Introduction

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Role of statistics in physics education: "A measurement without error bars is not a measurement." Unfortunately these are only dead words in standard physics education.


Everybody knows this

\Delta m = \frac{1}{\sqrt{N}}\Delta m_i\,

But what if

\vec{m} = f(\vec{x}) \,

and if also


\langle \Delta m_i \Delta m_j \rangle = \Sigma_{ij} \,

with

\Sigma_{ij} \neq 0 \,


This can get complicated


What if we have two vector-valued measurements

\vec{m}_1 = f_1(\vec{x}) + \vec \varepsilon_1 \,
\vec{m}_2 = f_2(\vec{x}) + \vec \varepsilon_2 \,

How can we get

\langle x_ix_j\rangle\,


So what is theory of measurements? It is

  • A clear and unified formalism for discussing questions about measurements and their interpretation.
  • Provides us with recipes for analysis (deriving \vec{x}\, from \vec{m}\,) in such a way, that we are sure we do not lose information.
  • Gives us ways to understand errors and uncertainties of analysis results.
  • But takes time to learn.
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