Guys, I'm trying to understand the concept of superposition in quantum physics. I've heard statements like an electron being in two places at once, but what does that actually mean? How is it explained mathematically? It seems illogical for something to both exist and not exist at the same time. Maybe there's a different perspective here compared to classical physics? How do you guys approach this concept?
What is superposition in quantum physics?
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Okay, so one of the most common analogies we use to understand superposition is Schrödinger's cat. But this seems more like a mix of quantum nonsense than a real analogy. In classical physics, it's impossible for an object to be in two places at once because its position is determined the moment you measure it. But in quantum mechanics, the state is defined by the wave function—an electron's position has a probability of being everywhere at once until you measure it.
Mathematically, this is expressed through linear combinations of wave functions. For example, an electron's spin-up (`|↑⟩`) and spin-down (`|↓⟩`) states in superposition can be written as `|ψ⟩ = α|↑⟩ + β|↓⟩`. Here, `α` and `β` are complex probability amplitudes—they give the probability distribution of which state the electron will be in when measured. That's why it seems like the electron is "both here and not here"—its probability is spread out, collapsing only when measured.