统计和严格动量守恒
Statistical and strict momentum conservation
摘要：
关于微观世界的能量和动量守恒定律是统计的还是严格的争论始于1924年，至今仍存在相互矛盾的观点。前者主要是理论上的支持，而后者已经被大量的实验所证实。通过将总波函数展开为子系统动量本征态乘积之和，说明了在子系统相互作用的封闭复合系统中，动量本征态的纠缠态形式原则上始终满足严格的动量守恒定律.常见的情况是，复合系统的两个子系统之一较大或较强，其状态在短时间内保持大致不变，纠缠态可以近似写成积态，这可以从Haroche小组2001年的论文中很容易地推导出来。所考虑的微观子系统可以近似地表示为它的不同动量本征态的叠加;因此，近似可以用来解释为什么该定律在统计上对子系统和任何单个粒子都成立，因为忽略了与大的子系统或环境的相互作用。因此，这两个动量守恒定律合理地成立，没有冲突。
英文摘要：
Arguments about the conservation laws of energy and momentum in the micro-world being statistical or strict began in 1924, and conflicting viewpoints remain today. The former is mainly supported theoretically, but the latter has been proved by many experiments. Here we explain that in principle, the strict conservation law of momentum always holds in the entangled state form of the momentum eigenstates of a closed composite system with interactions among subsystems, by expanding the total wave function to the sum of the products of momentum eigenstates of subsystems. Common scenario is that one of the two subsystems of a composite system is large or strong, its state remains approximately unchanged in a short time and the entangled state can be approximately written as a product state, which can be easily deduced from the paper of Haroche's group in 2001. The considered micro-subsystem can be approximately represented as the superposition of its different momentum eigenstates; therefore, the approximation can be used to explain why the law holds statistically for the subsystem and for any single particle due to neglecting the interactions with the large subsystem or the environment. So the two momentum conservation laws reasonably hold without conflicts.
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