To be, or not to be? Hamlet Act 3, Scene 1

Kurt Gödel and Albert Einstein were close friends. They took long walks together at the Institute for Advanced Study in Princeton during the middle part of the twentieth century. Gödel was younger than Einstein. He was born a year after Einstein’s Miracle Year of 1905. Einstein, the physicist, was the discoverer of General Relativity, the theory that combined the Special Theory with gravity. It predicted that space and time actually behaved nothing like our common experience of space and time. This had been experimentally verified. Gödel, the great mathematician and logician, had proved that logical self-referential systems could not discover everything that was true about themselves. These two great thinkers put their minds together and came up with a physical system that had the strange logical properties of logical self-referential systems. To see what they discovered, we need to understand the concept of world lines.

World lines are displayed in Figure~\ref{fig:PictureWorldLines.jpg}. A world line is basically a trajectory of an object as it moves through space and time. If an object is moving at a constant speed, then the trajectory is a straight line on a plot that has time on the vertical axis and space on the horizontal. If the object is not traveling at a constant speed, then the trajectory is not a straight line. It wiggles. The trajectory, however, still moves from the lower parts of the graph to the higher parts.

Gödel did something very clever. He found a solution of Einstein’s field equations in which the world lines circled back on themselves. This means that if you were traveling along a world line you would eventually encounter yourself as a baby. Suppose you kill yourself as a baby. Would you still be alive? It would be disturbing if you were both alive and dead. Unlike quantum mechanics, Einstein’s theory does not address ambiguity explicitly. The great challenge of modern physics is to unite the general theory of relativity with quantum mechanics. This has not yet been done.

Gödel s contribution was that he found a specific solution to the field equations in which world lines circled back on themselves. This solution has not been seen in nature, so it is speculative if this solution actually exists. I (RDJ) will say, however, that the solutions to the field equations tend to appear in nature. A good example is the black hole.\index{black hole} Black holes started out as a singular strange solution of the field equations. The solution made the prediction that extremely massive objects that completely contorted the fabric of space and time existed. This solution was initially a curiosity. A candidate for a black hole in nature, Cygnus X1\index{Cygnus X1}, was discovered when I was a graduate student in physics in the late 1970s. Now black holes in the universe are as common as ants on honey. They are believed to be at the center of every galaxy.