advanced_tools:group_theory:poincare_group

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advanced_tools:group_theory:poincare_group [2018/05/04 09:53] jakobadmin ↷ Links adapted because of a move operation |
advanced_tools:group_theory:poincare_group [2020/09/07 06:41] 14.161.7.200 [Why is it interesting?] |
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<tabbox Intuitive> | <tabbox Intuitive> | ||

- | The Poincare [[advanced_tools:group_theory|group]] is the mathematical tool that we use to describe the [[basic_tools:symmetry|symmetry]] of [[theories:special_relativity|special relativity]]. | + | The Poincare [[advanced_tools:group_theory|group]] is the mathematical tool that we use to describe the [[basic_tools:symmetry|symmetry]] of [[models:special_relativity|special relativity]]. |

The starting point for Einstein on his road towards what is now called special relativity was the experimental observation that the speed of light has the same value in all inertial frames of reference. This curious fact of nature was discovered by the famous [[experiments:michelson_morley|Michelson-Morley experiment]]. | The starting point for Einstein on his road towards what is now called special relativity was the experimental observation that the speed of light has the same value in all inertial frames of reference. This curious fact of nature was discovered by the famous [[experiments:michelson_morley|Michelson-Morley experiment]]. | ||

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The Poincare group is the set of all transformations that leave the speed of light invariant. Thus, the Poincare group yields all possible transformations between allowed frames of reference. This is incredibly useful, when we want to write down fundamental laws of nature. The fundamental laws should be valid in all allowed frames of reference, otherwise they would be quite useless. | The Poincare group is the set of all transformations that leave the speed of light invariant. Thus, the Poincare group yields all possible transformations between allowed frames of reference. This is incredibly useful, when we want to write down fundamental laws of nature. The fundamental laws should be valid in all allowed frames of reference, otherwise they would be quite useless. | ||

- | In practice, we can use our knowledge of all transformations inside the Poincare group to write down equations that are invariant under all these transformations. These equations then hold in all allowed frames of reference. This is such a strong restriction on the possible equations that is is almost enough to derive the most important equations of fundamental physics: the Dirac equation, the Klein-Gordon equation and the Maxwell-Equations. | + | In practice, we can use our knowledge of all transformations inside the Poincare group to write down equations that are invariant under all these transformations. These equations then hold in all allowed frames of reference. This is such a strong restriction on the possible equations that is almost enough to derive the most important equations of fundamental physics: the Dirac equation, the Klein-Gordon equation and the Maxwell-Equations. |

<blockquote>"//The Hilbert space of one-particle states is always an irreducible | <blockquote>"//The Hilbert space of one-particle states is always an irreducible |

advanced_tools/group_theory/poincare_group.txt · Last modified: 2020/09/07 06:41 by 14.161.7.200

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