@0celo7: "
This is a deterministic classical system, not a probabilistic quantum one." -- As far as I understand the OP question it is concerned with attributing and measuring momentum values, e.g. of objects (such as $A$) wrt. to suitable systems (such as $\mathcal S$). There doesn't seem to be any requirement or exclusion being made concerning some categorizazion as "
classical or
quantum"; whatever you might mean by that. "
doesn't $\hbar =0$
[...]?" -- Perhaps you mean cases or limits in which $$\frac{m_A~c^2~\Delta \tau_A}{\hbar} \gg 1 $$ ? ... —
user12262 3 hours ago