Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

1.9K
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
1.9K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

2.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
2.1K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

12.1K
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
12.1K
The Uncertainty Principle04:08

The Uncertainty Principle

34.5K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
34.5K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.6K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.6K
Uncertainty in Measurement: Reading Instruments02:46

Uncertainty in Measurement: Reading Instruments

55.6K
Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
55.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Valorization of <i>Zanthoxylum bungeanum</i> Maxim. Leaf By-Products: Comparative Aroma Profiling with Pericarps Across Extraction Strategies.

Foods (Basel, Switzerland)·2026
Same author

Testing Genuine Multipartite Nonlocality via an Inflated Network with Multicopy Entangled States.

Physical review letters·2026
Same author

Analytic Nonadiabatic Derivative Couplings Using Noncollinear Spin-Flip TDDFT.

Journal of chemical theory and computation·2026
Same author

The Gut-Bone Axis: Molecular Mechanisms and Therapeutic Perspectives in Skeletal Homeostasis.

Frontiers in bioscience (Landmark edition)·2026
Same author

Propyl gallate mitigates diabetic liver injury via suppressing SLC7A11/GPX4-mediated hepatic ferroptosis and modulating gut-liver axis.

Biochemical pharmacology·2026
Same author

DISCERN: Dual-Aptamer-Initiated Sensing Circuit <i>via</i> Engineered Nanozyme for Leukemia Stem Cells Phenotyping.

ACS sensors·2026
Same journal

Turbulent flow in a vortex separator with a directed pipe inlet.

Scientific reports·2026
Same journal

Systematic characteristic evaluation of clay-based cementitious material derived from calcium carbide residue and waste tile powder.

Scientific reports·2026
Same journal

Retraction Note: Improvement of a rapid diagnostic application of monoclonal antibodies against avian influenza H7 subtype virus using Europium nanoparticles.

Scientific reports·2026
Same journal

Applying large language models to spam detection in the Kazakh low-resource language setting.

Scientific reports·2026
Same journal

An open-source 3D printing system enabling in-situ freeze-thaw processing of hydrogels.

Scientific reports·2026
Same journal

An enhanced EfficientNet framework for automated waste classification using cosine annealing and label smoothing.

Scientific reports·2026
See all related articles

Related Experiment Video

Updated: Mar 24, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

8.9K

Weighted Uncertainty Relations.

Yunlong Xiao1,2, Naihuan Jing1,3, Xianqing Li-Jost2

  • 1School of Mathematics, South China University of Technology, Guangzhou 510640, China.

Scientific Reports
|March 18, 2016
PubMed
Summary
This summary is machine-generated.

Researchers developed new weighted uncertainty relations for quantum mechanics. These relations offer optimal lower bounds for all quantum states, improving upon previous work by Maccone and Pati.

More Related Videos

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations
09:07

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Published on: September 16, 2015

9.5K
Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling
06:04

Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling

Published on: January 17, 2025

1.8K

Related Experiment Videos

Last Updated: Mar 24, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

8.9K
Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations
09:07

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Published on: September 16, 2015

9.5K
Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling
06:04

Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling

Published on: January 17, 2025

1.8K

Area of Science:

  • Quantum mechanics
  • Quantum information theory

Background:

  • Maccone and Pati introduced stronger uncertainty relations based on the sum of variances.
  • One of their relations is nontrivial only for non-eigenstates of the summed observables.

Purpose of the Study:

  • To derive a generalized family of weighted uncertainty relations.
  • To provide an optimal lower bound applicable to all quantum states.
  • To extend these relations to multi-observable scenarios.

Main Methods:

  • Derivation of a novel family of weighted uncertainty relations.
  • Mathematical formulation for multi-observable cases.

Main Results:

  • A new set of weighted uncertainty relations is established.
  • An optimal lower bound for the weighted sum of variances is obtained.
  • The derived relations remove the restriction on quantum states being eigenstates.

Conclusions:

  • The new weighted uncertainty relations offer a more general and optimal framework.
  • These findings advance the understanding of uncertainty in quantum systems.
  • The generalization to multi-observable cases broadens the applicability of uncertainty relations.