Graviton Physics: A Concise Tutorial on the Quantum Field Theory of Gravitons, Graviton Noise, and Gravitational Decoherence
Abstract
:1. Matching the Main Themes with Different Readers’ Backgrounds and Needs
2. Gravitational Waves: Metric Perturbations of Minkowski Spacetime
2.1. Linear Perturbations
2.2. Polarization Tensors and Degrees of Freedom
2.3. Quantized Gravitational Wave in Minkowski Spacetime
3. Quantum Field Theory: Green’s Functions and Graviton States
3.1. Vacuum State
3.2. Coherent State
3.3. Squeezed Coherent State
4. Influence of Gravitons: Langevin Equation for Geodesic Separation
5. Graviton Noise: Master Equation for Gravitational Decoherence
5.1. Quantum Brownian Motion: Decoherence in the Configuration Space Basis
5.1.1. Phenomenology: Decoherence of a Quantum Particle in an Ohmic High Temperature Bath
5.1.2. Exact Non-Markovian Master Equation for a Quantum System in a General Environment
5.1.3. System and Bath with Time-Dependent Frequencies, Squeezed Thermal Bath, Quantum Field
5.2. Gravitational Decoherence Happens in the Energy Basis, Not in the Configuration Space Basis
5.2.1. Major Differences from Brownian Motion with Bilinear Interactions
5.2.2. A Markovian Master Equation for Gravitational Decoherence
6. Cosmology: Metric Perturbations in De Sitter Spacetime
6.1. Wave Equation of the Metric Perturbation
6.2. Gravitons in the De Sitter Spacetime
6.3. Infrared Behavior
7. Graviton Physics Is Low-Energy, Perturbative, Non-Planck-Scale, Quantum Gravity
7.1. Classical Gravity: General Relativity and Perturbative Gravity—Gravitational Waves
7.2. Quantum Gravity at Planck Energy: Theories for the Microscopic Constituents of Spacetime
7.3. Gravitons, Even at Today’s Low Energy, Carry the Quantum Signature of Perturbative Gravity
7.4. Constrained Degrees of Freedom Cannot Convey the Quantum Nature of Gravity
7.5. What Does Quantization Entail in Quantum Gravity?
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Machinery of the Influence Functional Formalism
1 | A noteworthy point is, mathematically, one can always construct a basis wherein a symmetric matrix is in a diagonal form. The physical reason why the reduced density matrix of a quantum system after interacting with its environment could, in time, become diagonal, is nontrivial. This is the idea behind Zurek’s ‘pointer-basis’, which depends on several factors, with the most salient of them all being the form of the interaction Hamiltonian. A good illustration of this point is in [23] |
2 | See Ref. [30] for the deficiencies of the CL equation, e.g., mathematically, the density operator is not positive-definite. It is worth mentioning an important class of the master equation, which is the most popular, called the Lindblad–Gorini–Kossakowski–Sudarshan equation [31,32]. The beauty of it is that it is completely positive, but it also has pathologies, e.g., it violates the uncertainty principle at very low temperatures [33,34,35], |
3 | This footnote is for readers interested in the non-Markovian dynamics of a massive system in a gravitational field with quantum noise. Indeed, in a cosmological setting, the effects of graviton noise are different from those in a Minkowski background spacetime. The extra time dependence due to cosmic expansion can impart non-Markovian attributes to systems that interact with gravitons. As seen in Equation (122), when the graviton constitutes the environment in the de Sitter space, its Green’s function is not simply a function of . Thus, in general, it cannot be put into a form proportional to a delta function or its derivatives. In addition, the infrared divergence may also prevent one from writing the Green’s function of the graviton in a form that may render the system dynamics Markovian. But this highly depends on the graviton state and the way the system is coupled to the graviton. Since the non-Markovian properties of gravitational systems make up an interesting topic of basic importance we have devoted a separate paper [47] to allow for a more systematic exposition of this issue. |
4 | The contents here mirror those in Section 2 of [5]. |
References
- DeWitt, B.S.; Brehme, R.W. Radiation damping in a gravitational field. Ann. Phys. 1960, 9, 220. [Google Scholar] [CrossRef]
- Misner, C.W.; Thorne, K.S.; Wheeler, J.A. Gravitation; W. H. Freeman: San Francisco, CA, USA, 1973. [Google Scholar]
- Hsiang, J.-T.; Hu, B.-L. No intrinsic decoherence of inflationary cosmological perturbations. Universe 2022, 8, 27. [Google Scholar] [CrossRef]
- Bravo, M.; Hsiang, J.-T.; Hu, B.L. Fluctuations-induced quantum radiation and reaction from an atom in a squeezed quantum field. Physics 2023, 5, 554–589. [Google Scholar] [CrossRef]
- Cho, H.-T.; Hu, B.-L. Quantum noise of gravitons and stochastic force on geodesic separation. Phys. Rev. D 2022, 105, 086004. [Google Scholar] [CrossRef]
- Cho, H.-T.; Hu, B.-L. Graviton noise on tidal forces and geodesic congruences. Phys. Rev. D 2023, 107, 084005. [Google Scholar] [CrossRef]
- Hsiang, J.-T.; Hu, B.L. Non-Markovian Abraham-Lorentz-Dirac equation: Radiation reaction without pathology. Phys. Rev. D 2022, 106, 125018. [Google Scholar] [CrossRef]
- Hsiang, J.-T.; Arısoy, O.; Hu, B.-L. Entanglement dynamics of coupled quantum oscillators in independent nonMarkovian baths. Entropy 2022, 24, 1814. [Google Scholar] [CrossRef] [PubMed]
- Dalvit, D.A.R.; Mazzitelli, F.D. Quantum corrections to the geodesic equation. AIP Conf. Proc. 1999, 484, 249. [Google Scholar]
- Parikh, M.; Wilczek, F.; Zahariade, G. Signature of the quantization of gravity at of gravitational wave detectors. Phys. Rev. D 2021, 104, 046021. [Google Scholar]
- Davies, E.B. The Quantum Theory of Open Systems; Academic Press: London, UK, 1976. [Google Scholar]
- Lindenberg, K.; West, B.J. The Nonequilibrium Statistical Mechanics of Open and Closed Systems; VCH Press: New York, NY, USA, 1990. [Google Scholar]
- Weiss, U. Quantum Dissipative Systems; World Scientific: Singapore, 1993. [Google Scholar]
- Breuer, H.P.; Petruccione, F. The Theory of Open Quantum Systems, 2nd ed.; Oxford University Press: Oxford, UK, 2007. [Google Scholar]
- Rivas, A.; Huelga, S.F. Open Quantum Systems: An Introduction; Springer: Berlin/Heidelberg, Germany, 2012. [Google Scholar]
- Vega, I.D.; Alonso, D. Dynamics of non-markovian open quantum systems. Rev. Mod. Phys. 2017, 89, 015001. [Google Scholar] [CrossRef]
- Zurek, W.H. Decoherence and the transition from quantum to classical. Phys. Today 1991, 44, 36. [Google Scholar] [CrossRef]
- Joos, E.; Zeh, H.D.; Kiefer, C.; Giulini, D.J.; Kupsch, J.; Stamatescu, I.O. Decoherence and the Appearance of a Classical World in Quantum Theory; Springer: Berlin/Heidelberg, Germany, 2017. [Google Scholar]
- Zurek, W.H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 2003, 75, 715. [Google Scholar] [CrossRef]
- Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 2004, 76, 1267. [Google Scholar] [CrossRef]
- Schlosshauer, M. Quantum decoherence. Phys. Rep. 2019, 831, 1. [Google Scholar] [CrossRef]
- Hu, B.L.; Paz, J.P.; Zhang, Y. Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. Phys. Rev. D 1992, 45, 2843. [Google Scholar] [CrossRef] [PubMed]
- Paz, J.P.; Habib, S.; Zurek, W.H. Reduction of the wave packet: Preferred observable and decoherence time scale. Phys. Rev. D 1993, 47, 488. [Google Scholar] [CrossRef] [PubMed]
- Halliwell, J.J.; Yu, T. Alternative derivation of the Hu-Paz-Zhang master equation of quantum Brownian motion. Phys. Rev. D 1996, 53, 2012. [Google Scholar] [CrossRef]
- Homa, G.; Bernád, J.Z.; Csordás, A. Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check. Phys. Rev. A 2023, 108, 012210. [Google Scholar] [CrossRef]
- Anastopoulos, C.; Hu, B.L. A Master equation for gravitational decoherence: Probing the textures of spacetime. Class. Quantum Gravity 2013, 30, 165007. [Google Scholar] [CrossRef]
- Blencowe, M. Effective field theory approach to gravitationally induced decoherence. Phys. Rev. Lett. 2013, 111, 021302. [Google Scholar] [CrossRef]
- Calzetta, E.; Hu, B.L. Nonequilibrium Quantum Field Theory; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar]
- Caldeira, A.O.; Leggett, A.J. Path integral approach to quantum Brownian motion. Phys. A 1983, 121, 587. [Google Scholar] [CrossRef]
- Homa, G.; Bernad, J.Z.; Lisztes, L. Positivity violations of the density operator in the Caldeira-Leggett master equation. Eur. Phys. J. D 2019, 73, 53, Erratum in Eur. Phys. J. D 2019, 73, 128. [Google Scholar] [CrossRef]
- Lindblad, G. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 1976, 48, 119. [Google Scholar] [CrossRef]
- Gorini, V.; Kossakowski, A.; Sudarshan, E.C.G. Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 1976, 17, 821. [Google Scholar] [CrossRef]
- Haake, F.; Reibold, R. Strong damping and low-temperature anomalies for the harmonic oscillator. Phys. Rev. A 1985, 32, 2462. [Google Scholar] [CrossRef] [PubMed]
- Garraway, B.M. Nonperturbative decay of an atomic system in a cavity. Phys. Rev. A 1997, 55, 2290. [Google Scholar] [CrossRef]
- Lampo, A.; Lim, S.H.; Wehr, J.; Massignan, P.; Lewenstein, M. Lindblad model of quantum Brownian motion. Phys. Rev. A 2016, 94, 042123. [Google Scholar] [CrossRef]
- Homa, G.; Csordás, A. Range of applicability of the Hu-Paz-Zhang master equation. Phys. Rev. A 2020, 102, 022206. [Google Scholar] [CrossRef]
- Grishchuk, L.; Sidorov, Y.V. Squeezed quantum states of relic gravitons and primordial density fluctuations. Phys. Rev. D 1990, 42, 3413. [Google Scholar] [CrossRef]
- Hu, B.L.; Matacz, A. Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions. Phys. Rev. D 1994, 49, 6612. [Google Scholar] [CrossRef]
- Hu, B.L.; Paz, J.P.; Zhang, Y. Quantum Brownian motion in a general environment. II. Nonlinear coupling and perturbative approach. Phys. Rev. D 1993, 47, 1576. [Google Scholar] [CrossRef] [PubMed]
- Unruh, W.G.; Zurek, W.H. Reduction of a wave packet in quantum Brownian motion. Phys. Rev. D 1989, 40, 1071. [Google Scholar] [CrossRef] [PubMed]
- Unruh, W.G. Notes on black-hole evaporation. Phys. Rev. D 1976, 14, 870. [Google Scholar] [CrossRef]
- Fulling, S.A.; Davies, P.C.W. Radiation from a moving mirror in two dimensional space-time: Conformal anomaly. Proc. R. Soc. Lond. A 1976, 348, 393. [Google Scholar]
- Davies, P.C.W.; Fulling, S.A. Radiation from moving mirrors and from black holes. Proc. R. Soc. Lond. A 1977, 356, 237. [Google Scholar]
- Hawking, S.W. Particle creation by black holes. Commun. Math. Phys. 1975, 43, 199. [Google Scholar] [CrossRef]
- Gibbons, G.; Hawking, S.W. Action integrals and partition functions in quantum gravity. Phys. Rev. D 1977, 15, 1752. [Google Scholar] [CrossRef]
- Boughn, S.; Rothman, T. Aspects of graviton detection: Graviton emission and absorption by atomic hydrogen. Class. Quantum Gravity 2006, 23, 5829. [Google Scholar] [CrossRef]
- Cho, H.T.; Hsiang, J.-T.; Hu, B.L. A non-Markovian master equation for masses in a quantum gravitational field: Graviton noise and gravitational decoherence. College of Electrical Engineering and Computer Science, National Taiwan University of Science and Technology, Taipei City, Taiwan. 2024; in preparation. [Google Scholar]
- Hu, B.L. Gravitational decoherence, alternative quantum theories and semiclassical gravity. J. Phys. Conf. Ser. 2014, 504, 012021. [Google Scholar] [CrossRef]
- Anastopoulos, C.; Hu, B.L. Gravitational decoherence: A thematic overview. AVS Quantum Sci. 2022, 4, 015602. [Google Scholar] [CrossRef]
- Hu, B.L. Emergent/quantum gravity: Macro/micro structures spacetime. J. Phys. Conf. Ser. 2009, 174, 012015. [Google Scholar] [CrossRef]
- Lagouvardos, M.; Anastopoulos, C. Gravitational decoherence of photons. Class. Quantum Gravity 2021, 38, 115012. [Google Scholar] [CrossRef]
- Oniga, T.; Wang, C.H.-T. Quantum gravitational decoherence of light and matter. Phys. Rev. D 2016, 93, 044027. [Google Scholar] [CrossRef]
- Bassi, A.; Großardt, A.; Ulbricht, H. Gravitational decoherence. Class. Quantum Gravity 2017, 34, 193002. [Google Scholar] [CrossRef]
- Zurek, W.H. Environment-induced superselection rules. Phys. Rev. D 1982, 26, 1862. [Google Scholar] [CrossRef]
- Joos, E.; Zeh, H.D. The emergence of classical properties through interaction with the environment. Z. Phys. B Condens. Matter. 1985, 59, 223. [Google Scholar] [CrossRef]
- Griffiths, R.B. Consistent histories and the interpretation of quantum mechanics. J. Stat. Phys. 1984, 36, 219. [Google Scholar] [CrossRef]
- Omnes, R. Logical reformulation of quantum mechanics. I. Foundations. J. Stat. Phys. 1988, 53, 893. [Google Scholar] [CrossRef]
- Omnes, R. Consistent interpretations of quantum mechanics. Rev. Mod. Phys. 1992, 64, 339. [Google Scholar] [CrossRef]
- Omnes, R. The Interpretation of Quantum Mechanics; Princeton University Press: Princeton, NJ, USA, 2018. [Google Scholar]
- Gell-Mann, M.; Hartle, J.B. Quantum mechanics in the light of quantum cosmology. In Complexity, Entropy, and the Physics of Information; CRC Press: Baton Rouge, LA, USA, 1990. [Google Scholar]
- Hartle, J.B. The quantum mechanics of cosmology. In Quantum Cosmology and Baby Universes; World Scientific: Singapore, 1990. [Google Scholar]
- Gell-Mann, M.; Hartle, J.B. Classical equations for quantum systems. Phys. Rev. D 1993, 47, 3345. [Google Scholar] [CrossRef] [PubMed]
- Hartle, J.B. Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime. Lectures at the 1992 Les Houches Summer School, “Gravitation and Quantizations”. 1993. Available online: https://web.physics.ucsb.edu/~quniverse/papers/nlh92.pdf (accessed on 1 December 2022).
- Hartle, J.B. The quantum mechanics of closed systems. In Directions in General Relativity; Cambridge University Press: Cambridge, UK, 1993; Volume 1. [Google Scholar]
- Hartle, J.B. The reduction of the state vector and limitations on measurement in the quantum mechanics of closed systems. In Directions in General Relativity; Cambridge University Press: Cambridge, UK, 1993; Volume 2. [Google Scholar]
- Halliwell, J.J. Decoherence in quantum cosmology. Phys. Rev. D 1989, 39, 2912. [Google Scholar] [CrossRef] [PubMed]
- Calzetta, E.; Hu, B.L. Decoherence of correlation histories. In Directions in General Relativity; Cambridge University Press: Cambridge, UK, 1993; Volume 2. [Google Scholar]
- Hsiang, J.-T.; Hu, B.L. Intrinsic entropy of squeezed quantum fields and nonequilibrium quantum dynamics of cosmological perturbations. Entropy 2021, 23, 1544. [Google Scholar] [CrossRef] [PubMed]
- Kanno, S.; Soda, J.; Tokuda, J. Noise and decoherence induced by gravitons. Phys. Rev. D 2021, 103, 044017. [Google Scholar] [CrossRef]
- Fulling, S.A. Nonuniqueness of canonical field quantization in Riemannian space-time. Phys. Rev. D 1973, 7, 2850. [Google Scholar] [CrossRef]
- Ford, L.H.; Parker, L. Infrared divergences in a class of Robertson-Walker universes. Phys. Rev. D 1977, 16, 245. [Google Scholar] [CrossRef]
- Ford, L.H.; Parker, L. Quantized gravitational wave perturbations in Robertson-Walker universes. Phys. Rev. D 1977, 16, 1601. [Google Scholar] [CrossRef]
- Allen, B. Vacuum states in de Sitter space. Phys. Rev. D 1985, 32, 3136. [Google Scholar] [CrossRef] [PubMed]
- Allen, B.; Folacci, A. Massless minimally coupled scalar field in de Sitter space. Phys. Rev. D 1987, 35, 3771. [Google Scholar] [CrossRef]
- Hollands, S.; Wald, R. Quantum fields in curved spacetime. Phys. Rep. 2015, 574, 1. [Google Scholar] [CrossRef]
- Kirsten, K.; Garriga, J. Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter–invariant vacuum. Phys. Rev. D 1993, 48, 567. [Google Scholar] [CrossRef]
- Hu, B.L.; O’Connor, D.J. Infrared behavior and finite-size effects in inflationary cosmology. Phys. Rev. Lett. 1986, 56, 1613. [Google Scholar] [CrossRef]
- Hu, B.L.; O’Connor, D.J. Symmetry behavior in curved spacetime: Finite size effect and dimensional reduction. Phys. Rev. D 1987, 36, 1701. [Google Scholar] [CrossRef]
- Starobinsky, A.A.; Yokoyama, J. Equilibrium state of a self-interacting scalar field in the de Sitter background. Phys. Rev. D 1994, 50, 6357. [Google Scholar] [CrossRef]
- Tsamis, N.C.; Woodard, R.P. The physical basis for infra-red divergences in inflationary quantum gravity. Class. Quantum Gravity 1994, 11, 2969. [Google Scholar] [CrossRef]
- Hu, B.L. Infrared behavior of quantum fields in inflationary cosmology—Issues and approaches: An overview. arXiv 2018, arXiv:1812.11851. [Google Scholar]
- Barceló, C.; Liberati, S.; Visser, M. Analogue Gravity. Liv. Rev. Relativ. 2011, 14, 3. [Google Scholar] [CrossRef]
- New Journal of Physics Focus Issue on Gravitational Quantum Physics. 2014. Available online: https://iopscience.iop.org/journal/1367-2630/page/Focus%20on%20Gravitational%20Quantum%20Physics (accessed on 14 July 2024).
- Carney, D.; Stamp, P.C.; Taylor, J.M. Tabletop experiments for quantum gravity: A user’s manual. Class. Quantum Gravity 2019, 36, 034001. [Google Scholar] [CrossRef]
- Bose, S.; Mazumdar, A.; Morley, G.W.; Ulbricht, H.; Toro, M.; Paternostro, M.; Geraci, A.A.; Barker, P.F.; Kim, M.S.; Milburn, G. A spin entanglement witness for quantum gravity. Phys. Rev. Lett. 2017, 119, 240401. [Google Scholar] [CrossRef]
- Marletto, C.; Vedral, V. Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity. Phys. Rev. Lett. 2017, 119, 240402. [Google Scholar] [CrossRef]
- Hu, B.L.; Verdaguer, E. Semiclassical and Stochastic Gravity: Quantum Field Effects on Curved Spacetime; Cambridge University Press: Cambridge, UK, 2020. [Google Scholar]
- Donoghue, J.F. General relativity as an effective field theory: The leading quantum corrections. Phys. Rev. D 1994, 50, 3874. [Google Scholar] [CrossRef]
- Burgess, C. Introduction to effective field theories and inflation. In Effective Field Theories in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School; Oxford Acadamic: Oxford, UK, 2020; Volume 108. [Google Scholar]
- Parikh, M.; Wilczek, F.; Zahariade, G. Quantum mechanics of gravitational waves. Phys. Rev. Lett. 2021, 127, 081602. [Google Scholar] [CrossRef]
- Wheeler, J.A. Relativity, Groups and Topology; DeWitt, B.S., DeWitt, C.M., Eds.; Gordon and Breach: New York, NY, USA, 1964. [Google Scholar]
- Hawking, S.W. Spacetime foam. Nucl. Phys. B 1978, 144, 349. [Google Scholar] [CrossRef]
- Oriti, D. Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Amelino-Camelia, G. Quantum-spacetime phenomenology. Liv. Rev. Relativ. 2013, 16, 5. [Google Scholar] [CrossRef]
- Hossenfelder, S. Experimental Search for Quantum Gravity; Springer: Cham, Switzerland, 2018. [Google Scholar]
- Brill, D.R.; Hartle, J.B. Method of the self-consistent field in general relativity and its application to the gravitational geon. Phys. Rev. B 1964, 135, 271. [Google Scholar] [CrossRef]
- Isaacson, R.A. Gravitational radiation in the limit of high frequency, I. The linear approximation and geometrical optics. Phys. Rev. 1968, 166, 1263. [Google Scholar] [CrossRef]
- Isaacson, R.A. Gravitational radiation in the limit of high frequency, II. Nonlinear terms and the effective stress tensor. Phys. Rev. 1968, 166, 1272. [Google Scholar] [CrossRef]
- Dyson, F. Is a graviton detectable? In Proceedings of the International Congress of Mathematical Physics, Aalborg, Denmark, 6 August 2012. [Google Scholar]
- Anastopoulos, C.; Hu, B.L. Comment on “A spin entanglement witness for quantum gravity” and on “Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity”. arXiv 2018, arXiv:1804.11315. [Google Scholar]
- Anastopoulos, C.; Hu, B.L. Quantum superposition of two gravitational cat states. Class. Quantum Gravity 2020, 37, 235012. [Google Scholar] [CrossRef]
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Hsiang, J.-T.; Cho, H.-T.; Hu, B.-L. Graviton Physics: A Concise Tutorial on the Quantum Field Theory of Gravitons, Graviton Noise, and Gravitational Decoherence. Universe 2024, 10, 306. https://doi.org/10.3390/universe10080306
Hsiang J-T, Cho H-T, Hu B-L. Graviton Physics: A Concise Tutorial on the Quantum Field Theory of Gravitons, Graviton Noise, and Gravitational Decoherence. Universe. 2024; 10(8):306. https://doi.org/10.3390/universe10080306
Chicago/Turabian StyleHsiang, Jen-Tsung, Hing-Tong Cho, and Bei-Lok Hu. 2024. "Graviton Physics: A Concise Tutorial on the Quantum Field Theory of Gravitons, Graviton Noise, and Gravitational Decoherence" Universe 10, no. 8: 306. https://doi.org/10.3390/universe10080306