Robert Brandenburger, a physicist at McGill University who was not involved in the study, said the new paper “sets a new standard for rigor in the mathematical analysis of the beginning of time.” In some cases, what at first glance appear to be singularities — points in space-time where mathematical descriptions lose meaning — may actually be illusions.
Classification of singularities
The central question facing Geshnijani, Lin and Quintin is whether there is a point before inflation where the laws of gravity break down in a singularity. The simplest example of a mathematical singularity is what happens to the function 1/X As X Approaching zero. The function takes a number X It takes one number as input and outputs another number. X It gets smaller and smaller, 1/X It gets bigger and bigger, approaching infinity. X When is zero, the function is no longer well-defined and can no longer be trusted as a description of reality.
But sometimes mathematicians can avoid singularities. For example, consider the prime meridian, which passes through Greenwich, England, at longitude zero. If we had a function of 1/longitude, it would run wild at Greenwich. But there’s actually nothing physically special about the outskirts of London. We can easily redefine longitude zero to pass through another place on Earth, and the function will behave perfectly fine as it approaches the Royal Observatory in Greenwich.
Something similar happens at the boundaries of mathematical models of black holes. In 1916, physicist Karl Schwarzschild solved the equations for spherical, non-rotating black holes, which contain a term whose denominator equals zero at the black hole’s event horizon (the surface surrounding the black hole from which nothing can escape). This led physicists to believe that the event horizon was a physical singularity. But eight years later, astronomer Arthur Eddington showed that the singularity vanished when a different coordinate system was used. Like the prime meridian, the event horizon is an illusion, a mathematical artifact called a coordinate singularity that arises only due to the choice of coordinates.
In contrast, at the center of a black hole, the density and curvature become infinite and cannot be resolved by using a different coordinate system. The laws of general relativity start to say gibberish. This is called a curvature singularity. It means that something is happening that cannot be explained by current physical and mathematical theories.
