Classical physics vs quantum physics

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jd12345
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Why do we say that classical physics is a lot different from quantum physics?

The laws that determine the macroscopic world should be derivable from quantum laws. So in a way the Newtonian or classical laws are basically quantum laws( maybe a bit approximated)
So why differentiate between macroscopic and microscopic world?
 
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Why do we say that classical physics is a lot different from quantum physics?
We don't (except by mistake). We say that quantum physics is different from classical physics :)

All dogs may be animals but not all animals are dogs.
All classical physics is a consequence of quantum - but not all quantum physics can be described classically.

Technically - classical physics is what QM does on average ... so the math is different.