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The Uncertainty Principle

The Uncertainty Principle

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...

Uncertainty in Measurement: Reading Instruments

Uncertainty 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...

Uncertainty: Overview

Uncertainty: 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.

Uncertainty in Measurement: Accuracy and Precision

Uncertainty 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.

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

Uncertainty: Confidence Intervals

Uncertainty: 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...

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Related Experiment Video

Updated: Feb 13, 2026

Estimation of Contact Regions Between Hands and Objects During Human Multi-Digit Grasping

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Published on: April 21, 2023

Processing Technology Selection for Municipal Sewage Treatment Based on a Multi-Objective Decision Model under

Xudong Chen¹, Zhongwen Xu², Liming Yao³

¹College of Management Science, Chengdu University of Technology, Chengdu 610059, China. chenxudong198401@163.com.

International Journal of Environmental Research and Public Health

|March 8, 2018

Summary

This study optimizes municipal sewage treatment plant construction by balancing environmental protection and economic benefits. A multi-objective decision model and genetic algorithm demonstrate effectiveness for sustainable urban water management.

Keywords:

multi-objective decision municipal sewage treatment processing technology selection

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Published on: April 18, 2013

Area of Science:

Environmental Engineering
Urban Planning
Operations Research

Background:

Municipal sewage treatment is critical for environmental protection and public health.
Balancing ecological sustainability with economic viability presents a significant challenge in sewage infrastructure development.
Optimizing the selection and design of sewage treatment plants requires a systematic decision-making framework.

Purpose of the Study:

To develop a general multi-objective decision model for optimizing the construction of municipal sewage treatment plants.
To integrate environmental protection and economic benefit considerations into the decision-making process.
To provide a practical tool for informed decision-making in sewage treatment infrastructure projects.

Main Methods:

Establishment of a multi-objective decision model incorporating site selection, processing technology, costs, and environmental impact indicators.
Application of a genetic algorithm to test and validate the decision model.
Case study analysis using a sewage treatment plant construction project in Chengdu.

Main Results:

The developed multi-objective decision model effectively optimizes municipal sewage treatment plant construction.
The genetic algorithm implementation confirmed the model's applicability and efficiency.
The study demonstrated a viable approach for balancing environmental and economic factors in infrastructure development.

Conclusions:

The multi-objective decision model offers a robust framework for optimizing sewage treatment plant construction.
This research provides valuable decision support for enhancing municipal sewage treatment strategies.
The findings contribute to more sustainable and cost-effective urban water management solutions.