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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 [[s:The Measure of Time|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 [[s:The Measure of Time|The Measure of Time]] (1898), Poincaré said, "

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.<ref>{{Citation

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.<ref>{{Citation

| last=Poincaré|first= Henri | year=1898 | title=The Measure of Time | journal=Revue de Métaphysique et de Morale | volume =6 | pages =1–13| title-link=s:The Measure of Time }}</ref>

| last=Poincaré|first= Henri | year=1898 | title=The Measure of Time | journal=Revue de Métaphysique et de Morale | volume =6 | pages =1–13| title-link=s:The Measure of Time }}</ref>

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.<ref name=action>{{Citation

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.<ref name=action>{{Citation

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。

1881年，庞加莱用<font color="#ff8000"> 双曲面模型Hyperboloid model</font>描述了<font color="#ff8000"> 双曲几何学Hyperbolic geometry</font>，提出了洛伦兹区间<math>x^2+y^2-z^2=-1</math>上不变的变换，使其在数学上等价于2+1维的<font color="#ff8000"> 洛伦兹变换</font>。此外，庞加莱的其他双曲几何模型(<font color="#ff8000"> 庞加莱圆盘模型，庞加莱半平面模型</font>)以及<font color="#ff8000"> 贝尔特拉米-克莱因Beltrami–Klein模型</font>都可以与相对论速度空间（见<font color="#ff8000"> 陀螺矢量空间</font>）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>

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>

In 1892 Poincaré developed a mathematical theory of light including polarization. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the Poincaré sphere. It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.

In 1892 Poincaré developed a mathematical theory of light including polarization. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the Poincaré sphere. It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions.

====Principle of relativity and Lorentz transformations相对论原理与洛伦兹变换====

====Principle of relativity and Lorentz transformations相对论原理与洛伦兹变换====