Difference between revisions of "Properties of Geodesics: Resolving an Apparent Conflict of Global Positioning System Evidence with General Relativity"

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==Abstract==
 
==Abstract==
  
A gedanken experiment is described that exposes an apparent conflict between the treatment of proper timekeeping on geodesics according to general relativity theory, as customarily understood, and empirical evidence such as that of the Global Positioning System. The paradox is resolved by noting that there may be many geodesics between two spacetime events, only one of which represents a global maximum of proper time. The cardinality of such nonuniqueness (which may be that of the continuum) at first seems to violate the property that a geodesic between two events always incurs a (local) extremum of proper time. However, to first order (hence to observationally significant order), all free-fall orbits that have the same period have the same proper time, so no first variations of the orbits within our solution set change the proper time?a consistency check on the geodesic (extremum) interpretation of such orbits.[[Category:Scientific Paper]]
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A gedanken experiment is described that exposes an apparent conflict between the treatment of proper timekeeping on geodesics according to general relativity theory, as customarily understood, and empirical evidence such as that of the Global Positioning System. The paradox is resolved by noting that there may be many geodesics between two spacetime events, only one of which represents a global maximum of proper time. The cardinality of such nonuniqueness (which may be that of the continuum) at first seems to violate the property that a geodesic between two events always incurs a (local) extremum of proper time. However, to first order (hence to observationally significant order), all free-fall orbits that have the same period have the same proper time, so no first variations of the orbits within our solution set change the proper time?a consistency check on the geodesic (extremum) interpretation of such orbits.
  
[[Category:Relativity]]
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[[Category:Scientific Paper|properties geodesics resolving apparent conflict global positioning evidence general relativity]]
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[[Category:Relativity|properties geodesics resolving apparent conflict global positioning evidence general relativity]]

Latest revision as of 19:50, 1 January 2017

Scientific Paper
Title Properties of Geodesics: Resolving an Apparent Conflict of Global Positioning System Evidence with General Relativity
Author(s) Tom Van Flandern, Thomas E Phipps, Michael H Brill, Ronald R Hatch
Keywords Global Positioning System, GPS, General Relativity, Special Relativity, Geodesic, Orbit, Timekeeping, Proper Time
Published 2008
Journal Physics Essays
Volume 21
Number 1
Pages 57-64

Abstract

A gedanken experiment is described that exposes an apparent conflict between the treatment of proper timekeeping on geodesics according to general relativity theory, as customarily understood, and empirical evidence such as that of the Global Positioning System. The paradox is resolved by noting that there may be many geodesics between two spacetime events, only one of which represents a global maximum of proper time. The cardinality of such nonuniqueness (which may be that of the continuum) at first seems to violate the property that a geodesic between two events always incurs a (local) extremum of proper time. However, to first order (hence to observationally significant order), all free-fall orbits that have the same period have the same proper time, so no first variations of the orbits within our solution set change the proper time?a consistency check on the geodesic (extremum) interpretation of such orbits.