Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
Abstract A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subre...
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2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)063 |
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| author | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin |
| author_facet | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin |
| author_sort | Julian De Vuyst |
| collection | DOAJ |
| description | Abstract A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subregion to a Type II crossed product, whose entropy reduces to the generalised entropy formula in a semiclassical limit. The observers thus used are also known as quantum reference frames (QRFs); as noted in our companion work [1], using different QRFs result in different algebras, and hence different entropies — so gravitational entropy is observer-dependent. Here, we provide an in-depth analysis of this phenomenon, with full derivations of many new results. Using the perspective-neutral QRF formalism, we extend previous constructions to allow for arbitrarily many observers, each carrying a clock with possibly degenerate energy spectra. We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. Unlike previous works, we allow the clocks and fields to be arbitrarily entangled. At leading order the von Neumann entropy still reduces to the generalised entropy, but linear corrections are typically non-vanishing and quantify the degree of entanglement between the clocks and fields. We also describe an ‘antisemiclassical’ regime as the opposite of the semiclassical one, with suppressed fluctuations of the clock energy; in this regime, we show how the clock may simply be ‘partially traced’ out when evaluating the entropy. Four explicit examples of observer-dependent entropy are then given, involving a gravitational interferometer, degenerate clock superselection, a semiclassical approximation applying to some clocks but not others, and differences between monotonic and periodic clocks. |
| format | Article |
| id | doaj-art-fa7058ef359f4d7db1237abcc443d2cf |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-fa7058ef359f4d7db1237abcc443d2cf2025-08-20T03:45:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-0120257111810.1007/JHEP07(2025)063Crossed products and quantum reference frames: on the observer-dependence of gravitational entropyJulian De Vuyst0Stefan Eccles1Philipp A. Höhn2Josh Kirklin3Qubits and Spacetime Unit, Okinawa Institute of Science and TechnologyQubits and Spacetime Unit, Okinawa Institute of Science and TechnologyQubits and Spacetime Unit, Okinawa Institute of Science and TechnologyQubits and Spacetime Unit, Okinawa Institute of Science and TechnologyAbstract A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subregion to a Type II crossed product, whose entropy reduces to the generalised entropy formula in a semiclassical limit. The observers thus used are also known as quantum reference frames (QRFs); as noted in our companion work [1], using different QRFs result in different algebras, and hence different entropies — so gravitational entropy is observer-dependent. Here, we provide an in-depth analysis of this phenomenon, with full derivations of many new results. Using the perspective-neutral QRF formalism, we extend previous constructions to allow for arbitrarily many observers, each carrying a clock with possibly degenerate energy spectra. We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. Unlike previous works, we allow the clocks and fields to be arbitrarily entangled. At leading order the von Neumann entropy still reduces to the generalised entropy, but linear corrections are typically non-vanishing and quantify the degree of entanglement between the clocks and fields. We also describe an ‘antisemiclassical’ regime as the opposite of the semiclassical one, with suppressed fluctuations of the clock energy; in this regime, we show how the clock may simply be ‘partially traced’ out when evaluating the entropy. Four explicit examples of observer-dependent entropy are then given, involving a gravitational interferometer, degenerate clock superselection, a semiclassical approximation applying to some clocks but not others, and differences between monotonic and periodic clocks.https://doi.org/10.1007/JHEP07(2025)063Gauge SymmetryModels of Quantum GravitySpace-Time Symmetries |
| spellingShingle | Julian De Vuyst Stefan Eccles Philipp A. Höhn Josh Kirklin Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy Journal of High Energy Physics Gauge Symmetry Models of Quantum Gravity Space-Time Symmetries |
| title | Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy |
| title_full | Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy |
| title_fullStr | Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy |
| title_full_unstemmed | Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy |
| title_short | Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy |
| title_sort | crossed products and quantum reference frames on the observer dependence of gravitational entropy |
| topic | Gauge Symmetry Models of Quantum Gravity Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP07(2025)063 |
| work_keys_str_mv | AT juliandevuyst crossedproductsandquantumreferenceframesontheobserverdependenceofgravitationalentropy AT stefaneccles crossedproductsandquantumreferenceframesontheobserverdependenceofgravitationalentropy AT philippahohn crossedproductsandquantumreferenceframesontheobserverdependenceofgravitationalentropy AT joshkirklin crossedproductsandquantumreferenceframesontheobserverdependenceofgravitationalentropy |