Eugene Leitl <firstname.lastname@example.org> wrote:
> Two systems in the same quantum state are indistinguishable. You can
> find the outline of a proof for that in the appendix of Tipler's
> 'The Physics of Immortality'. I don't understand which 'counting'
> you refer to, but that proof says there cannot be any measurement
> procedure to distinguish one object from the other. Finis.
I think everyone would agree that they are identical, but are they one system? By counting, I mean you have two molecules of water. They are indistinguishable from each other. Both are identical H2O. Are there two molecules of water, or one molecule of water somehow existing in two locations? How would you count indistinguishable systems. The debate lead to the point that some claimed there were multiple indistinguishable systems, where some claimed that there was only one such system, seemingly in multiple places concurrently.
> Of course this is pretty useless, for no macroscopic objects occupy
> the same quantum state.
Is this because of random motions, such as Browning(?) random vibration? That is, each macro object may look the same, but all their atoms can't hold in the exact same positon as its copy, because the atoms randomly move around?
> But we are talking about the user front end,
> right? If _I_, the user, cannot distinguish between an object, and
> a copy, then it is meaningless to make the distinction between them,
Yes, for utility purposes of one of the objects. But in counting total objects, they must be distinquished by position to count them. The example I was quoting lead to the situation where a square room was declared to have one wall, because it was "meaningless to make a distinction between them." There still are x number of objects, even if they are all identical, right? When two objects become identical or indistinguishable, they don't suddenly merge into a single object, do they?
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