Related papers: Uncertainty principles for the Fock space
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…
We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called…
The idea of possible time or space variations of the `fundamental' constants of nature, although not new, is only now beginning to be actively considered by large numbers of researchers in the particle physics, cosmology and astrophysics…
A deformation of the Fock space based on the finite difference replacement for the derivative is introduced. The deformation parameter is related to the dimension of the finite analogue of the Fock space.
We prove that zero sets for distinct Fock spaces are not the same, this is an answer of a question asked by K. Zhu in \cite[Page. 209]{Zhu}.
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
A phenomenological model of unstable particles based on uncertainty principle is discussed in quantum field approach. We show that the simplest quantum field description of mass uncertainty makes it possible to account finite width effects…
We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…
I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of…
The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms,…
The space rotation invariance hypothesis is examined. The basic space-time properties and the physical object description from this point of view are considered. An $\omega$-invariance as an approximation of the space rotation invariance…
Motivated by inequalities in Fourier analysis, we present an improvement on the lower bound for the sign uncertainty principle of Bourgain, Clozel and Kahane in high dimensions. Additionally, our methods can be used to match the existing…
We discuss time measurement in quantum gravity. Using general relativity for large distances and the uncertainty principle we find a minimum time interval of the order of the Planck time, therefore the uncertainty in time measurment is…
Time variation of fundamental constants would not be surprising in the framework of theories involving extra dimensions. The variation of any one constant is likely to be correlated with variations of others in a pattern that is diagnostic…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…