[论文解读] Einstein's Discovery of Gravitational Waves 1916-1918

Galina Weinstein|arXiv (Cornell University)|Feb 12, 2016

Relativity and Gravitational Theory参考文献 4被引用 3

一句话总结

本文分析了爱因斯坦在1916–1918年间对引力波的发展过程，揭示其推导中存在一个关键的数学错误，该错误导致他得出三种波型——纵向波、横向波以及一种新型波——的原因在于其对单式坐标条件的限制。在同事证明只有第三种波型在该坐标系中携带能量后，爱因斯坦放弃了该条件，最终正确发现了平面横向引力波。

ABSTRACT

In his 1916 ground-breaking general relativity paper Einstein had imposed a restrictive coordinate condition, his field equations were valid for coordinate systems which are unimodular. Later, Einstein published a paper on gravitational waves. The solution presented in this paper did not satisfy the above restrictive condition. In his gravitational waves paper, Einstein concluded that gravitational fields propagate at the speed of light. The solution is the Minkowski flat metric plus a small disturbance propagating in a flat spacetime. Einstein calculated the small deviation from Minkowski metric in a manner analogous to that of retarded potentials in electrodynamics. However, in obtaining the above derivation, Einstein made a mathematical error. This error caused him to obtain three different types of waves compatible with his approximate field equations: longitudinal waves, transverse waves and a new type of wave. Einstein added an Addendum in which he suggested that in systems in unimodular coordinates only waves of the third type occur and these waves transport energy. He became obsessed with his unimodular coordinates. Einstein's colleagues demonstrated to him that in the coordinate system in unimodular coordinates the gravitational wave of a mass point carry no energy, but Einstein tried to persuade them that he had actually not made a mistake in his gravitational waves paper. Einstein, however, eventually accepted his colleagues results and dropped the restrictive unimodular coordinates. This finally led him to discover plane transverse gravitational waves.

研究动机与目标

• 澄清1916至1918年间爱因斯坦引力波理论的历史发展过程。
• 识别爱因斯坦在引力波推导中所犯的数学错误及其后果。
• 分析爱因斯坦对单式坐标依赖及其对波能量传播的影响。
• 追踪爱因斯坦结果与同事反驳意见之间冲突的解决过程。
• 解释放弃单式坐标条件如何导致横向引力波的正确表述。

提出的方法

• 分析爱因斯坦1916年广义相对论论文，重点关注单式坐标条件的引入及其对场方程的限制性影响。
• 研究爱因斯坦1918年的引力波论文，其中他采用类似于电动力学中推迟势的微扰方法推导解。
• 识别推导中导致产生三种不同波型而非正确横向波的数学错误。
• 评估附录中爱因斯坦声称仅第三种波型在单式坐标系中携带能量的作用。
• 回顾爱因斯坦同事的论证，证明在单式坐标系中，点质量源产生的引力波不携带能量。
• 追踪爱因斯坦在这些批评之后思想的转变，最终放弃单式坐标条件并发现横向波。

实验结果

研究问题

• RQ1 爱因斯坦在1918年引力波推导中犯了什么数学错误？
• RQ2 为什么爱因斯坦坚持认为在单式坐标系中只有第三种波型携带能量？
• RQ3 爱因斯坦的同事如何挑战他关于单式坐标系中能量传输的结论？
• RQ4 限制性的单式坐标条件在何种程度上扭曲了引力波的本质？
• RQ5 放弃单式坐标条件如何导致爱因斯坦正确推导出横向引力波？

主要发现

• 爱因斯坦在1918年引力波推导中存在数学错误，导致得出三种波型：纵向波、横向波以及一种新型波。
• 在单式坐标系中，爱因斯坦声称仅第三种波型携带能量，但其同事证明对于点质量源而言这是错误的。
• 爱因斯坦的同事证明，在单式坐标系中引力波不携带能量，与爱因斯坦的断言相矛盾。
• 在长期坚持后，爱因斯坦接受了同事的分析，并放弃了单式坐标条件。
• 去除单式约束后，爱因斯坦得以正确推导出平面横向引力波。
• 这一修正标志着物理上正确的引力波形式——即横向、以光速传播的引力波——的最终确立。