Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

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.

Collapse dynamics and Hilbert-space stochastic processes

Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi–Rimini–Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical features of the superposition generated, including also the effect of a finite reaction time of the measuring apparatus. We find that collapse dynamics is sensitive to the number of detectors and the physical properties of the photon-detector quantum states superposition.

Thick-Wall Elastic Collapse for Casing Design

Summary Elastic collapse is an important piece of the tubular collapse formulation in API TR 5C3 (2008) and ISO/TR 10400 (2007). Elastic collapse is significant because it is independent of the strength of the tubing, for example, K-55 and Q-125 have the same resistance to elastic collapse. Advanced collapse models, such as Klever and Tamano (2006), require a thick-wall collapse result as part of their formulation. What would the effect of a thick wall have on elastic collapse? There really is no way to tell from the classic formulation. The primary issue is whether the elastic collapse formula overpredicts or underpredicts collapse pressure. The developers of the API collapse equation thought the thin-wall equation overpredicted collapse pressure and put in terms to reduce the predictions. Other studies suggested the opposite effect. What is needed is a formulation that is based on an elastic solution for a thick-wall cylinder, but that can derive the classic solution for a thin wall. The elastic equations for a thick-walled cylinder exist, known as the Kirsch equations (Kirsch 1898). A new set of physically reasonable boundary conditions are proposed for the Kirsch equation, which was then used to determine the collapse resistance for a thick-wall pipe. This result also yielded the classic result in the limit because t/D is small. The thick-wall elastic collapse formula is then applied to the standard API TR 5C3 (2008) collapse formulation and to the Klever-Tamano formulation (Klever and Tamano 2006).

Collapse and Measures of Consciousness

There has been an upsurge of interest lately in developing Wigner’s hypothesis that conscious observation causes collapse by exploring dynamical collapse models in which some purportedly quantifiable aspect(s) of consciousness resist superposition. Kremnizer–Ranchin, Chalmers–McQueen and Okon–Sebastián have explored the idea that collapse may be associated with a numerical measure of consciousness. More recently, Chalmers–McQueen have argued that any single measure is inadequate because it will allow superpositions of distinct states of equal consciousness measure to persist. They suggest a satisfactory model needs to associate collapse with a set of measures quantifying aspects of consciousness, such as the “Q-shapes” defined by Tononi et al. in their “integrated information theory” (IIT) of consciousness. I argue here that Chalmers–McQueen’s argument against associating a single measure with collapse requires a precise symmetry between brain states associated with different experiences and thus does not apply to the only case where we have strong intuitions, namely human (or other terrestrial biological) observers. In defence of Chalmers–McQueen’s stance, it might be argued that idealized artificial information processing networks could display such symmetries. However, I argue that the most natural form of any theory (such as IIT) that postulates a map from network states to mind states is one that assigns identical mind states to isomorphic network states (as IIT does). This suggests that, if such a map exists, no familiar components of mind states, such as viewing different colours, or experiencing pleasure or pain, are likely to be related by symmetries.