The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Pekka Lahti - One of the best experts on this subject based on the ideXlab platform.
-
heisenberg s Uncertainty Principle
Physics Reports, 2007Co-Authors: Paul Busch, Teiko Heinonen, Pekka LahtiAbstract:Heisenberg's Uncertainty Principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this Principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The Uncertainty Principle is shown to appear in three manifestations, in the form of Uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of Uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the Uncertainty Principle.
Michele Maggiore - One of the best experts on this subject based on the ideXlab platform.
-
quantum groups gravity and the generalized Uncertainty Principle
Physical Review D, 1994Co-Authors: Michele MaggioreAbstract:We investigate the relationship between the generalized Uncertainty Principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincar\'e algebra obey a deformed Heisenberg algebra from which the generalized Uncertainty Principle follows. The result indicates that in the $\ensuremath{\kappa}$-deformed Poincar\'e algebra a minimal observable length emerges naturally.
-
the algebraic structure of the generalized Uncertainty Principle
Physics Letters B, 1993Co-Authors: Michele MaggioreAbstract:We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ is the algebraic structure which underlies the generalized Uncertainty Principle in quantum gravity. The deformed algebra and therefore the form of the generalized Uncertainty Principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in Δp/MPL. We also briefly comment on possible implications for Lorentz at the Planck scale.
Paul Busch - One of the best experts on this subject based on the ideXlab platform.
-
heisenberg s Uncertainty Principle
Physics Reports, 2007Co-Authors: Paul Busch, Teiko Heinonen, Pekka LahtiAbstract:Heisenberg's Uncertainty Principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this Principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The Uncertainty Principle is shown to appear in three manifestations, in the form of Uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of Uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the Uncertainty Principle.
Pan Lian - One of the best experts on this subject based on the ideXlab platform.
-
Uncertainty Principle for the quaternion fourier transform
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Pan LianAbstract:Abstract The two-sided quaternion Fourier transform was introduced for the analysis of 2D linear time-invariant partial-differential systems. It has been shown to be a powerful tool in image processing. In this paper, several Uncertainty inequalities for the two-sided quaternion Fourier transform are given with optimal constants, including the Pitt's inequality, logarithmic Uncertainty inequality, Hausdorff–Young inequality, Hirschman's entropy inequality, generalized Heisenberg inequality, local Uncertainty Principle and qualitative Uncertainty Principle.
L. Cohen - One of the best experts on this subject based on the ideXlab platform.
-
The Uncertainty Principle: global, local, or both?
IEEE Transactions on Signal Processing, 2004Co-Authors: P.j. Loughlin, L. CohenAbstract:We address the issue of the relation between local quantities and the Uncertainty Principle. We approach the problem by defining local quantities as conditional standard deviations, and we relate these to the Uncertainty product appearing in the standard Uncertainty Principle. We show that the Uncertainty product for the average local standard deviations is always less than or equal to the standard Uncertainty product and that it can be arbitrarily small. We apply these results to the short-time Fourier transform/spectrogram to explore the commonly held notion that the Uncertainty Principle somehow limits local quantities. We show that, indeed, for the spectrogram, there is a lower bound on the local Uncertainty product of the spectrogram due to the windowing operation of this method. This limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit. We also examine the local Uncertainty product for a large class of time-frequency distributions that satisfy the usual Uncertainty Principle, including the Wigner distribution, the Choi-Williams distribution, and many other commonly used distributions. We obtain an expression for the local Uncertainty product in terms of the signal and show that for these distributions, the local Uncertainty product is less than that of the spectrogram and can be arbitrarily small. Extension of our approach to an entropy formulation of the Uncertainty Principle is also considered.
-
The Uncertainty Principle in signal analysis
Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis, 1994Co-Authors: L. CohenAbstract:We give a simple derivation for the covariance of time and frequency. The simplicity remains when applied to arbitrary variables. We show that the covariance enters into the Uncertainty Principle in a fundamental way. Also we present a seeming paradox: the Uncertainty Principle depends only on the marginals, but the marginals carry no information about covariance. Then how is it possible that the Uncertainty Principle involves the covariance? The resolution of the paradox clarifies a number of issues regarding the existence of well behaved manifestly positive joint distributions of time and frequency.