Why does tha physicist believe," a measurement without a quoted error is meaningless "?
Please help!!
Suppose you tell your friend that you have an object that is 90.4 cm +/- 0.1 cm long. That means you think the length of the object is closest to 90.4 cm but it could be as little as 90.3 cm or as much as 90.5 cm (or any value between those extremes). On the other hand you might quote 90 cm +/- 1 cm so it means you think the object is closest to 90 cm but it could be as little as 89 cm or as much as 91 cm (or values between). Therefore, without knowing the possible error you have an estimate of the length of the object but that's all it is; i.e., an estimate.
A physicist believes that a measurement without a quoted error is meaningless because uncertainty is inherent in any measurement. In science, it is essential to quantify and communicate the uncertainty associated with a measurement to provide a complete understanding of the result.
When we perform an experimental measurement, various sources of error can influence the outcome. These errors can arise from limitations in the equipment, the nature of the phenomenon being measured, or even human factors. For example, a digital scale may have a limited precision, or a stopwatch may have a variation in reaction time when starting and stopping it.
By providing a quoted error, scientists express the range within which they believe the true value lies. This uncertainty interval helps other researchers evaluate and reproduce the experiment, leading to more reliable and robust scientific results.
Additionally, the quoted error allows for more accurate data analysis and conclusions. It enables physicists to assess the significance of differences between measurements, perform statistical analyses, and make predictions with confidence intervals.
To determine the error associated with a measurement, scientists employ various statistical and analytical methods. These methods consider factors such as experimental design, measurement precision, and deviations from ideal conditions. By carefully assessing and quantifying these uncertainties, physicists can provide a more complete and reliable understanding of their measurements.
In summary, a physicist believes that a measurement without a quoted error is meaningless because it fails to capture the inherent uncertainty in the measurement process. By quantifying and communicating this uncertainty, scientists ensure that their results are robust, reproducible, and accurately reflect the limitations of the measurement.