What is internal space translation?
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INTERNAL SPACE TRANSLATION
In our expressions above we have tacitly taken a mixture of the a”active view ” and the “passive view” of transformations. That means for translations we have transformed space (moving the origin, etc.) leaving the vector invariant, which is linked closely to the standard verbal description of symmetries: we transform the coordinate axes leaving the vector pointing as it was before. For rotations we have not yet given enough detail to make out what we are doing, but for boosts we have taken the alternative “active view” where we change , leaving the origin invariant. A little thought shows that these two approaches are inverse; i.e., an active transformation is always the inverse of the corresponding passive one. From here on we shall carefully use active transformations! The two views are obviously equivalent.
INTERNAL SPACE TRANSLATION
In our expressions above we have tacitly taken a mixture of the a”active view ” and the “passive view” of transformations. That means for translations we have transformed space (moving the origin, etc.) leaving the vector invariant, which is linked closely to the standard verbal description of symmetries: we transform the coordinate axes leaving the vector pointing as it was before. For rotations we have not yet given enough detail to make out what we are doing, but for boosts we have taken the alternative “active view” where we change , leaving the origin invariant. A little thought shows that these two approaches are inverse; i.e., an active transformation is always the inverse of the corresponding passive one. From here on we shall carefully use active transformations! The two views are obviously equivalent.
HARSSNI100:
Super explanation QHM
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