Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell‐Mann in relation to the fundamental processes. This move provides further support to Schwinger's “symbolic” derivation of quantum mechanics from measurement.
Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell‐Mann in relation to the fundamental processes. This move provides further support to Schwinger's “symbolic” derivation of quantum mechanics from measurement.
Julian Schwinger provided to physics a mathematical reconstruction of quantum mechanics on the basis of the characteristics of sequences of measurements occurring at the atomic level of physical structure. The central component of this reconstruction is an algebra of symbols corresponding to quantum measurements, conceived of as discrete processes, which serve to relate experience to theory; collections of outcomes of identically circumscribed such measurements are attributed expectation values, which constitute the predictive content of the theory. The outcomes correspond to certain phase parameters appearing in the corresponding symbols, which are complex numbers, the algebra of which he finds by a process he refers to as 'induction'. Schwinger assumed these (individually unpredictable) phase parameters to take random, uniformly distributed definite values within a natural range. I have previously suggested that the 'principle of plenitude' may serve as a basis in principle for the occurrence of the definite measured values that are those members of the collections of measurement outcomes from which the corresponding observed statistics derive (Jaeger 2015Found. Phys.45, 806-819. (doi:10.1007/s10701-015-9893-6)). Here, I evaluate Schwinger's assumption in the context of recent critiques of the notion of randomness and explicitly relate the randomness of these phases with the principle of plenitude and, in this way, provide a fundamental grounding for the objective, physically irreducible probabilities, conceived of as graded possibilities, that are attributed to measurement outcomes by quantum mechanics.
The outcomes of quantum measurements are generally considered to be random, but despite the fact that this randomness is an important element in quantum information theory, its nature is not well understood. In this thesis, we study several issues relating to the origin and certification of quantum randomness and unpredictability. One of the key results in forming our understanding of quantum mechanics as an intrinsically indeterministic theory is the Kochen-Specker theorem, which shows the impossibility to consistently assign simultaneous noncontextual definite values to all quantum mechanical observables prior to measurement. However, the theorem, under the assumption that any definite values must be noncontextual, only strictly shows that some observables must be value indefinite. We strengthen this result, proving a stronger variant of the Kochen-Specker theorem showing that, under the same assumption, if a system is prepared in an arbitrary state j i, then every observable A is value indefinite unless j i is an eigenstate of A. The indeterministic nature of quantum measurements does little to explain how the quality of quantum randomness differs from classical randomness. We show that, subject to certain physical assumptions, a sequence of bits generated by the measurement of value indefinite observables is guaranteed, in the infinite limit, to be strongly incomputable. We further discuss how this can be used to build a quantum random number generator certified by value indefiniteness. Next, we study the notion of unpredictability, which is central to the concept of (quantum) randomness. In doing so, we propose a formal model of prediction that can be used to asses the predictability of arbitrary physical experiments. We investigate how the quantum features of value indefiniteness and complementarity can be used to certify different levels of unpredictability, and show that the outcome of a single measurement of a value indefinite quantum observable is formally unpredictable. Finally, we study the relation between this notion of unpredictability and the computability-theoretic certification of quantum randomness.
Quantum Physics is usually defined as a theory that affirms a primary role of randomness and probability. Eleven well-known quantum experiments are examined and the result is the coexistence of both random and causal type behaviour. We need both to describe experiments. Quantum Mechanics states the general overcoming of causality and this statement constitutes an unlimited generalization, not supported by experience. Determinism and indeterminism are philosophical systems, that universalize causality or chance. The crucial point is the difference between epistemic and intrinsic randomness. In the first aspect, randomness does not have a fundamental meaning, in the second, randomness of the individual event is explained, but the detection of high stable regularities remains to be explained. The article addresses the question of entanglement and various aspects of probability theory, including the law of large numbers, arriving at the thesis that many relevant questions are unresolved. A causal description is in quantum mechanics impossible in principle, given its assumptions. In order not to contradict experience, both points of view are necessary, causal and random. This is the state of the research, to return to and start again from.
The paper addresses the issue of stochastic behavior in quantum systems. The causes of the unpredictability of measurement outcomes in quantum mechanics are analyzed. The fundamental postulate of quantum mechanics is formulated, and on its basis a clear and consistent general concept of measurements in quantum mechanics is developed. The principles of designing an instrument that operates in accordance with Bohr's postulates are outlined. A model of the corresponding measurement process is proposed in the simplest case of a spin 1/2 particle in a constant magnetic field. It is shown that there is no difference between the nature of the stochastic behavior of quantum and classical systems.
Abstract Quantum mechanics is our most successful and versatile account of the basic constituents of matter, of their interaction and of their compounds. We introduce the theory via a sketch of its history and lay out its mathematical structure in some detail. Before this background we address the important and controversial question of how to interpret that structure. We contextualise our own position, which is linked to our account of ontological emergence as detailed in Chap. 2 , and which is mathematically best expressed in the Heisenberg picture of quantum dynamics. Indeterminism and irreversible processes are fundamental for our approach. We discuss the dialectics of the deterministic challenge to our position and argue that indeterminism in the form of quantum randomness has turned from a philosophical riddle to a technological resource. This claim is supported by a discussion of quantum information science, including some of its basic protocols. Towards the end of the chapter we argue that agency and quantum mechanics come as a package deal. For one, quantum mechanics describes the world as offering open possibilities for the future at a fundamental physical level, which is needed for real higher-order organisation, including agency. Of course, this does not in any way show that the actual existence of agents in our world is guaranteed. But it does show that general agency scepticism has no basis in physics. Second, we show that quantum mechanics is best understood as a theory that describes our agential interactions with nature, and not as a theory that represents nature from the point of view of an inert, detached observer.
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.