If there's one lesson that philosophers seem to have learned from quantum mechanics it is that the quantum realm is governed by indeterministic laws. However, in 1952 David Bohm constructed a deterministic theory and proved that it is empirically equivalent to quantum mechanics. One of the three conditions that are together sufficient for the empirical adequacy of Bohm's theory is the statistical postulate. This postulate demands a very particular initial condition to hold for ensembles of quantum systems. I argue that the statistical postulate requires a justification. A justification would consist of showing how the dynamics of Bohm's theory is able to generate the initial conditions specified by the statistical postulate. I examine two deterministic justifications of the statistical postulate, one by Valentini and the other by Durr, Goldstein and Zanghi. I explain precisely the ways in which they are lacking. The basic problem is that crucial dynamical details are missing, ones needed to complete the justification. Whether these missing bits can be filled in is an open question. Until a justification is at hand, and its application to real-world ensembles is clarified, the empirical adequacy of Bohm's theory remains an open question. Bohm himself proposed a stochastic or indeterministic justification for the statistical postulate. It has been shown that the dynamics of this stochastic theory does not have the resources to justify the statistical postulate. In addition I show that the mathematical argument Bohm uses in his justification is flawed. Other stochastic theories do justify the statistical postulate but have other problems. The issue of indeterminism in the quantum realm is far from settled. Bohm's deterministic dynamics enables an investigation into the limits (if any) of a deterministic dynamics for the quantum realm. The properties of Bohm's deterministic equations of motion remain largely unknown. What we do know is that if the quantum realm is indeterministic it will not be for any of the reasons we have so far been given.
If there's one lesson that philosophers seem to have learned from quantum mechanics it is that the quantum realm is governed by indeterministic laws. However, in 1952 David Bohm constructed a deterministic theory and proved that it is empirically equivalent to quantum mechanics. One of the three conditions that are together sufficient for the empirical adequacy of Bohm's theory is the statistical postulate. This postulate demands a very particular initial condition to hold for ensembles of quantum systems. I argue that the statistical postulate requires a justification. A justification would consist of showing how the dynamics of Bohm's theory is able to generate the initial conditions specified by the statistical postulate. I examine two deterministic justifications of the statistical postulate, one by Valentini and the other by Durr, Goldstein and Zanghi. I explain precisely the ways in which they are lacking. The basic problem is that crucial dynamical details are missing, ones needed to complete the justification. Whether these missing bits can be filled in is an open question. Until a justification is at hand, and its application to real-world ensembles is clarified, the empirical adequacy of Bohm's theory remains an open question. Bohm himself proposed a stochastic or indeterministic justification for the statistical postulate. It has been shown that the dynamics of this stochastic theory does not have the resources to justify the statistical postulate. In addition I show that the mathematical argument Bohm uses in his justification is flawed. Other stochastic theories do justify the statistical postulate but have other problems. The issue of indeterminism in the quantum realm is far from settled. Bohm's deterministic dynamics enables an investigation into the limits (if any) of a deterministic dynamics for the quantum realm. The properties of Bohm's deterministic equations of motion remain largely unknown. What we do know is that if the quantum realm is indeterministic it will not be for any of the reasons we have so far been given.
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.
Abstract Is the world deterministic and can we ever know whether it is or is not so? This chapter critically evaluates recent results that bear on these issues, and points out the relation to probabilities. While results from classical physics are neither fully relevant nor conclusive, quantum mechanics is often assumed to establish indeterminism beyond doubt. However, whether the quantum world is indeterministic crucially depends on how the measurement problem is solved. There are both deterministic and indeterministic contenders in this field, some of them empirically equivalent to another one. This is shown using the deterministic Bohm theory and Nelsonsion mechanics, which is indeterministic. Two arguments that purport to establish indeterminism and that rely on Gleason's theorem and on Conway and Kochen's recent Free Will Theorem are shown to be wanting.
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the problem of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.
A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail.
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name principle of infinite precision). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on finite information quantities (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem.'' We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').
According to the widely accepted opinion, classical (statistical) physics does not support objective indeterminism, since the statistical laws of classical physics allow a deterministic hidden background, while --- as Arthur Fine writes polemizing with Grünbaum --- "{\sl the antilibertarian position finds little room to breathe in a statistical world if we take laws of the quantum theory as exemplars of the statistical laws in such a world. So, it appears that, contrary to what Grünbaum claims, the libertarians' 'could have done otherwise' does indeed find support from indeterminism if we take the indeterministic laws to be of the sort found in the quantum theory.}" In this paper I will show that, quite the contrary, quantum mechanics does not save free will. For instance, the EPR experiments are compatible with a deterministic world. They admit a deterministic local hidden parameter description if the deterministic model is 'allowed' to describe not only the measurement outcomes, but also the outcomes of the 'decisions' whether this or that measurement will be performed. So, the derivation of the freedom of the will from quantum mechanics is a tautology: from the assumption that the world is indeterministic it is derived that the world cannot be deterministic.