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- https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/01%3A_Special_Relativity/1.02%3A_The_Spacetime_IntervalIn Newtonian mechanics, the length of an object is invariant. That is, if you use a different coordinate system to mark locations, the result you get for the length does not change. In Special Relativ...In Newtonian mechanics, the length of an object is invariant. That is, if you use a different coordinate system to mark locations, the result you get for the length does not change. In Special Relativity, however, it is a combination of distance and time that is invariant from one coordinate system to another. We call this the spacetime interval.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/01%3A__Relativity/1.04%3A_Time_DilationTime dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location)....Time dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location). Observers moving at a relative velocity v do not measure the same elapsed time between two events. Proper time Δτ is the time measured in the reference frame where the start and end of the time interval occur at the same location.
- 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/Mechanics_and_Relativity_(Idema)/12%3A_Spacetime_Diagrams/12.03%3A_Worldlines_and_Proper_Time
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/15%3A_Special_Relativity/15.10%3A_Time_DilationThe interval s between two events is clearly independent of the orientation any reference frames, and is the same when referred to two reference frames that may be inclined to each other. But the co...The interval s between two events is clearly independent of the orientation any reference frames, and is the same when referred to two reference frames that may be inclined to each other. But the components of the vector joining two events, or their projections on to the time axis or a space axis are not at all expected to be equal.
- https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/04%3A_Trip_to_Canopus/4.09%3A_Relativity_of_SimultaneityThe so-called Twin Paradox is resolved by noticing that between the Earth-clock reading of 3.96 years, taken from the outward rocket lookout station at turnaround and the Earth-clock reading of 198.04...The so-called Twin Paradox is resolved by noticing that between the Earth-clock reading of 3.96 years, taken from the outward rocket lookout station at turnaround and the Earth-clock reading of 198.04 years, taken by the returning-rocket lookout station at turnaround, there is a difference of 194.08 years."
- https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Introduction_to_Physics_(Park)/05%3A_Unit_4-_Modern_Physics_-_Quantum_Mechanics_Special_Relativity_and_Nuclear_and_Particle_Physics/13%3A_Special_Relativity/13.03%3A_Simultaneity_and_Time_DilationTwo simultaneous events are not necessarily simultaneous to all observers—simultaneity is not absolute. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to...Two simultaneous events are not necessarily simultaneous to all observers—simultaneity is not absolute. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to another observer. Observers moving at a relative velocity do not measure the same elapsed time for an event. Proper time is measured by an observer at rest relative to the event being observed and implies that relative velocity cannot exceed the speed of light.
- https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9D__Modern_Physics/2%3A_Foundations_of_Special_Relativity/2.2%3A_The_Nature_of_TimeWe continue in the same manner as Einstein – with what he called "thought experiments." These are simply logical arguments that lead to inescapable conclusions if the relativity principle is correct. ...We continue in the same manner as Einstein – with what he called "thought experiments." These are simply logical arguments that lead to inescapable conclusions if the relativity principle is correct. Some of the most startling of these conclusions are related to the nature of time.
- https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/01%3A_Spacetime_Overview/1.03%3A_Events_and_Intervals_AloneIn this book we often call the proper time the wristwatch time and the proper clock the wristwatch to emphasize that the proper clock is carried so that it is "present" at each of the two events as th...In this book we often call the proper time the wristwatch time and the proper clock the wristwatch to emphasize that the proper clock is carried so that it is "present" at each of the two events as the events occur.
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/28%3A_Special_Relativity/28.02%3A_Simultaneity_and_Time_DilationTwo simultaneous events are not necessarily simultaneous to all observers—simultaneity is not absolute. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to...Two simultaneous events are not necessarily simultaneous to all observers—simultaneity is not absolute. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to another observer. Observers moving at a relative velocity do not measure the same elapsed time for an event. Proper time is measured by an observer at rest relative to the event being observed and implies that relative velocity cannot exceed the speed of light.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/05%3A__Relativity/5.04%3A_Time_DilationTime dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location)....Time dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location). Observers moving at a relative velocity v do not measure the same elapsed time between two events. Proper time Δτ is the time measured in the reference frame where the start and end of the time interval occur at the same location.
