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The Leggett-Garg inequalities are a set of inequalities obeyed by classicalsystems but violated in quantum theory. Their violation has been taken asevidence that quantum theory lacks a `realistic' formulation. However inaddition to realism the derivation of the Leggett-Garg inequalities relies onanother, more obscure assumption of `non-invasive measurability.' Thesignificance of this assumption and the consequences for the interpretation ofviolations of the Leggett-Garg inequalities have been hotly debated. In thispaper we present a pedagogical introduction to the issues, focussing on thesignificance of non-invasive measurability. We give a simple derivation of theLeggett-Garg inequalities paying particular attention to where and when the twoassumptions are used, and we give an example of a realist but notnon-invasively measurable hidden variable theory which violates them. We alsodiscuss recent attempts to experimentally implement non-invasive measurementsvia so called `undetectable measurements' and we show that even undetectablemeasurements are not necessarily non-invasive.

The Leggett-Garg Inequalities and Non-Invasive Measurability