Darren New wrote:
> andrel wrote:
>> I don't want to spoil your gedanken experiment, but in modern physics 
>> you can not distinguish one (e.g.) hydrogen atom from another.
> 
> You say this, but it's not actually true.  You cannot distinguish two 
> hydrogen atoms as long as you ignore the stuff that lets you distinguish 
> them.  Like, say, their positions.

no.

> Certainly the hydrogen atoms in my coffee are distinguishable from the 
> hydrogen atoms emitting light eight minutes ago in the sun.

nope

> Basically, science has a list of "things it's safe to ignore when 
> replicating an experiment."  Given that list, hydrogen atoms are 
> indistinguishable. But there's still a list.
Sorry, no. It may sound counterintuitive but there isn't. A proton does 
not have a position, but a peaked distribution in one place with a small 
but finite change that it is somewhere else entirely. If you have two 
protons, you have a distribution with two peaks with an amplitude large 
enough for two protons. Nothing more and individuality is a meaningless 
concept here. I am trying to find a macroscopic equivalent, but I can't, 
yet.
> 
> It's like saying "pennies are indistinguishable, from a spending point 
> of view. I can replace one penny with any other penny."  

There is a difference between the (sub)atomic and the macroscopic range. 
In the latter common sense is just that, in the former not.

> Yet I'll still 
> get arrested for putting all your pennies in my bank account.
> 
No as long as we assume that you exchanged all your pennies with mine 
simultaneously, I don't see why anyone would bother. ;)
Don't try this at home though, the number of pennies in this house will 
probably not exceed 2, mainly because we use a different currency.

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