Editing Twin paradox (section)

==Resolution of the paradox in special relativity==

The paradoxical aspect of the twins' situation arises from the fact that at any given moment the travelling twin's clock is running slow in the earthbound twin's inertial frame, but based on the relativity principle one could equally argue that the earthbound twin's clock is running slow in the travelling twin's inertial frame.<ref name='Ohanian'>{{cite book|last=Ohanian|first=Hans|title=Special relativity: a modern introduction|date=2001|publisher=Physics Curriculum and Instruction|location=Lakeville, MN|isbn=0971313415}}</ref><ref name='Harris'>{{cite book|last=Harris|first=Randy|title=Modern Physics|date=2008|publisher=Pearson Addison-Wesley|location=San Francisco, CA|isbn=978-0805303087}}</ref><ref name='Rindler'>{{cite book|last=Rindler|first=W|title=Introduction to special relativity|date=2006|publisher=Oxford University Press|location=Oxford, UK|isbn=9780198567318}}</ref> One proposed resolution is based on the fact that the earthbound twin is at rest in the same inertial frame throughout the journey, while the travelling twin is not: in the simplest version of the thought-experiment, the travelling twin switches at the midpoint of the trip from being at rest in an inertial frame which moves in one direction (away from the Earth) to being at rest in an inertial frame which moves in the opposite direction (towards the Earth). In this approach, determining which observer switches frames and which does not is crucial. Although both twins can legitimately claim that they are at rest in their own frame, only the traveling twin experiences acceleration when the spaceship engines are turned on. This acceleration, measurable with an accelerometer, makes his rest frame temporarily non-inertial. This reveals a crucial asymmetry between the twins' perspectives: although we can predict the aging difference from both perspectives, we need to use different methods to obtain correct results.

===Role of acceleration===
Although some solutions attribute a crucial role to the acceleration of the travelling twin at the time of the turnaround,<ref name='Ohanian'/><ref name='Harris'/><ref name='Rindler'/><ref name='Weidner'>{{cite book|last=Weidner|first=Richard|title=Physics|url=https://archive.org/details/physics0000weid|url-access=registration|date=1985|publisher=Allyn and Bacon|location=Needham Heights, MA|isbn=0205111556}}</ref> others note that the effect also arises if one imagines two separate travellers, one outward-going and one inward-coming, who pass each other and synchronize their clocks at the point corresponding to "turnaround" of a single traveller. In this version, physical acceleration of the travelling clock plays no direct role;<ref name="Einstein, A. 1923 pp. 38">Einstein, A., Lorentz, H.A., Minkowski, H., and Weyl, H. (1923). [[Arnold Sommerfeld]]. ed. ''The Principle of Relativity.'' Dover Publications: Mineola, NY. pp. 38–49.</ref><ref name='Kogut'>{{cite book |title=Introduction to Relativity: For Physicists and Astronomers |first1=John B. |last1=Kogut |publisher=Academic Press |year=2012 |isbn=978-0-08-092408-3 |page=35 |url=https://books.google.com/books?id=9AKPpSxiN4IC}} [https://books.google.com/books?id=9AKPpSxiN4IC&pg=PA35 Extract of page 35]</ref><ref name='Minguzzi'/> "the issue is how long the world-lines are, not how bent".<ref name='Maudlin'>{{cite book|last=Maudlin|first=Tim|title=Philosophy of physics : space and time|date=2012|publisher=Princeton University Press|location=Princeton|isbn=9780691143095|pages=77–83}}</ref> The length referred to here is the Lorentz-invariant length or "proper time interval" of a trajectory which corresponds to the elapsed time measured by a clock following that trajectory (see Section [[#Difference_in_elapsed_time as_a_result_of_differences_in_twins'_spacetime_paths|Difference in elapsed time as a result of differences in twins' spacetime paths]] below). In Minkowski spacetime, the travelling twin must feel a different history of accelerations from the earthbound twin, even if this just means accelerations of the same size separated by different amounts of time,<ref name='Maudlin'/> however "even this role for acceleration can be eliminated in formulations of the twin paradox in curved spacetime, where the twins can fall freely along space-time geodesics between meetings".<ref name='Debs_Redhead'/>

===Relativity of simultaneity===
[[Image:Twin Paradox Minkowski Diagram.svg|thumb|right|333px|[[Minkowski diagram]] of the twin paradox. There is a difference between the trajectories of the twins: the trajectory of the ship is equally divided between two different inertial frames, while the Earth-based twin stays in the same inertial frame.]]
For a moment-by-moment understanding of how the time difference between the twins unfolds, one must understand that in special relativity there is no concept of ''absolute present''. For different inertial frames there are different sets of events that are simultaneous in that frame. This [[relativity of simultaneity]] means that switching from one inertial frame to another requires an adjustment in what slice through spacetime counts as the "present". In the spacetime diagram on the right, drawn for the reference frame of the Earth-based twin, that twin's world line coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the ''planes of simultaneity'' for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnaround, the traveling twin calculates the age of the Earth-based twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnaround, if he recalculates, he will measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin. When one transfers from the outgoing inertial frame to the incoming inertial frame there is a jump discontinuity in the age of the Earth-based twin<ref name='Ohanian'/><ref name='Harris'/><ref name='Kogut'/><ref name="Wheeler, J. 1992 pp. 38, 170">Wheeler, J., Taylor, E. (1992). ''Spacetime Physics, second edition.'' W. H. Freeman: New York, pp. 38, 170-171.</ref><ref name="Einstein et al 1923">Einstein, A., Lorentz, H.A., Minkowski, H., and Weyl, H. (1923). Arnold Sommerfeld. ed. ''The Principle of Relativity.'' Dover Publications: Mineola, NY. p. 38.</ref> (6.4 years in the [[#Specific example|example]] above).