The physics literature contains many claims that elementary particles have been observed: such observational claims are, of course, important for the development of existential knowledge. Regarding claimed observations of short-lived unstable particles in particular, the use of the word 'observation' is based on the convention in physics that the observation of a short-lived unstable particle can be claimed when its
predicted decay products have been observed with a significance of 5 sigma. This paper, however, shows that this 5 sigma convention is inconsistent with existing concepts of observation by showing that unstable particles with a lifetime of less than 0.01 attosecond are fundamentally unobservable both from the perspective of Fox's recent concepts of direct and indirect observation, and from the perspective of Van Fraassen's notion of observability. This cognitive inaccessibility of parts of the subatomic world has far-reaching implications for physics, not the least of which is that the aforementioned convention is untenable: claims that such short-lived unstable particles have been observed will thus have to be retracted. The main implications are two incompleteness theorems for physics, respectively stating (i) that experiments cannot prove completeness of a physical theory predicting short-lived unstable particles, and (ii) that experiments cannot prove correctness of such a theory|one can at most test its empirical adequacy. On a general note, the conclusion is that the importance of philosophical arguments for particle physics is herewith demonstrated: it is, thus, a widespread misconception that philosophical arguments can be completely avoided.