Question

So I'm reading Something Deeply Hidden by Sean Carroll, and he's talking about the differences between quantum and classical realities. I mean by just general human "logic," you'd think that what we experience in our physical world i.e classical mechanics must apply to all states, right? Even though we know this isn't true, it's simply mind boggling that it'd be any different! Basically what I'm getting at is how does this quantum reality change into classical? How come the minuscule aspect of our universe experiences something one way i.e the wave function, and then magically bigger "stuff" experiences another, i.e Newton's laws? How do they coexist with one another? It's almost as if in one world 2 + 2 = 4, and in another, the "properties" are different to where 2 + 2 = 5 simultaneously.

Answer 1

I will try to answer all your questions to the best of my knowledge as I had understood. It won't be a complete answer. But I hope it's helpful.

I would like to say that the statement of coexistence of Newtonian and quantum mechanics is not a correct one. The term we need is approximation. Classical mechanics is an approximation of quantum mechanics for larger objects. Quantum is the general formulation applicable to every relams(except relativistic). If we need to combine relativity with quatuqu mechanics, then we a the most general theory called quantum field theory. Similarly the analogy of 2+2 is 4 in one World and 5 in another is also inappropriate.

In older times people were trying to explain what there observed. This eventually led to the birth of classical mechanics. If you follow history, you could see that , a significantly large time after the birth of classical mechanics, there arised problems that where unexplicable using classical mechanics, like Black body radiation, photo electric effect, Compton effect. The birth of quantum mechanics was because of plancks attempt to explain black body radiation. He tried to explain experimental results by a mathematical guess. But it was from the physical implication of that mathematical explaination that the quantum mechanics originated. After that Schrodinger, Heisenberg, Dirac etc developed it. The success of quantum mechanics is that it could explain these phenomenas and it's prediction were observed. My point is quantum mechanics was formulated from any preceding theories, it just explained things precisely so that we can't reject it. Yes it shows results against out common sense like the concept of probability. Quantum tunnelling Is a example which is impossible classically. But without it we couldn't explain the alpha decay. It is notable that Einstien was always against the concept of quantum mechanics. His famous qoute that "god doesn't play dice" shows his view.

Wavefunction of a particle is a purely mathematical quantity which doesn't have any physical significance. But the square of this quantity is proportional to the probability of finding that particle at that point. It is the solution to schrodinger equation, something that we can't arrive from any theories. But the new formulation of quantum mechanics agrees with Newtonian under appropriate limiting condition and it explains experimental findings.

The reason behind these wave aspects is because of the dual nature of matter and radiation. Infact the only confusion in quantum mechanics is due to this dual nature. It means that, radiation has a particle nature in it (it explains photoelectric effect), similarly particle has wave nature (Davisson and germer expt confirmed wave nature of electron) they are called de Broglie waves whose wavelength is inversely proportional to the momentum of the particle. Hence the wave nature of macroscopic things are so small that we won't notice it.

I tried to explain many concepts as the question is general. Drop a comment if there is any doubts