WheelerDeWittGleichung

The Wheeler-DeWitt equation is a fundamental equation in theoretical physics, specifically within the framework of quantum gravity. It arises from attempts to combine quantum mechanics with general relativity, aiming to describe the quantum state of the entire universe. Named after physicists John Archibald Wheeler and Bryce DeWitt, who formulated it independently in the 1960s, the equation is often regarded as the quantum analogue of the classical Einstein field equations of general relativity.

The Wheeler-DeWitt equation describes a wave function of the universe, denoted as Ψ, which encapsulates the probability amplitude for different configurations of spacetime geometry and matter fields. Unlike conventional quantum mechanics, the equation does not explicitly depend on time, reflecting the "problem of time" in quantum gravity—an issue stemming from the fact that time in general relativity is dynamic and intertwined with space, contrasting with the fixed time parameter in standard quantum theory.

Mathematically, the Wheeler-DeWitt equation is a functional differential equation, acting on an infinite-dimensional space called superspace, which represents all possible three-dimensional geometries. Its solutions provide insights into the quantum behavior of spacetime, including concepts such as initial conditions of the universe and quantum cosmological phenomena like tunneling and wave function collapse.

The equation has played a crucial role in the development of canonical quantum gravity and quantum cosmology, although it remains a theoretical construct with limited direct experimental validation. Its study continues to influence ongoing research in understanding the quantum nature of gravity and the early universe.