The Kochen–Specker theorem, developed in 1967 by Simon Kochen and Ernst Specker, is a fundamental result in quantum foundations. It shows that non-contextual hidden variable theories cannot reproduce the predictions of quantum mechanics.
Here’s what that means:
- Non-contextuality is the classical idea that the value of a measurement (like spin or position) exists independently of how or with what other quantities it is measured.
- In a non-contextual hidden variable theory, every observable property has a predetermined value, no matter how it’s tested.
The Kochen–Specker theorem proves that such an assumption cannot be true in quantum mechanics. It shows that:
- Quantum measurements are contextual—the outcome depends on which other measurements are being performed alongside it.
- There is no consistent way to assign definite values to all quantum properties independent of measurement context.
This theorem is especially powerful because:
- Unlike Bell’s theorem, it doesn’t require entanglement or multiple particles—it applies even to single quantum systems like a spin-1 particle.
- It strengthens the idea that quantum properties don’t exist as fixed attributes prior to measurement.
In essence, the Kochen–Specker theorem tells us that quantum reality is fundamentally different from classical intuition:
What you choose to measure influences what is real.