Related papers: Wave-like behaviour in (0,1) binary sequences
In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
Given a sequence of real numbers $\{\psi(n)\}_{n\in\mathbb{N}}$ with $0\leq \psi(n)<1$, let $W(\psi)$ denote the set of $x\in[0,1]$ for which $|xn-m|<\psi(n)$ for infinitely many coprime pairs $(n,m)\in\mathbb{N}\times\mathbb{Z}$. The…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
A quantum binary experiment consists of a pair of density operators on a finite dimensional Hilbert space. An experiment E is called \epsilon-deficient with respect to another experiment F if, up to \epsilon, its risk functions are not…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an…
We explore spinning, precessing, unequal mass binary black holes to display the long term orbital angular momentum, $\vec{L}$, flip dynamics. We study two prototypical cases of binaries with mass ratios $q=1/7$ and $q=1/15$ and a misaligned…
The physical states of matter and fields are represented in the quantum theory with complex valued wavefunctions, or more generally by quantum states in an abstract linear vector space. Determining the physical nature of wavefunctions…
Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder…
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a…
We discuss the relation between the "compositeness" of an s-wave bound state, as derived from a related partial wave scattering amplitude, and the corresponding spatial probability densities, for the case of spherically symmetric,…
The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|\psi\rangle$ is determined by $P(a)=|\langle a|\psi\rangle|^{2}$. Despite its great success in…
The probabilistic interpretation of quantum mechanics has been a point of discussion since the earliest days of the theory. The development of quantum technologies transfer these discussions from philosophical interest to practical…
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is now described not just as two extreme cases of wave and…
The sizes of subsets of the natural numbers are typically quantified in terms of asymptotic (linear) and logarithmic densities. These concepts have been generalized to weighted $w$-densities, where a specific weight function $w$ plays a key…