What Came Before the Big Bang?

Robert Brandenberger, a physicist astatine McGill University who was not progressive with the study, said the caller insubstantial “sets a caller modular of rigor for the analysis” of the mathematics of the opening of time. In immoderate cases, what appears astatine archetypal to beryllium a singularity—a constituent successful space-time wherever mathematical descriptions suffer their meaning—may successful information beryllium an illusion.

A Taxonomy of Singularities

The cardinal contented confronting Geshnizjani, Ling, and Quintin is whether determination is simply a constituent anterior to ostentation astatine which the laws of gravity interruption down successful a singularity. The simplest illustration of a mathematical singularity is what happens to the relation 1/x arsenic x approaches zero. The relation takes a fig x arsenic an input, and outputs different number. As x gets smaller and smaller, 1/x gets larger and larger, approaching infinity. If x is zero, the relation is nary longer good defined: It can’t beryllium relied upon arsenic a statement of reality.

Sometimes, however, mathematicians tin get astir a singularity. For example, see the premier meridian, which passes done Greenwich, England, astatine longitude zero. If you had a relation of 1/longitude, it would spell berserk successful Greenwich. But there’s not really thing physically peculiar astir suburban London: You could easy redefine zero longitude to walk done immoderate different spot connected Earth, and past your relation would behave perfectly usually erstwhile approaching the Royal Observatory successful Greenwich.

Something akin happens astatine the bound of mathematical models of achromatic holes. The equations that picture spherical nonrotating achromatic holes, worked retired by the physicist Karl Schwarzschild successful 1916, person a word whose denominator goes to zero astatine the lawsuit skyline of the achromatic hole—the aboveground surrounding a achromatic spread beyond which thing tin escape. That led physicists to judge that the lawsuit skyline was a carnal singularity. But 8 years aboriginal the astronomer Arthur Eddington showed that if a antithetic acceptable of coordinates is used, the singularity disappears. Like the premier meridian, the lawsuit skyline is an illusion: a mathematical artifact called a coordinate singularity, which lone arises due to the fact that of the prime of coordinates.

At a achromatic hole’s center, by contrast, the density and curvature spell to infinity successful a mode that can’t beryllium eliminated by utilizing a antithetic coordinate system. The laws of wide relativity commencement spewing retired gibberish. This is called a curvature singularity. It implies that thing is taking spot that’s beyond the quality of existent carnal and mathematical theories to describe.