Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function ($e.g.$ mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic’ realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true’ (Markovian) collapse models and non-Markovian models.
Unlike Bohmian mechanics, collapse models modify the predictions of orthodox quantum mechanics. To avoid predictions that have already been empirically ruled out, non-Markovian collapse models (NMCMs), with smooth-in-time noise, have been proposed. However, such NMCMs are mathematically challenging to derive and simulate.
In this paper we show that NMCMs can be easily derived and understood within a Bohmian framework, as follows. In standard NMCMs, one adds to the system an auxiliary quantum bath in order to construct the system collapse dynamics, so that averaging over the noise is the same as tracing over that ‘non-physical’ bath. Here we introduce Bohmian variables for this auxiliary bath only, with standard Bohmian dynamics. Then the “conditional wavefunction” for the system, conditioned on those auxiliary Bohmian variables, reproduces exactly the NMCM.
Our work explains complicated stochastic non-Markovian dynamics in terms of simple deterministic Markovian dynamics of a larger system with hidden variables. This suggests that to take NMCMs seriously one should take seriously the auxiliary bath as a physical system, as well as its Bohmian variables.
 David Bohm. A suggested interpretation of the quantum theory in terms of “hidden” variables. i. Phys. Rev., 85: 166–179, Jan 1952a. 10.1103/PhysRev.85.166.
 David Bohm. A suggested interpretation of the quantum theory in terms of “hidden” variables. ii. Phys. Rev., 85: 180–193, Jan 1952b. 10.1103/PhysRev.85.180.
 Detlef Dürr and Stefan Teufel. Bohmian mechanics: the physics and mathematics of quantum theory. Springer Science & Business Media, Berlin, Germany, 2009.
 Sheldon Goldstein. Bohmian mechanics. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, fall 2016 edition, 2016. URL https://plato.stanford.edu/archives/fall2016/entries/qm-bohm/.
 G. C. Ghirardi, A. Rimini, and T. Weber. Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D, 34: 470–491, Jul 1986. 10.1103/PhysRevD.34.470.
 Angelo Bassi and GianCarlo Ghirardi. Dynamical reduction models. Phys. Rep., 379 (5): 257 – 426, 2003. ISSN 0370-1573. 10.1016/S0370-1573(03)00103-0.
 Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, and Hendrik Ulbricht. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys., 85: 471–527, Apr 2013a. 10.1103/RevModPhys.85.471.
 J. S. Bell. The theory of local beables. Epistemological Letters, 9 (11), 1976. (Reproduced in Ref. BellCollection.).
 Valia Allori. Primitive ontology in a nutshell. International Journal of Quantum Foundations, 1 (2): 107–122, 2015. URL http://www.ijqf.org/archives/2394.
 Valia Allori, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghì. On the common structure of bohmian mechanics and the ghirardi–rimini–weber theory dedicated to giancarlo ghirardi on the occasion of his 70th birthday. Br. J. Philos. Sci., 59 (3): 353–389, 2008. 10.1093/bjps/axn012.
 Valia Allori, Sheldon Goldstein, Roderich Tumulka, and Nino Zanghì. Predictions and primitive ontology in quantum foundations: a study of examples. Br. J. Philos. Sci., 65 (2): 323–352, 2014. 10.1093/bjps/axs048.
 Marko Toros, Sandro Donadi, and Angelo Bassi. Bohmian mechanics, collapse models and the emergence of classicality. J. Phys. A: Math. Theor., 49 (35): 355302, 2016. 10.1088/1751-8113/49/35/355302.
 Jay Gambetta and H. M. Wiseman. Interpretation of non-markovian stochastic schrödinger equations as a hidden-variable theory. Phys. Rev. A, 68: 062104, Dec 2003a. 10.1103/PhysRevA.68.062104.
 Angelo Bassi and GianCarlo Ghirardi. Dynamical reduction models with general gaussian noises. Phys. Rev. A, 65: 042114, Apr 2002. 10.1103/PhysRevA.65.042114.
 Stephen L. Adler and Angelo Bassi. Collapse models with non-white noises. J. Phys. A: Math. Theor., 40 (50): 15083, 2007. 10.1088/1751-8113/40/50/012.
 Stephen L. Adler and Angelo Bassi. Collapse models with non-white noises: Ii. particle-density coupled noises. J. Phys. A: Math. Theor., 41 (39): 395308, 2008. 10.1088/1751-8113/41/39/395308.
 Angelo Bassi and Luca Ferialdi. Non-markovian quantum trajectories: An exact result. Phys. Rev. Lett., 103: 050403, Jul 2009a. 10.1103/PhysRevLett.103.050403.
 Angelo Bassi and Luca Ferialdi. Non-markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties. Phys. Rev. A, 80: 012116, Jul 2009b. 10.1103/PhysRevA.80.012116.
 Luca Ferialdi and Angelo Bassi. Exact solution for a non-markovian dissipative quantum dynamics. Phys. Rev. Lett., 108: 170404, Apr 2012a. 10.1103/PhysRevLett.108.170404.
 Philip Pearle. Combining stochastic dynamical state-vector reduction with spontaneous localization. Phys. Rev. A, 39: 2277–2289, Mar 1989. 10.1103/PhysRevA.39.2277.
 Gian Carlo Ghirardi, Philip Pearle, and Alberto Rimini. Markov processes in hilbert space and continuous spontaneous localization of systems of identical particles. Phys. Rev. A, 42: 78–89, Jul 1990. 10.1103/PhysRevA.42.78.
 Nicolas Gisin. Weinberg’s non-linear quantum mechanics and supraluminal communications. Phys. Lett. A, 143 (1-2): 1–2, 1990. 10.1016/0375-9601(90)90786-N.
 Joseph Polchinski. Weinberg’s nonlinear quantum mechanics and the einstein-podolsky-rosen paradox. Phys. Rev. Lett., 66: 397–400, Jan 1991. 10.1103/PhysRevLett.66.397.
 Angelo Bassi and Kasra Hejazi. No-faster-than-light-signaling implies linear evolution. a re-derivation. Eur. J. Phys., 36 (5): 055027, 2015. 10.1088/0143-0807/36/5/055027.
 Angelo Bassi, Detlef Dürr, and Günter Hinrichs. Uniqueness of the equation for quantum state vector collapse. Phys. Rev. Lett., 111: 210401, Nov 2013b. 10.1103/PhysRevLett.111.210401.
 Howard M. Wiseman and Lajos Diósi. Complete parameterization, and invariance, of diffusive quantum trajectories for markovian open systems. Chem. Phys., 268 (1): 91 – 104, 2001. ISSN 0301-0104. 10.1016/S0301-0104(01)00296-8.
 Wayne C. Myrvold. Relativistic markovian dynamical collapse theories must employ nonstandard degrees of freedom. Phys. Rev. A, 96: 062116, Dec 2017. 10.1103/PhysRevA.96.062116.
 C. Jones, T. Guaita, and A. Bassi. Impossibility of extending the ghirardi-rimini-weber model to relativistic particles. Phys. Rev. A, 103: 042216, Apr 2021. 10.1103/PhysRevA.103.042216.
 Antoine Tilloy. Time-local unraveling of non-Markovian stochastic Schrödinger equations. Quantum, 1: 29, September 2017. ISSN 2521-327X. 10.22331/q-2017-09-19-29.
 L. Diósi and L. Ferialdi. General non-markovian structure of gaussian master and stochastic schrödinger equations. Phys. Rev. Lett., 113: 200403, Nov 2014. 10.1103/PhysRevLett.113.200403.
 Richard Phillips Feynman and Frank Lee Vernon. The theory of a general quantum system interacting with a linear dissipative system. Ann. Phys. (N Y), 24: 118–173, 1963. 10.1016/0003-4916(63)90068-X.
 Walter T. Strunz. Linear quantum state diffusion for non-markovian open quantum systems. Phys. Lett. A, 224 (1): 25 – 30, 1996. ISSN 0375-9601. 10.1016/S0375-9601(96)00805-5.
 Lajos Diósi and Walter T Strunz. The non-markovian stochastic schrödinger equation for open systems. Phys. Lett. A, 235 (6): 569–573, 1997. 10.1016/S0375-9601(97)00717-2.
 Jay Gambetta and H. M. Wiseman. Non-markovian stochastic schrödinger equations: Generalization to real-valued noise using quantum-measurement theory. Phys. Rev. A, 66: 012108, Jul 2002. 10.1103/PhysRevA.66.012108.
 Jay Gambetta and H. M. Wiseman. Modal dynamics for positive operator measures. Found. Phys., 34 (3): 419–448, Mar 2004. ISSN 1572-9516. 10.1023/B:FOOP.0000019622.81881.f8.
 Jay Gambetta and Howard Wiseman. A non-markovian stochastic schrodinger equation developed from a hidden variable interpretation. Proceedings of SPIE – The International Society for Optical Engineering, 5111, 05 2003b. 10.1117/12.496938.
 J. Gambetta and H. M. Wiseman. Interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory. Phys. Rev. A, 68 (6): 062104, Dec 2003c. 10.1103/PhysRevA.68.062104.
 W Struyve and H Westman. A minimalist pilot-wave model for quantum electrodynamics. Proc. R. Soc. A., 463 (2088): 3115–3129, 2007. 10.1098/rspa.2007.0144.
 Nicolas Gisin. Indeterminism in physics, classical chaos and bohmian mechanics: Are real numbers really real? Erkenntnis, Oct 2019. ISSN 1572-8420. 10.1007/s10670-019-00165-8.
 J. S. Bell. On the Einstein-Podolsy-Rosen paradox. Physics, 1: 195, 1964. (Reproduced in Ref. BellCollection.).
 Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman. A strong no-go theorem on the wigner’s friend paradox. Nature Physics, 2020. 10.1038/s41567-020-0990-x.
 H. M. Wiseman and E. G. Cavalcanti. Causarum Investigatio and the two Bell’s theorems of John Bell. In Reinhold Bertlmann and Anton Zeilinger, editors, Quantum [Un]speakables II: Half a Century of Bell’s Theorem, The Frontiers Collection, pages 119–142, Switzerland, 2017. Springer.
 A. Shimony. Controllable and uncontrollable non-locality. In Susumu Kamefuchi, editor, Foundations of Quantum Mechanics in the Light of New Technology, pages 225–230, Tokyo, 1984. Physical Society of Japan.
 H. M. Wiseman, E. G. Cavalcanti, and Eleanor G. Rieffel. A `thoughtful’ local friendliness no-go theorem. in preparation, 2021.
 J. S. Bell. Beables for quantum field theory. Technical Report TH.4035/84, CERN, Geneva, 1984. (Reproduced in Ref. BellCollection.).
 A Sudbery. Objective interpretations of quantum mechanics and the possibility of a deterministic limit. J. Phys. A: Math. Gen., 20 (7): 1743, 1987. 10.1088/0305-4470/20/7/020.
 J. Gambetta, T. Askerud, and H. M. Wiseman. Jumplike unravelings for non-Markovian open quantum systems. Phys. Rev. A, 69 (5): 052104, May 2004. 10.1103/PhysRevA.69.052104.
 J Butterfield and B Marsh. Non-locality and quasiclassical reality in kent’s formulation of relativistic quantum theory. Journal of Physics: Conference Series, 1275: 012002, Sep 2019. ISSN 1742-6596. 10.1088/1742-6596/1275/1/012002.
 E. A. Novikov. Functionals and the random-force method in turbulence theory. JETP, 20: 5, 1965. URL http://www.jetp.ac.ru/cgi-bin/dn/e_020_05_1290.pdf.
 M. Bell, K. Gottfried, and M. Veltman, editors. John S. Bell on the Foundations of Quantum Mechanics. World Scientific, Singapore, 2001.
 Guillermo Albareda, Kevin Lively, Shunsuke A. Sato, Aaron Kelly, and Angel Rubio, “Conditional wavefunction theory: a unified treatment of molecular structure and nonadiabatic dynamics”, arXiv:2107.01094.
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