Editing Conservation of energy (section)

==General relativity==
General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim that energy is no longer meaningfully conserved in any identifiable form.<ref>Harrison, E. R. (1995). Mining energy in an expanding universe. The Astrophysical Journal, 446, 63.</ref><ref name=leaking>{{cite news |author1=Tamara M. Davis |title=Is the Universe Leaking Energy? |url=https://www.scientificamerican.com/article/is-the-universe-leaking-energy/ |access-date=25 September 2022 |work=Scientific American |date=2010}}</ref>

[[John Baez]]'s view is that energy–momentum conservation is not well-defined except in certain special cases. Energy-momentum is typically expressed with the aid of a [[stress–energy–momentum pseudotensor]]. However, since [[Pseudotensor|pseudotensors]] are not tensors, they do not transform cleanly between reference frames. If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the [[Friedmann–Lemaître–Robertson–Walker metric]] that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined.<ref>{{cite web|url=http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html|title=Is Energy Conserved in General Relativity?|author1=Michael Weiss |author2=John Baez |access-date=5 January 2017|archive-url=https://web.archive.org/web/20070605041426/http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html|archive-date=5 June 2007|url-status=dead}}</ref> Besides being dependent on the coordinate system, pseudotensor energy is dependent on the type of pseudotensor in use; for example, the energy exterior to a [[Kerr–Newman black hole]] is twice as large when calculated from Møller's pseudotensor as it is when calculated using the [[Einstein pseudotensor]].<ref>{{cite journal |last1=Duerr |first1=Patrick M. |title=Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |date=February 2019 |volume=65 |pages=1–14 |doi=10.1016/j.shpsb.2018.07.002|bibcode=2019SHPMP..65....1D |s2cid=126366668 }}</ref>

For asymptotically flat universes, Einstein and others salvage conservation of energy by introducing a specific global gravitational potential energy that cancels out mass-energy changes triggered by spacetime expansion or contraction. This global energy has no well-defined density and cannot technically be applied to a non-asymptotically flat universe; however, for practical purposes this can be finessed, and so by this view, energy is conserved in our universe.<ref>{{cite news |last1=Moskowitz |first1=Clara |title=Fact or Fiction?: Energy Can Neither Be Created Nor Destroyed |url=https://www.scientificamerican.com/article/energy-can-neither-be-created-nor-destroyed/ |access-date=25 September 2022 |work=Scientific American |date=2014 |language=en}}</ref><ref name="Energy Is Not Conserved"/> [[Alan Guth]] stated that the universe might be "the ultimate free lunch", and theorized that, when accounting for gravitational potential energy, the net energy of the Universe is [[zero-energy universe|zero]].<ref>{{cite news |title=Confronting the Multiverse: What 'Infinite Universes' Would Mean |url=https://www.space.com/31465-is-our-universe-just-one-of-many-in-a-multiverse.html |access-date=25 September 2022 |work=Space.com |date=23 December 2015 |language=en}}</ref>