Measurement problem and the Born rule

6 problems

• Can the Born rule be derived from unitary quantum mechanics alone?

  Contested

  The Born rule says the chance of an outcome is the squared size of its amplitude (the complex number attached to that outcome). Some argue it follows from symmetry or from rational betting in a universe that never collapses; others argue these derivations assume what they set out to prove.

• Why does a measurement produce one definite outcome?

  Open

  When a detector interacts with a particle in a superposition (a blend of states), the Schrodinger equation predicts a blended detector, yet one reading is always seen. The question is what physical process or rule selects that single reading.

• Is there three-path interference beyond what the Born rule allows?

  Open

  The Born rule implies that interference always comes from pairs of paths, so a three-slit pattern is fixed by the two-slit and one-slit patterns. A leftover three-path term would show the Born rule is wrong.

• How large can a Wigner friend be while violating Local Friendliness?

  Partially resolved

  In Wigner's friend experiments an outside observer treats a friend who has made a measurement as a quantum system. The 2020 test used single photons as the friend; small agent-like programs on a quantum computer gave violations in 2026, and the open question is how large and how isolated the friend can be made while the violation survives.

• Optimal overlap of epistemic states in $\psi$-epistemic hidden-variable models

  Open

  One view holds that the wave function only describes knowledge of a deeper physical state, so two different wave functions could correspond to the same underlying reality. Theorems show such shared reality must shrink rapidly as the number of quantum levels grows, but the exact limit is unknown.

• A pilot-wave theory for interacting quantum fields without preferred foliation

  Partially resolved

  Bohmian mechanics (pilot-wave theory) gives particles definite paths guided by the wave function and reproduces quantum predictions, but its nonlocal guidance seems to need a preferred notion of 'now' across space, which relativity lacks. Whether a fully relativistic version exists for interacting fields is open.