Abstract We consider how Bohmian mechanics characterizes the behavior of physical systems paying particular attention to what it means to make a measurement in the theory and how one should understand the empirical content of one’s records. We discuss the sense in which a measurement record selects a branch of the quantum-mechanical state and, hence, why the empirical content of the record is well-understood as being given by the effective wave function in configuration space. We conclude by considering the virtues and vices of Bohmian mechanics given how it accounts for our experience. This includes reflecting on how the theory explains surreal trajectories and EPR-Bell type nonlocal correlations.
Abstract We consider how Bohmian mechanics characterizes the behavior of physical systems paying particular attention to what it means to make a measurement in the theory and how one should understand the empirical content of one’s records. We discuss the sense in which a measurement record selects a branch of the quantum-mechanical state and, hence, why the empirical content of the record is well-understood as being given by the effective wave function in configuration space. We conclude by considering the virtues and vices of Bohmian mechanics given how it accounts for our experience. This includes reflecting on how the theory explains surreal trajectories and EPR-Bell type nonlocal correlations.
Abstract Each formulation of quantum mechanics we consider in the book seeks to explain why we have determinate measurement records distributed according to the standard quantum statistics. The explanation we get relies on the metaphysical assumptions that underlie the particular theory. Metaphysics here does real explanatory work in accounting for our experience. While it is not at all clear what specific metaphysical commitments best explain our experience, one can distinguish between different types and degrees of empirical adequacy each formulation provides. Stronger notions of empirical adequacy might be characterized in terms of such things as the plausibility that one’s experience in fact supervenes on the sort of records a particular theory provides and the richness of the account of experience provided by the theory.
Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.
The popular impression of Bohmian mechanics is that it is standard quantum mechanics with the addition of some extra gadgets---exact particle positions and a guiding equation for particle trajectories---the advantages being that the gadgets pave the way for a resolution of the measurement problem that eschews state vector reduction while restoring the determinism lost in standard quantum mechanics. In fact, the Bohmian mechanics departs in significant ways from standard quantum mechanics. By itself this is not a basis for criticism; indeed, it makes Bohmian mechanics all the more interesting. But Bohmian mechanics is not, as the popular impression would have it, empirically equivalent to standard quantum mechanics in terms of probabilistic predictions for the outcomes of measurements of quantum observables. Indeed, in physically important applications to systems for which standard quantum mechanics delivers empirically well-confirmed probabilistic predictions, the sophisticated form of Bohmian mechanics designed to prove the global existence of Bohmian particle trajectories fails to deliver unequivocal predictions---of even a probabilistic variety---for the future behavior of said systems. Possible responses to this lacuna are discussed.
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.
This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.
Standard quantum mechanics famously disallows to simultaneously measure particle position and momentum with arbitrary precision. In contrast, Bohmian mechanics, a hidden-variable interpretation, at the same time ascribes reality to the positions and momenta of quantum particles at the cost of a nonlocal ontology [1]. It thus allows to conceive of definite particle trajectories, while being fully compatible with the standard theory in all empirical predictions. To record such trajectories [2] we consider two optical settings using weak measurements in order to investigate different features of particle propagation in the Bohmian picture.