狭义相对论的微观推导：运动时空晶格的简谐振荡
A microscopic derivation of Special Relativity: simple harmonic oscillations of a moving space-time lattice
摘要：
狭义相对论$^1$的出发点是洛伦兹变换，它本质上描述了空间和时间的绝对测量的缺乏。当人们把第二相对论假设应用于惯性观察者时，这些效应就产生了。在这里，我证明了有一种非常优雅的方式来解释自然界如何确切地实施狭义相对论，这迫使我们得出结论，爱因斯坦的伟大理论已经揭示了空间和时间的量子化。该模型提出，在微观上，时空的结构类似于由相同的“弹性弹簧”连接的晶格点或“刻度”（用于测量）组成的晶体。当静止时，“弹簧”处于其自然状态。然而，当被置于运动状态并用于测量静止的物体时，晶格会以爱因斯坦的固体热容理论所描述的方式有效地振动，结果是“刻度”变宽，因为均方根分离现在增加了。我通过该理论的基本假设，即关系$\frac{v^2}{c^2} = e^{-\fracε{kT}}$，将振动温度$T$与运动速度$v$联系起来，其中$ε$是晶格谐振子的能量量子。一个移动的观察者用这样一个振动的晶格测量距离，得到的结果正好是由洛伦兹变换给出的结果。除了它显而易见的美丽之外，这种方法还为理解空间和时间提供了许多新的前景。例如，该模型的一个结论是，时空，像质量一样，原则上可以转换为能量。
英文摘要：
The starting point of the theory of Special Relativity$^1$ is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity Postulate to inertial observers. Here I demonstrate that there is a very elegant way of explaining how exactly nature enforces Special Relativity, which compels us to conclude that Einstein's great theory has already revealed quantization of space and time. The model proposes that microscopically the structure of space-time is analogous to a crystal which consists of lattice points or `tickmarks' (for measurements) connected by identical `elastic springs'. When at rest the `springs' are at their natural states. When set in motion and used to measure objects at rest, however, the lattice effectively vibrates in a manner described by Einstein's theory of the heat capacity of solids, with consequent widening of the `tickmarks' because the root-mean-square separation now increases. I associate a vibration temperature $T$ with the speed of motion $v$ via the fundamental postulate of this theory, viz. the relation $\frac{v^2}{c^2} = e^{-\fracε{kT}}$ where $ε$ is a quantum of energy of the lattice harmonic oscillator. A moving observer who measures distances with such a vibrating lattice obtains results which are precisely those given by the Lorentz transformation. Apart from its obvious beauty, this approach provides many new prospects in understanding space and time. For example, a consequence of the model is that space-time, like mass, can in principle be converted to energy.
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