Conditions are formulated under which a representation of an intrinsic C*- algebra of (often quasilocal) observables of an infinite system is appropriate to describe measurement-type processes: such a representation should allow for the description of robust experiments, it should be separable, and the pointer observable should be in its weak closure. If the pointer values are discrete the existence of such a measurement representation can be proven. If the pointer can take continuously many values, then the existence can only be proven under the additional assumptions of having an asymptotically Abelian system or dealing with type I representations. In the constructed measurement representations the pointer observable turns out to be classical. The structure of the representation suggests that spontaneous symmetry breaking might be a physical explanation of the emergence of the classical pointer.
Conditions are formulated under which a representation of an intrinsic C*- algebra of (often quasilocal) observables of an infinite system is appropriate to describe measurement-type processes: such a representation should allow for the description of robust experiments, it should be separable, and the pointer observable should be in its weak closure. If the pointer values are discrete the existence of such a measurement representation can be proven. If the pointer can take continuously many values, then the existence can only be proven under the additional assumptions of having an asymptotically Abelian system or dealing with type I representations. In the constructed measurement representations the pointer observable turns out to be classical. The structure of the representation suggests that spontaneous symmetry breaking might be a physical explanation of the emergence of the classical pointer.
Quantum mechanics cannot be applied within a closed system. Inevitable measurement process in quantum mechanics is usually treated separately from the basic principles of the framework and requires outside observer of the system. In this paper, we propose that the quantum measurement process is actually a physical process associated with the ubiquitous mechanism of spontaneous symmetry breaking. Based on this proposal, we construct a quantum measurement model in which the mixed state evolves into a pure state as the dynamical pro-coherence process. Furthermore, the classically distinguishable pointer parameter emerges as the c-number order parameter in the formalism of closed time-path quantum field theory. We also discuss the precision of the measurement and the possible deduction of the Born probability postulate.
The theory of decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an open quantum evolution (or channel) can be characterized in terms of observables of the initial system. We use this approach to show that information which is broadcast into many parts of the environment can be encoded in a single observable. This supports a model of decoherence where the pointer observable can be an arbitrary positive operator-valued measure (POVM). This generalization makes it possible to characterize the emergence of a realistic classical phase-space. In addition, this model clarifies the relationships among the information preserved in the system, the information flowing from the system to the environment (measurement), and the establishment of correlations between the system and the environment.
We follow Kofler and Brukner (2007 Phys. Rev. Lett. 99 180403) in studying the conditions under which a classical picture emerges from the results of not too accurate quantum measurements made on large macroscopic objects. We show that for such objects, consisting of a large number of microscopic elements obeying quantum laws, the Central Limit theorem guarantees the existence of classical values for collective variables, even if the corresponding operators do not commute. Owing to localisation of the overall wave function in any chosen representation, these values can be measured to a small relative error without significantly altering the state of the object. We study a simple model, which includes a rudimentary observer capable of detecting in the coordinate space the position of a macroscopic pointer. The pointer can be employed to measure such quantities, not directly accessible to the observer, as linear or angular momenta. A purely classical picture arises provided the measurements are made on macroscopic objects. Results of measurements, made on small quantum objects, cannot be predicted with certainty, but acquire certain objectivity when encoded in macroscopic pointers’ positions accessible to all observers. Our estimates show that the classical conditions could, in principle, be realised for systems with number of constituent parts of the order of the Avogadro constant. It is possible that the approach captures the essential features of the quantum-to-classical behaviour, although its extension to more realistic systems is likely to be required.
Quantum measurement is ultimately a physical process, resulting from an interaction between the measured system and a measurement apparatus. Considering the physical process of measurement within a thermodynamic context naturally raises the following question: how can the work and heat resulting from the measurement process be interpreted? In the present manuscript, we model the measurement process for an arbitrary discrete observable as a measurement scheme. Here, the system to be measured is first unitarily coupled with a measurement apparatus, and subsequently the apparatus is measured by a pointer observable, thus producing a definite measurement outcome. The work can therefore be interpreted as the change in internal energy of the compound of system-plus-apparatus due to the unitary coupling. By the first law of thermodynamics, the heat is the subsequent change in internal energy of this compound due to the measurement of the pointer observable. However, in order for the apparatus to serve as a stable record for the measurement outcomes, the pointer observable must commute with the Hamiltonian, and its implementation must be repeatable. Given these minimal requirements, we show that the heat will necessarily be a classically fluctuating quantity.
Since the mechanism of spontaneous symmetry breaking has such a relevant impact for the description of physical systems, its explanation should be based on physical considerations with a direct operational meaning. To this purpose, it is useful to recognize that the operational/experimental description of a physical system (not necessarily quantum!) involves the following elements: the set A of its measurable quantities, briefly called observables ; the measurement of the time evolution of the observables; the set ∑ of configurations or states in which the system may be prepared, according to well defined protocols of experimental preparations; the measurement of an observable A , when the system is in the state ω is operationally defined by the experimental expectation 〈A〉 ω
Central thesis: Quantum theory contains stable closure without universal completion. Quantum field theory repeatedly resists the classical assumption that every physically meaningful structure must correspond to an independently complete object. A quantum state can be definite relative to one observable while remaining unresolved relative to another; separated alternatives can retain phase relations and later interfere; composite systems can possess globally definite relational structure without factorizing into independently complete subsystems; gauge-related field configurations can represent a single physical state; effective descriptions depend systematically on scale; and local field degrees of freedom need not correspond to independently realizable asymptotic particles. This paper investigates whether these apparently different structures admit a common representation as forms of partial closure. A closure is defined as a physically meaningful stabilization or equivalence relative to a specified context, probe family, observable algebra, quotient, scale, or asymptotic condition. It is partial when stable disclosure exists while additional physically relevant structure remains latent, relational, global, scale-dependent, or otherwise outside that closure. The framework distinguishes redundant fibers from latent physical fibers through a future-distinguishability criterion and introduces reclosure for later sensitivity to information not exhausted by an earlier closure. Interference becomes phase-sensitive reclosure; incompatible measurements instantiate noncommuting closure; entanglement instantiates nonfactorizable closure; contextuality becomes a failure of local closures to assemble into one global classical assignment; gauge symmetry becomes quotient closure; renormalization becomes scale-relative effective closure; confinement exemplifies asymptotic closure restriction; and Berry, Wilson, and flavor-cycle invariants exemplify closed relational cycles retaining invariant memory. Two restricted theory-space applications are developed: a one-generation hypercharge calculation in which Yukawa invariance and anomaly cancellation fix relative hypercharges up to overall normalization, and a minimal representation reconstruction under explicit low-dimensional and minimality assumptions. The resulting Typed Quantum Partial Closure Representation Theorem is a representation theorem rather than a derivation theorem. The framework is therefore presently a unifying reconstruction program whose decisive future test is whether closure principles can generate restrictions or predictions not already contained in the formalisms they reorganize. Keywords: quantum field theory; partial closure; reclosure; gauge symmetry; effective field theory; entanglement; contextuality; confinement; asymptotic states; anomaly cancellation; flavor mixing