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00:59Uncertainty: Overview
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.
03:37Uncertainty in Measurement: Accuracy and Precision
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.
01:10Propagation of Uncertainty from Systematic Error
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 particular...
02:46Uncertainty in Measurement: Reading Instruments
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...
00:59Propagation of Uncertainty from Random Error
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...
00:54Uncertainty: Confidence Intervals
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 't,' or...
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Related Experiment Video
Updated: Jun 17, 2026
11:55
Cryo-Structured Illumination Microscopic Data Collection from Cryogenically Preserved Cells
Published on: May 28, 2021
Summary
Image restoration is limited by information degradation and the uncertainty principle. Achieving perfect image restoration, especially from smeared signals, is physically unrealizable and may require infinite energy.
Area of Science:
- Physics
- Information Theory
- Quantum Mechanics
Background:
- Image restoration is challenged by information degradation due to signal distortion.
- The process is fundamentally linked to spacetime constraints and quantum principles.
Purpose of the Study:
- To explore the physical interpretations and limitations of image restoration techniques.
- To discuss the relationship between information and energy in the context of image restoration.
Main Methods:
- Analysis based on information theory to explain inverse filter unrealizability.
- Application of concepts from the theory of relativity and quantum mechanics (Heisenberg's uncertainty principle).
- Discussion of the information-energy relationship.
Main Results:
- Image restoration from distorted signals is feasible only if a detectability condition is met, with restored images approaching a time criterion.
- Restoring images from smeared signals is physically unrealizable, potentially requiring infinite energy.
Conclusions:
- The detectability condition is crucial for feasible image restoration.
- Perfect image restoration from smeared data is physically impossible under normal energy constraints.