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S1h. Can all quantum states be realized in Nature?
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No. Many mathematically conceivable states do not exist in Nature, 
for example, that of water at an absolute temperature of zero.

Quantum mechanics does not demand that all states are realizable.
For a number of tiny systems with a few levels, all states are 
realizable with reasonable precision. However, the larger the system 
the fewer states are realized. 

The number of states realized at a given time of very large systems 
such as human beings or galaxy clusters is even so small that it 
can be approximately counted!