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.
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.
This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of quantum mechanics.
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the sense that the solution will bring new physics, i.e. new testable predictions, hence it is not merely a matter of interpretation of a frozen formalism. I argue that the two popular ways around the measurement problem, many-worlds and Bohmian-like mechanics, do, de facto, introduce effective collapses when "I" interact with the quantum system. Hence, surprisingly, in many-worlds and Bohmian mechanics, the "I" plays a more active role than in alternative models, like e.g. collapse models. Finally, I argue that either there are several kinds of stuffs out there, i.e. physical dualism, some stuff that respects the superposition principle and some that doesn't, or there are special configurations of atoms and photons for which the superposition principle breaks down. Or, and this I argue is the most promising, the dynamics has to be modified, i.e. in the form of a stochastic Schrödinger equation.
Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to govern the motion of the matter. 1. Introduction2. Bohmian Mechanics3. Ghirardi, Rimini, and Weber3.1. GRWm3.2. GRWf3.3. Empirical equivalence between GRWm and GRWf4. Primitive Ontology4.1. Primitive ontology and physical equivalence4.2. Primitive ontology and symmetry4.3. Without primitive ontology4.4. Primitive ontology and quantum state5. Differences between BM and GRW5.1. Primitive ontology and quadratic functionals5.2. Primitive ontology and equivariance6. A Plethora of Theories6.1. Particles, fields, and flashes6.2. Schrödinger wave functions and many-worlds7. The Flexible Wave Function7.1. GRWf without collapse7.2. Bohmian mechanics with collapse7.3. Empirical equivalence and equivariance8. What is a Quantum Theory without Observers?
Bohmian mechanics and Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of the Schr\\"odinger equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about matter moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of space-time points. The role of the wave function then is to guide the motion of the matter.
It is argued that in Bohmian mechanics the effective wave function of a subsystem of the universe does not encode the influences of other par-ticles on the subsystem. This suggests that the ontology of Bohmian mechanics does not consist only in Bohmian particles and their posi-tions. It is nonetheless pointed out that since the wave function in configuration space may represent the state of ergodic motion of non-Bohmian particles in three-dimensional space, the ontology of Bohmian mechanics may still consist only in particles. Bohmian mechanics, which is also called the de Broglie-Bohm theory, is a realistic alternative to standard quantum mechanics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete realistic description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. It has been a hot topic of debate how to interpret the wave function in the theory. Recently Esfeld et al (2013) further developed the nomological interpretation of the wave function, as suggested by Dürr, Goldstein and Zangh̀ı (1997), Goldstein and Teufel (2001) and Goldstein and Zangh̀ı (2012). They argued that the ontology of Bohmian mechanics consists only in Bohmian particles and their positions, and in particular, the effective wave function of a subsystem of the universe encodes the influences of other particles in the universe on the subsystem. In this note, we will argue that this interesting view may be problematic. The Bohmian law of motion is expressed by two equations, a guiding equation for the configuration of particles in three-dimensional space and the Schrödinger equation, describing the time evolution of the wave function, which enters the guiding equation. The law can be formulated as follows: dQ(t) dt = vΨ(t)(Q(t)). (1)
Dedicated to the memory of J. S. Bell. Abstract. The quantum formalism is a \\measurement " formalism|a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrodinger's equation for a system of particles when we merely insist that \\particles " means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We nd that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by \\ = j j 2. " A crucial ingredient in our analysis of the origin of this randomness is the notion of the eective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate. KEY WORDS: Quantum randomness; quantum uncertainty; hidden variables; eective wave function; collapse of the wave function; the measurement problem; Bohm's causal inter-pretation of quantum theory; pilot wave; foundations of quantum mechanics. 1.