Robert Brandenberger, a physicist at McGill University who was not involved in the study, said the new paper “sets a new standard of rigor for the analysis” of early mathematics. In some cases, what at first appears to be a singularity (a point in space-time where mathematical descriptions lose their meaning) may actually be an illusion.
A taxonomy of singularities
The central question facing Geshnizjani, Ling and Quintin is whether there is a point before inflation at which the laws of gravity break down singularly. The simplest example of a mathematical singularity is what happens to the function 1/x as x approaches zero. The function takes a number. x as input and generates another number. As x gets smaller and smaller, 1/x It gets bigger and bigger, approaching infinity. Yeah x is zero, the function is no longer well defined: it cannot be trusted as a description of reality.
Sometimes, however, mathematicians can get around a singularity. For example, consider the prime meridian, which passes through Greenwich, England, at longitude zero. If you had a 1/length function, it would go crazy in Greenwich. But there’s actually nothing physically special about suburban London: you could easily redefine longitude zero to pass somewhere else on Earth, and then your function would behave perfectly normally as you approach the Royal Greenwich Observatory.
Something similar occurs at the limits of mathematical models of black holes. The equations describing non-rotating spherical black holes, developed by physicist Karl Schwarzschild in 1916, have a term whose denominator reaches zero at the black hole’s event horizon: the surface surrounding a black hole beyond which it swims. can escape. That led physicists to believe that the event horizon was a physical singularity. But eight years later, astronomer Arthur Eddington showed that if a different set of coordinates is used, the singularity disappears. Like the prime meridian, the event horizon is an illusion: a mathematical artifact called a coordinate singularity, which only arises due to the choice of coordinates.
At the center of a black hole, by contrast, density and curvature go to infinity in a way that cannot be eliminated using a different coordinate system. The laws of general relativity start to spout gibberish. This is called curvature singularity. It implies that something is happening that is beyond the ability of current physical and mathematical theories to describe.
