Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
1Laboratoire Méthodes Formelles, Inria Saclay, France
2Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Vienna
3Quantum Group, Department of Computer Science, University of Oxford
4Department of Physics, Imperial College London
5Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa
6Department of Physics and Astronomy, University College London, London
7Faculty of Physics, University of Vienna
8Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, Zürich, Switzerland
9Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
Published: | 2023-08-22, volume 7, page 1088 |
Eprint: | arXiv:1809.05093v3 |
Doi: | https://doi.org/10.22331/q-2023-08-22-1088 |
Citation: | Quantum 7, 1088 (2023). |
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Abstract
Given the importance of quantum reference frames (QRFs) to both quantum and gravitational physics, it is pertinent to develop a systematic method for switching between the descriptions of physics relative to different choices of QRFs, which is valid in both fields. Here we continue with such a unifying approach, begun in [Quantum 4, 225 (2020)], whose key ingredient is a symmetry principle, which enforces physics to be relational. Thanks to gauge related redundancies, this leads to a perspective-neutral structure which contains all frame choices at once and via which frame perspectives can be consistently switched. Formulated in the language of constrained systems, the perspective-neutral structure is the constraint surface classically and the gauge invariant Hilbert space in the Dirac quantized theory. By contrast, a perspective relative to a specific frame corresponds to a gauge choice and the associated reduced phase and Hilbert space. QRF changes thus amount to a gauge transformation. We show that they take the form of `quantum coordinate changes'. We illustrate this in a general mechanical model, namely the relational $N$-body problem in 3D space with rotational and translational symmetry. This model is especially interesting because it features the Gribov problem so that globally valid gauge fixing conditions, and hence relational frame perspectives, are absent. The constraint surface is topologically non-trivial and foliated by 3-, 5- and 6-dimensional gauge orbits, where the lower dimensional orbits are a set of measure zero. The $N$-body problem also does not admit globally valid canonically conjugate pairs of Dirac observables. These challenges notwithstanding, we exhibit how one can construct the QRF transformations for the 3-body problem. Our construction also sheds new light on the generic inequivalence of Dirac and reduced quantization through its interplay with QRF perspectives.
![](https://quantum-journal.org/wp-content/uploads/2023/08/gaugefixing.jpg)
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► References
[1] A. Vanrietvelde, P. A. Höhn, F. Giacomini, and E. Castro-Ruiz, ``A change of perspective: switching quantum reference frames via a perspective-neutral framework,'' Quantum 4 (2020) 225, arXiv:1809.00556 [quant-ph].
https://doi.org/10.22331/q-2020-01-27-225
arXiv:1809.00556
[2] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, ``Quantum mechanics and the covariance of physical laws in quantum reference frames,'' Nature Commun. 10 no. 1, (2019) 494, arXiv:1712.07207 [quant-ph].
https://doi.org/10.1038/s41467-018-08155-0
arXiv:1712.07207
[3] B. S. DeWitt, ``Quantum theory of gravity. I. The canonical theory,'' Phys.Rev. 160 (1967) 1113–1148.
https://doi.org/10.1103/PhysRev.160.1113
[4] C. Rovelli, Quantum Gravity. Cambridge University Press, 2004.
https://doi.org/10.1017/CBO9780511755804
[5] C. Rovelli, ``Quantum reference systems,'' Class.Quant.Grav. 8 (1991) 317–332.
https://doi.org/10.1088/0264-9381/8/2/012
[6] C. Rovelli, ``What is observable in classical and quantum gravity?,'' Class.Quant.Grav. 8 (1991) 297–316.
https://doi.org/10.1088/0264-9381/8/2/011
[7] K. Kuchař, ``Time and interpretations of quantum gravity,'' Int.J.Mod.Phys.Proc.Suppl. D20 (2011) 3–86. Originally published in the Proc. 4th Canadian Conf. on General Relativity and Relativistic Astrophysics, eds. G. Kunstatter, D. Vincent and J. Williams (World Scientific, Singapore, 1992).
https://doi.org/10.1142/S0218271811019347
[8] C. J. Isham, Canonical Quantum Gravity and the Problem of Time, pp. 157–287. Springer Netherlands, Dordrecht, 1993.
https://doi.org/10.1007/978-94-011-1980-1_6
[9] J. D. Brown and K. V. Kuchař, ``Dust as a standard of space and time in canonical quantum gravity,'' Phys. Rev. D 51 (May, 1995) 5600–5629.
https://doi.org/10.1103/PhysRevD.51.5600
[10] B. Dittrich, ``Partial and complete observables for Hamiltonian constrained systems,'' Gen.Rel.Grav. 39 (2007) 1891–1927, arXiv:gr-qc/0411013 [gr-qc].
https://doi.org/10.1007/s10714-007-0495-2
arXiv:gr-qc/0411013
[11] B. Dittrich, ``Partial and complete observables for canonical General Relativity,'' Class.Quant.Grav. 23 (2006) 6155–6184, arXiv:gr-qc/0507106 [gr-qc].
https://doi.org/10.1088/0264-9381/23/22/006
arXiv:gr-qc/0507106
[12] J. Tambornino, ``Relational Observables in Gravity: a Review,'' SIGMA 8 (2012) 017, arXiv:1109.0740 [gr-qc].
https://doi.org/10.3842/SIGMA.2012.017
arXiv:1109.0740
[13] T. Thiemann, Modern Canonical Quantum General Relativity. Cambridge University Press, 2007.
https://doi.org/10.1017/CBO9780511755682
[14] M. Bojowald, P. A. Höhn, and A. Tsobanjan, ``An Effective approach to the problem of time,'' Class. Quant. Grav. 28 (2011) 035006, arXiv:1009.5953 [gr-qc].
https://doi.org/10.1088/0264-9381/28/3/035006
arXiv:1009.5953
[15] M. Bojowald, P. A. Höhn, and A. Tsobanjan, ``Effective approach to the problem of time: general features and examples,'' Phys.Rev. D83 (2011) 125023, arXiv:1011.3040 [gr-qc].
https://doi.org/10.1103/PhysRevD.83.125023
arXiv:1011.3040
[16] P. A. Höhn, E. Kubalova, and A. Tsobanjan, ``Effective relational dynamics of a nonintegrable cosmological model,'' Phys.Rev. D86 (2012) 065014, arXiv:1111.5193 [gr-qc].
https://doi.org/10.1103/PhysRevD.86.065014
arXiv:1111.5193
[17] B. Dittrich, P. A. Höhn, T. A. Koslowski, and M. I. Nelson, ``Can chaos be observed in quantum gravity?,'' Phys. Lett. B769 (2017) 554–560, arXiv:1602.03237 [gr-qc].
https://doi.org/10.1016/j.physletb.2017.02.038
arXiv:1602.03237
[18] B. Dittrich, P. A. Höhn, T. A. Koslowski, and M. I. Nelson, ``Chaos, Dirac observables and constraint quantization,'' arXiv:1508.01947 [gr-qc].
arXiv:1508.01947
[19] Y. Aharonov and L. Susskind, ``Charge Superselection Rule,'' Phys. Rev. 155 (1967) 1428–1431.
https://doi.org/10.1103/PhysRev.155.1428
[20] Y. Aharonov and L. Susskind, ``Observability of the sign change of spinors under $2{\pi}$ rotations,'' Phys. Rev. 158 (Jun, 1967) 1237–1238.
https://doi.org/10.1103/PhysRev.158.1237
[21] Y. Aharonov and T. Kaufherr, ``Quantum frames of reference,'' Phys. Rev. D 30 (Jul, 1984) 368–385.
https://doi.org/10.1103/PhysRevD.30.368
[22] S. D. Bartlett, T. Rudolph, and R. W. Spekkens, ``Reference frames, superselection rules, and quantum information,'' Rev. Mod. Phys. 79 (2007) 555–609, arXiv:quant-ph/0610030.
https://doi.org/10.1103/RevModPhys.79.555
arXiv:quant-ph/0610030
[23] S. D. Bartlett, T. Rudolph, R. W. Spekkens, and P. S. Turner, ``Quantum communication using a bounded-size quantum reference frame,'' New Journal of Physics 11 no. 6, (2009) 063013, arXiv:0812.5040.
https://doi.org/10.1088/1367-2630/11/6/063013
arXiv:0812.5040
[24] G. Gour and R. W. Spekkens, ``The resource theory of quantum reference frames: manipulations and monotones,'' New Journal of Physics 10 no. 3, (Mar, 2008) 033023.
https://doi.org/10.1088/1367-2630/10/3/033023
[25] M. C. Palmer, F. Girelli, and S. D. Bartlett, ``Changing quantum reference frames,'' Phys. Rev. A89 no. 5, (2014) 052121, arXiv:1307.6597 [quant-ph].
https://doi.org/10.1103/PhysRevA.89.052121
arXiv:1307.6597
[26] S. D. Bartlett, T. Rudolph, R. W. Spekkens, and P. S. Turner, ``Degradation of a quantum reference frame,'' New Journal of Physics 8 no. 4, (2006) 58, arXiv:quant-ph/0602069.
https://doi.org/10.1088/1367-2630/8/4/058
arXiv:quant-ph/0602069
[27] A. R. Smith, M. Piani, and R. B. Mann, ``Quantum reference frames associated with noncompact groups: The case of translations and boosts and the role of mass,'' Physical Review A 94 no. 1, (2016) 012333, arXiv:1602.07696.
https://doi.org/10.1103/PhysRevA.94.012333
arXiv:1602.07696
[28] D. Poulin and J. Yard, ``Dynamics of a quantum reference frame,'' New J. Phys. 9 no. 5, (2007) 156–156, arXiv:quant-ph/0612126.
https://doi.org/10.1088/1367-2630/9/5/156
arXiv:quant-ph/0612126
[29] M. Skotiniotis, B. Toloui, I. T. Durham, and B. C. Sanders, ``Quantum Frameness for CPT Symmetry,'' Phys. Rev. Lett. 111 no. 2, (2013) 020504, arXiv:1306.6114 [quant-ph].
https://doi.org/10.1103/PhysRevLett.111.020504
arXiv:1306.6114
[30] L. Loveridge, P. Busch, and T. Miyadera, ``Relativity of quantum states and observables,'' EPL (Europhysics Letters) 117 no. 4, (2017) 40004, arXiv:1604.02836.
https://doi.org/10.1209/0295-5075/117/40004
arXiv:1604.02836
[31] J. Pienaar, ``A relational approach to quantum reference frames for spins,'' arXiv:1601.07320 [quant-ph].
arXiv:1601.07320
[32] R. M. Angelo, N. Brunner, S. Popescu, A. J. Short, and P. Skrzypczyk, ``Physics within a quantum reference frame,'' Journal of Physics A: Mathematical and Theoretical 44 no. 14, (2011) 145304, arXiv:1007.2292.
https://doi.org/10.1088/1751-8113/44/14/145304
arXiv:1007.2292
[33] P. A. Höhn and M. P. Müller, ``An operational approach to spacetime symmetries: Lorentz transformations from quantum communication,'' New J. Phys. 18 no. 6, (2016) 063026, arXiv:1412.8462 [quant-ph].
https://doi.org/10.1088/1367-2630/18/6/063026
arXiv:1412.8462
[34] P. A. Guérin and Č. Brukner, ``Observer-dependent locality of quantum events,'' New J. Phys. 20 no. 10, (2018) 103031, arXiv:1805.12429 [quant-ph].
https://doi.org/10.1088/1367-2630/aae742
arXiv:1805.12429
[35] O. Oreshkov, F. Costa, and Č. Brukner, ``Quantum correlations with no causal order,'' Nature Commun. 3 (2012) 1092, arXiv:1105.4464 [quant-ph].
https://doi.org/10.1038/ncomms2076
arXiv:1105.4464
[36] L. Hardy, ``The Construction Interpretation: Conceptual Roads to Quantum Gravity,'' arXiv:1807.10980 [quant-ph].
arXiv:1807.10980
[37] J. Barbour and B. Bertotti, ``Mach's principle and the structure of dynamical theories,'' Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 382 no. 1783, (1982) 295–306.
https://doi.org/10.1098/rspa.1982.0102
[38] F. Mercati, Shape Dynamics: Relativity and Relationalism. Oxford University Press, 2018.
https://doi.org/10.1093/oso/9780198789475.001.0001
[39] P. A. Höhn, ``Reflections on the information paradigm in quantum and gravitational physics,'' J. Phys. Conf. Ser. 880 no. 1, (2017) 012014, arXiv:1706.06882 [hep-th].
https://doi.org/10.1088/1742-6596/880/1/012014
arXiv:1706.06882
[40] P. A. Dirac, Lectures on Quantum Mechanics. Yeshiva University Press, 1964.
[41] M. Henneaux and C. Teitelboim, Quantization of Gauge Systems. Princeton University Press, 1992.
https://doi.org/10.2307/j.ctv10crg0r
[42] L. Hardy, ``Implementation of the Quantum Equivalence Principle,'' in Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics. 3, 2019. arXiv:1903.01289 [quant-ph].
arXiv:1903.01289
[43] M. Zych, F. Costa, and T. C. Ralph, ``Relativity of quantum superpositions,'' arXiv:1809.04999 [quant-ph].
arXiv:1809.04999
[44] C. Rovelli, ``Why Gauge?,'' Found. Phys. 44 no. 1, (2014) 91–104, arXiv:1308.5599 [hep-th].
https://doi.org/10.1007/s10701-013-9768-7
arXiv:1308.5599
[45] A. Ashtekar and G. t. Horowitz, ``On the canonical approach to quantum gravity,'' Phys. Rev. D26 (1982) 3342–3353.
https://doi.org/10.1103/PhysRevD.26.3342
[46] V. Guillemin and S. Sternberg, ``Geometric quantization and multiplicities of group representations,'' Inventiones mathematicae 67 (10, 1982) 515–538.
https://doi.org/10.1007/BF01398934
[47] Y. Tian and W. Zhang, ``An analytic proof of the geometric quantization conjecture of guillemin-sternberg,'' Inventiones mathematicae 132 no. 2, (1998) 229–259.
https://doi.org/10.1007/s002220050223
[48] P. Hochs and N. Landsman, ``The guillemin–sternberg conjecture for noncompact groups and spaces,'' Journal of K-theory 1 no. 3, (2008) 473–533, arXiv:math-ph/0512022.
https://doi.org/10.1017/is008001002jkt022
arXiv:math-ph/0512022
[49] M. J. Gotay, ``Constraints, Reduction, and Quantization,'' J. Math. Phys. 27 (1986) 2051–2066.
https://doi.org/10.1063/1.527026
[50] K. V. Kuchař, ``Covariant Factor Ordering of Gauge Systems,'' Phys. Rev. D 34 (1986) 3044–3057.
https://doi.org/10.1103/PhysRevD.34.3044
[51] A. Ashtekar, Lectures on Nonperturbative Canonical Gravity, vol. 6 of Advances series in astrophysics and cosmology. World Scientific.
https://doi.org/10.1142/1321
[52] K. Schleich, ``Is reduced phase space quantization equivalent to Dirac quantization?,'' Class. Quant. Grav. 7 (1990) 1529–1538.
https://doi.org/10.1088/0264-9381/7/8/028
[53] G. Kunstatter, ``Dirac versus reduced quantization: A Geometrical approach,'' Class. Quant. Grav. 9 (1992) 1469–1486.
https://doi.org/10.1088/0264-9381/9/6/005
[54] P. Hajicek and K. V. Kuchar, ``Constraint quantization of parametrized relativistic gauge systems in curved space-times,'' Phys. Rev. D41 (1990) 1091–1104.
https://doi.org/10.1103/PhysRevD.41.1091
[55] J. D. Romano and R. S. Tate, ``Dirac Versus Reduced Space Quantization of Simple Constrained Systems,'' Class. Quant. Grav. 6 (1989) 1487.
https://doi.org/10.1088/0264-9381/6/10/017
[56] R. Loll, ``Noncommutativity of constraining and quantizing: A U(1) gauge model,'' Phys. Rev. D41 (1990) 3785–3791.
https://doi.org/10.1103/PhysRevD.41.3785
[57] J. Barbour, T. Koslowski, and F. Mercati, ``Identification of a gravitational arrow of time,'' Phys. Rev. Lett. 113 no. 18, (2014) 181101, arXiv:1409.0917 [gr-qc].
https://doi.org/10.1103/PhysRevLett.113.181101
arXiv:1409.0917
[58] J. Barbour, T. Koslowski, and F. Mercati, ``Entropy and the Typicality of Universes,'' arXiv:1507.06498 [gr-qc].
arXiv:1507.06498
[59] C. Isham, ``Topological and global aspects of quantum theory,'' in Relativity, Groups and Topology II, Les Houches Summer School, 1983, B. DeWitt and R. Stora, eds., p. 1062. North Holland, Amsterdam, 1984.
[60] R. G. Littlejohn and M. Reinsch, ``Internal or shape coordinates in the n-body problem,'' Physical Review A 52 no. 3, (1995) 2035.
https://doi.org/10.1103/PHYSREVA.52.2035
[61] R. G. Littlejohn and M. Reinsch, ``Gauge fields in the separation of rotations and internal motions in the n-body problem,'' Reviews of Modern Physics 69 no. 1, (1997) 213.
https://doi.org/10.1103/RevModPhys.69.213
[62] D. Marolf, ``Refined algebraic quantization: Systems with a single constraint,'' arXiv:gr-qc/9508015 [gr-qc].
arXiv:gr-qc/9508015
[63] D. Marolf, ``Group averaging and refined algebraic quantization: Where are we now?,'' arXiv:gr-qc/0011112 [gr-qc].
arXiv:gr-qc/0011112
[64] A. Kempf and J. R. Klauder, ``On the implementation of constraints through projection operators,'' J. Phys. A34 (2001) 1019–1036, arXiv:quant-ph/0009072 [quant-ph].
https://doi.org/10.1088/0305-4470/34/5/307
arXiv:quant-ph/0009072
[65] D. N. Page and W. K. Wootters, ``Evolution without evolution: Dynamics described by stationary observables,'' Phys. Rev. D27 (1983) 2885.
https://doi.org/10.1103/PhysRevD.27.2885
[66] P. A. Höhn, A. R. H. Smith, and M. P. E. Lock, ``Trinity of relational quantum dynamics,'' Phys. Rev. D 104 no. 6, (2021) 066001, arXiv:1912.00033 [quant-ph].
https://doi.org/10.1103/PhysRevD.104.066001
arXiv:1912.00033
[67] P. A. Höhn, A. R. H. Smith, and M. P. E. Lock, ``Equivalence of approaches to relational quantum dynamics in relativistic settings,'' Front. in Phys. 9 (2021) 181, arXiv:2007.00580 [gr-qc].
https://doi.org/10.3389/fphy.2021.587083
arXiv:2007.00580
[68] K. Kuchař, ``Covariant factor ordering of gauge systems,'' Phys. Rev. D 34 (Nov, 1986) 3044–3057.
https://doi.org/10.1103/PhysRevD.34.3044
[69] D. McMullan and J. Paterson, ``Covariant Factor Ordering of Gauge Systems Using Ghost Variables. 1. Constraint Rescaling,'' J. Math. Phys. 30 (1989) 477.
https://doi.org/10.1063/1.528414
[70] B. P. Dolan, ``BRST symmetry and quantum mechanics on homogeneous spaces,'' Journal of Physics A: Mathematical and General 23 no. 20, (Oct, 1990) 4439–4453.
https://doi.org/10.1088/0305-4470/23/20/006
[71] J. M. Yang, ``Switching quantum reference frames for quantum measurement,'' Quantum 4 (2020) 283, arXiv:1911.04903 [quant-ph].
https://doi.org/10.22331/q-2020-06-18-283
arXiv:1911.04903
[72] P. A. Höhn and A. Vanrietvelde, ``How to switch between relational quantum clocks,'' New J. Phys. 22 no. 12, (2020) 123048, arXiv:1810.04153 [gr-qc].
https://doi.org/10.1088/1367-2630/abd1ac
arXiv:1810.04153
[73] P. A. Höhn, ``Switching Internal Times and a New Perspective on the ‘Wave Function of the Universe’,'' Universe 5 no. 5, (2019) 116, arXiv:1811.00611 [gr-qc].
https://doi.org/10.3390/universe5050116
arXiv:1811.00611
[74] J. De Vuyst, P. A. Höhn, and A. Tsobanjan to appear.
[75] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, ``Relativistic Quantum Reference Frames: The Operational Meaning of Spin,'' Phys. Rev. Lett. 123 no. 9, (2019) 090404, arXiv:1811.08228 [quant-ph].
https://doi.org/10.1103/PhysRevLett.123.090404
arXiv:1811.08228
[76] V. Guillemin and S. Sternberg, Symplectic techniques in physics. Cambridge University Press, Cambridge, 1990.
https://doi.org/10.1088/0031-9112/36/4/042
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[40] Sylvain Carrozza and Philipp A. Höhn, "Edge modes as reference frames and boundary actions from post-selection", Journal of High Energy Physics 2022 2, 172 (2022).
[41] Flaminia Giacomini and Achim Kempf, "Second-quantized Unruh-DeWitt detectors and their quantum reference frame transformations", Physical Review D 105 12, 125001 (2022).
[42] Lucien Hardy, "Implementation of the Quantum Equivalence Principle", arXiv:1903.01289, (2019).
[43] T. Favalli and A. Smerzi, "A model of quantum spacetime", AVS Quantum Science 4 4, 044403 (2022).
[44] Anne-Catherine de la Hamette, Stefan L. Ludescher, and Markus P. Müller, "Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames", Physical Review Letters 129 26, 260404 (2022).
[45] Shadi Ali Ahmad, Thomas D. Galley, Philipp A. Höhn, Maximilian P. E. Lock, and Alexander R. H. Smith, "Quantum Relativity of Subsystems", Physical Review Letters 128 17, 170401 (2022).
[46] Philipp A. Hoehn, Isha Kotecha, and Fabio M. Mele, "Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics", arXiv:2308.09131, (2023).
[47] Carlo Rovelli, "Gauge Is More Than Mathematical Redundancy", One Hundred Years of Gauge Theory; Past, Present and Future Perspectives 107 (2020).
[48] Carlo Cepollaro and Flaminia Giacomini, "Quantum generalisation of Einstein's Equivalence Principle can be verified with entangled clocks as quantum reference frames", arXiv:2112.03303, (2021).
[49] Martin Bojowald, "Noncovariance of the dressed-metric approach in loop quantum cosmology", Physical Review D 102 2, 023532 (2020).
[50] Marion Mikusch, Luis C. Barbado, and Časlav Brukner, "Transformation of spin in quantum reference frames", Physical Review Research 3 4, 043138 (2021).
[51] Jianhao M. Yang, "Switching Quantum Reference Frames for Quantum Measurement", Quantum 4, 283 (2020).
[52] Shadi Ali Ahmad, Wissam Chemissany, Marc S. Klinger, and Robert G. Leigh, "Quantum Reference Frames from Top-Down Crossed Products", arXiv:2405.13884, (2024).
[53] Cristina Cîrstoiu, Kamil Korzekwa, and David Jennings, "Robustness of Noether's Principle: Maximal Disconnects between Conservation Laws and Symmetries in Quantum Theory", Physical Review X 10 4, 041035 (2020).
[54] Martin Bojowald and Artur Tsobanjan, "Quantization of Dynamical Symplectic Reduction", Communications in Mathematical Physics 382 1, 547 (2021).
[55] M. F. Savi and R. M. Angelo, "Quantum resource covariance", Physical Review A 103 2, 022220 (2021).
[56] Ashmeet Singh, "Quantum Space, Quantum Time, and Relativistic Quantum Mechanics", arXiv:2004.09139, (2020).
[57] Rodolfo Gambini, Luis Pedro García-Pintos, and Jorge Pullin, "Single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties", Physical Review A 100 1, 012113 (2019).
[58] Andrzej Góźdź, Marek Góźdź, and Aleksandra Pędrak, "Projection evolution and quantum spacetime", arXiv:1910.11198, (2019).
[59] Martin Bojowald and Artur Tsobanjan, "Algebraic properties of quantum reference frames: Does time fluctuate?", arXiv:2211.04520, (2022).
[60] Martin Bojowald, Luis Martínez, and Garrett Wendel, "Relational evolution with oscillating clocks", Physical Review D 105 10, 106020 (2022).
[61] Lee Smolin, "Quantum reference frames and triality", arXiv:2007.05957, (2020).
[62] Houri Ziaeepour, "\boldmath $SU(\infty)$ Quantum Gravity: Emergence of Gravity in an Infinitely Divisible Quantum Universe", arXiv:2301.02813, (2023).
[63] Matheus Fritsch Savi and Renato Moreira Angelo, "Quantum resource covariance", arXiv:2005.09612, (2020).
[64] Jan Głowacki, "Operational Quantum Frames: An operational approach to quantum reference frames", arXiv:2304.07021, (2023).
[65] Ashmeet Singh, "Quantum space, quantum time, and relativistic quantum mechanics", Quantum Studies: Mathematics and Foundations 9 1, 35 (2022).
[66] Jackson R. Fliss, Alexander Frenkel, Sean A. Hartnoll, and Ronak M Soni, "Minimal Areas from Entangled Matrices", arXiv:2408.05274, (2024).
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