How can macroscopic objects in real world have always-true cause-effect relationships when underlying quantum world is probabilistic? How does it not ever produce results different than what is predicted by Newtonian physics, except for borderline cases?
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Expectation values (of position, for example) in QM track the classical analogues. For large objects, position is localized and so is momentum (given the relative smallness of planck’s constant) - which keeps the position localized. In turn, this means that the expectation values of position closely match what we actually observe.
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A simple way to understand this is to realize that a macroscopic object consists of trillions of individual quantum systems whose QM properties average out into Newtonian behavior as the number of particles in the system is increased.
The only exceptions to this rule are lasers, superconductors and condensates like liquid helium. In each of these special cases, those quantum properties get writ large for us by arranging for most of the quantum particles to not average themselves out but to instead (roughly speaking) all settle into the same state.
niels nielsen
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Statistical mechanics is a field that gives some good perspective to this. It's quite common that the math works out where you have an equation to describe your system, and there is a variable $N$ in your equation for the number of particles. If $N$ is a small value, the equation and your system still look very quantum. But once $N$ is large values, or you take the limit of the equation as $N$ approaches infinity (called the thermodynamic limit), you then see the system's macroscopic laws. This article might be of interest: https://arxiv.org/abs/1402.7172
Urb
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Chylomicron
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