models:special_relativity
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models:special_relativity [2018/05/26 14:12] jakobadmin [Why is it interesting?] |
models:special_relativity [2023/04/02 03:32] (current) edi [Concrete] |
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| + | * [[https://terrytao.files.wordpress.com/2013/01/relativistic1.pdf|Notes on Special Relativity for High-School Students]] by Field Medalist Terrence Tao | ||
| * [[https://arxiv.org/abs/physics/0302045|Nothing but Relativity]] by Palash B. Pal | * [[https://arxiv.org/abs/physics/0302045|Nothing but Relativity]] by Palash B. Pal | ||
| * [[http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf|Derivation of the Lorentz Transformation]] by Yakovenko | * [[http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf|Derivation of the Lorentz Transformation]] by Yakovenko | ||
| * [[http://aapt.scitation.org/doi/pdf/10.1119/1.11622|A simple method for illustrating the difference between the homogeneous and inhomogeneous Lorentz groups]] by Y. S. Kim | * [[http://aapt.scitation.org/doi/pdf/10.1119/1.11622|A simple method for illustrating the difference between the homogeneous and inhomogeneous Lorentz groups]] by Y. S. Kim | ||
| * [[http://aapt.scitation.org/doi/abs/10.1119/1.11632|Representing arbitrary boosts for undergraduates]] by Charles P. Frahm | * [[http://aapt.scitation.org/doi/abs/10.1119/1.11632|Representing arbitrary boosts for undergraduates]] by Charles P. Frahm | ||
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| + | ---- | ||
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| + | **Distance in Space vs. Space-Time:** | ||
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| + | The diagram below illustrates the difference between distance in Euclidean space (left-hand side) and "distance" (actually proper time) in space-time according to Einstein's special theory of relativity (right-hand side). Time dilation is shown in red. For a more detailed explanation of this diagram see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#space_time_dist|Fun with Symmetry]]. | ||
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| + | [{{ :models:space_time_dist.jpg?nolink }}] | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
| + | Mathematically, special relativity is the statement that all laws of physics are invariant under the [[advanced_tools:group_theory:poincare_group|Poincare group]]. | ||
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| + | ---- | ||
| In special relativity spacetime denotes the configuration space of a __single__ point particle. We denote the Minkowski spacetime by $Q$, i.e., $\mathbb{R}^{3+1}\ni(x^0,\ldots,x^n)$ with the [[advanced_tools:minkowski_metric|Minkowksi metric]] | In special relativity spacetime denotes the configuration space of a __single__ point particle. We denote the Minkowski spacetime by $Q$, i.e., $\mathbb{R}^{3+1}\ni(x^0,\ldots,x^n)$ with the [[advanced_tools:minkowski_metric|Minkowksi metric]] | ||
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| <cite>One more derivation of the Lorentz transformation by Jean-Marc Levy-Leblond</cite></blockquote> | <cite>One more derivation of the Lorentz transformation by Jean-Marc Levy-Leblond</cite></blockquote> | ||
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| + | ---- | ||
| The [[experiments:michelson_morley|Michelson-Morley experiment]] demonstrated that the speed of light is the same in all frames of reference. Special relativity is the correct theory that incorporates this curious fact of nature. | The [[experiments:michelson_morley|Michelson-Morley experiment]] demonstrated that the speed of light is the same in all frames of reference. Special relativity is the correct theory that incorporates this curious fact of nature. | ||
models/special_relativity.1527336743.txt.gz · Last modified: 2018/05/26 12:12 (external edit)
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