We show that Quantum Mechanics is consistent with the λ-dominant regime of the Law from Bit framework, where information is predominantly distributed rather than localized. Bell's theorem and its experimental confirmations established that quantum correlations cannot be explained by local hidden variables. We interpret this as information operating in λ-mode. Combined with Paper V (GR as α-regime), this suggests GR and QM are complementary descriptions connected by α + λ + 1/2 = 0.
We show that Quantum Mechanics is consistent with the λ-dominant regime of the Law from Bit framework, where information is predominantly distributed rather than localized. Bell's theorem and its experimental confirmations established that quantum correlations cannot be explained by local hidden variables. We interpret this as information operating in λ-mode. Combined with Paper V (GR as α-regime), this suggests GR and QM are complementary descriptions connected by α + λ + 1/2 = 0.
Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting of alpha; similarly for the other side and the setting beta. From this equation John Bell derived a simple inequality that is violated by the predictions of quantum mechanics, which is generally taken to imply that quantum mechanics is a nonlocal theory. But, by combining Richard Feynman's formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the "space of all paths," SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, (2) has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set lambda of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set lambda is nonmeasurable, and therefore the above equation is meaningless in SP.
While Bell’s theorem is traditionally seen as a total rejection of local classical models in quantum mechanics, this paper argues that such a conclusion relies on the narrow assumption of "joint definiteness." Bell’s derivation requires a single hidden state, λ, to account for all possible measurement outcomes simultaneously, which implies that the measurement apparatus remains microscopically unchanged regardless of its settings. However, because physical instruments are composed of matter, their internal microstates necessarily vary with the chosen settings, meaning the relevant hidden variables are setting-dependent. This physical reality prevents the formation of a global joint probability distribution, placing these types of models outside the mathematical constraints of Bell’s and Fine’s theorems. Consequently, the authors conclude that while Bell’s theorem remains mathematically sound, it only excludes hidden-variable models that ignore the setting-dependent nature of the measuring apparatus, leaving the door open for classical descriptions of physical reality.
The standard formalism of quantum mechanics is one of the most successful theoretical constructions in the history of science. Its predictions have been confirmed to extraordinary precision. This paper explores a question it never asked --- and assumed closed without ever testing it. Bell's theorem rules out local hidden variables, and a continuously oscillating variable is no exception: sampled at the instant of measurement, it is still local. What the post-Bell consensus never tested is a different question --- whether quantum unpredictability could rest on a dynamic, deterministic substrate whose properties oscillate, with each measurement capturing a snapshot of that oscillation. In such a model, quantum outcomes are unpredictable --- as the result of a die throw is unpredictable --- without being indeterminate in the ontological sense claimed by the Copenhagen interpretation. [Proposed] We derive a falsifiable prediction: two successive weak measurements on a system governed by a dynamic hidden variable should exhibit a correlation function oscillating at frequency 2ω, where ω is the characteristic oscillation frequency of the hidden variable. Standard quantum mechanics predicts oscillation at ω with amplitude proportional to the measurement strength g. These two predictions are experimentally distinguishable with current technology at frequencies up to ∼1015 Hz.
This year we celebrate 100 years of quantum mechanics (QM). Incorrect interpretations of QM and incorrect mental models of the invisible details of quantum phenomena lead to paradoxes. To explain these, we advocate the statistical contextual interpretation (SCI) of quantum mechanics. State vectors (wave functions) and various operators are purely mathematical entities that permit quantitative probabilistic predictions. “State vector” describes an ensemble of identically prepared physical systems, and a specific “operator” represents a class of equivalent measurements of a physical observable. A collapse of wavefunction is not a mysterious and instantaneous physical process; a collapsed quantum state describes a new ensemble of physical systems prepared in a particular way. A value of a physical observable, such as a spin projection, associated with a pure quantum ensemble is a characteristic of this ensemble created by its interaction with measuring instruments. Probabilities are objective properties of random experiments in which empirical frequencies stabilize. Following Einstein, SCI rejects the claim that QM provides a complete description of individual physical systems, but it remains agnostic about whether a more detailed subquantum description can be found or is necessary. In conformity with Bohr contextuality, SCI rejects Bell-local and Bell-causal hidden variable models. Nevertheless, by incorporating into a probabilistic model contextual hidden variable measuring instruments, long distance quantum correlations studied in Bell tests can be explained without evoking quantum nonlocality or retro-causality. SCI allows the explanation of several quantum phenomena without evoking quantum magic. SCI does not claim to provide a complete description of quantum phenomena; in fact, it is unknown whether quantum probabilities even provide a complete description of existing experimental data. Time series of experimental data may contain much more information than is obtained using empirical frequencies and histograms. Therefore, predictable completeness of QM must be tested and not taken for granted.
Quantum entanglement, the phenomenon whereby two or more quantum systems exhibit correlations that cannot be explained by any local hidden-variable theory, has evolved from a philosophical curiosity debated by Einstein, Podolsky, and Rosen in 1935 into the foundational resource of an emerging technological revolution. This narrative review traces the conceptual development of entanglement from the EPR paradox through Bell's theorem, the experimental violation of Bell inequalities, and the emergence of quantum information science as a unifying framework. Drawing on the original EPR argument, Bell's seminal 1964 theorem, the experimental work of Aspect et al., the quantum information synthesis of Nielsen and Chuang, the review of entanglement theory by Horodecki et al., and the foundational perspectives of Brukner and Zeilinger, the review covers the mathematical characterization of entanglement, its role in quantum computation and quantum cryptography, and the ongoing debate about the interpretation of quantum mechanics that entanglement continues to fuel.
Abstract Quantum mechanics is a more accurate description of the microscopic world than classical mechanics, and quantum information, which is governed by the laws of quantum mechanics, is a more accurate description of information theory. The quantum laws of physics are fundamentally different from the classical laws and so, therefore, is the resulting information processing. In one limit, quantum information reduces to classical information; otherwise, quantum information is a much more general concept that allows information-processing protocols that have no classical analogue whatsoever. This chapter discusses the basics of quantum information, some differences between bits and qubits, quantum cryptography, trace and partial-trace operations, extension of Hilbert spaces, Schmidt decomposition, generalised measurements, CP-maps and positive operator-valued measurements, and the postulates of quantum mechanics.