## Cosmology and Relativity

By 1915 Einstein had generalized his theory of relativity and founded the science of cosmology. General relativity is really a set of complicated differential equations. There are many solutions because one may choose various parameters in the equations, and also postulate what are called the initial and boundary conditions.

At present we cannot observe either the beginning or the edge of the universe (if it has an edge). Therefore the choice of initial and boundary conditions is arbitrary. Mathematicians start with initial and boundary conditions that seem good to them, solve the equations, and then see if the resulting model of the universe looks at all like the present universe. It would be more logical to write down present conditions in the present universe and then solve the general relativity equations backwards until we knew the conditions at the beginning. However, this procedure is much more difficult that solving the equations in the forward direction.

The values of the parameters and the conditions chosen may make the equations easy, difficult, or impossible to solve. Naturally Einstein and other physicists and mathematicians found most of the easy solutions first.

There is nothing wrong with solving the easy cases first. In doing so we may learn something that will make solving the harder cases easier or at least possible. The parameters and conditions that make for easy solution do not necessarily correspond to reality. The problem with solving only the easy cases is the temptation to jump to philosophical conclusions that don’t correspond to reality before doing the hard work necessary to solve a realistic case. Even great scientists are not immune to this temptation, as we shall see.

Willem de Sitter (Dutch astronomer, 1872–1934) found the first non-static solution in 1917. In his solution, the universe consists of empty space and time only. The solution is interesting to mathematicians, but it doesn’t correspond to reality. The solution describes a universe with zero matter density in it. Material objects (including us) exist in our universe. One may solve the equations for an empty universe, but such a universe could not have living, rational beings in it to find the solution.

In 1922 Alexander Friedmann (Russian mathematician, 1888–1925) found a solution that depends directly on the density of matter and energy in the universe. His was the accepted model until recently, when astronomers discovered that the expansion of the universe is accelerating. Now many physicists and mathematicians are working to extend and modify his solution, or to find another solution that includes accelerating expansion.

At present we cannot observe either the beginning or the edge of the universe (if it has an edge). Therefore the choice of initial and boundary conditions is arbitrary. Mathematicians start with initial and boundary conditions that seem good to them, solve the equations, and then see if the resulting model of the universe looks at all like the present universe. It would be more logical to write down present conditions in the present universe and then solve the general relativity equations backwards until we knew the conditions at the beginning. However, this procedure is much more difficult that solving the equations in the forward direction.

The values of the parameters and the conditions chosen may make the equations easy, difficult, or impossible to solve. Naturally Einstein and other physicists and mathematicians found most of the easy solutions first.

There is nothing wrong with solving the easy cases first. In doing so we may learn something that will make solving the harder cases easier or at least possible. The parameters and conditions that make for easy solution do not necessarily correspond to reality. The problem with solving only the easy cases is the temptation to jump to philosophical conclusions that don’t correspond to reality before doing the hard work necessary to solve a realistic case. Even great scientists are not immune to this temptation, as we shall see.

Willem de Sitter (Dutch astronomer, 1872–1934) found the first non-static solution in 1917. In his solution, the universe consists of empty space and time only. The solution is interesting to mathematicians, but it doesn’t correspond to reality. The solution describes a universe with zero matter density in it. Material objects (including us) exist in our universe. One may solve the equations for an empty universe, but such a universe could not have living, rational beings in it to find the solution.

In 1922 Alexander Friedmann (Russian mathematician, 1888–1925) found a solution that depends directly on the density of matter and energy in the universe. His was the accepted model until recently, when astronomers discovered that the expansion of the universe is accelerating. Now many physicists and mathematicians are working to extend and modify his solution, or to find another solution that includes accelerating expansion.