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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: 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...

Propagation of Uncertainty from Random Error

Propagation 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...

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Related Experiment Video

Updated: Feb 8, 2026

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Published on: May 8, 2018

Stereotactic Ablative Radiotherapy Uncertainties: Delineation, Setup and Motion.

Ming Yang¹, Robert Timmerman¹

¹Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX.

Seminars in Radiation Oncology

|June 24, 2018

Summary

Stereotactic ablative radiotherapy (SAbR) offers potent tumor ablation, differing from conventional methods. Precise targeting and margin strategies are crucial for SAbR

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Stereotactically-guided Ablation of the Rat Auditory Cortex, and Localization of the Lesion in the Brain

Stereotactically-guided Ablation of the Rat Auditory Cortex, and Localization of the Lesion in the Brain

Published on: October 11, 2017

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Last Updated: Feb 8, 2026

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Treatment of Liver Metastases Using an Internal Target Volume Method for Stereotactic Body Radiotherapy

Published on: May 8, 2018

Dynamic Lung Tumor Tracking for Stereotactic Ablative Body Radiation Therapy

Dynamic Lung Tumor Tracking for Stereotactic Ablative Body Radiation Therapy

Published on: June 7, 2015

Stereotactically-guided Ablation of the Rat Auditory Cortex, and Localization of the Lesion in the Brain

Stereotactically-guided Ablation of the Rat Auditory Cortex, and Localization of the Lesion in the Brain

Published on: October 11, 2017

Area of Science:

Radiation Oncology
Medical Physics

Background:

Stereotactic ablative radiotherapy (SAbR) is biologically distinct from conventionally fractionated radiotherapy.
SAbR aims for functional incapacitation of targeted tissue, unlike conventional methods that cause repairable injury.

Purpose of the Study:

To highlight the need for novel strategic approaches to uncertainties and margins in SAbR.
To emphasize the importance of minimizing target size in SAbR while ensuring complete tumor coverage.

Main Methods:

The abstract discusses the biological distinctiveness of SAbR.
It contrasts SAbR's ablative nature with the repairable injury from conventional radiotherapy.
It outlines the need for new strategies to manage uncertainties like tumor motion and dose variations.

Main Results:

SAbR causes functional incapacitation of targeted tissue.
Conventional radiotherapy doses are more likely to be repaired by normal tissue than tumor.
Effective SAbR requires precise management of uncertainties and appropriate margins.

Conclusions:

A sophisticated and rigorous approach to uncertainties and margins is warranted for SAbR.
Minimizing target volumes in SAbR is essential to avoid missing tumor deposits.
The potency and clinical potential of SAbR necessitate advanced treatment planning.