Editing Spacetime (section)

=== Is spacetime really curved? ===
In Poincaré's [[conventionalist]] views, the essential criteria according to which one should select a Euclidean versus non-Euclidean geometry would be economy and simplicity. A realist would say that Einstein discovered spacetime to be non-Euclidean. A conventionalist would say that Einstein merely found it ''more convenient'' to use non-Euclidean geometry. The conventionalist would maintain that Einstein's analysis said nothing about what the geometry of spacetime ''really'' is.<ref name="Murzi">{{cite web|last1=Murzi|first1=Mauro|title=Jules Henri Poincaré (1854–1912)|url=http://www.iep.utm.edu/poincare/#H4|publisher=Internet Encyclopedia of Philosophy (ISSN 2161-0002)|access-date=9 April 2018|archive-date=23 December 2020|archive-url=https://web.archive.org/web/20201223123326/http://www.iep.utm.edu/poincare/#H4|url-status=live}}</ref>

Such being said,
:# Is it possible to represent general relativity in terms of flat spacetime?
:# Are there any situations where a flat spacetime interpretation of general relativity may be ''more convenient'' than the usual curved spacetime interpretation?

In response to the first question, a number of authors including Deser, Grishchuk, Rosen, Weinberg, etc. have provided various formulations of gravitation as a field in a flat manifold. Those theories are variously called "[[bimetric gravity]]", the "field-theoretical approach to general relativity", and so forth.<ref name="Deser1970">{{cite journal|last1=Deser|first1=S.|title=Self-Interaction and Gauge Invariance|journal=General Relativity and Gravitation|date=1970|volume=1|issue=18|pages=9–8|arxiv=gr-qc/0411023|bibcode=1970GReGr...1....9D|doi=10.1007/BF00759198|s2cid=14295121}}</ref><ref name="Grishchuk1984">{{cite journal|last1=Grishchuk|first1=L. P.|last2=Petrov|first2=A. N.|last3=Popova|first3=A. D.|title=Exact Theory of the (Einstein) Gravitational Field in an Arbitrary Background Space–Time|journal=Communications in Mathematical Physics|date=1984|volume=94|issue=3|pages=379–396|url=https://projecteuclid.org/download/pdf_1/euclid.cmp/1103941358|access-date=9 April 2018|bibcode=1984CMaPh..94..379G|doi=10.1007/BF01224832|s2cid=120021772|archive-date=25 February 2021|archive-url=https://web.archive.org/web/20210225061922/https://projecteuclid.org/download/pdf_1/euclid.cmp/1103941358|url-status=live}}</ref><ref name="Rosen1940">{{cite journal|last1=Rosen|first1=N.|title=General Relativity and Flat Space I|journal=Physical Review|date=1940|volume=57|issue=2|pages=147–150|doi=10.1103/PhysRev.57.147|bibcode=1940PhRv...57..147R}}</ref><ref name="Weinberg1964">{{cite journal|last1=Weinberg|first1=S.|title=Derivation of Gauge Invariance and the Equivalence Principle from Lorentz Invariance of the S-Matrix|journal=Physics Letters|date=1964|volume=9|issue=4|pages=357–359|doi=10.1016/0031-9163(64)90396-8|bibcode=1964PhL.....9..357W}}</ref> Kip Thorne has provided a popular review of these theories.<ref name="Thorne1995">{{cite book|last1=Thorne|first1=Kip|title=Black Holes & Time Warps: Einstein's Outrageous Legacy|date=1995|publisher=W. W. Norton & Company|isbn=978-0-393-31276-8}}</ref>{{rp|397–403}}

The flat spacetime paradigm posits that matter creates a gravitational field that causes rulers to shrink when they are turned from circumferential orientation to radial, and that causes the ticking rates of clocks to dilate. The flat spacetime paradigm is fully equivalent to the curved spacetime paradigm in that they both represent the same physical phenomena. However, their mathematical formulations are entirely different. Working physicists routinely switch between using curved and flat spacetime techniques depending on the requirements of the problem. The flat spacetime paradigm is convenient when performing approximate calculations in weak fields. Hence, flat spacetime techniques tend be used when solving gravitational wave problems, while curved spacetime techniques tend be used in the analysis of black holes.<ref name="Thorne1995" />{{rp|397–403}}