# Are all superposition principles related?

Are all superposition principles related? Is there a relationship between the microscopic superposition principle and the macroscopic superposition principle? Does the microscopic one lend to the macroscopic one?

Clarification:

• By "microscopic superposition principle," I mean the ability for quantum states to superimpose ($$\tfrac{1}{\sqrt 2} (|\psi_1\rangle + |\psi_2 \rangle )$$ and all that jazz).
• By "macroscopic superposition principle," I mean the way we add up multiple vectors to compute a final result, such as in Newton's 2nd Law $$\mathbf a = \frac{1}{m} \sum_i \mathbf F_i$$ or with Electric fields $$\mathbf E = \frac{1}{4 \pi \epsilon_0} \iiint \frac{dq}{|\mathbf r - \mathbf r'|^2} \hat r$$.

Mathematically they're simply related in that vectors obey the superposition principle and everything you've listed ($$|\psi\rangle, \mathbf{E}, \mathbf{a}$$ etc.) are all vectors.
If you're comparing $$\psi=\alpha\psi_1+\beta\psi_2$$ to an integral of a gravitational force or electric field, you're comparing apples and oranges: the quantum mechanics superposition state is a fundamental property of the particle; it must exist if there are various allowed states. But for the 'macroscopic superposition', it's just because you're examining the forces caused by several different objects, hence the 'superposition'.