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The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…
This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…
It is widely believed that classical electromagnetism is either unphysical or inconsistent, owing to pathological behavior when self-force and radiation reaction are non-negligible. We argue that there is no inconsistency as long as it is…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
We analyze seemingly contradictory claims in the literature about the role played by decoherence in ensuring classical behavior for the chaotically tumbling satellite Hyperion. We show that the controversy is resolved once the very…
We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified and how it can be measured. We focus on environment induced decoherence…
A quantum decaying system can reveal its nonclassical behavior by being noninvasively measured. Correlations of weak measurements in the noninvasive limit violate the classical bound for a universal class of systems. The violation is…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
If we reduce coherence in a given quantum system, the result is an increase in entropy. Does this necessarily convert this quantum system into a classical system? The answer to this question is No. The decrease of coherence means more…
The nonclassicality of single-mode quantum states is studied in relation to the entanglement created by a beam splitter. It is shown that properly defined quantifications -- based on the quantum superposition principle -- of the amounts of…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
This paper proposes a basic theory on physical reality, and a new foundation for quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization procedure, but…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…