Editing Equivalence principle (section)

=== Einstein equivalence principle ===
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What is now called the "Einstein equivalence principle" states that the weak equivalence principle holds, and that:
{{block indent|em=1.5|text=''the outcome of any local, non-gravitational test experiment is independent of the experimental apparatus' velocity relative to the gravitational field and is independent of where and when in the gravitational field the experiment is performed.''<ref name="Lāmmerzahl">{{Cite book |last1=Haugen |first1=Mark P. |title=Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space. Lecture Notes in Physics |last2=Lämmerzahl |first2=Claus |year=2001 |isbn=978-3-540-41236-6 |volume=562 |pages=195–212 |chapter=Principles of Equivalence: Their Role in Gravitation Physics and Experiments That Test Them. |journal=Gyros |bibcode=2001LNP...562..195H |doi=10.1007/3-540-40988-2_10 |arxiv=gr-qc/0103067 |s2cid=15430387}}</ref>}}
Here ''local'' means that experimental setup must be small compared to variations in the gravitational field, called [[tidal forces]]. The ''test'' experiment must be small enough so that its gravitational potential does not alter the result.

The two additional constraints added to the weak principle to get the Einstein form − (1) the independence of the outcome on relative velocity (local [[Lorentz invariance]]) and (2) independence of "where" (known as local positional invariance) − have far reaching consequences. With these constraints alone Einstein was able to predict the [[gravitational redshift]].<ref name="Lāmmerzahl" /> Theories of gravity that obey the Einstein equivalence principle must be "metric theories", meaning that trajectories of freely falling bodies are [[geodesics]] of symmetric metric.<ref name=Will2014/>{{rp|9}}

Around 1960 [[Leonard I. Schiff]] conjectured that any complete and consistent theory of gravity that embodies the weak equivalence principle implies the Einstein equivalence principle; the conjecture can't be proven but has several plausibility arguments in its favor.<ref name=Will2014/>{{rp|20}} Nonetheless, the two principles are tested with very different kinds of experiments.

The Einstein equivalence principle has been criticized as imprecise, because there is no universally accepted way to distinguish gravitational from non-gravitational experiments (see for instance Hadley<ref>{{cite journal |first=Mark J. |last=Hadley |doi=10.1007/BF02764119 |journal=Foundations of Physics Letters |volume=10 |issue=1 |title=The Logic of Quantum Mechanics Derived from Classical General Relativity |pages=43–60 |year=1997 |arxiv=quant-ph/9706018|bibcode = 1997FoPhL..10...43H |citeseerx=10.1.1.252.6335 |s2cid=15007947 }}</ref> and Durand<ref>{{cite journal | last1 = Durand | first1 = Stéphane | year = 2002| title = An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel | url = http://stacks.iop.org/ob/4/S351 | journal = Journal of Optics B: Quantum and Semiclassical Optics | volume = 4 | issue = 4 | pages = S351–S357| doi = 10.1088/1464-4266/4/4/319 | bibcode = 2002JOptB...4S.351D }}</ref>).