Related papers: Limits of reductionism and the measurement problem
It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally…
Describing the solutions of inverse problems arising in signal or image processing is an important issue both for theoretical and numerical purposes. We propose a principle which describes the solutions to convex variational problems…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
Several theories have been advanced recently which appear to offer a resolution to that portion of the measurement problem which previously dealt with a possible reduction of the state vector in a subjective fashion by the brain, mind or…
It is shown that it is possible to measure the Schr\"odinger wave of a single quantum system. This provides a strong argument for associating physical reality with a quantum state of a single system in sharp contrast with the usual approach…
Endeavoring to formulate an exhaustive solution to the measurement problem in view of the theory of decoherence leads to a better understanding of the status of the collapse and of the emergence of classicality, thanks to a precise…
We study generalizations of the Schr\"odinger problem in statistical mechanics in two directions: when the density is constrained at more than two times, and when the joint law of the initial and final positions for the particles is…
In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.
The paper [1] considers a spherical cloak described by three radially varying acoustical quantities. For a given radial mass density in the cloak the question posed is whether the remaining two parameters, tangential density and…
A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system…
The Quantum Measurement Problem is arguably one of the most debated issues in the philosophy of Quantum Mechanics, since it represents not only a technical difficulty for the standard formulation of the theory, but also a source of…
We describe a certain "self-similar" family of solutions to the free Schroedinger equation in all dimensions, and derive some consequences of such solutions for two specific problems.
It is shown that any theory that has certain properties has a measurement problem, in the sense that it makes predictions that are incompatible with measurement outcomes being absolute (that is, unique and non-relational). These properties…
In this paper we study the (classical) Frobenius problem, namely the problem of finding the largest integer that cannot be represented as a nonnegative integral combination of given relatively prime (strictly) positive integers (known as…
We provide an affirmative answer to the question posed in the title. Our argument is based on a treatment of the Schroedinger dynamics of the composite of a quantum microsystem, S, and a macroscopic measuring apparatus, I, consisting of N…
We consider the nonlinear Schrodinger equation with a modified spatial dispersion, given either by an homogeneous Fourier multiplier, or by a bounded Fourier multiplier. Arguments based on ordinary differential equations yield ill-posedness…