A photographer tries to capture light interference, but has only one lens and the ability to change exposure time. A similar challenge faces cosmologists studying quantum imprints in the cosmic microwave background — the afterglow of the Big Bang. The classic Bell test requires two devices: each measures a property of a pair of particles. Yet telescopes see only the temperature of the sky at different points — a single quantity. How, then, to test the quantum entanglement born in the first moments?
The solution came via the temporal Bell inequality. Instead of comparing two different measurements at one point in space, one compares the same measurement at two different times. This is like an echo: the same sound returns with a delay, and distortions reveal the path it traveled. The authors applied this idea to the early universe, replacing the usual initial state (Bunch–Davies vacuum) with a coherent one — a kind of "jittery" but ordered background.
The result surprised: no violation of the temporal Bell inequality occurred. Quantum correlations were not strong enough for this test. But the value of the correlator itself, a numerical measure of the connection between measurements at different times, differs noticeably between the coherent and squeezed vacuum states. Even without violating the inequality, one can distinguish one initial state from another. So a photographer, not getting the desired shot, still understands from the film grain what light fell on the lens.
Such an approach opens the door to "quantum archaeology": by measuring today's sky, one can peer into the very beginning of time and understand in which quantum state our universe was born. And just as a photographer reconstructs the light picture from a single lens, cosmologists reconstruct the quantum past from a single observable.
Temporal Bell inequalities were first proposed to test quantum effects in systems where two particles cannot be measured simultaneously — for example, in a single quantum dot.
In Isaac Asimov's novel "The End of Eternity," time travelers change reality by observing consequences. Here, observing the sky at different epochs can itself reveal the quantum past.