更改

In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.

In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.

In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.

In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.

In 1892 Poincaré developed a mathematical theory of light including [[polarization (waves)|polarization]]. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the [[Poincaré sphere (optics)|Poincaré sphere]].<ref>{{Cite book|author=Poincaré, H. |year=1892|title=Théorie mathématique de la lumière II|location=Paris|publisher=Georges Carré|chapter-url=https://archive.org/details/thoriemathma00poin|chapter=Chapitre XII: Polarisation rotatoire}}</ref> 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.<ref>{{Cite journal|author=Tudor, T.|year=2018|title=Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics|journal=Symmetry|volume=10|issue=3|pages=52|doi=10.3390/sym10030052|doi-access=free}}</ref>

In 1892 Poincaré developed a mathematical theory of light including [[polarization (waves)|polarization]]. His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the [[Poincaré sphere (optics)|Poincaré sphere]].<ref>{{Cite book|author=Poincaré, H. |year=1892|title=Théorie mathématique de la lumière II|location=Paris|publisher=Georges Carré|chapter-url=https://archive.org/details/thoriemathma00poin|chapter=Chapitre XII: Polarisation rotatoire}}</ref> 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.<ref>{{Cite journal|author=Tudor, T.|year=2018|title=Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics|journal=Symmetry|volume=10|issue=3|pages=52|doi=10.3390/sym10030052|doi-access=free}}</ref>

<blockquote>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:

<blockquote>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:

| author=Poincaré, H. | year=1900 | title= Les relations entre la physique expérimentale et la physique mathématique | journal=Revue Générale des Sciences Pures et Appliquées | volume =11 | pages =1163–1175 | url=http://gallica.bnf.fr/ark:/12148/bpt6k17075r/f1167.table}}. Reprinted in "Science and Hypothesis", Ch. 9–10.</ref>

| author=Poincaré, H. | year=1900 | title= Les relations entre la physique expérimentale et la physique mathématique | journal=Revue Générale des Sciences Pures et Appliquées | volume =11 | pages =1163–1175 | url=http://gallica.bnf.fr/ark:/12148/bpt6k17075r/f1167.table}}. Reprinted in "Science and Hypothesis", Ch. 9–10.</ref>

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.<ref name=louis>{{Citation|author=Poincaré, Henri|year=1913|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=The Foundations of Science (The Value of Science)|pages=297–320|publisher=Science Press|place=New York|postscript=; article translated from 1904 original}} available in [https://books.google.com/books/about/The_Foundations_of_Science.html?id=mBvNabP35zoC&pg=PA297 online chapter from 1913 book]</ref>

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.<ref name=louis>{{Citation|author=Poincaré, Henri|year=1913|chapter=[[s:The Principles of Mathematical Physics|The Principles of Mathematical Physics]]|title=The Foundations of Science (The Value of Science)|pages=297–320|publisher=Science Press|place=New York|postscript=; article translated from 1904 original}} available in [https://books.google.com/books/about/The_Foundations_of_Science.html?id=mBvNabP35zoC&pg=PA297 online chapter from 1913 book]</ref>

In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.<ref name="univ-nantes">

In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance." In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz.<ref name="univ-nantes">

and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is invariant. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of four-vectors. Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907.

and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is invariant. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of four-vectors. Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907.

证明了任意函数“左”(右)必为“数”(Lorentz 用另一个论点设置“数”)的整数，从而使变换形成一个组。在1906年庞加莱论文的放大版本中，他指出组合 x ^ 2 + y ^ 2 + z ^ 2-c ^ 2 </math > 是不变的。他指出，洛伦兹变换是通过引入 < math > ct sqrt {-1} </math > 作为第四个虚数坐标，仅仅是在原点四维上的一个旋转，并且他使用了早期形式的四向量。庞加莱在1907年对其新力学的四维重新表述缺乏兴趣，因为他认为，将物理学翻译成四维几何学的语言将需要为有限的利润付出太多的努力。因此，在1907年，赫尔曼·闵可夫斯基 · 马丁发现了这个概念的后果。

并证明了任意函数<math>\ell\left(\varepsilon\right)</math>对于所有<math>\varepsilon</math>必须是统一的（Lorentz通过一个不同的参数设置<math>\ell = 1</math>），以使变换形成一个组。在1906年发表的论文的放大版中，庞加莱指出组合<math>x^2+ y^2+ z^2- c^2t^2</math>是不变的。他通过引入<math>ct\sqrt{-1}</math>作为第四个虚坐标，指出Lorentz变换仅仅是四维空间中绕原点的旋转，他使用了四个向量的早期形式。庞加莱在1907年表示对他的新力学的四维重新表述不感兴趣，因为在他看来，将物理学翻译成四维几何的语言需要付出太多的努力才能获得有限的益处。1907年，由赫尔曼·明科夫斯基（Hermann Minkowski）提出了这个概念的后果。

 

{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.3, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=255–257 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz3.html}}</ref>

{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.3, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=255–257 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz3.html}}</ref>

In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.<ref name="univ-nantes2">{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.4, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=257–258 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz4.html}}</ref>

In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law.<ref name="univ-nantes2">{{Citation | author=Poincaré, H. | year=2007 | editor=Walter, S. A. | contribution= 38.4, Poincaré to H. A. Lorentz, May 1905 | title=La correspondance entre Henri Poincaré et les physiciens, chimistes, et ingénieurs |pages=257–258 |place=Basel | publisher=Birkhäuser|contribution-url=http://henripoincarepapers.univ-nantes.fr/chp/text/lorentz4.html}}</ref>

Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote:<ref name="1905 paper">[http://www.academie-sciences.fr/pdf/dossiers/Poincare/Poincare_pdf/Poincare_CR1905.pdf] (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.</ref>

庞加莱后来在1905年6月5日巴黎科学院会议上发表了一篇论文，其中讨论了这些问题。在出版的版本中，他这样写道：<ref name="1905 paper">[http://www.academie-sciences.fr/pdf/dossiers/Poincare/Poincare_pdf/Poincare_CR1905.pdf] (PDF) Membres de l'Académie des sciences depuis sa création : Henri Poincare. Sur la dynamique de l' electron. Note de H. Poincaré. C.R. T.140 (1905) 1504–1508.</ref>

Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems:

Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems:

像其他人一样，庞加莱(1900)发现了质量和电磁能量之间的关系。在研究作用力/反作用力原理和洛伦兹理论之间的冲突时，他试图确定当电磁场包括在内时，重心是否仍以均匀速度运动。能量携带质量并且批评以太解决方案来补偿上述问题的可能性:

像其他人一样，庞加莱(1900)发现了质量和电磁能量之间的关系。在研究作用力/反作用力原理和洛伦兹理论之间的冲突时，他试图确定当电磁场包括在内时，重心是否仍以均匀速度运动。<font color="#32CD32">能量携带质量和用有争议的乙太解决方案来弥补上述问题的可能性the possibility that energy carries mass and criticized the ether solution to compensate the above-mentioned problems</font>

<blockquote>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:

<blockquote>The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:

::<math>x^\prime = k\ell\left(x + \varepsilon t\right)\!,\;t^\prime = k\ell\left(t + \varepsilon x\right)\!,\;y^\prime = \ell y,\;z^\prime = \ell z,\;k = 1/\sqrt{1-\varepsilon^2}.</math></blockquote>

::<math>x^\prime = k\ell\left(x + \varepsilon t\right)\!,\;t^\prime = k\ell\left(t + \varepsilon x\right)\!,\;y^\prime = \ell y,\;z^\prime = \ell z,\;k = 1/\sqrt{1-\varepsilon^2}.</math></blockquote>

He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass <math>\gamma m</math>, Abraham's theory of variable mass and Kaufmann's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Madame Curie.

He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass <math>\gamma m</math>, Abraham's theory of variable mass and Kaufmann's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Madame Curie.

他还讨论了另外两个无法解释的效应: (1)洛伦兹变质量理论暗示的质量不守恒，亚伯拉罕变质量理论和考夫曼关于快速运动电子质量的实验，以及(2)居里夫人镭实验中的能量不守恒。

他还讨论了另外两个无法解释的效应: (1)洛伦兹变质量理论<math>\gamma m</math>暗示的质量不守恒，亚伯拉罕变质量理论和考夫曼关于快速运动电子质量的实验，以及(2)居里夫人镭实验中的能量不守恒。

and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is [[Invariant (mathematics)|invariant]]. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of [[four-vector]]s.<ref name=long>{{Citation

and showed that the arbitrary function <math>\ell\left(\varepsilon\right)</math> must be unity for all <math>\varepsilon</math> (Lorentz had set <math>\ell = 1</math> by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination <math>x^2+ y^2+ z^2- c^2t^2</math> is [[Invariant (mathematics)|invariant]]. He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing <math>ct\sqrt{-1}</math> as a fourth imaginary coordinate, and he used an early form of [[four-vector]]s.<ref name=long>{{Citation

| author=Poincaré, H. | year=1906 | title=Sur la dynamique de l'électron (On the Dynamics of the Electron) | journal=Rendiconti del Circolo Matematico Rendiconti del Circolo di Palermo | volume =21 | pages =129–176

| author=Poincaré, H. | year=1906 | title=Sur la dynamique de l'électron (On the Dynamics of the Electron) | journal=Rendiconti del Circolo Matematico Rendiconti del Circolo di Palermo | volume =21 | pages =129–176

It was Albert Einstein's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m&nbsp;=&nbsp;E/c² that resolved Poincaré's paradox, without using any compensating mechanism within the ether. 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.

It was Albert Einstein's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m&nbsp;=&nbsp;E/c² that resolved Poincaré's paradox, without using any compensating mechanism within the ether. 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.

阿尔伯特 · 爱因斯坦(Albert Einstein)的质能等效(mass-energy equivalence，1905)概念解决了庞加莱悖论(poincaré 佯谬) ，而没有使用以太中的任何补偿机制。赫兹振子在发射过程中失去了质量，动量在任何一个框架中都是守恒的。然而，关于庞加莱的重心问题的解决方案，爱因斯坦指出，庞加莱的公式和他自己1906年的公式在数学上是等价的。

阿尔伯特 · 爱因斯坦(Albert Einstein)的质能等效(mass-energy equivalence，1905)概念解决了<font color="#ff8000"> 庞加莱悖论(poincaré 佯谬)</font>，而没有使用以太中的任何补偿机制。<font color="#ff8000"> 赫兹振子Hertzian oscillato</font>在发射过程中失去了质量，动量在任何一个框架中都是守恒的。然而，关于庞加莱的重心问题的解决方案，爱因斯坦指出，庞加莱的公式和他自己1906年的公式在数学上是等价的。

| doi=10.1007/BF03013466| bibcode=1906RCMP...21..129P| hdl=2027/uiug.30112063899089 | s2cid=120211823 | url=https://zenodo.org/record/1428444| hdl-access=free }} (Wikisource translation)</ref> Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit.<ref>Walter (2007), Secondary sources on relativity</ref> So it was [[Hermann Minkowski]] who worked out the consequences of this notion in 1907.

| doi=10.1007/BF03013466| bibcode=1906RCMP...21..129P| hdl=2027/uiug.30112063899089 | s2cid=120211823 | url=https://zenodo.org/record/1428444| hdl-access=free }} (Wikisource translation)</ref> Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit.<ref>Walter (2007), Secondary sources on relativity</ref> So it was [[Hermann Minkowski]] who worked out the consequences of this notion in 1907.

 

====Mass–energy relation质量-能量关系====

====Mass–energy relation质量-能量关系====