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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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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.
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Propagation of Uncertainty from Random Error00:59

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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...
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The Uncertainty Principle04:08

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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...
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Propagation of Uncertainty from Systematic Error01:10

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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...
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Second Uniqueness Theorem01:16

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Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
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Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Universal uncertainty relations.

Shmuel Friedland1, Vlad Gheorghiu2, Gilad Gour3

  • 1Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045, USA.

Physical Review Letters
|January 31, 2014
PubMed
Summary
This summary is machine-generated.

Quantum theory

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics

Background:

  • Uncertainty relations in quantum theory limit simultaneous measurement precision.
  • Modern approaches use entropic measures, but other quantifiers are possible.

Purpose of the Study:

  • To identify the most general uncertainty quantifiers beyond entropy.
  • To develop a more universal and fine-grained uncertainty relation.

Main Methods:

  • Derived uncertainty quantifiers based on invariance under relabeling of outcomes.
  • Introduced a vector-type uncertainty relation using majorization order.
  • Showcased how this generates scalar uncertainty relations.

Main Results:

  • Schur-concave functions are identified as the most general uncertainty quantifiers.
  • A fine-grained, vector-type uncertainty relation is established, generalizing previous work.
  • This new relation generates an infinite family of scalar uncertainty relations.

Conclusions:

  • The developed uncertainty relation is universal, capturing the core of quantum uncertainty.
  • This framework offers a more comprehensive understanding of quantum measurement limitations.