Two lots sit in the same hat, and no one knows which one the first hand will draw. In quantum mechanics, a similar uncertainty arises when two particles form an entangled pair: the state of each on its own is undefined, but together they are linked so that the result of measuring one instantly agrees with the result of measuring the other. Standard theory says that upon measurement the superposition randomly "collapses" into one of the options, but it does not explain why that particular one came up or how the second particle learns about it without any signal.

A new work proposes looking at this puzzle differently. The author lifts the entangled state into a broader mathematical space where all the ways of distributing a hidden phase between the particles become visible, a kind of "tilt" of the superposition. These ways fall into two classes that are indistinguishable in the usual description but yield opposite measurement outcomes when the particles are separated. If a pair of photons belongs to the first class, then measuring the polarization of one will give, say, horizontal, and of the other vertical; for the second class the outcomes swap places.

The key idea is that the phase is randomly set when the pair is prepared or when it is separated, and it is this phase that steers the collapse of the wave function in each subsystem. The sequence of outcomes for one particle looks random because the phase class is chosen at random, while correlations between the particles arise automatically since they share the phase. This explains both the anticorrelations in the singlet state Ψ− and the behavior of the three-particle GHZ state, where under some polarizer settings all three photons pass, and under others only half of the triples do.

Such a mechanism requires neither hidden variables nor superluminal signals: collapse turns out to be a consequence of interference within each particle, guided by the shared phase. This preserves all the predictions of quantum mechanics and is consistent with violations of Bell inequalities, since the phase is not a classical local quantity. It remains an open question when exactly the phase is fixed, at preparation, at separation, or at the moment of measurement, and this can be tested experimentally by comparing the emission rates of separated and unseparated excited atoms.

If you look at the hat with the lots once more, it is now clear that the "randomness" of the draw was predetermined by an invisible mark made before the hands parted. Quantum mechanics may be arranged the same way: the measurement outcome of each particle is set in advance by the shared phase, yet remains random for the observer until they look into their half of the pair.