models:special_relativity
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models:special_relativity [2018/05/06 13:41] jakobadmin [Intuitive] |
models:special_relativity [2023/04/02 03:32] (current) edi [Concrete] |
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| - the speed of light in a vacuum has the same value for all (inertial) observers. | - the speed of light in a vacuum has the same value for all (inertial) observers. | ||
| - | These two postulates taken together tell us that space and time are not absolute but must be relative, i.e. change depending on the observer. Otherwise, it isn't possible that different moving observers always measure exactly the same value for the speed of light. | + | These two postulates taken together tell us that space and time are not absolute but must be relative, i.e. change depending on the observer. Otherwise, it isn't possible that different moving observers always measure exactly the same value for the speed of light. This was discovered by the famous [[experiments:michelson_morley|Michelson Morley experiment]]. |
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| * A particularly nice intuitive introduction is the free online book [[https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/|Einstein for Everyone]] by John D. Norton | * A particularly nice intuitive introduction is the free online book [[https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/|Einstein for Everyone]] by John D. Norton | ||
| * The basic idea of relativity is nicely explained here: https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/the-first-principle-of-relativity/ | * The basic idea of relativity is nicely explained here: https://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/the-first-principle-of-relativity/ | ||
| - | * http://www.wetsavannaanimals.net/wordpress/galileo-groups-and-light/ | + | * [[http://www.wetsavannaanimals.net/wordpress/galileo-groups-and-light/|Of Galileo, Groups and What’s So Special about the Speed of Light]] by Rod Vance |
| * It's About Time: Understanding Einstein's Relativity by Mermin is a great book for laymen on special relativity. | * It's About Time: Understanding Einstein's Relativity by Mermin is a great book for laymen on special relativity. | ||
| * [[http://www.spacetimetravel.org/|Relativity visualized]] - a website by Ute Krause and Corvin Zahn | * [[http://www.spacetimetravel.org/|Relativity visualized]] - a website by Ute Krause and Corvin Zahn | ||
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| <tabbox Concrete> | <tabbox Concrete> | ||
| - | Best beginner Special Relativity Textbooks are: | + | The best beginner Special Relativity Textbooks are: |
| * Special Relativity by French | * Special Relativity by French | ||
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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 | ||
| + | |||
| + | ---- | ||
| + | |||
| + | **Distance in Space vs. Space-Time:** | ||
| + | |||
| + | 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]]. | ||
| + | |||
| + | [{{ :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]]. | ||
| + | |||
| + | |||
| + | ---- | ||
| 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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| We can therefore conclude that our free particle moves unaccelerated along a straight line. | We can therefore conclude that our free particle moves unaccelerated along a straight line. | ||
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| + | <blockquote>We believe that special relativity at the present time stands | ||
| + | as a universal theory describing the structure of a common space-time arena in which | ||
| + | all fundamental processes take place. All the laws of physics are constrained by special | ||
| + | relativity acting as a sort of ”super law”. | ||
| + | |||
| + | <cite>One more derivation of the Lorentz transformation by Jean-Marc Levy-Leblond</cite></blockquote> | ||
| + | |||
| + | ---- | ||
| + | |||
| 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. | ||
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