$$ \hatH \Psi = 0 $$
The PDF typically introduces the Hartle–Hawking no-boundary proposal , where the universe’s wave function is defined as a path integral over compact Euclidean four-geometries. Key topics include:
This equation implies that the total energy of the universe is zero—the positive energy of matter is exactly canceled by the negative energy of gravity. Because the right side is zero, the wave function does not explicitly depend on time, leading to the "problem of time" in quantum gravity. 2. Primary Proposals for the Initial State wave function of the universe pdf
The famous consequence is that at very early times, the universe’s time dimension behaves like a fourth spatial dimension. There is no "time before the Big Bang" because the concept of time emerges smoothly from a purely spatial, closed geometry—much like the North Pole is the "boundary" of the Earth: you can go north until you reach the pole, but there is no point north of the pole.
The universe may not need a creator, but it does need a wave function. And that wave function is waiting for you in PDF form. $$ \hatH \Psi = 0 $$ The PDF
The primary literature regarding the wave function of the universe is dense and mathematically rigorous. Because the field is decades old, many of the foundational texts exist as scanned typewritten manuscripts or digitized journal articles available primarily through university repositories and archives.
The tunneling wave function is typically larger for universes that begin at a specific, small size and then inflate. It favors universes that are spatially infinite or open. The mathematics involves a where the universe tunnels through a potential barrier, similar to alpha decay in nuclear physics. The universe may not need a creator, but
For decades, these two theories existed in separate domains. However, as cosmologists peered closer to the Big Bang—the singularity where the universe was infinitely dense and small—the need to unify them became urgent. Out of this necessity was born the Wheeler-DeWitt equation, a formulation that attempts to describe the .