方向传播。两束光被反射回来并重新叠加，产生干涉条纹。
| Component | Function |
| Light source | Provides a coherent beam of light |
| Half-silvered mirror | Splits the beam into two perpendicular paths |
| Two plane mirrors | Reflect the beams back to the beam splitter |
| Telescope/screen | Observes the interference pattern |
An important design detail was the use of multiple reflections to increase the effective path length to about 11 m. The whole apparatus was mounted on a heavy stone slab floating in mercury, allowing it to rotate smoothly without vibration.
一个重要的设计细节是利用多次反射将有效光路长度增加到约 11 m。整个装置安装在一块浮在水银中的沉重石板上，以便无振动地平稳旋转。
4. Expected Fringe Shift | 预期的条纹移动
For a light beam travelling parallel to the aether wind, the total time for the round trip is the sum of the outward and return times:
t₁ = L/(c − v) + L/(c + v) = 2Lc/(c² − v²)
For the perpendicular arm, the beam travels along the hypotenuse of a right triangle, so the round-trip time is:
t₂ = 2L/√(c² − v²)
Using a Taylor expansion for v ≪ c, the time difference is approximately:
Δt = t₁ − t₂ ≈ Lv²/c³
When the apparatus is rotated by 90°, the roles of the arms interchange, doubling the expected fringe shift. The predicted number of fringes is:
N = 2Lv²/(c²λ) ≈ 0.4 fringes
With L ≈ 11 m, λ ≈ 550 nm and v²/c² ≈ 10⁻⁸, the experiment should have revealed about four-tenths of a fringe shift. Such a shift was well within the sensitivity of the apparatus.
对于平行于以太风传播的光束，往返总时间为去程与回程时间之和：
t₁ = L/(c − v) + L/(c + v) = 2Lc/(c² − v²)
对于垂直方向的光束，光沿直角三角形的斜边传播，因此往返时间为：
t₂ = 2L/√(c² − v²)
利用 v ≪ c 的泰勒展开，时间差近似为：
Δt = t₁ − t₂ ≈ Lv²/c³
当装置旋转 90° 时，两臂角色互换，预期条纹移动加倍。因此预测的条纹数为：
N = 2Lv²/(c²λ) ≈ 0.4 条
取 L ≈ 11 m，λ ≈ 550 nm，v²/c² ≈ 10⁻⁸，实验应当观察到约十分之四条条纹移动。这样的移动量远在仪器灵敏度范围之内。
5. The Null Result | 零结果
Michelson and Morley observed essentially no shift in the interference pattern. The measured fringe shift was less than about 0.01 fringes, far below the expected 0.4 fringes. Even after repeated trials and rotation of the apparatus, no periodic variation corresponding to an aether wind appeared.
迈克耳孙和莫雷几乎没有观察到干涉条纹的移动。实测条纹移动小于约 0.01 条，远低于预期的 0.4 条。即使反复实验并旋转装置，也没有出现与以太风对应的周期性变化。
This null result implied that the speed of light is the same in all directions, regardless of the Earth’s motion. It contradicted the aether hypothesis and created a major puzzle for classical physics.
这一零结果意味着，无论地球如何运动，光速在各方向上都相同。它与以太假说直接矛盾，给经典物理学带来了重大难题。
6. Ad Hoc Explanations | 特设解释
Some physicists tried to rescue the aether concept. One idea was that the Earth drags the aether along with it, but this contradicted other observations such as stellar aberration. Another explanation, proposed independently by George FitzGerald and Hendrik Lorentz, was that an object moving through the aether contracts in the direction of motion by a factor of √(1 − v²/c²).
一些物理学家试图挽救以太概念。一种观点认为地球会拖曳周围的以太，但这与恒星光行差等观测矛盾。另一种解释由乔治·菲茨杰拉德和亨德里克·洛伦兹独立提出：物体沿运动方向会收缩，收缩因子为 √(1 − v²/c²)。
L = L₀√(1 − v²/c²)
This length contraction would reduce the parallel arm enough to make the light travel times equal, explaining the null result. However, it was introduced specifically to explain the experiment and seemed artificial. There was no direct evidence for such a contraction at the time.
这种长度收缩会使平行方向的光臂缩短，从而令两束光的传播时间相等，解释零结果。然而，这一假说是为了解释实验而专门引入的，显得人为而牵强。当时并没有直接证据支持这种收缩。
7. Einstein’s Principle of the Constancy of Light | 爱因斯坦的光速不变原理
In 1905, Albert Einstein published his special theory of relativity, based on two postulates. First, the laws of physics are the same in all inertial reference frames. Second, the speed of light in vacuum is constant and independent of the motion of the source or the observer. This second postulate explains the Michelson-Morley result without any need for an aether or a special reference frame.
1905 年，阿尔伯特·爱因斯坦发表了狭义相对论，其基础是两条基本假设。第一条：物理学定律在所有惯性参考系中都相同。第二条：真空中的光速是恒定的，与光源或观察者的运动无关。第二条假设解释了迈克耳孙-莫雷实验的结果，无需以太或任何特殊参考系。
According to Einstein, there is no absolute rest frame in the universe. Light does not require a medium; it propagates by the electromagnetic field itself. The aether hypothesis became unnecessary.
按照爱因斯坦的观点，宇宙中不存在绝对静止参考系。光不需要介质，它依靠电磁场自身传播。因此，以太假说变得多余。
8. Consequences and Significance | 推论与意义
The constancy of light has profound consequences. Time and space are not absolute. Two observers moving relative to each other will measure different time intervals and different distances. The relevant formulas are:
光速不变性具有深远的推论。时间和空间不再是绝对的。两个相对运动的观察者会测得不同的时间间隔和不同的距离。相关公式为：
Δt = Δt₀/√(1 − v²/c²), L = L₀√(1 − v²/c²)
The first equation describes time dilation: moving clocks run slower. The second describes length contraction: moving objects shorten along the direction of motion. Moreover, simultaneity is relative: two events that happen at the same time in one frame may happen at different times in another.
第一个公式描述时间膨胀：运动的时钟走得慢。第二个公式描述长度收缩：运动的物体沿运动方向缩短。此外，同时性也是相对的：在一个参考系中同时发生的事件，在另一个参考系中可能并不同时。
The Michelson-Morley experiment thus became one of the key experimental foundations for special relativity. It showed that the speed of light is invariant, and it replaced the idea of an absolute aether frame with a symmetric view of all inertial observers.
因此，迈克耳孙-莫雷实验成为狭义相对论的关键实验基础之一。它表明光速不变，并以此替代了绝对以太参考系观念，确立了所有惯性观察者的对称地位。
9. Modern Confirmations | 现代验证
Modern versions of the Michelson-Morley experiment have been performed with much higher precision. Using laser interferometers and optical cavities, physicists have tested whether the speed of light depends on direction or on the Earth’s motion. These experiments constrain any directional variation of light speed to less than about one part in 10⁻¹⁵.
现代的迈克耳孙-莫雷型实验已使用更高精度的技术完成。通过激光干涉仪和光学谐振腔，物理学家检验了光速是否随方向或地球运动而变化。这些实验将光速的方向性变化限制在约 10⁻¹⁵ 分之一以下。
Today the speed of light in vacuum is fixed exactly by definition: c = 299 792 458 m/s. The metre is defined using the distance light travels in a tiny fraction of a second. The constancy of light is therefore not merely a theory but also the foundation of the international system of measurement.
如今，真空中的光速被定义为精确值：c = 299 792 458 m/s。米的定义正是基于光在一秒的极短分数内传播的距离。因此，光速不变不仅是理论结论，更是国际单位制的基础。
10. Exam Take-Aways | 考点总结
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