If we are thinking about alternatives in everyday life, their relation is usually an “exclusive or”: The sky is blue OR green. It cannot be both at the same time. In [[quantum mechanics]], states can be connected with an AND. In the commonly used analogy of [[Schrödinger’s Cat|Schrödinger's cat]], the cat is both dead AND alive. More fundamentally (and not to unnecessarily kill anybody’s pets), [[Electron|electrons]] have a degree of freedom called [[Spin|spin]]. [[Spin]] is a [[Discreteness|discrete]] quantity and we can imagine it as an arrow. This arrow can either point up or down. Wait, actually it can point up AND down if the electron’s spin state is in a superposition. Importantly, the AND operator that we use to write the superposition here does not relate to our lack of knowledge about the system. Let’s consider a classical system to make the distinction. Imagine a box of blue and green balls. You don’t know how many balls of each color are in there, but you know that there are only two kinds of balls (blue and green). Upon drawing you know that the ball must be blue OR green. This is not a superposition, it is just a lack of knowledge. The probability of drawing a blue or a green ball depends solely on the amount of blue/green balls in the box. In [[Quantum Mechanics|quantum physics]], we call this a mixture. ![[balls.excalidraw.light.svg]] In contrast, a quantum ball only takes on a specific color upon [[Measurement|measuring]] it. Imagine measurements as taking a snapshot of the ball and the ball has to commit to a color. Before we measure the ball, we can still modify it inside its box without measuring it. These operations can modify the probabilities to see blue or green. This idea of late [[Measurement|measurements]] only after many manipulations is a key ingredient for modern [[Quantum Technologies]] like [[Quantum Simulation]] and [[Quantum Computer|Quantum Computing]]. For a concrete example of a superposition in mathematical language, see [[Qubit]]. >[!read]- Further Reading >- [[Entanglement]] >- [[Measurement]] >- [[Heisenberg Uncertainty Principle]] >- [[Discreteness]] >- [[Quantum Mechanics]] >- [[Qubit]] >[!ref]- References