Editing Albert Einstein (section)

==== Equations of motion ====
{{Main|Einstein–Infeld–Hoffmann equations}}
In general relativity, gravitational force is reimagined as curvature of [[spacetime]]. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by [[John Archibald Wheeler]] that has become proverbial among physicists summarizes the theory: {{qi|Spacetime tells matter how to move; matter tells spacetime how to curve.}}<ref name="Wheeler">{{Cite book|last=Wheeler|first=John Archibald|url={{GBurl|id=zGFkK2tTXPsC|p=235}}|title=Geons, Black Holes, and Quantum Foam: A Life in Physics|date=18 June 2010|publisher=W. W. Norton & Company|isbn=978-0-393-07948-7|language=en|author-link=John Archibald Wheeler}}</ref><ref>{{Cite journal|last=Kersting|first=Magdalena|date=May 2019|title=Free fall in curved spacetime—how to visualise gravity in general relativity|journal=[[Physics Education]] |volume=54|issue=3|pages=035008|doi=10.1088/1361-6552/ab08f5|bibcode=2019PhyEd..54c5008K |s2cid=127471222 |issn=0031-9120|doi-access=free|hdl=10852/74677|hdl-access=free}}</ref> The [[Einstein field equations]] cover the latter aspect of the theory, relating the curvature of spacetime to the distribution of matter and energy. The [[geodesic equation]] covers the former aspect, stating that freely falling bodies follow [[Geodesics in general relativity|lines that are as straight as possible in a curved spacetime]]. Einstein regarded this as an "independent fundamental assumption" that had to be postulated in addition to the field equations in order to complete the theory. Believing this to be a shortcoming in how general relativity was originally presented, he wished to derive it from the field equations themselves. Since the equations of general relativity are non-linear, a lump of energy made out of pure gravitational fields, like a black hole, would move on a trajectory which is determined by the Einstein field equations themselves, not by a new law. Accordingly, Einstein proposed that the field equations would determine the path of a singular solution, like a black hole, to be a geodesic. Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from applying the field equations to the motion of a [[gravitational singularity]], but this claim remains disputed.<ref>{{cite journal|last=Tamir |first=M |url=http://philsci-archive.pitt.edu/9158/1/Tamir_-_Proving_the_Principle.pdf |title=Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory |journal=Studies in History and Philosophy of Modern Physics |volume=43 |number=2 |pages=137–154 |year=2012 |doi=10.1016/j.shpsb.2011.12.002|bibcode=2012SHPMP..43..137T }}</ref><ref>{{cite book|last=Malament |first=David |chapter=A Remark About the "Geodesic Principle" in General Relativity |author-link=David Malament |chapter-url=http://philsci-archive.pitt.edu/5072/1/GeodesicLaw.pdf |title=Analysis and Interpretation in the Exact Sciences |pages=245–252 |series=The Western Ontario Series in Philosophy of Science |volume=78 |publisher=Springer |year=2012 |editor-last1=Frappier |editor-first1=M. |editor-last2=Brown |editor-first2=D. |editor-last3=DiSalle |editor-first3=R. |doi=10.1007/978-94-007-2582-9_14 |isbn=978-94-007-2581-2 |quote=Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein's equation (or the conservation principle) alone. Other assumptions are needed to derive the theorems in question.}}</ref>