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第647行： − 庞加莱在经度局建立国际时区的工作使他考虑如何使地球上静止的时钟（相对于绝对空间（或“发光以太”）以不同的速度移动）如何同步。与此同时，荷兰理论家亨德里克·洛伦兹正在将麦克斯韦的理论发展成带电粒子（“电子”或“离子”）运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量（没有物理解释），叫做“本地时间”<math>t^\prime = t-v x/c^2 \,</math>+ − 庞加莱在法国经度管理局关于建立国际时区的工作使他思考如何使地球上静止的时钟以不同的速度相对于绝对空间(或称为“以太时间”)进行同步。与此同时，荷兰理论家亨德里克 · 洛伦兹正在将麦克斯韦理论发展成一个关于带电粒子(“电子”或“离子”)运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量(没有物理解释) ，叫做“本地时间” t ^ prime = t-v x/c ^ 2 − + − + − 并且引入了长度收缩假说来解释光学和电学实验相对于以太探测运动的失败(见 Michelson-Morley 实验)。 第661行：
第659行： − 庞加莱是洛伦兹理论的不断解释者(有时也是友好的批评者)。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了 Lorentz 的理论，并由此提出了许多现在与狭义相对论有关的见解。在《时间的度量》(1898)中，庞加莱说:+ 第667行：
第665行： − 稍加思考就足以理解所有这些自我肯定本身没有任何意义。他们只能根据惯例生一个。”他还认为，科学家必须把光速的恒定性作为一个假设，才能给物理理论提供最简单的形式。+ − − and introduced the hypothesis of [[length contraction]] to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson–Morley experiment]]).<ref>{{Citation − 基于这些假设，他在1900年讨论了洛伦兹关于当地时间的“奇妙发明” ，并指出，当移动的时钟通过交换假定在移动的框架中以相同速度向两个方向移动的光信号而实现同步时，就产生了这一假设。+ + + 第687行：
第685行： − 在1881年庞加莱用双曲几何描述了双曲面模型变换，公式化的变换保持洛伦兹区间不变。此外，poincaré 的其他双曲几何模型(庞加莱圆盘模型，庞加莱半平面模型)以及 Beltrami-Klein 模型可以与相对论速度空间相关(见回旋向量空间)。+ − | last=Poincaré|first= Henri | year=1900 | title=La théorie de Lorentz et le principe de réaction | journal=Archives Néerlandaises des Sciences Exactes et Naturelles | volume =5 | pages =252–278| title-link=s:fr:La théorie de Lorentz et le principe de réaction }}. See also the [http://www.physicsinsights.org/poincare-1900.pdf English translation]</ref>+ 第697行：
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第708行： − 并在1904年将其命名为相对性原理，根据这一理论，没有任何物理实验能够区分匀速运动状态和静止状态。+ 第876行：
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→Work on relativity相对论部分的工作
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math>
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous aether"), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math>
在经度局建立国际时区的工作使庞加莱考虑如何使地球上静止的时钟（相对于绝对空间（或“<font color="#ff8000">以太Luminiferous aether</font>”）以不同的速度移动）进行同步。与此同时，荷兰理论家亨德里克·洛伦兹正在将麦克斯韦理论发展成带电粒子（“电子”或“离子”）运动及其与辐射相互作用的理论。1895年，洛伦兹引入了一个辅助量（没有物理解释），叫做“本地时间”<math>t^\prime = t-v x/c^2 \,</math>
====Local time====
==== Local time本地时间====
and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment).
and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment).
并且引入了长度收缩假说来解释光学和电学实验相对于<font color="#ff8000"> 以太</font>探测运动的失败(见 迈克尔逊·莫利Michelson-Morley 实验)。
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "[[luminiferous aether]]"), could be synchronised. At the same time Dutch theorist [[Hendrik Lorentz]] was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math><ref>{{Citation|title=A broader view of relativity: general implications of Lorentz and Poincaré invariance|volume=10|first1=Jong-Ping|last1=Hsu|first2=Leonardo|last2=Hsu|publisher=World Scientific|year=2006|isbn=978-981-256-651-5|page=37
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "[[luminiferous aether]]"), could be synchronised. At the same time Dutch theorist [[Hendrik Lorentz]] was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" <math>t^\prime = t-v x/c^2 \,</math><ref>{{Citation|title=A broader view of relativity: general implications of Lorentz and Poincaré invariance|volume=10|first1=Jong-Ping|last1=Hsu|first2=Leonardo|last2=Hsu|publisher=World Scientific|year=2006|isbn=978-981-256-651-5|page=37
Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "
Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "
庞加莱一直是洛伦兹理论的解释者（有时是友好的批评家）。作为一个哲学家，庞加莱对“更深层的意义”很感兴趣。因此，他解释了洛伦兹的理论，并由此提出了许多与<font color="#ff8000"> 狭义相对论</font>相关的见解。在《时间的度量》(1898)中，庞加莱说
|url=https://books.google.com/books?id=amLqckyrvUwC}}, [https://books.google.com/books?id=amLqckyrvUwC&pg=PA37 Section A5a, p 37]</ref>
|url=https://books.google.com/books?id=amLqckyrvUwC}}, [https://books.google.com/books?id=amLqckyrvUwC&pg=PA37 Section A5a, p 37]</ref>
A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form.
A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form.
“稍加反思就足以理解，所有这些肯定本身都没有意义。只有在约定成立的情况下，才能成立。”他还认为，科学家必须将光速的恒定性作为一个假设，以使物理理论具有最简单的形式。
Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.
Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.
基于这些假设，他在1900年对洛伦兹关于本地时间的“奇妙发明”进行了讨论，并指出，当移动的时钟通过交换假定在移动帧中以相同速度在两个方向上传播的光信号来同步时，就出现了这种情况。
and introduced the hypothesis of [[length contraction]] to explain the failure of optical and electrical experiments to detect motion relative to the aether (see [[Michelson–Morley experiment]]).<ref>{{Citation
| last=Lorentz|first= Hendrik A. | authorlink=Hendrik Lorentz| year=1895 | title=Versuch einer theorie der electrischen und optischen erscheinungen in bewegten Kõrpern | place =Leiden| publisher=E.J. Brill| title-link=s:de:Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern }}</ref>
| last=Lorentz|first= Hendrik A. | authorlink=Hendrik Lorentz| year=1895 | title=Versuch einer theorie der electrischen und optischen erscheinungen in bewegten Kõrpern | place =Leiden| publisher=E.J. Brill| title-link=s:de:Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern }}</ref>
In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. In addition, Poincaré's other models of hyperbolic geometry (Poincaré disk model, Poincaré half-plane model) as well as the Beltrami–Klein model can be related to the relativistic velocity space (see Gyrovector space).
In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. In addition, Poincaré's other models of hyperbolic geometry (Poincaré disk model, Poincaré half-plane model) as well as the Beltrami–Klein model can be related to the relativistic velocity space (see Gyrovector space).
1881年，庞加莱用双曲面模型描述了双曲几何学，提出了洛伦兹区间<math>x^2+y^2-z^2=-1</math>不变的变换，使其在数学上等价于2+1维的洛伦兹变换。此外，庞加莱的其他双曲几何模型(庞加莱圆盘模型，庞加莱半平面模型)以及贝尔特拉米-克莱因Beltrami–Klein模型都可以与相对论速度空间（见陀螺矢量空间）相关。
caré|first= Henri | year=1900 | title=La théorie de Lorentz et le principe de réaction | journal=Archives Néerlandaises des Sciences Exactes et Naturelles | volume =5 | pages =252–278| title-link=s:fr:La théorie de Lorentz et le principe de réaction }}. See also the [http://www.physicsinsights.org/poincare-1900.pdf English translation]</ref>
1892年庞加莱发展了包括偏振在内的光的数学理论。他关于偏振器和延迟器作用于代表极化状态的球体的观点称为庞加莱球。证明了庞加莱球具有一个基本的洛伦兹对称性，可以作为洛伦兹变换和速度加法的几何表示。
1892年庞加莱发展了包括偏振在内的光的数学理论。他关于偏振器和延迟器作用于代表极化状态的球体的观点称为庞加莱球。证明了庞加莱球具有一个基本的洛伦兹对称性，可以作为洛伦兹变换和速度加法的几何表示。
====Principle of relativity and Lorentz transformations====
====Principle of relativity and Lorentz transformations相对论原理与洛伦兹变换====
{{Further|History of Lorentz transformations#Poincare|History of Lorentz transformations#Poincare3|label1=History of Lorentz transformations - Poincaré (1881)|label2=History of Lorentz transformations - Poincaré (1905)}}
{{Further|History of Lorentz transformations#Poincare|History of Lorentz transformations#Poincare3|label1=History of Lorentz transformations - Poincaré (1881)|label2=History of Lorentz transformations - Poincaré (1905)}}
{{更进一步|洛伦兹变换的历史#庞加莱|洛伦兹变换的历史#庞加莱3 | label1=洛伦兹变换的历史-庞加莱（1881）| label2=洛伦兹变换的历史-庞加莱（1905）}}
He discussed the "principle of relative motion" in two papers in 1900
He discussed the "principle of relative motion" in two papers in 1900
and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.
and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest.
并在1904年将其命名为<font color="#ff8000"> 相对性原理Principle of relativity</font>，根据这一理论，没有任何物理实验能够区分匀速运动状态和静止状态。
In 1881 Poincaré described [[hyperbolic geometry]] in terms of the [[hyperboloid model]], formulating transformations leaving invariant the [[Lorentz interval]] <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions.<ref>{{Cite journal|author=Poincaré, H.|year=1881|title=Sur les applications de la géométrie non-euclidienne à la théorie des formes quadratiques|journal=Association Française Pour l'Avancement des Sciences|volume=10|pages=132–138|url=http://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1881af.pdf}}{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{Cite journal|author=Reynolds, W. F.|year=1993|title=Hyperbolic geometry on a hyperboloid|journal=The American Mathematical Monthly|volume=100|issue=5|pages=442–455|jstor=2324297|doi=10.1080/00029890.1993.11990430}}</ref> In addition, Poincaré's other models of hyperbolic geometry ([[Poincaré disk model]], [[Poincaré half-plane model]]) as well as the [[Beltrami–Klein model]] can be related to the relativistic velocity space (see [[Gyrovector space]]).
In 1881 Poincaré described [[hyperbolic geometry]] in terms of the [[hyperboloid model]], formulating transformations leaving invariant the [[Lorentz interval]] <math>x^2+y^2-z^2=-1</math>, which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions.<ref>{{Cite journal|author=Poincaré, H.|year=1881|title=Sur les applications de la géométrie non-euclidienne à la théorie des formes quadratiques|journal=Association Française Pour l'Avancement des Sciences|volume=10|pages=132–138|url=http://henripoincarepapers.univ-nantes.fr/chp/hp-pdf/hp1881af.pdf}}{{Dead link|date=June 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{Cite journal|author=Reynolds, W. F.|year=1993|title=Hyperbolic geometry on a hyperboloid|journal=The American Mathematical Monthly|volume=100|issue=5|pages=442–455|jstor=2324297|doi=10.1080/00029890.1993.11990430}}</ref> In addition, Poincaré's other models of hyperbolic geometry ([[Poincaré disk model]], [[Poincaré half-plane model]]) as well as the [[Beltrami–Klein model]] can be related to the relativistic velocity space (see [[Gyrovector space]]).
While this is the view of most historians, a minority go much further, such as [[E. T. Whittaker]], who held that Poincaré and Lorentz were the true discoverers of relativity.<ref>Whittaker 1953, Secondary sources on relativity</ref>
While this is the view of most historians, a minority go much further, such as [[E. T. Whittaker]], who held that Poincaré and Lorentz were the true discoverers of relativity.<ref>Whittaker 1953, Secondary sources on relativity</ref>
===Algebra and number theory===
===Algebra and number theory===