一种离散有限的过去真时方法
A discrete and finite approach to past proper time
摘要：
函数$γ(x)=\frac{1}{\sqrt{1-x^2}}$在数学物理中起着重要的作用，例如在$x=β$与$β=\frac{v}{c}$或$β=\frac{pc}{E}$的情况下作为相对论性时间膨胀的因子。基于上述考虑，研究$γ(x)$的幂级数展开是合理的。在这里，它与二项分布的关系被示出，特别是事实上，幂级数的和对应于返回到伯努利随机行走的起点（局部坐标、配置或状态）的概率。所以$γ(x)$和相应的时间与收益概率之和成正比。在$x=1$或$v=c$的情况下，随机游走是对称的。附录中介绍了带吸收障碍的随机游动。这里基本上显示了基本的数学事实，并给出了参考资料，大多数解释留给读者。
英文摘要：
The function $γ(x)=\frac{1}{\sqrt{1-x^2}}$ plays an important role in mathematical physics, e.g. as factor for relativistic time dilation in case of $x=β$ with $β=\frac{v}{c}$ or $β=\frac{pc}{E}$. Due to former considerations it is reasonable to study the power series expansion of $γ(x)$. Here its relationship to the binomial distribution is shown, especially the fact, that the summands of the power series correspond to the return probabilities to the starting point (local coordinates, configuration or state) of a Bernoulli random walk. So $γ(x)$ and with that also proper time is proportional to the sum of the return probabilities. In case of $x=1$ or $v=c$ the random walk is symmetric. Random walks with absorbing barriers are introduced in the appendix. Here essentially the basic mathematical facts are shown and references are given, most interpretation is left to the reader.
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