[632.3.1] Experimental uncertainties limit also the ability to distinguish different states. [632.3.2] Two states are experimentally indistinguishable (or metrologically equivalent) if they cannot be distinguished by measurements. [632.3.3] Let denote the maximal number of experiments that can be performed to distinguish the states of the system. [632.3.4] Let with denote the observables in these experiments, and let () be the experimental resolutions or accuracy that can be attained for . [632.3.5] Two states with

(24) |

for all are called metrologically equivalent or experimentally indistinguishable with respect to the observables . [632.3.6] The sets of indistinguishable states

(25) |

are -neighborhoods of in the weak* topology [17]. [632.3.7] The algebra generated by the elements will be called macroscopic algebra.

[632.4.1] In the following
and
will be assumed.
[632.4.2] The -neighborhoods of
-almost invariant states, i.e. the sets
with for small
will be the candidates for local (in time) stationary states.