Quantum Superposition
Quantum superposition is the principle that a quantum system can exist in a linear combination of two or more distinct states simultaneously, with the combination itself being a valid physical state, until a measurement forces an outcome corresponding to one of the constituent states.
Curious
Superposition is the idea that a quantum system doesn't have to be in one definite state or another — it can be in a combination of both at once. This is fundamentally different from a classical coin spinning in the air, which is secretly either heads or tails the whole time even before it lands; we just don't know which yet.
A famous illustration is Erwin Schrödinger's 1935 thought experiment: a cat sealed in a box with a mechanism triggered by a random quantum event (radioactive decay) that could kill it. Taken literally and naively, quantum mechanics would say the cat is in a superposition of alive and dead until someone opens the box and looks. Schrödinger actually proposed this scenario to highlight how strange and seemingly absurd it would be if quantum superposition applied unmodified to large, everyday objects — not as an endorsement of literal alive-and-dead cats.
In practice, superpositions of macroscopic objects like cats decohere (lose their quantum superposition character) almost instantly due to interactions with their environment, which is why we never actually observe superposed cats, coins, or people — but individual atoms, electrons, and photons can be kept in superposition and experimentally verified to behave accordingly.
Exploring
Mathematically, if |ψ₁⟩ and |ψ₂⟩ are both valid quantum states of a system, then any linear combination is also a valid state:
| Symbol | Quantity | Notes |
|---|---|---|
| α, β | Complex probability amplitudes | |α|² + |β|² = 1 for normalisation |
| |ψ₁⟩, |ψ₂⟩ | Basis states | Possible outcomes of a measurement |
Upon measurement, the system is found in state |ψ₁⟩ with probability |α|² and in state |ψ₂⟩ with probability |β|² — this is the Born rule applied to a discrete, two-state system rather than a continuous position wave function. This underlies the mathematical basis of the double-slit experiment: a particle passing through two slits is in a superposition of "went through slit 1" and "went through slit 2," and the interference pattern observed on a screen is a direct experimental signature of this superposition, not merely ignorance of which slit was actually used.
Worked example: A qubit is prepared in the state |ψ⟩ = (1/√2)|0⟩ + (1/√2)|1⟩. The probability of measuring 0 is |1/√2|² = 1/2, and the probability of measuring 1 is also |1/√2|² = 1/2 — an equal superposition, analogous to a fair coin, except the "50/50-ness" reflects a genuine feature of the quantum state rather than hidden classical information.
Deep Dive
Superposition is a direct mathematical consequence of the linearity of the Schrödinger equation: if Ψ₁ and Ψ₂ are both solutions for a given Hamiltonian, then any linear combination c₁Ψ₁ + c₂Ψ₂ is also a solution. This is the quantum mechanical analogue of the principle of superposition familiar from classical wave phenomena (e.g., two overlapping water waves add linearly) — but with the crucial difference that the coefficients c₁, c₂ are complex probability amplitudes rather than classical wave amplitudes, and the squared magnitudes of these amplitudes determine measurement probabilities via the Born rule rather than a directly observable classical intensity.
Decoherence: The reason macroscopic superpositions (like Schrödinger's hypothetical cat) are never observed is decoherence — rapid, effectively irreversible entanglement between a quantum system and its environment (air molecules, photons, thermal vibrations) that destroys the coherent phase relationships between superposed states, causing the system to behave, for all practical purposes, as if it had collapsed into one definite outcome. Decoherence theory, developed substantially by H. Dieter Zeh in the 1970s and Wojciech Zurek from the 1980s onward, explains the appearance of classical, definite outcomes from underlying quantum superposition without necessarily requiring a separate, additional "collapse" postulate — though whether decoherence alone fully resolves the measurement problem, or whether an additional interpretive ingredient is needed, remains actively debated.
Interpretational status: The Copenhagen interpretation treats superposition as ending in a genuine, irreducible collapse upon measurement. The many-worlds interpretation denies collapse: all branches of a superposition continue to exist, with the observer's own state becoming entangled with, and effectively split across, all possible outcomes. Both interpretations agree completely on experimentally verified predictions for measurement statistics; they differ in the underlying physical picture of what happens to the "other" branches of the superposition.
Concept Relationship Map
Requires: wave function, linear algebra
Enables: quantum computing, quantum entanglement [PENDING], double-slit interference
Commonly confused with: classical ignorance about a pre-existing definite state (ruled out by Bell's theorem for entangled systems)
Sources
- Schrödinger, E. (1935). "Die gegenwärtige Situation in der Quantenmechanik." Naturwissenschaften, 23(48), 807–812.
- Zurek, W.H. (2003). "Decoherence, einselection, and the quantum origins of the classical." Reviews of Modern Physics, 75(3), 715–775.
- Griffiths, D.J., Schroeter, D.F. (2018). Introduction to Quantum Mechanics, 3rd ed. Cambridge University Press, Ch. 1, 12.