用修正的距离公式研究离散时空中的相对论时间膨胀和长度收缩
Relativistic Time Dilation and Length Contraction in Discrete Space-Time using a Modified Distance Formula
摘要：
在这项工作中，洛伦兹收缩和时间膨胀的相对论性现象推导出使用修改后的距离公式适用于离散空间。这个新的距离公式与毕达哥拉斯定理不同，但在距离大于普朗克长度时收敛于毕达哥拉斯定理。首先，将考虑在过去70年中由不同的人开发的四个候选公式。其中三个公式在最好地描述离散空间的条件下是相同的;然后在本文的其余部分中使用该方程。它表明，这个新的距离公式是适用于所有的尺寸尺度，从普朗克长度向上，并解决了两个主要的历史问题与离散时空模型。它解决的一个问题是在离散空间中保持各向同性。它解决的第二个问题是，普遍认为模型中的空间“原子”概念与狭义相对论所要求的这个原子的洛伦兹收缩是不相容的。利用新的距离公式，证明了无论两个参考系的相对速度如何，空间原子都不会发生洛伦兹收缩。它还表明，时间原子的时间膨胀不会发生。还讨论了任何物体能够以光速在本工作中导出的特定时间段内旅行的可能性。
英文摘要：
In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges to it for distances large relative to the Planck length. First, four candidate formulas developed by different people over the last 70 years will be considered. Three of the formulas are shown to be identical for conditions that best describe discrete space; this equation is then used in the rest of the paper. It is shown that this new distance formula is applicable to all size-scales, from the Planck length upwards, and solves two major historical problems associated with a discrete space-time model. One problem it solves is maintaining isotropy in discrete space. The second problem it solves is the commonly perceived incompatibility of the model's concept of an immutable "atom" of space and the Lorentz contraction of this atom required by special relativity. With the new distance formula, it is shown that the Lorentz contraction of the atom of space does not occur regardless of the relative velocities of two reference frames. It is also shown that time dilation of the atom of time does not occur. Also discussed is the possibility of any object being able to travel at the speed of light for specific temporal durations derived in this work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
