帕斯夸尔·乔丹对光的波粒二象性难题的解答
Pascual Jordan's resolution of the conundrum of the wave-particle duality of light
摘要：
1909年，爱因斯坦导出了黑体辐射中能量涨落的均方公式。这个公式是波项和粒子项之和。在1925年与玻恩和海森堡的Dreimaennerarbeit的一个关键贡献中，乔丹表明，人们可以在一个简单的量子化波模型中恢复这两项。因此，这两个术语并不需要单独的机制，而是来自一个一致的动力学框架。一些作者认为，各种无穷大使乔丹的结论无效。在本文中，我们捍卫约旦的论点，反对这种批评。特别是，我们注意到，在一个狭窄的频率范围内的波动，这是约旦计算，是完全有限的。然而，我们也注意到，约旦的论点是不完整的。用现代术语来说，乔丹计算了整个系统能量本征态中一个子系统能量的量子不确定性，而热涨落则是这个量在这些态的系综上的平均值。尽管如此，我们的总体结论是，乔丹的论点基本上是合理的，他应该因为解决了量子物理发展中的一个重大难题而受到赞扬。
英文摘要：
In 1909, Einstein derived a formula for the mean square energy fluctuation in black-body radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1925 Dreimaennerarbeit with Born and Heisenberg, Jordan showed that one recovers both terms in a simple model of quantized waves. So the two terms do not require separate mechanisms but arise from a single consistent dynamical framework. Several authors have argued that various infinities invalidate Jordan's conclusions. In this paper, we defend Jordan's argument against such criticism. In particular, we note that the fluctuation in a narrow frequency range, which is what Jordan calculated, is perfectly finite. We also note, however, that Jordan's argument is incomplete. In modern terms, Jordan calculated the quantum uncertainty in the energy of a subsystem in an energy eigenstate of the whole system, whereas the thermal fluctuation is the average of this quantity over an ensemble of such states. Still, our overall conclusion is that Jordan's argument is basically sound and that he deserves credit for resolving a major conundrum in the development of quantum physics.
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。
