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- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/17%3A_Relativistic_Mechanics/17.05%3A_Geometry_of_Space-timeFour dimensional space-time.
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_I_(Raymond)/04%3A_Special_Relativity/4.02%3A_Spacetime_Thinking_in_Special_RelativityNotice that it is physically possible for an object to have a world line which connects event O at the origin and the events A and D in Figure \(\PageIndex{3}\):, since the slope of the resulting worl...Notice that it is physically possible for an object to have a world line which connects event O at the origin and the events A and D in Figure \(\PageIndex{3}\):, since the slope of the resulting world line would exceed unity, and thus represent a velocity less than the speed of light.
- https://phys.libretexts.org/Courses/Grand_Rapids_Community_College/PH246_Calculus_Physics_II_(2025)/14%3A__Relativity/14.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/01%3A__Relativity/1.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/05%3A__Relativity/5.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/05%3A__Relativity/5.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_I_(Raymond)/04%3A_Special_Relativity/4.01%3A_Galilean_Spacetime_ThinkingFigure \(\PageIndex{2}\):: The left panel shows the world line in the unprimed reference frame, while the right panel shows it in the primed frame, which moves to the right at speed U relative to the ...Figure \(\PageIndex{2}\):: The left panel shows the world line in the unprimed reference frame, while the right panel shows it in the primed frame, which moves to the right at speed U relative to the unprimed frame. (The “prime” is just a label that allows us to distinguish the axes corresponding to the two reference frames.)
