Does entanglement describe continuity at the micro level?

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I'm a new poster; I hope don't violate rules or policy.
Am I wrong, or is the rule essentially that a particle isn't finished interacting with the last particle on it's world path unless and until it interacts with a third? This isn't what I might have guessed about physical continuity, but it seems to be the gist of it.
An entangled particle that has been transported miles reminds me of Shrodinger's cat riding in an effectively "impervious to everything box."
Am I not getting this? Is every particle entangled until it arrives at the next interaction in it's world path?
 
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