更改

正是[[阿尔伯特·爱因斯坦]]的[[质能守恒]]（1905年）的概念，一个以辐射或热的形式损失能量的物体，其质量损失量为''m''&nbsp;=&nbsp;''E''/''c''²<ref name=darrigol>Darrigol 2005, Secondary sources on relativity</ref> 解决了庞加莱悖论，没有使用以太内部的任何补偿机制。<ref>{{Citation|author=Einstein, A. |year=1905b |title=Ist die Trägheit eines Körpers von dessen Energieinhalt abhängig? |journal=Annalen der Physik |volume=18 |issue=13 |pages=639–643 |bibcode=1905AnP...323..639E |doi= 10.1002/andp.19053231314 |url=http://www.physik.uni-augsburg.de/annalen/history/papers/1905_18_639-641.pdf |archive-url=https://web.archive.org/web/20050124051500/http://www.physik.uni-augsburg.de/annalen/history/papers/1905_18_639-641.pdf |url-status=dead |archive-date=24 January 2005}}请参阅 [http://www.fourmilab.ch/etexts/einstein/specrel/www English translation]。</ref> The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent.<ref>{{Citation|author=Einstein, A. |year=1906 |title=Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie |journal=Annalen der Physik |volume=20 |pages=627–633 |doi=10.1002/andp.19063250814 |issue=8 |bibcode=1906AnP...325..627E |url= http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf |archive-url=https://web.archive.org/web/20060318060830/http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf |url-status=dead |archive-date=18 March 2006}}</ref>

正是[[阿尔伯特·爱因斯坦]]的[[质能守恒]]（1905年）的概念，一个以辐射或热的形式损失能量的物体，其质量损失量为''m''&nbsp;=&nbsp;''E''/''c''²<ref name=darrigol>Darrigol 2005, Secondary sources on relativity</ref> 解决了庞加莱悖论，没有使用以太内部的任何补偿机制。<ref>{{Citation|author=Einstein, A. |year=1905b |title=Ist die Trägheit eines Körpers von dessen Energieinhalt abhängig? |journal=Annalen der Physik |volume=18 |issue=13 |pages=639–643 |bibcode=1905AnP...323..639E |doi= 10.1002/andp.19053231314 |url=http://www.physik.uni-augsburg.de/annalen/history/papers/1905_18_639-641.pdf |archive-url=https://web.archive.org/web/20050124051500/http://www.physik.uni-augsburg.de/annalen/history/papers/1905_18_639-641.pdf |url-status=dead |archive-date=24 January 2005}}请参阅 [http://www.fourmilab.ch/etexts/einstein/specrel/www English translation]。</ref> The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent.<ref>{{Citation|author=Einstein, A. |year=1906 |title=Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie |journal=Annalen der Physik |volume=20 |pages=627–633 |doi=10.1002/andp.19063250814 |issue=8 |bibcode=1906AnP...325..627E |url= http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf |archive-url=https://web.archive.org/web/20060318060830/http://www.physik.uni-augsburg.de/annalen/history/papers/1906_20_627-633.pdf |url-status=dead |archive-date=18 March 2006}}</ref>

====Gravitational waves====

====Gravitational waves引力波====

The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing, instead of previously used "Analysis situs". Some important concepts were introduced by Enrico Betti and Bernhard Riemann. But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894.

The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing, instead of previously used "Analysis situs". Some important concepts were introduced by Enrico Betti and Bernhard Riemann. But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894.

这个主题是由 Felix Klein 在他的《爱尔兰根纲领(1872)中明确定义的: 任意连续变换的几何不变量，一种几何学。正如利斯廷所建议的那样，引入了术语“拓扑” ，而不是之前使用的“分析位置”。一些重要的概念是由 Enrico Betti 和波恩哈德·黎曼介绍的。但是对于任何维度的空间来说，这门科学的基础都是由庞加莱创造的。他的第一篇关于这个主题的文章发表于1894年。

这个主题是由 <font color="#ff8000"> 费利克斯·克莱因Felix Klein</font>在他的《爱尔兰根纲领(1872)中明确定义的: 任意连续变换的几何不变量，一种几何学。正如利斯廷所建议的那样，引入了术语“拓扑” ，而不是之前使用的“分析位置”。一些重要的概念是由 恩里科·贝蒂Enrico Betti 和波恩哈德·黎曼介绍的。但是对于任何维度的空间来说，这门科学的基础都是由庞加莱创造的。他的第一篇关于这个主题的文章发表于1894年。

In 1905 Henri Poincaré first proposed [[gravitational waves]] (''ondes gravifiques'') emanating from a body and propagating at the speed of light.<ref name="1905 paper" /> ''"Il importait d'examiner cette hypothèse de plus près et en particulier de rechercher quelles modifications elle nous obligerait à apporter aux lois de la gravitation. C'est ce que j'ai cherché à déterminer; j'ai été d'abord conduit à supposer que la propagation de la gravitation n'est pas instantanée, mais se fait avec la vitesse de la lumière."''

In 1905 Henri Poincaré first proposed [[gravitational waves]] (''ondes gravifiques'') emanating from a body and propagating at the speed of light.<ref name="1905 paper" /> ''"Il importait d'examiner cette hypothèse de plus près et en particulier de rechercher quelles modifications elle nous obligerait à apporter aux lois de la gravitation. C'est ce que j'ai cherché à déterminer; j'ai été d'abord conduit à supposer que la propagation de la gravitation n'est pas instantanée, mais se fait avec la vitesse de la lumière."''

 

His research in geometry led to the abstract topological definition of homotopy and homology. He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group. Poincaré proved a formula relating the number of edges, vertices and faces of n-dimensional polyhedron (the Euler–Poincaré theorem) and gave the first precise formulation of the intuitive notion of dimension.

His research in geometry led to the abstract topological definition of homotopy and homology. He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group. Poincaré proved a formula relating the number of edges, vertices and faces of n-dimensional polyhedron (the Euler–Poincaré theorem) and gave the first precise formulation of the intuitive notion of dimension.

他对几何的研究导致了同伦和同调的抽象拓扑定义。他还首先介绍了组合拓扑的基本概念和不变量，如 Betti 数和基本群。证明了 n 维多面体的边数、顶点数和面数的一个公式(欧拉-庞加莱定理) ，给出了直观维数概念的第一个精确表达式。

他对几何的研究导致了<font color="#ff8000"> 同伦和同调Homotopy and Homology</font>的抽象拓扑定义。他还首先介绍了组合拓扑的基本概念和不变量，如 贝蒂Betti 数和基本群。证明了 n 维多面体的边数、顶点数和面数的一个公式(欧拉-庞加莱定理) ，给出了直观维数概念的第一个精确表达式。

====Poincaré and Einstein====

====Poincaré and Einstein====