Classical physics vs quantum physics

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Classical physics and quantum physics are fundamentally connected, with classical laws emerging as approximations of quantum laws at macroscopic scales. The distinction arises not from a difference in nature but from the mathematical frameworks used to describe each realm. While all classical physics can be derived from quantum principles, not all quantum phenomena can be captured by classical theories. This leads to the perception that classical and quantum physics are vastly different, despite their underlying relationship. Ultimately, quantum mechanics provides a more comprehensive understanding of physical laws, encompassing both the microscopic and macroscopic worlds.
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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.
 
We often see discussions about what QM and QFT mean, but hardly anything on just how fundamental they are to much of physics. To rectify that, see the following; https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/66a6a6005101a2ffa86cdd48/original/a-derivation-of-maxwell-s-equations-from-first-principles.pdf 'Somewhat magically, if one then applies local gauge invariance to the Dirac Lagrangian, a field appears, and from this field it is possible to derive Maxwell’s...
I read Hanbury Brown and Twiss's experiment is using one beam but split into two to test their correlation. It said the traditional correlation test were using two beams........ This confused me, sorry. All the correlation tests I learnt such as Stern-Gerlash are using one beam? (Sorry if I am wrong) I was also told traditional interferometers are concerning about amplitude but Hanbury Brown and Twiss were concerning about intensity? Isn't the square of amplitude is the intensity? Please...
This is still a great mystery, Einstein called it ""spooky action at a distance" But science and mathematics are full of concepts which at first cause great bafflement but in due course are just accepted. In the case of Quantum Mechanics this gave rise to the saying "Shut up and calculate". In other words, don't try to "understand it" just accept that the mathematics works. The square root of minus one is another example - it does not exist and yet electrical engineers use it to do...