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- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/03%3A_Differential_Geometry/3.05%3A_Intrinsic_QuantitiesModels can be dangerous, because they can tempt us to impute physical reality to features that are purely extrinsic, i.e., that are only present in that particular model. This is as opposed to intrins...Models can be dangerous, because they can tempt us to impute physical reality to features that are purely extrinsic, i.e., that are only present in that particular model. This is as opposed to intrinsic features, which are present in all models, and which are therefore logically implied by the axioms of the system itself. The existence of lunes is clearly an intrinsic feature of non-Euclidean geometries, because intersection of lines was defined before any model has even been proposed.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/02%3A_Geometry_of_Flat_Spacetime/2.09%3A_Three_Spatial_Dimensions_(Part_2)where we assume that the square has negligible size, so that all four Lorentz boosts act in a way that preserves the origin of the coordinate systems. (We have no convenient way in our notation L(. . ...where we assume that the square has negligible size, so that all four Lorentz boosts act in a way that preserves the origin of the coordinate systems. (We have no convenient way in our notation L(. . .) to describe a transformation that does not preserve the origin.) The first transformation, L(−vˆy), changes coordinates measured by the original gyroscope-defined frame to new coordinates measured by the new gyroscope-defined frame, after the box has been accelerated in the positive y …
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/02%3A_Geometry_of_Flat_Spacetime/2.06%3A_The_Light_ConeIn Newtonian physics, causal relationships fell into two classes: (1) could potentially cause any event that lay in its future or (2) could have been caused by any event in its past. In a Lorentz spa...In Newtonian physics, causal relationships fell into two classes: (1) could potentially cause any event that lay in its future or (2) could have been caused by any event in its past. In a Lorentz spacetime, there is a third class of events that are too far away from in space, and too close in time, to allow any cause and effect relationship, since causality’s maximum velocity is c . The boundary of this set is formed by the lines with slope ±1 on a (t,x) plot. This is referred to as the light
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.35%3A_Einstein_RelativityThe Maxwell equations are inconsistent with Galilean relativity. Here we review Einstein's solution to this problem, which preserves the principle of relativity, and replaces the Galilean transformati...The Maxwell equations are inconsistent with Galilean relativity. Here we review Einstein's solution to this problem, which preserves the principle of relativity, and replaces the Galilean transformation with a Lorentz transformation.
