Mathematical formalism for nonlocal spontaneous collapse in quantum field theory. (English) Zbl 1528.81018
Summary: Previous work has shown that spontaneous collapse of Fock states of identical fermions can be modeled as arising from random Rabi oscillations between two states. In this paper, a mathematical formalism is presented to incorporate this into many-body quantum field theory. This formalism allows for nonlocal collapse in the context of a relativistic system. While there is no absolute time-ordering of events, this approach allows for a coherent narrative of the collapse process.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 81T10 | Model quantum field theories |
| 81U90 | Particle decays |
| 30H20 | Bergman spaces and Fock spaces |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 81R30 | Coherent states |
References:
| [1] | Ghirardi, GC; Rimini, A.; Weber, T., Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D, 34, 470 (1986) · Zbl 1222.82047 · doi:10.1103/PhysRevD.34.470 |
| [2] | Ghirardi, GC; Pearle, P.; Rimini, A., Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles, Phys. Rev. A, 42, 78 (1990) · doi:10.1103/PhysRevA.42.78 |
| [3] | Diósi, L., Models for universal reduction of macroscopic quantum fluctuations, Phys. Rev. A, 40, 1165 (1989) · doi:10.1103/PhysRevA.40.1165 |
| [4] | Penrose, R., On gravity’s role in quantum state reduction, General Relativity and Gravitation, 28, 581 (1996) · Zbl 0855.53046 · doi:10.1007/BF02105068 |
| [5] | Everett, H., Relative state formulation of quantum mechanics, Rev. Mod. Phys., 29, 454 (1957) · doi:10.1103/RevModPhys.29.454 |
| [6] | Wallace, D., The Emergent Multiverse (2014), Oxford University Press · Zbl 1290.81001 |
| [7] | Brown, HR, Everettian quantum mechanics, Contemporary Physics, 60, 299 (2019) · doi:10.1080/00107514.2020.1733846 |
| [8] | Diósi, L.; Lukács, B., In favor of a Newtonian quantum gravity, Annalen der Physik, 499, 488 (1987) · doi:10.1002/andp.19874990703 |
| [9] | Diósi, L., Planck length challenges non-relativistic quantum mechanics of large masses, J. Physics: Conference Series, 1275, 012007 (2019) |
| [10] | Diósi, L., On the conjectured gravity-related collapse rate \(E_{\Delta }/\hbar\) of massive quantum superpositions, AVS Quantum Sci., 4, 015605 (2022) · doi:10.1116/5.0077919 |
| [11] | Penrose, R.; Bertlmann, R.; Zeilinger, A., John Bell, state reduction, and quanglement, Quantum (Un)speakables: From Bell to Quantum Information, 319 (2002), Springer · doi:10.1007/978-3-662-05032-3_23 |
| [12] | Penrose, R., On the gravitization of quantum mechanics 1: Quantum state reduction, Foundations of Physics, 44, 557 (2014) · Zbl 1311.81009 · doi:10.1007/s10701-013-9770-0 |
| [13] | Albert, DZ, The foundations of quantum mechanics and the approach to thermodynamic equilibrium, Brit. J. Phil. Sci., 45, 669 (1994) · doi:10.1093/bjps/45.2.669 |
| [14] | Martin, J.; Vennin, V., On the choice of the collapse operator in cosmological Continuous Spontaneous Locatization (CSL) theories, Eur. Phys. J. C, 81, 516 (2021) · doi:10.1140/epjc/s10052-021-09290-7 |
| [15] | Diósi, L., Spontaneous wave function collapse with frame dragging and induced gravity, Quantum Rep., 1, 277 (2019) · doi:10.3390/quantum1020025 |
| [16] | Bedingham, D.; Pearle, P., Continuous-spontaneous-localization scalar-field relativistic collapse model, Phys. Rev. Research, 1, 033040 (2019) · doi:10.1103/PhysRevResearch.1.033040 |
| [17] | Cowan, CW; Tumulka, R., Epistemology of wave function collapse in quantum physics, Brit. J. Phil. Sci., 67, 405 (2016) · Zbl 1359.81015 · doi:10.1093/bjps/axu038 |
| [18] | Carlesso, M.; Ferialdi, L.; Bassi, A., Colored collapse models from the non-interferometric perspective, Eur. Phys. J. D, 72, 159 (2018) · doi:10.1140/epjd/e2018-90248-x |
| [19] | Snoke, DW, A model of spontaneous collapse with energy conservation, Foundations of Physics, 51, 100 (2021) · Zbl 1483.81178 · doi:10.1007/s10701-021-00507-z |
| [20] | Zurek, W., Probabilities from entanglement, Born’s rule \(p_k = |\psi_k|^2\) from envariance, Phys. Rev. A, 71, 052105 (2005) · Zbl 1227.81062 · doi:10.1103/PhysRevA.71.052105 |
| [21] | Daley, A., Quantum trajectories and open many-body quantum systems, Adv Phys, 63, 77 (2014) · doi:10.1080/00018732.2014.933502 |
| [22] | Albert, DZ, After physics (2016), Harvard University Press |
| [23] | Einstein, A.; Podolsky, B.; Rosen, N., Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev., 47, 777 (1935) · Zbl 0012.04201 · doi:10.1103/PhysRev.47.777 |
| [24] | Aharanov, Y.; Albert, DZ, States and observables in relativistic quantum field theories, Physical Review D, 21, 3316 (1980) · doi:10.1103/PhysRevD.21.3316 |
| [25] | Aharonov, Y.; Albert, DZ, Can we make sense out of the measurement process in relativistic quantum mechanics?, Phys. Rev. D, 24, 359 (1981) · doi:10.1103/PhysRevD.24.359 |
| [26] | Myrvold, WC, On peaceful coexistence: is the collapse postulate incompatible with relativity?, Studies in History and Philosophy of Science Part B, 33, 435 (2002) · Zbl 1222.83020 · doi:10.1016/S1369-8486(02)00004-3 |
| [27] | Aharonov, Y.; Anandan, J.; Vaidman, L., Meaning of the wave function, Phys Rev A, 47, 4616 (1993) · doi:10.1103/PhysRevA.47.4616 |
| [28] | Snoke, DW, Solid State Physics: Essential Concepts (2020), Cambridge University Press · Zbl 1429.82001 · doi:10.1017/9781108123815 |
| [29] | Fleming, GN; Brown, HR; Harré, R., Hyperplane-dependent quantized fields and Lorentz invariance, Philosophical Foundations of Quantum Field Theory (1988), Clarendon Press · Zbl 0641.53075 |
| [30] | Aurich, R.; Reinhardt, D., Determining our peculiar velocity from the aberration in the cosmic microwave background, Monthly Not. Royal Astron. Soc., 506, 3259 (2021) · doi:10.1093/mnras/stab1897 |
| [31] | Consoli, M.; Pluchino, A., Cosmic Microwave Background and the issue of a fundamental preferred frame, Eur. Phys. J. Plus, 133, 295 (2018) · doi:10.1140/epjp/i2018-12136-5 |
| [32] | Jacobs, K.; Steck, DA, A straightforward introduction to continuous quantum measurement, Contemporary Physics, 47, 279 (2006) · doi:10.1080/00107510601101934 |
| [33] | Oreshkov, O.; Bru, TA, Weak measurements are universal, Phys. Rev. Lett., 95, 110409 (2005) · doi:10.1103/PhysRevLett.95.110409 |
| [34] | Clerk, A.; Devoret, M.; Girvin, S.; Marquardt, F.; Schoelkopf, R., Introduction to quantum noise, measurement, and amplification, Rev. Modern Phys., 82, 1155 (2010) · Zbl 1205.81001 · doi:10.1103/RevModPhys.82.1155 |
| [35] | Tumulka, R., A relativistic version of the Ghirardi-Rimini-Weber model, J. Statistical Physics, 125, 825 (2006) · Zbl 1106.81013 · doi:10.1007/s10955-006-9227-3 |
| [36] | Hellwig, KE; Kraus, K., Formal description of measurements in local quantum field theory, Phys. Rev. D, 1, 566 (1970) · doi:10.1103/PhysRevD.1.566 |
| [37] | Cramer, J., The Quantum Handshake (2016), Springer · Zbl 1358.81001 · doi:10.1007/978-3-319-24642-0 |
| [38] | Cramer, J., Kastner, R.E.: Quantifying absorption in the transactional interpretation, arXiv:1711.04501 |
| [39] | Kastner, R., The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility (2012), Cambridge University Press · Zbl 1487.81002 · doi:10.1017/CBO9780511675768 |
| [40] | Kastner, R.E.: The relativistic transactional interpretation and the quantum direct-action theory. arXiv:2101.00712 · Zbl 1223.81033 |
| [41] | Tipler, FJ, Quantum nonlocality does not exist, Proc. Natl Acad Sci USA, 111, 11281 (2014) · Zbl 1355.81019 · doi:10.1073/pnas.1324238111 |
| [42] | Davies, PCW, Extension of Wheeler-Feynman quantum theory to the relativistic domain, I. Scattering processes. J. Phys. A, 4, 836 (1971) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
