Wave | Function Of The Universe Pdf [cracked]

Hartle, J. B., & Hawking, S. W. (1983). Wave function of the universe . Physical Review D, 28(12), 2960.

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. wave function of the universe pdf

Introduced in the seminal 1983 paper Wave function of the Universe , this theory suggests the universe is spatially closed and has no boundary in the past. It uses a Euclidean path integral over compact four-geometries, effectively smoothing out the Big Bang singularity into a rounded "North Pole" of spacetime where time and space become indistinguishable. Hartle, J

[ \Psi[h_ij, \phi] \approx \int \mathcalDg , \mathcalD\Phi , e^-I_E[g, \Phi] ] (1983)