Why isn't Newtonian mechanics valid in Quantum world? Suppose you isolate an alpha particle and accelerate it in absolute vacuum. Why it doesn't follow the equation $F=ma$? If Newtonian mechanics is invalid in quantum world, what is the guarantee that Quantum mechanics is valid in macroscopic world?
[Physics] Newtonian Mechanics and Quantum mechanics
newtonian-mechanicsquantum mechanics
Best Answer
The answers to "why" questions in physics end up in "because it has been observed to be so"
When science progressed into the realm of the microscopic, of dimensions the size of an atom, i.e. less than a nanometer, it was observed that newtonian mechanics and classical electrodynamics were in contradiction with experiments, could not explain them. For example, they could not explain :
1) Photelectric effect
2) The table of elements which showed regularities unexpected by a simple atomic (a la Demokritos) nature following newtonian mechanics and classical electricity
3) The light spectra. The existence of the hydrogen atom which forced the quantum mechanical view finally, because a differential equation was found which completely described the energy levels seen in the light spectrum of the atom. There was no explanation using using classical electromagnetism and newtonian mechanics
4) Interference effects seen in particles, like electrons, as if they were waves: individual electrons passing through slits showed an intensity pattern appropriate to waves not to newtonian particles
At the microscopic level, forces don't have a meaning, because nothing touches directly anything else. There are intermediate force carriers of what is perceived as "force" macroscopically.
The guarantee that macroscopically the newtonian mechanics and classical electrodynamics appear as we have validated them experimentally is that all of quantum mechanical behavior rests on h_bar, a very small number which is irrelevant for the distances and energies we move and observe macroscopically. There is a smooth mathematical transition from the QM regime to the classical regime.