This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called"Epistemic Constraint."Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid's fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
Quantum theory challenges the view that individual measurement outcomes are predefined and independent of the measurement context. Yet the quantum state itself -- the catalogue of probabilities for all possible measurements -- is usually assumed to be well defined. We argue that this assumption tacitly relies on measurements being performed relative to ideal, infinitely-resourceful reference frames. We show that, when measurements are made relative to non-ideal quantum reference frames, the probabilities themselves become indefinite: even in the limit of arbitrarily large number of runs, the relative frequencies may remain uncertain. The uncertainty is irreducible in a quantum-mechanical sense, as we show by proving a Bell-type theorem for relative frequencies. We further propose a quantum-optical implementation of these relational measurements based on pulsed homodyne detection. Our findings motivate an extension of the notion of the quantum state to regimes constrained by finite resources. We expect them to be especially relevant at the interface between quantum theory and general relativity, where the resources and information available in a bounded region of spacetime are fundamentally limited.
Esteban Castro-Ruiz, Nathan Cohen, L. Barbado et al.· 0 citations
Initially proposed by Hugh Everett III as the “theory of the universal wave function,” the many worlds interpretation has since been developed and refined into one of the most influential ways of giving meaning to quantum mechanics. This volume explores the idea that if one adopts the many worlds interpretation, then one can avoid what Einstein called “spooky action at a distance,” the non-locality that is supposed to be a consequence of quantum entanglement according to other approaches. The essays in this volume articulate a clear and defensible formulation of the argument from locality for preferring the many worlds interpretation of quantum mechanics over its rivals and evaluate it. They question in what sense those in quantum foundations should care about locality, in particular, whether and how an interpretation of quantum mechanics must avoid action at a distance in order to maintain consistency with special relativity. Finally, these essays assess whether the many worlds theory needs a particular metaphysical or mathematical interpretation in order to achieve the aim of providing a local interpretation of quantum mechanics.
In their strongest usage, quantum reference frames have been described as referring to"the measurements performed by a superposed lab","the perspective of a quantum particle","the point of view of a superposed observer", etc. While exciting, these operational proposals have remained brief and ambiguous, leading to misinterpretations and criticism. Here, we provide a detailed specification and defense of the notion of a position-superposed lab or observer. We argue that this requires no exotic claims about quantum physics and raises no greater interpretive difficulty than ordinary quantum measurements. We then derive several consequences of taking this operational meaning seriously. We stress that the position-superposed observers that define quantum references frames are different from, and considerably less problematic than, the outcome-superposed observers considered in Wigners'friend scenarios. In particular, we show that outcomes obtained by a position-superposed observer may (without decohering the superposition) be broadcast to a well-localised one, in contrast with Wigner's friend scenarios, which require the outcomes to remain internal to the system at hand. Finally, we defend the possibility to roleplay a quantum reference frame from a classical reference frame.
The physical content of a theory is not intrinsically tied to any single mathematical formalism. Both classical and quantum mechanics admit equivalent representations, notably in phase space and in Hilbert space, related by the Wigner-Weyl correspondence. While this correspondence has long been studied in mathematical physics, its foundational and operational implications are often left implicit. Here we give a systematic account of what changes, and what does not, when classical and quantum theories are expressed in each other's native language. This representational viewpoint separates artifacts (such as the appearance of non-positivity or negativity under certain maps) from robust structural distinctions that persist across representations, in particular noncommutativity and its $\hbar$-dependent $\star$-deformation of the classical algebra. We develop the comparison at the level of states, kinematics, and dynamics, and extend it to measurement by formulating both outcome statistics and state-update rules within the same framework.
S. Schlegel, Borivoje Daki'c, Flavio Del Santo· 0 citations
Textbook quantum superposition refers to the feature that certain linear combinations of Hilbert space rays, each representing a valid quantum state, are themselves valid states. This notion is not operational, and it relies on the underlying Hilbert space formalism. Recent proposals for experimental tests of indefinite causal order, as well as tests probing the non-classicality of gravity, pivot on superposition, thereby calling for a theory-independent, operational formalisation of the concept. Here, we define superposition within the framework of Generalised Probabilistic Theories, based on observed statistics in prepare-and-measure experiments. Using this, we formulate three superposition principles to investigate which structural features of quantum theory carry over to other theories. We study conditions under which these principles carry over from subsystems to their compositions; to this end, we show that the quantum tensor product emerges as the largest composition rule for quantum systems respecting all three principles. Furthermore, we show how non-classical features such as entanglement and preparational uncertainty can be viewed as special forms of superposition.
Quantum mechanics is among the most successful physical theories, yet its formulation and empirical testing rely on classical structures. Following Lev Landau and Niels Bohr, this reliance is not merely pragmatic: quantum observables acquire empirical meaning only relative to classical reference frames, and, in practice, quantization starts from classical models. At the same time, the two domains display forms of mutual irreducibility: intrinsically quantum features (that is, spin and exchange statistics) have no counterpart in the phase-space ontology of classical point-particle mechanics, while classical trajectory chaos does not arise straightforwardly from unitary quantum evolution in closed systems. A hierarchy is commonly established between classical and quantum theories, namely, a claim of ontological and explanatory priority according to which quantum mechanics is fundamental and classical mechanics is only a limiting case. This claim is less secure than is often assumed; therefore, the traditional hierarchy deserves to be examined. In this paper, we argue that a quantum–classical framework provides an effective and structurally faithful representation of empirically accessible physical systems in regimes where quantum and classical degrees of freedom coexist within a single, consistent effective dynamical description. To give this point of view a firm theoretical basis, we discuss the quasi-Lie formal structure underlying quantum–classical hybrid dynamics, with applications ranging from gravity and condensed matter to open, driven systems in biology and complex media.
A. Sergi, A. Migliore, A. Messina· Physics· 0 citations