jmcasey@pacific.net.sg writes:
> I hear what you're saying, but...
>
> >Heisenberg tells us that there is a point where the change to a physical system
> >is so small that there is no change at all.
>
> ...surely this challenges the concept of emergence? I'm imagining
>the subatomic equivalent of the butterfly in Beijing "causing" the
>thunderstorm in Toronto. Are *all* the changes which are so small as
>to "be" no change at all, still no change in aggregate? (If not, of
>course, they were never really *no* change.)
Actually, all the tiny quantum fluctuations together do have emergent and noticeable effects. Heisenberg only showed that measurement uncertainties will always be larger than a certain level, essentially placing a limit on how well we (or anything else) can distinguish quantum states. Even tiny quantum noise that cannot be detected itself can add together to create "macro" effects such as coupling constants and shielding of electron charges (if I remember my Feynmann lectures right).
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