  Since the development of micro- and nanolasers, the question of laser
threshold has been subject to debate. Different definitions have been used to
try and establish its occurrence, often encountering major obstacles. We
examine a set of common physical definitions which we apply to measurements
taken in a micro-VCSEL. Their predictions not only clearly disagree, pointing
to different pump values at which the laser should cross threshold, but they
also correspond to autocorrelation values which demonstrate very low field
coherence. A topological analysis of the rate equations, with average
spontaneous emission added to the lasing mode, clearly identifies the
contradictions and explains the origin of the discrepancies. Additional
considerations help understanding the failure of the approach and highlight the
path towards a unique and general definition of threshold in all lasers,
irrespective of their sizes. A critical scrutiny of the assumptions made in the
rate equations with spontaneous emission illustrates their strength and
weaknesses and better defines the bounds within which their predictions hold.
We remark in the conclusions how the main results of this paper could hold for
other small systems.
