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Observer Time from Causality in Perturbative Quantum Gravity

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Elapsed proper time, defined by light-cone intersections, becomes a quantum operator in perturbative quantum gravity, with a nonzero commutator at order $G_N$.

desk verdict Genuinely new lightbulb-clock definition of observer time, but the headline commutator rests on an asserted gauge equivalence and an imported two-point function. read the letter →

arxiv 2506.16109 v1 pith:DTDSLRYD submitted 2025-06-19 hep-th gr-qchep-ph

Allic Sivaramakrishnan This is my paper
classification hep-thgr-qchep-ph PACS 04.60.-m04.62.+v
keywords propertimelightbulbclockperturbativequantumgravityeffectivefieldtheorynonlocalobservablegravitonvacuumfluctuationssynchronizationinterferometernoise
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes an operational definition of elapsed proper time in perturbative quantum gravity: the time between light signals exchanged by inertial observers, defined by intersections of worldlines and future light cones. It then feeds this 'lightbulb clock' time through the gravitational path integral, so metric fluctuations $h_{\mu\nu}$ turn the elapsed time into a quantum variable. At leading order $O(G_N)$ the two-point correlator of elapsed time is computed in closed form, and its commutator is nonzero for ticks shorter than a full round trip and zero outside it. The conclusion is that this causal notion of time is a genuine quantum operator and that clock synchronization fails in a computable way in perturbative quantum gravity.

What carries the argument

The lightbulb clock: elapsed proper time $\tau_3-\tau_1$ is defined by flashing a light from worldline $x_1$ at $\tau_1$, recording the unique future-light-cone intersection $\tau_2$ on worldline $x_2$, and the return intersection $\tau_3$ on $x_1$. The paper quantizes this by expanding $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$, imposing the worldline equations of motion, and path-integrating over $h$; in synchronous gauge the worldlines stay fixed and the null ray's perturbed trajectory supplies $\tau_2,\tau_3$ order by order. The load-bearing computation is the connected two-point function $\langle\tau(t)\tau(0)\rangle_c$, which becomes an integral of the graviton Wightman function $\langle h_{zz}(x)h_{zz}(x')\rangle$ along the unperturbed null rays; evaluating this integral, with a residual transverse-traceless gauge choice, produces the commutator.

What would settle it

Repeat the path-integral computation in a different gauge, such as harmonic gauge, and check whether the $O(G_N)$ commutator $\langle[\tau(t),\tau(0)]\rangle$ is unchanged; if the gauge-invariant regulator yields a different function of $u=t/2L$, the central claim fails.

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Extended reading notes

Core claim

The central claim is that an observer's elapsed proper time, defined by light-cone intersections rather than coordinates, does not commute with itself at different tick times after quantization. In flat space with two inertial worldlines separated by $L$, the leading vacuum expectation value is $\langle[\tau(t),\tau(0)]\rangle = -i \frac{8}{3}G_N(3-12u+18u^2-8u^3)$ for $0<u<1$ and zero for $u>1$, with $u=t/2L$. The same analysis for a clock-synchronization protocol gives $\langle[\tau_3(t),\tau_3(0)]\rangle = i \frac{16G_N}{3}(u-1)^3$ in the same interval. Since free graviton fields commute outside the light cone, the nonzero commutator shows elapsed time is an intrinsically nonlocal functional of the metric, and the paper takes it as evidence that time is a quantum operator in quantum gravity.

Load-bearing premise

The construction rests on assuming the future light cone of one observer's flash intersects the other worldline exactly once at every perturbative order in the metric fluctuation; if quantum fluctuations cause multiple or no intersections, the elapsed time is not uniquely defined and the path-integral correlators collapse.

Editorial extensions

If this is right

  • Elapsed proper time is a quantum operator: $\langle[\tau(t),\tau(0)]\rangle\neq 0$ for $0<t<2L$, so time measurements do not commute in the vacuum.
  • No universal clock synchronization survives in perturbative quantum gravity: the synchronized-time commutator $\langle[\tau_3(t),\tau_3(0)]\rangle$ is nonzero for $0<u<1$.
  • The result reproduces and extends earlier interferometer proper-time analyses: the $O(h)$ round-trip time is recovered, and the $O(h^2)$ connected correlator is the leading quantum-gravity contribution to the toy-interferometer observable.
  • The same light-cone intersection procedure defines a diffeomorphism-invariant, all-orders-in-$G_N$ prescription for geometric observables, so the framework applies beyond time measurements alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if time is genuinely noncommuting, any notion of a global time coordinate in quantum gravity must break down at $O(G_N)$; protocols that exchange light signals will inherit an irreducible timing uncertainty from vacuum gravitons.
  • Editorial inference: the same construction could define a nonlocal quantum length between worldlines, with a commutator of analogous support, connecting the result to relational observables beyond time.
  • Editorial inference: the commutator signature for $0<u<1$ is, in principle, a falsifiable prediction for the spectrum of timing noise in long-baseline interferometers, although the effect is far below current sensitivity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This paper proposes a relational observable—elapsed proper time defined by a 'lightbulb clock' in which future light cones from one inertial worldline intersect a second worldline, and the return signal defines τ3−τ1. The construction is then quantized by expanding g=η+h and performing a path integral over h, with τ1 serving as a fixed parameter. The paper computes τ3 to O(h^2) in synchronous gauge (Eqs. (8)–(11), Appendix C), identifies the O(G_N) connected two-point function as an integral of the h_zz Wightman function (Eq. (14)), and, using the explicit Wightman function reviewed from [13] in Appendix D, obtains the commutator ⟨[τ(t),τ(0)]⟩ shown in Eq. (16) (and the synchronization version in Eq. (18)), concluding that proper time is a quantum operator. Appendices A and B relate the clock to detector correlators and bulk-point singularities.

Significance. The idea of defining an observer's time through causal light-cone intersections and promoting it to a path-integral operator is attractive and could connect relational observables to interferometer experiments; the paper is clear that the leading-order term in τ3 agrees with [26]. If Eq. (16) is established, it gives a concrete, falsifiable prediction of nonzero commutativity for a time observable, which is a nontrivial conceptual result. The manuscript is honest about its assumptions, and the O(h^2) perturbative setup is standard. However, the paper's central quantitative output is not independently derived: Eq. (15) is quoted from the overlapping [13], and the gauge identification behind it is asserted rather than proven. The significance is therefore conditional on closing that gap.

major comments (2)
  1. [Section III, Eq. (14) and following paragraph] The central computation replaces the synchronous-gauge h_zz entering Eq. (14) with the transverse-traceless vacuum Wightman function, using 'residual gauge freedom in synchronous gauge.' This is not proven. Synchronous gauge leaves only restricted residual transformations (ξ_0 independent of t and ∂_0 ξ_i = −∂_i ξ_0), and the TT condition imposes additional constraints on the spatial components; the paper does not show that these residual transformations remove the non-TT (scalar and longitudinal) parts of the particular integrated correlator ⟨∫ h_zz ∫ h_zz⟩, nor that those parts cancel at O(G_N). Since Eq. (15) is taken from [13] rather than derived in this paper, and since Eq. (16) is the paper's main quantitative result, this is a load-bearing gap that must be closed by a direct derivation of Eq. (15) in synchronous gauge or by an explicit gauge-invariance argument for the truncated correlator.
  2. [Section IIB, path-integral definition] The path-integral definition (3)–(5) assumes that the light-cone intersection equations have a unique solution τ3(τ1,h) to all perturbative orders, stated as the assumption that small h 'does not violate the lightbulb clock conditions at any perturbative order.' This is plausible locally by the implicit function theorem near the background solution, but it is not established that caustics, multiple intersections, or loss of intersection do not occur for finite time intervals or for generic small fluctuations h. If multiple branches exist, the integrals (3) and (5) require a branch choice; without one, the observable is not fully defined to all orders. The O(G_N) result may be unaffected, but the paper's claim to an all-orders definition needs this assumption either removed or explicitly defended.
minor comments (4)
  1. [Title and header] The title in the abstract appears with a line-break artifact ('Gravi ty'); the author name in the full text is also given as 'Allic Sivaramakrishnan', which should be checked against the arXiv metadata for consistency.
  2. [Section III, Eqs. (14)–(15)] The notation x_p(t,t') in Eq. (14) is inconsistent with the earlier notation x_p(t_1, λ); please unify the notation so that the fixed initial proper time and the integration variable are clearly distinguished.
  3. [Section III, after Eq. (16)] The explanation that ⟨[τ(t),τ(0)]⟩ vanishes for u>1 because local graviton commutators vanish outside the light cone is heuristic, since τ is a nonlocal functional of h; the sentence should be phrased as an interpretation rather than a derivation.
  4. [Appendix E] In Eq. (E1), the logarithms contain arguments like 2Lu and 2L(1+u) that mix a length scale L with the dimensionless u; this is harmless dimensionally but should be written with explicit dimensionless ratios (for example, t/(2L), |t−2L|/(2L), and (t+2L)/(2L)) to avoid confusion.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central commutator follows from a parameter-free Wightman function that is re-derived in Appendix D, and the self-citation to [13] is independent support rather than an input-equivalent construction.

full rationale

The paper's central result, Eq. (16), is obtained by taking the imaginary part of Eq. (15), which is a parameter-free two-point function. Eq. (15) is explicitly attributed to [13], but Appendix D re-derives the needed free graviton Wightman function from the standard mode expansion and polarization sum, so the closed form does not reduce to a fitted input or to the paper's own conclusion by construction. The lightbulb-clock definition in Section II is a classical, diffeomorphism-invariant construction, and the perturbative computation in Section III (Eqs. 8-14) follows from solving the null and timelike geodesic equations; no parameter is fitted to a subset of data and then renamed as a prediction. The self-citation to [13] is load-bearing for the final analytic integral, but it is independent support: it is parameter-free, it is based on stated physical assumptions, and it is externally falsifiable as an interferometer response prediction, so it does not constitute circularity under the review rules. The potentially fragile step is the assertion that residual gauge freedom in synchronous gauge makes Eq. (14) exactly the transverse-traceless correlator of [13]; this is an unproven gauge equivalence that could affect correctness, but it is not a circular reduction by construction. The explicit assumption in Section IIB that light-cone intersections remain unique at all perturbative orders is an assumption about the validity of the construction, not a circular step.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the validity of perturbative quantum gravity as an EFT, the existence and uniqueness of light-cone intersections under fluctuations, and the correctness of the imported Wightman function. No free parameters are fitted; the masses of the observers and the separation L are fixed by initial conditions. No new entities are introduced.

assumptions (4)
  • domain assumption Small metric fluctuations preserve the unique intersection of future light cones with observer worldlines at every perturbative order.
    Section IIB: 'Crucially, we assume that when h is small, it does not violate the lightbulb clock conditions at any perturbative order.' Without this, τ2 and τ3 are not well-defined functions of h.
  • domain assumption Perturbative quantum gravity as an effective field theory, with path integral over h around a fixed background, is valid for defining these observables.
    Eq (3) and surrounding text define ⟨τ3⟩ = ∫ D[h] τ3 e^{-iS[h]}. This presumes the standard EFT treatment of graviton fluctuations.
  • domain assumption The Wightman function of h in transverse-traceless gauge and its closed-form integral, Eq (15), are correct as reviewed from [13].
    Appendix D labels this as 'Additional review from [13]'. The present paper does not independently derive or verify this central integral.
  • domain assumption Observers can be modeled as point masses on geodesics with back-reaction included through the worldline action.
    Section IIA and Eq (4). This is the standard relational-observer model, but the paper does not discuss its range of validity for realistic extended observers.

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Cite this review

Pith. "Pith review of Observer Time from Causality in Perturbative Quantum Gravity." pith.science (2026). https://pith.science/paper/DTDSLRYD

@misc{pith2026250616109,
  author       = {Pith},
  title        = {Pith review of: Observer Time from Causality in Perturbative Quantum Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DTDSLRYD}},
  note         = {Machine review of arXiv:2506.16109}
}
abstract

It is unclear whether an observable notion of time exists in quantum gravity even in principle because spacetime itself fluctuates. We propose a form of observable time in perturbative quantum gravity. First, we define an elapsed proper time in curved space using intersections of worldlines and future light cones. Here, time arises from causality via the dependence on light cones. We then propose that performing the gravitational path integral describes quantum gravity corrections to this notion of proper time at all orders in $G_N$. Using this prescription, we compute the leading quantum gravity corrections to two-point correlation functions of elapsed time. We find that the commutators can be nonzero, showing this notion of time is a quantum operator in quantum gravity.

Figures

Figures reproduced from arXiv: 2506.16109 by the authors.

Figure 1
Figure 1. FIG. 1. One “tick” of a lightbulb clock built from inertial [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The diagram that computes the connected two [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Graph of detector output, specifically [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

54 extracted references · 8 canonical work pages · cited by 3 Pith papers

  1. [13]

    Observational signatures of quantum gravity in interferometers,

    E. P. Verlinde and K. M. Zurek, “Observational signatures of quantum gravity in interferometers,” Phys. Lett. B 822 (2021) 136663, arXiv:1902.08207 [gr-qc]

    arXiv 2021

  2. [26]

    Takesaki, Tomita’sTheory of Modular Hilbert Algebras and Its Applications

    M. Takesaki, Tomita’sTheory of Modular Hilbert Algebras and Its Applications. Lecture Notes in Mathematics. Springer-Verlag, 1970

    work page 1970

  3. [1]

    Observables in Quantum Gravity: from Theory to Experiment

    − τ ′ 1)⟩. The times τ2, τ3 have become quantum operators. 1 Im- posing the equations of motion for the worldlines and performing the path integral over hµν was a procedure studied in [19]. The main novel feature of our work is to define proper-time correlators in this setup. III. PROPER-TIME CORRELATORS We now compute the two-point correlators of proper t...

    work page 2025

  4. [2]

    Gravitational entropy is observer-dependent,

    J. De Vuyst, S. Eccles, P. A. Hoehn, and J. Kirklin, “Gravitational entropy is observer-dependent,” arXiv:2405.00114 [hep-th]

    arXiv

  5. [3]

    Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy,

    J. De Vuyst, S. Eccles, P. A. Hoehn, and J. Kirklin, “Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy,” arXiv:2412.15502 [hep-th]

    arXiv

  6. [4]

    An algebra of observables for de Sitter space,

    V. Chandrasekaran, R. Longo, G. Penington, and E. Witten, “An algebra of observables for de Sitter space,” JHEP 02 (2023) 082, arXiv:2206.10780 [hep-th]

    arXiv 2023

  7. [5]

    Quantum gravity observables: observation, algebras, and mathematical structure,

    S. B. Giddings, “Quantum gravity observables: observation, algebras, and mathematical structure,” arXiv:2505.22708 [hep-th]

    arXiv

  8. [6]

    Introduction to the effective field theory description of gravity,

    J. F. Donoghue, “Introduction to the effective field theory description of gravity,” in Advanced School on Effective Theories. 6, 1995. arXiv:gr-qc/9512024

    arXiv 1995

Show all 54 references
  1. [7]

    Quantum gravity in everyday life: General relativity as an effective field theory,

    C. P. Burgess, “Quantum gravity in everyday life: General relativity as an effective field theory,” Living Rev. Rel. 7 (2004) 5–56, arXiv:gr-qc/0311082

    2004 arXiv

  2. [8]

    Noise and decoherence induced by gravitons,

    S. Kanno, J. Soda, and J. Tokuda, “Noise and decoherence induced by gravitons,” Phys. Rev. D 103 no. 4, (2021) 044017, arXiv:2007.09838 [hep-th]

    2021 arXiv

  3. [9]

    Signatures of the quantization of gravity at gravitational wave detectors,

    M. Parikh, F. Wilczek, and G. Zahariade, “Signatures of the quantization of gravity at gravitational wave detectors,” Phys. Rev. D 104 no. 4, (2021) 046021, arXiv:2010.08208 [hep-th]

    2021 arXiv

  4. [10]

    Quantum Mechanics of Gravitational Waves,

    M. Parikh, F. Wilczek, and G. Zahariade, “Quantum Mechanics of Gravitational Waves,” Phys. Rev. Lett. 127 no. 8, (2021) 081602, arXiv:2010.08205 [hep-th]

    2021 arXiv

  5. [11]

    The Noise of Gravitons,

    M. Parikh, F. Wilczek, and G. Zahariade, “The Noise of Gravitons,” Int. J. Mod. Phys. D 29 no. 14, (2020) 2042001, arXiv:2005.07211 [hep-th]

    2020 arXiv

  6. [12]

    On vacuum fluctuations in quantum gravity and interferometer arm fluctuations,

    K. M. Zurek, “On vacuum fluctuations in quantum gravity and interferometer arm fluctuations,” Phys. Lett. B 826 (2022) 136910, arXiv:2012.05870 [hep-th]

    2022 arXiv

  7. [14]

    Response of interferometers to the vacuum of quantum gravity,

    D. Carney, M. Karydas, and A. Sivaramakrishnan, “Response of interferometers to the vacuum of quantum gravity,” arXiv:2409.03894 [hep-th]

    arXiv

  8. [15]

    Advanced ligo,

    J. Aasi et al., “Advanced ligo,” Classical and quantum gravity 32 no. 7, (2015) 074001

    2015

  9. [16]

    Photon-Counting Interferometry to Detect Geontropic Space-Time Fluctuations with GQuEST,

    S. M. Vermeulen et al., “Photon-Counting Interferometry to Detect Geontropic Space-Time Fluctuations with GQuEST,” Phys. Rev. X 15 no. 1, (2025) 011034, arXiv:2404.07524 [gr-qc]

    2025 arXiv

  10. [17]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation. 1973

    1973

  11. [18]

    Ligo technical document ligo-t0900043,

    “Ligo technical document ligo-t0900043,” https://dcc.ligo.org/public/0000/T0900043/011/ LIGO-T0900043-11.pdf. 6

  12. [19]

    Maggiore, Gravitational Waves

    M. Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments. Oxford University Press, 2007

    2007

  13. [20]

    Diffeomorphism-invariant observables and their nonlocal algebra,

    W. Donnelly and S. B. Giddings, “Diffeomorphism-invariant observables and their nonlocal algebra,” Phys. Rev. D 93 no. 2, (2016) 024030, arXiv:1507.07921 [hep-th] . [Erratum: Phys.Rev.D 94, 029903 (2016)]

    2016 arXiv

  14. [21]

    Observables, gravitational dressing, and obstructions to locality and subsystems,

    W. Donnelly and S. B. Giddings, “Observables, gravitational dressing, and obstructions to locality and subsystems,” Phys. Rev. D 94 no. 10, (2016) 104038, arXiv:1607.01025 [hep-th]

    2016 arXiv

  15. [22]

    Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance,

    C. Goeller, P. A. Hoehn, and J. Kirklin, “Diffeomorphism-invariant observables and dynamical frames in gravity: reconciling bulk locality with general covariance,” arXiv:2206.01193 [hep-th]

    arXiv

  16. [23]

    Characterization of standard clocks by means of light rays and freely falling particles,

    V. Perlick, “Characterization of standard clocks by means of light rays and freely falling particles,” General Relativity and Gravitation 19 no. 11, (Nov., 1987) 1059–1073. https://doi.org/10.1007/BF00759142

    1987 doi

  17. [24]

    On the Radar method in general-relativist ic spacetimes,

    V. Perlick, “On the Radar method in general-relativist ic spacetimes,” Astrophys. Space Sci. Libr. 349 (2008) 131–152, arXiv:0708.0170 [gr-qc]

    2008 arXiv

  18. [25]

    Maggiore, Gravitational waves, vol

    M. Maggiore, Gravitational waves, vol. 2. Oxford university press, 2008

    2008

  19. [27]

    Proper Time Observables of General Gravitational Perturbations in Laser Interferometry-based Gravitational Wave Detectors,

    V. S. H. Lee and K. M. Zurek, “Proper Time Observables of General Gravitational Perturbations in Laser Interferometry-based Gravitational Wave Detectors,” arXiv:2408.03363 [hep-ph]

    arXiv

  20. [28]

    Correlators of Worldline Prope r Length,

    A. Sivaramakrishnan, “Correlators of Worldline Prope r Length,” arXiv:2406.17205 [hep-th]

    arXiv

  21. [29]

    Spectrum of Hawking Radiation and Huygens’ Principle,

    H. Ooguri, “Spectrum of Hawking Radiation and Huygens’ Principle,” Phys. Rev. D 33 (1986) 3573

    1986

  22. [30]

    CFT unitarity and the AdS Cutkosky rules,

    D. Meltzer and A. Sivaramakrishnan, “CFT unitarity and the AdS Cutkosky rules,” JHEP 11 (2020) 073, arXiv:2008.11730 [hep-th]

    2020 arXiv

  23. [31]

    On-shell correlators and color-kinematics duality in curved symmetric spacetimes,

    C. Cheung, J. Parra-Martinez, and A. Sivaramakrishnan, “On-shell correlators and color-kinematics duality in curved symmetric spacetimes,” JHEP 05 (2022) 027, arXiv:2201.05147 [hep-th]

    2022 arXiv

  24. [32]

    Modular Fluctuations in Cosmology,

    L. Aalsma and S.-E. Bak, “Modular Fluctuations in Cosmology,” arXiv:2503.04886 [hep-th]

    arXiv

  25. [33]

    Generalized entropy for general subregions in quantum gravity,

    K. Jensen, J. Sorce, and A. J. Speranza, “Generalized entropy for general subregions in quantum gravity,” JHEP 12 (2023) 020, arXiv:2306.01837 [hep-th]

    2023 arXiv

  26. [34]

    Algebras, regions, and observers,

    E. Witten, “Algebras, regions, and observers,” Proc. Symp. Pure Math. 107 (2024) 247–276, arXiv:2303.02837 [hep-th]

    2024 arXiv

  27. [35]

    Quantum mechanics and observers for gravity in a closed universe,

    D. Harlow, M. Usatyuk, and Y. Zhao, “Quantum mechanics and observers for gravity in a closed universe,” arXiv:2501.02359 [hep-th]

    arXiv

  28. [36]

    The gravitational path integral from an observer’s point of view,

    A. I. Abdalla, S. Antonini, L. V. Iliesiu, and A. Levine, “The gravitational path integral from an observer’s point of view,” arXiv:2501.02632 [hep-th]

    arXiv

  29. [37]

    Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory,

    J. C. Fewster, D. W. Janssen, L. D. Loveridge, K. Rejzner, and J. Waldron, “Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory,” Commun. Math. Phys. 406 no. 1, (2025) 19, arXiv:2403.11973 [math-ph]

    2025 arXiv

  30. [38]

    Quantum reference frames from top-down crossed products,

    S. Ali Ahmad, W. Chemissany, M. S. Klinger, and R. G. Leigh, “Quantum reference frames from top-down crossed products,” Phys. Rev. D 110 no. 6, (2024) 065003, arXiv:2405.13884 [hep-th]

    2024 arXiv

  31. [39]

    Crossed products, conditional expectations and constraint quantization,

    M. S. Klinger and R. G. Leigh, “Crossed products, conditional expectations and constraint quantization,” Nucl. Phys. B 1006 (2024) 116622, arXiv:2312.16678 [hep-th]

    2024 arXiv

  32. [40]

    Gravity and the crossed product,

    E. Witten, “Gravity and the crossed product,” JHEP 10 (2022) 008, arXiv:2112.12828 [hep-th]

    2022 arXiv

  33. [41]

    Toward stringy horizons,

    E. Gesteau and H. Liu, “Toward stringy horizons,” arXiv:2408.12642 [hep-th]

    arXiv

  34. [42]

    A background-independent algebra in quantum gravity,

    E. Witten, “A background-independent algebra in quantum gravity,” JHEP 03 (2024) 077, arXiv:2308.03663 [hep-th]

    2024 arXiv

  35. [43]

    Direct detection of a single photon by humans,

    J. N. Tinsley, M. I. Molodtsov, R. Prevedel, D. Wartmann, J. Espigul´ e-Pons, M. Lauwers, and A. Vaziri, “Direct detection of a single photon by humans,” Nature Communications 7 no. 1, (2016) 12172

    2016

  36. [44]

    Energy Correlators in Perturbative Quantum Gravity,

    E. Herrmann, M. Kologlu, and I. Moult, “Energy Correlators in Perturbative Quantum Gravity,” arXiv:2412.05384 [hep-th]

    arXiv

  37. [45]

    Energy Correlators: A Journey From Theory to Experiment,

    I. Moult and H. X. Zhu, “Energy Correlators: A Journey From Theory to Experiment,” arXiv:2506.09119 [hep-ph]

    arXiv

  38. [46]

    Local bulk S-matrix elements and CFT singularities,

    M. Gary, S. B. Giddings, and J. Penedones, “Local bulk S-matrix elements and CFT singularities,” Phys. Rev. D 80 (2009) 085005, arXiv:0903.4437 [hep-th]

    2009 arXiv

  39. [47]

    Negative energy, superluminosity and holography,

    J. Polchinski, L. Susskind, and N. Toumbas, “Negative energy, superluminosity and holography,” Phys. Rev. D 60 (1999) 084006, arXiv:hep-th/9903228

    1999 arXiv

  40. [48]

    Holography from Conformal Field Theory,

    I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully , “Holography from Conformal Field Theory,” JHEP 10 (2009) 079, arXiv:0907.0151 [hep-th]

    2009 arXiv

  41. [49]

    Writing CFT correlation functions as AdS scattering amplitudes,

    J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 03 (2011) 025, arXiv:1011.1485 [hep-th]

    2011 arXiv

  42. [50]

    String scattering in flat space and a scaling limit of Yang-Mills correlators,

    T. Okuda and J. Penedones, “String scattering in flat space and a scaling limit of Yang-Mills correlators,” Phys. Rev. D 83 (2011) 086001, arXiv:1002.2641 [hep-th]

    2011 arXiv

  43. [51]

    Looking for a bulk point,

    J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,” JHEP 01 (2017) 013, arXiv:1509.03612 [hep-th]

    2017 arXiv

  44. [52]

    Holographic cameras: an eye for the bulk,

    S. Caron-Huot, “Holographic cameras: an eye for the bulk,” JHEP 03 (2023) 047, arXiv:2211.11791 [hep-th]

    2023 arXiv

  45. [53]

    Looking at bulk points in general geometries,

    S. Caron-Huot, J. Chakravarty, and K. Namjou, “Looking at bulk points in general geometries,” arXiv:2502.14963 [hep-th]

    arXiv

  46. [54]

    Towards a Reconstruction of General Bulk Metrics,

    N. Engelhardt and G. T. Horowitz, “Towards a Reconstruction of General Bulk Metrics,” Class. Quant. Grav. 34 no. 1, (2017) 015004, arXiv:1605.01070 [hep-th]. 7 Appendix A: Proper time from detector correlators Here we sketch how proper time can be defined opera- tionally in a m...

    2017 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.