arXiv physics/00050342000-05physics.gen-ph

相对论作为时空测量的量子力学

Relativity as the quantum mechanics of space-time measurements

Richard Lieu

备注：: 17 pages, 3 figures

摘要：

一个简单的空间和时间的微观模型能证明狭义相对论是一个系综的宏观（集合）行为吗？这个问题将分三个部分进行研究。首先，它表明，洛伦兹变换正式源于第一相对性公设（FRP）{ \it单独}，如果时空量子化是一个基本的物理定律，必须包括作为公设的一部分。然而，一个重要的推论是，当带有长度和时间基本单位的测量设备（例如，每个时间段都滴答作响的时钟）均匀地“移动”时，它们似乎是在用更大的单位进行测量。其次，量子尺寸的这种明显增加可以归因于与运动相关的额外波动，这可以通过使用温度参数来精确地描述热搅动谐振子。这对平坦时空的微观性质提供了严格的限制：它是一个量子化振子阵列。第三，由于上述发展表明，加速帧的时空阵列不能处于热平衡，（即，它将具有温度分布），该方法适用于{ \it any}点物体的场加速的情况，这对应于阵列中的温度“尖峰”。结果表明，声子传导的能量向外输运意味着在低速时力的平方反比定律，而在高速时则是完整的史瓦西度规。新理论的一个预测是，当两个惯性观测者相对移动太快时，或者当场太强时，非谐修正将修改时间膨胀等效应，并将导致不对称，这意味着FRP在这个极端极限下可能无法持续。

英文摘要：

Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation formally stems from the First Relativity Postulate (FRP) {\it alone} if space-time quantization is a fundamental law of physics which must be included as part of the Postulate. An important corollary, however, is that when measuring devices which carry the basic units of lengths and time (e.g. a clock ticking every time quantum) are `moving' uniformly, they appear to be measuring with larger units. Secondly, such an apparent increase in the sizes of the quanta can be attributed to extra fluctuations associated with motion, which are precisely described in terms of a thermally agitated harmonic oscillator by using a temperature parameter. This provides a stringent constraint on the microscopic properties of flat space-time: it is an array of quantized oscillators. Thirdly, since the foregoing development would suggest that the space-time array of an accelerated frame cannot be in thermal equilibrium, (i.e. it will have a distribution of temperatures), the approach is applied to the case of acceleration by the field of {\it any} point object, which corresponds to a temperature `spike' in the array. It is shown that the outward transport of energy by phonon conduction implies an inverse-square law of force at low speeds, and the full Schwarzschild metric at high speeds. A prediction of the new theory is that when two inertial observers move too fast relative to each other, or when fields are too strong, anharmonic corrections will modify effects like time dilation, and will lead to asymmetries which implies that the FRP may not be sustainable in this extreme limit.

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英文摘要：

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