>[!abstract] >The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. > >In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called "problem of time" ("Wheeler-DeWitt equation", 2025). >[!quote] >In the Schrödinger equation, we have $d$ by $dt$, the derivative with respect to $t$, time of the quantum state. And according to the naive version of quantum gravity [the Wheeler-DeWitt equation], that should vanish (Carroll, 2025). The Wheeler-DeWitt equation is at the heart of the [[Problem of time|problem of time]]. While time is fundamental in the Schrödinger equation which is central to quantum mechanics, it disappears in the Wheeler-DeWitt equation which is central to quantum gravity. This absence would suggest that time is an emergent property of the universe rather than fundamental. ## References - Carroll, S. (Host). (2025, January 6). Does time exist? (No. 300) [Audio podcast episode]. In *Mindscape*. https://www.preposterousuniverse.com/podcast/2025/01/06/300-solo-does-time-exist/ - Wheeler-DeWitt equation. (2025, April 09). In *Wikipedia*. https://en.wikipedia.org/w/index.php?title=Wheeler–DeWitt_equation&oldid=1274071907