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Einstein’s theory of general relativity is one of the crowning achievements of 20th century science. It describes gravity as a geometric property of the fabric of spacetime.  

Today, this idea is one of the cornerstones of modern physics but it was not without its birth pangs. A point of particular controversy is a term in Einstein’s equations called the cosmological constant.  This constant is a kind of pressure that influences the Universe’s rate of expansion.

Einstein’s original equations did not have this constant. These equations predicted that the Universe would contract if gravity were too strong or expand if it were too weak.

But Einstein believed the Universe was static and so added a term that would provide some kind of pressure to counteract the force of gravity. 

A few years later, George Lamaitre and Edwin Hubble discovered that the Universe was indeed expanding. This caused Einstein to remove the constant. He later called his failure to predict the expansion of the Universe from the original equations, the biggest blunder of his life.

All this is well known as part of the famous story of general relativity.

But today, Alex Harvey at New York University in New York, adds an interesting twist to the tale. Harvey has unearthed and re-interpreted a note by Erwin Schrodinger about Einstein’s addition of the constant and also studied Einstein’s reply.

The correspondence took place between 1918 and 1921, soon after Einstein first published his ideas. The purpose of Schrodinger’s note is to discuss the properties of the new constant that Einstein added and what form it must take. 

Einstein’s reply is short and direct. He points out that Schrodinger’s approach allows the constant to be fixed or to vary.  He goes on to say that this leads to “a non-observable negative density in interstellar space” and to the question of how this might vary throughout spacetime. 

Harvey says this is remarkable because Einstein is describing the central problem that modern cosmologists face in the search for dark energy. 

To be fair, Einstein gives the notion short shrift.  He dismisses it saying: “The course taken by Herr Schrodinger does not appear possible to me because it leads too deeply into the thicket of hypotheses.”

That’s interesting because this is exactly the headache that modern cosmologists have in formulating a structure for dark energy today. “In the late 1990’s, Einstein’s concern about a “thicket of hypotheses” became real, ” says Harvey.

That’s when astronomers discovered that not only was the Universe expanding but that this expansion is accelerating.

From a theoretical point of view, the cosmological constant ought to explain this but nobody knows what form it must take. Today, the problem is how to extract this form from Einstein’s thicket of hypotheses. 

Nobody knows whether this debate between Einstein and Schrodinger continued.  Harvey says he knows of no other correspondence on the topic.

In fact, Schrodinger does not appear to have considered the constant again. But of course, Einstein did and went on to entirely change his view, eventually denouncing the constant altogether. 

That’s all the more reason why Harvey’s insight is a fascinating and important footnote in the history of the cosmological constant.

Ref: arxiv.org/abs/1211.6338: How Einstein Discovered Dark Energy

 

 

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