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Theory of relativity
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== Modern applications == Far from being simply of theoretical interest, relativistic effects are important practical engineering concerns. Satellite-based measurement needs to take into account relativistic effects, as each satellite is in motion relative to an Earth-bound user, and is thus in a different frame of reference under the theory of relativity. Global positioning systems such as [[GPS]], [[GLONASS]], and [[Galileo (satellite navigation)|Galileo]], must account for all of the relativistic effects in order to work with precision, such as the consequences of the Earth's gravitational field.<ref>Ashby, N. Relativity in the Global Positioning System. ''Living Rev. Relativ.'' '''6''', 1 (2003). {{doi|10.12942/lrr-2003-1}}{{cite web |url=http://relativity.livingreviews.org/Articles/lrr-2003-1/download/lrr-2003-1Color.pdf |title=Archived copy |access-date=2015-12-09 |url-status=dead |archive-url=https://web.archive.org/web/20151105155910/http://relativity.livingreviews.org/Articles/lrr-2003-1/download/lrr-2003-1Color.pdf |archive-date=2015-11-05 }}</ref> This is also the case in the high-precision measurement of time.<ref name=Francis2002>{{cite journal|last=Francis|first=S.|author2=B. Ramsey|author3=S. Stein|author4=Leitner, J.|author5=Moreau, J.M.|author6=Burns, R.|author7=Nelson, R.A.|author8=Bartholomew, T.R.|author9=Gifford, A.|title=Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble|journal=Proceedings 34th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting|date=2002|pages=201β214|url=http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf|access-date=14 April 2013|url-status=dead|archive-url=https://web.archive.org/web/20130217211012/http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf|archive-date=17 February 2013}}</ref> Instruments ranging from electron microscopes to particle accelerators would not work if relativistic considerations were omitted.<ref>{{cite book |title=Einstein's Mirror |edition=illustrated |first1=Tony |last1=Hey |first2=Anthony J. G. |last2=Hey |first3=Patrick |last3=Walters |publisher=Cambridge University Press |date=1997 |isbn=978-0-521-43532-1 |page=x (preface) |url=https://archive.org/details/isbn_9780521435321|url-access=registration }}</ref>
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