Not really. The issue is that you aren't the same from one moment to the other in the natural world either. You constantly change, large parts of your body even get rebuild regularly. So demanding 'quantum level perfection' of a copy just doesn't mesh with the ever changing mess that is the real you.
As long as the copy is 'good enough', which can be far away from the uncertainty principle, it really shouldn't make a difference to the though experiment.
Given: If the technology exists to create “good-enough” copies of a human, the tech to create “good-enough” copies of a habitat should also exist.
Experiment:
1) Create X copies of a controlled habitat
2) Create X copies of N humans, where N > 1
3) Place human copies into habitat copies
4) Observe
What is the expected percentage that the humans will behave identically? For how long? It’s probably best to start with one human per habitat, but I think “more than one human” is the more interesting question.
I can’t find the name of the condition right now, but sometimes people fall into loops, where they will ask the same series of questions and give the same responses each time until they recover. It happened to my grandmother once after a mini-stroke, and there’s a Radiolab episode about it which I also can’t find. So that lends credibility to the hypothesis that if the environments are “good enough,” there will be no divergence. I’m curious to know how long that could possibly last.
> I can’t find the name of the condition right now, but sometimes people fall into loops, where they will ask the same series of questions and give the same responses each time until they recover
Anecdotally, my mother did that sometimes during the mid-to-late stages of her Alzheimer’s (before we had to send her to a care home, but after she was failing the Clock test).
My one experience of edible cannabis (in retrospect I don’t think it was just cannabis), my partner at the time said I was repeating the same sentences. Not that I know for certain: myself, I had the subjective feeling of all working memories going direct into long-term memory without touching short-term memory.
As long as the copy is 'good enough', which can be far away from the uncertainty principle, it really shouldn't make a difference to the though experiment.