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Example: Buckling of a rod: It is easy to know the previous position of a buckled rod, but it is impossible to predict the direction of buckling from the unbuckled position.

Does causality play any role in this buckling situation? The situation looks non causal when looking forward in time (prediction), and causal when looking backwards in time (history).

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    The word is "indeterministic" rather than "non-causal", and it is not future/past that matters here. What matters is sensitivity to initial/final conditions. It is not that buckling is indeterministic but rather that small perturbations in the initial state give rise to widely diverging forward solutions. There are similar effects in weather predictions and deterministic chaos systems generally, and there are symmetric examples for backward solutions. See Norton's dome for genuine indeterminism.
    – Conifold
    Oct 15, 2021 at 8:30
  • There's a whole set of physics used by engineers to treat deformation, strain, fracture propagation & so on: en.wikipedia.org/wiki/Deformation_(physics) On causality in general, see: 'Is the idea of a causal chain physical (or even scientific)?' philosophy.stackexchange.com/questions/70930/… In the Many Worlds interpretation, where quantum indeterminism is involved, all the outcomes happen, preserving determinism across the worlds as a whole.
    – CriglCragl
    Oct 15, 2021 at 10:58
  • In the finite element method, there is the possibility that the present were determined not only all past times but future too, contrary to the usual initial state condition. But I have not yet understood much.
    – Cretin2
    Dec 27, 2021 at 14:22

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