Editing Quantum gravity (section)

=== Problem of time ===
{{Main|Problem of time}}
A conceptual difficulty in combining quantum mechanics with general relativity arises from the contrasting role of time within these two frameworks. In quantum theories, time acts as an independent background through which states evolve, with the [[Hamiltonian (quantum mechanics)|Hamiltonian operator]] acting as the [[Translation operator (quantum mechanics)|generator of infinitesimal translations]] of quantum states through time.<ref>{{Cite book|title=Modern Quantum Mechanics|last1=Sakurai|first1=J. J.|last2=Napolitano|first2=Jim J.|date=2010-07-14|publisher=Pearson|isbn=978-0-8053-8291-4|edition=2|page=68|language=en}}</ref> In contrast, general relativity [[Einstein field equations|treats time as a dynamical variable]] which relates directly with matter and moreover requires the Hamiltonian constraint to vanish.<ref>{{Cite book|url=https://books.google.com/books?id=vDWvUBiNgNkC|title=Cosmology and Gravitation: Xth Brazilian School of Cosmology and Gravitation; 25th Anniversary (1977–2002), Mangaratiba, Rio de Janeiro, Brazil|last1=Novello|first1=Mario|last2=Bergliaffa|first2=Santiago E.|date=2003-06-11|publisher=Springer Science & Business Media|isbn=978-0-7354-0131-0|page=95|language=en}}</ref> Because this variability of time has been [[Gravitational time dilation#Experimental confirmation|observed macroscopically]], it removes any possibility of employing a fixed notion of time, similar to the conception of time in quantum theory, at the macroscopic level.