In everyday life, time flows on its own, like a river past its banks. But in quantum gravity, things are different: time does not flow; it emerges from relations between objects, like a pattern in a carpet that is only visible when viewed from a certain spot.
Physicists have long sought a way to honestly describe how quantum systems change when the clock is not an external device but part of the system itself. In the new work, a universal formula has been derived: the operator governing evolution is built solely from quantum constraints and conditions on the chosen reference frame. It is as if the conductor of an orchestra were also an instrument, and the score dictated both his playing and the overall rhythm.
The formula works for any theory with well-defined quantum constraints — from models of quantum cosmology to loop quantum gravity. It shows that evolution is not imposed from outside but is born from the very structure of the theory. This is a step toward understanding how time appears in a world where space and matter are not yet separated.
This approach recalls the old idea that time is not an absolute river but rather a web woven from interactions. The formula provides a tool to unravel this web without cutting it.
In quantum gravity, clocks cannot be infinitely precise: the very act of measuring time affects the system being measured, as if looking at a thermometer slightly warmed the water.
In Greg Egan's novel Schild's Ladder, the laws of physics depend on the choice of observer, and characters travel between regions with different mathematics — the new formula resembles an attempt to find an invariant language for such worlds.