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By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation.

So logic says "if" there exists closed system by non-conservative momentum, then there is a explicit physical experiment which has different result by translation.

please give such an experiment explicitly (preferably as simple as possible or creative).

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    $\begingroup$ what do you mean by " closed system by non-conservative momentum"? $\endgroup$
    – Luessiaw
    Commented Jul 3 at 1:44
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    $\begingroup$ Are you asking if a system with explicit boundaries violates translational invariance and is therefor not momentum conserving? Yes. Mechanical systems that are setting limits to the motion of their internal masses are definitely not momentum conserving. $\endgroup$
    – FlatterMann
    Commented Jul 3 at 4:50

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Experiments on crystals are translationally variant because the crystal structure is only the same up to translations that reproduce the same structure, in such cases there is "crystal momentum" associated with discrete as opposed to continuous invariance of translations.

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