Related papers: How to Secure Valid Quantizations
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…