Friedmann’s Models of the Universe

Alexander Friedmann was a brilliant mathematician who also had a penchant for science and technology.  After enduring both the First World War and the Russian revolution in 1917, Friedmann was eventually introduced to Einstein’s Theory of General Relativity.  It may have been a combination of his delayed exposure to the theory and Russia’s relative isolation from the rest of the world that allowed Friedmann to ignore Einstein’s (and most other physicists’) view of the universe as static and formulate an entirely new and radical approach.

While Einstein started with the assumption that the universe is static and introduced the cosmological constant to counter the effect of gravity, which, under his view, would eventually lead to the collapse of the universe, Friedmann ignored the cosmological constant and then looked at general relativity to see what kind of universe it predicted.  First of all, Friedmann’s model was one of a dynamic universe, one that had started with an initial expansion (the term Big Bang wouldn’t come along for some 30 years).  This initial expansion led to three possible results:

friedmann models
friedmann models (Photo credit: Wikipedia)

First, if the initial expansion wasn’t great enough, gravity would eventually pull the universe back in on itself.  Like a ball thrown upward, the universe would at first move quickly, then slow to a complete and brief (in cosmological terms) time, and then begin to contract ever faster.  Friedmann envisioned it then expanding again, endlessly like a bouncing ball.

Secondly, if the initial expansion was great enough, the universe would continue to expand infinitely.

The third view was a middle ground in which the initial expansion was enough so that the universe would continue to expand, though slower and slower, never quite stopping.  It is like the problem of the rabbit and the lettuce.  Each second a rabbit moves one-half of the remaining distance between himself and a piece of lettuce.  For example, the rabbit starts out four feet from the lettuce.  In the first second he moves two feet closer.  The second second he moves one foot closer.  The third second he moves six inches closer and so forth.  Does he ever reach the lettuce?  The answer is, no, he never covers the remaining half-distance to the lettuce.  Similarly Friedmann’s third model never quite reaches a point where gravity overcomes expansion, though the rate of expansion continually slows until, like the rabbit, the universe is creeping forward.

Friedmann thus proposed a model of the universe based on general relativity that did not match the model proposed by the creator of the Theory of General Relativity, Albert Einstein.  Although Einstein would admit that Friedmann’s view was mathematically correct based on general relativity, he claimed it was scientifically irrelevant because the universe was static.

Friedmann was eventually proven correct, but he did not live to see himself vindicated as Einstein had done with his theory.  Friedmann died of a serious illness, probably typhoid fever, in a delirium, reportedly lecturing to an imaginary audience.  Part of Friedmann’s problem was that his notion was too radical.  He suffered the same fate as Copernicus in that the scientific world simply wasn’t ready for his view of the universe.  Another problem was that he locked horns with Einstein himself, the world’s foremost cosmologist at the time.  Finally, Friedmann, a mathematician, was not an astronomer and was therefore an outsider to the cosmological world.  Though Friedmann’s papers were published during his lifetime they received almost no notice and would not until they were rediscovered by a Belgian scientist, Georges Lemaitre.


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