*expect*young scientists to move mountains.

Any measurement of a particle presumably involves some sort of interaction that changes its quark content. The change may be small, maybe even negligible, but nonetheless there is always a logical distinction between an observed value and the theoretical concept of the energy of an isolated particle. The customary way of assessing this is to make many observations, so consider a series of $N$ measurements with results noted by $E^{1}, \, E^{2}, \, E^{3} \ \ldots \ E^{\it{k}} \ \ldots \ E^{\it{N}}$. These observed values are related to $E$ the theoretical idea of energy by

$E = \tilde{E} \pm \delta E$

where $\tilde{E}$ is a typical or representative value called the**experimental average**. The other number $\delta E$ describes the variation in observed values, it is called the

**experimental uncertainty**. For 'good' measurements $\delta E$ is small enough so that $E$ and $\tilde{E}$ are interchangeable thus reconciling theory and observation. Usually the experimental average is determined from the arithmetic mean of the set of observations

$\tilde{E} = \frac{1}{ N} \sum_{k=1}^{N} \; E^{k}$

and the experimental uncertainty is represented by their standard deviation$\delta E = \sqrt{ \frac{1}{N} \sum_{k=1}^{N} \left( E ^{k} - \tilde{E} \right)^{2} \; }$

Another important number is the coefficient of variation in the data which is defined by the ratio $\delta E / \tilde{E}$. The inverse of this quantity is known as the signal-to-noise ratio$\varsigma = 10 \log{ \left(\tilde{E} / \delta E \right) }$ (dB)

expressed on a logarithmic scale in units of decibels.Here is a link to the most recent version of this content, including the full text.

Energy Measurements |