Related papers: Contextual unification of classical and quantum ph…
Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both physics and mathematics as a whole…
Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
In his book `Physics and Philosophy', Heisenberg suggested that the quantum world is one of ``potentialities or possibilities'' and that the classical realm is one of ``things or facts''. After ascertaining that his categories most…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
All our statements about the physical world are expressed in terms of everyday notions and thus in terms of classical physics. This necessity is behind each of our attempt to extract meaning out of empirical data and to communicate this…
A correspondence of classical to quantum physics studied by Schr\"{o}\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities…
We propose an improved variant of the third-quantization scheme, for the spatially homogeneous and isotropic cosmological models in Einstein gravity coupled with a neutral massless scalar field. Our strategy is to specify a semi-Riemannian…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…