Dangers of Unphysical Regions

We discuss the appearance of negative numbers of events in radiochemical experiments and negative squared antineutrino mass $m^2_{\bar{\nu}_e}$ in tritium beta decay. Going beyond the standard discussion about how to extract upper limits in those cases, we show that the problem is much more profound. We explain the circumstances which are the likely cause of the persistently negative values of $m^2_{\bar{\nu}_e}$ in all modern tritium beta decay experiments.