  Distinguishability plays a major role in quantum and statistical physics.
When particles are identical their wave function must be either symmetric or
antisymmetric under permutations and the number of microscopic states, which
determines entropy, is counted up to permutations. When the particles are
distinguishable, wavefunctions have no symmetry and each permutation is a
different microstate. This binary and discontinuous classification raises a few
questions: one may wonder what happens if particles are almost identical, or
when the property that distinguishes between them is irrelevant to the physical
interactions in a given system. Here I sketch a general answer to these
questions. For any pair of non-identical particles there is a timescale,
$\tau_d$, required for a measurement to resolve the differences between them.
Below $\tau_d$, particles seem identical, above it - different, and the
uncertainty principle provides a lower bound for $\tau_d$. Thermal systems
admit a conjugate temperature scale, $T_d$. Above this temperature the system
appears to equilibrate before it resolves the differences between particles,
below this temperature the system identifies these differences before
equilibration. As the physical differences between particles decline towards
zero, $\tau_d \to \infty$ and $T_d \to 0$.
