Einstein’s Invention of Cosmology
By Asghar Qadir
In 2005, we are celebrating the World Year of Physics as the centenary of Einstein’s annus mirables – the year of miracles!
In 1905, Einstein shook the world three times. In a series of five papers and his Ph D thesis, he demonstrated the reality of molecules by measuring them and explained Brownian motion (which had bothered biologists for some time). He explained the photoelectric effect. His paper on special relativity changed the world.
In this article, I will discuss how his general theory led him to formulate “cosmology” the study of the Universe as a whole.
Einstein’s general relativity gives only small corrections to Newtonian predictions when applied at solar system scales. Einstein wanted to see relativity dominate. The theory is nonlinear. This means that a small change in the beginning can have arbitrarily large effects later. Consequently, if its effects are to dominate, no part of the Universe however far away can be neglected. The Universe must be viewed as a whole. Thus was born the scientific study of cosmology. Surprisingly, “classical (Newtonian) cosmology” was developed only after relativistic cosmology.
Einstein had stated new principles in 1905 and 1916 to formulate special and general relativity. In 1917, he followed the same procedure again. The cosmological principle states that physics is invariant under shift of position and time. So the Universe must look the same everywhere and in all directions. Further, it must also be unchanging. Mach’s principle states that the frame of reference in which Newton’s second law of motion holds is that in which the universe is at rest on average. Thus inertia is due to the presence of other matter. This links gravity with inertia.
Einstein found that there are no solutions to his original equations of general relativity satisfying the cosmological principle. They all required that the density change with time. So Einstein modified his equations by introducing a “cosmological constant”, yielding a finite size eternal Universe model. De Sitter found another solution corresponding to an empty eternal Universe of finite size, in which points would be pushed away from each other. This was shown to be equivalent to a model of an expanding Universe. In 1922, Friedman re-discovered Einstein’s discarded solutions of an expanding Universe.
Light from sources moving away from us is red-shifted. From 1925 - 1929, Hubble found that galaxies are red-shifted on average; the further they are the faster they seem to recede. This is like points marked on a balloon move away from each other. In effect the Universe is expanding. Einstein later called the introduction of the constant “the greatest blunder of my life”, as he missed the opportunity of predicting the expansion of the Universe from his theory.
If one took a film of the expanding Universe and ran it backwards the entire Universe that we see would reach a point about 13 billion years ago. This is the beginning of the Universe, called the “big bang” – an unfortunate name since it brings to mind an explosion in a (confined) space instead of an “explosion” of the space itself. There is nothing outside the Universe (by definition) as it is a space without boundary, much like the surface of a ball is finite but has no boundary. Similarly, there is nothing before the Universe – everything started at the big bang.
An obvious problem with this picture is that all the matter that we see must have been at one point in the beginning, like a giant atom. As the Universe expanded the atom could break, but there should be many large atoms around today. What is found is that the entire Universe is composed of hydrogen (having the smallest atom), helium (having the next smallest atom) and precious little else. What else there is has largely been “cooked” in the nuclear furnaces of the stars. This means that there must have been a lot of radiant energy at the time – a hot big bang! This heat stopped the formation of the giant atom. As the Universe expanded it cooled, like a giant refrigerator. This allowed the formation of the smaller nuclei before they moved so far from each other that there could be no more formed. If this theory is true the remnants of that radiation should be around today. The remnant radiation was observed in the 1960s and this discovery was awarded the Nobel Prize. Cosmology as an observational science was born.
The big successes of the theory, the explanation of the abundances of elements (and their isotopes) and the background radiation, became a serious embarrassment as they worked too well. The radiation came out uniform to two parts in a hundred thousand. Considering that the Universe is very lumpy, with planets, stars, galaxies, clusters of galaxies that are spread on enormous filaments with huge voids between, it should not be possible to get perfectly uniform radiation. In 1992, the Cosmic Background Explorer (COBE) found slight bumps in the background that may just about fit with the observed lumpiness. This level of uniformity was explained by Alan Guth, with modifications by Andre Linde, by effectively reviving the cosmological constant at the very early stages of the Universe.
Another embarrassment was that the total amount of matter inferred from the observed motion of galaxies and their clusters in the Universe, is not allowed by the theory for the abundance of elements. There must be some exotic matter that we have not seen so far. An observational problem arose at the end of the last century that the large scale behaviour of the Universe requires three times as much energy density as seen from the motion of galaxies and clusters. This requires that the supposed vacuum stores energy, which is provided by the cosmological constant. It may appear that Einstein’s greatest blunder was not much of a blunder after all, but the current reasoning is not why it was introduced. At the time it was a blunder.
The writer, a distinguished National Professor of the Higher Education Commission of Pakistan, is currently associated with the centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad. This is the final article of a fire-part series