两个永相合杆可能有不同的固有长度
Two Permanently Congruent Rods May Have Different Proper Lengths
摘要：
我们将全等视为几何学中相等的基本定义之一，并将其与狭义相对论的物理学相对立。我们表明，两个非刚性杆永久保持一致，在其共同的膨胀或压缩可能有不同的瞬时适当的长度（当测量在同一时间的各自的参考时钟），如果他们有不同的质量分布在他们的长度。或者，只有在它们各自的时钟的不同但严格相关的时刻测量时，它们的正确长度才能相等。导出的两个永久全等变化物体的瞬时固有长度之比的表达式明确地包含了物体质量分布的信息。对于两个参考时钟的读数比率也是如此，对于这两个参考时钟，各自适当长度的瞬时测量产生相同的结果。在这两种情况下，通常被认为是纯运动学的特性取决于质量分布，这是一种动态特性。这是一个壮观的演示动态方面的几何已经在框架内的狭义相对论。
英文摘要：
We scrutinize congruence as one of the basic definitions of equality in geometry and pit it against physics of Special Relativity. We show that two non-rigid rods permanently kept congruent during their common expansion or compression may have different instantaneous proper lengths (when measured at the same time of their respective reference clocks) if they have different mass distributions over their lengths. Alternatively, their proper lengths can come out equal only when measured at different but strictly correlated moments of time of their respective clocks. The derived expression for the ratio of instantaneous proper lengths of two permanently congruent changing objects explicitly contains information about the objects mass distribution. The same is true for the ratio of readings of the two reference clocks, for which the instantaneous measurements of respective proper lengths produce the same result. In either case the characteristics usually considered as purely kinematic depend on mass distribution, which is a dynamic property. This is a spectacular demonstration of dynamic aspect of geometry already in the framework of Special Relativity.
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