Related papers: Three-space from quantum mechanics
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under…
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…
Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…
Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed…
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
This paper deals with the Newton--Wigner position observable for Poincar\'e-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton--Wigner theorem in the quantum…
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…
The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
In this paper we identify a hidden premise in Bell's theorem: measurability of the underlying space. But our system (the space of all paths, SP) is not measurable, although it replicates the predictions of standard quantum mechanics. Using…
This paper serves as a preparation of work that focuses on extracting cosmological sectors from Loop Quantum Gravity. We start with studying the extraction of subsystems from classical systems. A classical Hamiltonian system can be reduced…
We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion,…