I find the following new paper “Einstein’s steady-state model of the universe” very interesting. The authors present a translation and analysis of an unpublished manuscript by Albert Einstein in which he proposed a “steady-state” model of the universe. They show that the manuscript appears to have been written **in early 1931**, and demonstrate that Einstein once considered a cosmic model in which the mean density of matter **in an expanding universe** remains constant due to a continuous creation of matter from empty space, a process he associated with the cosmological constant. x

*Einstein, Hubble, Michelson, Campbell, Adams, and others. Einstein wrote the equation: Is Ricci tensor zero in all components? on the blackboard in the library of the Mount Wilson Observatory in Pasadena, California, Jan. 1931.* Here

**In 1922**, Aleksandr Friedmann published a dynamical universe model. Friedmann discovered non-static models with a cosmological constant equal to zero or not equal to zero. This was a prediction of an expanding or a contracting universe of which Einstein’s (static) and de Sitter worlds were special cases. Friedmann’s model with a cosmological constant equal to zero was the simplest general relativity universe. See my paper

**In 1929** Edwin Hubble announced the discovery that the actual universe is apparently expanding. In the years beyond 1930, the tide turned in favor of dynamical models of the universe. The discovery was hailed as fulfilling the prediction of general relativity. **In January 1931 **Einstein became aware of this revolution during a visit to Caltech in Pasadena. Einstein discussed his general theory of relativity and cosmological model at length with Richard Tolman and Hubble, and viewed the skies through the colossal telescope at Mount Wilson. Hubble accompanied Einstein while he examined evidence that demonstrated that the universe was expanding. Upon his return to Berlin the new experimental and theoretical findings have led Einstein to drop his old suggestions in favor of new ones, **the dynamical universe**. x

Einstein found that models of **the expanding universe** could be achieved without any mention of the cosmological constant. In **April 1931** Einstein published his new findings in a short paper, “On the Cosmological problem of General Relativity”; in this paper he studied Friedmann’s non-static solution of the field equations of the general theory of relativity, of which the line element corresponded to a cosmological constant equal to zero. x

In an **August 1931** paper De Sitter adopted this line element with a cosmological constant equal to zero. A few months later, on **January 1932**, when both De Sitter and Einstein were visiting Mount Wilson Observatory, they wrote a joint paper in which they presented the Einstein-De Sitter universe following Einstein’s lead without the cosmological term. See my paper

*Einstein writes the equation: Is Ricci tensor zero in all components? on the blackboard in the library of the Mount Wilson Observatory, Pasadena, California, Jan. 1931.* here

The authors of the paper “Einstein’s steady-state model of the universe” found a new manuscript, according to which, **in early 1931** Einstein proposed a ‘steady-state’ model of the universe. They claim that this model is in marked contrast to **previously known** Einsteinian models of the cosmos (**both static and dynamic**) but anticipates the well-known steady-state theories of Hoyle, Bondi and Gold. x

Hence, I assume that perhaps sometime **between January 1931 **(Einstein’s visit to Caltech)** and March 1931**, Einstein embarked on developing a “steady-state” model, but eventually renounced this idea; **in April 1931** he adopted the line element with a cosmological constant equal to zero, Friedmann’s non-static solution. x

The authors of the paper, “Einstein’s steady-state model of the universe”, write that Einstein’s steady-state model **contains a fundamental flaw **and suggest it was discarded for this reason. x

It is reasonable to assume that Einstein had renounced the “steady-state” model **before April 1931**, and then he was ready to publish his **April 1931 **paper. Einstein dropped the cosmological term publicly and returned to the unmodified field equations of general relativity, and accepted Friedmann’s model with a cosmological constant equal to zero. x

Why did Einstein consider a “steady-state” model of the universe? it seems that the authors do not consider Mach’s principle. Einstein invented a finite and spatially closed static universe, bounded in space (and introduced the cosmological constant for this purpose), according to the idea of inertia having its origin in an interaction between the mass under consideration and all of the other masses in the universe, which he called “Mach’s ideas”, later called, “Mach’s principle”.

Mach’s Principle was of utmost importance to Einstein. Later Hermann Bondi and Thomas Gold came up with the idea of a steady-state theory of the expanding universe. They were fascinated by Mach’s principle, and spoke about the difficulties “concerned with the absolute state of rotation of a body. Mach examined this problem very thoroughly and all the advances in theory which have been made have not weakened the force of his argument. According to ‘Mach’s Principle’ inertia is an influence exerted by the aggregate of distant matter which determines the state of motion of the local frame of reference by means of which rotation of acceleration is measured…. …. The stationary character of the universe permits us to assume very strong interactions and yet to have permanent laws of nature. Only in this way can Mach’s principle be truly satisfied…” See my paper

A most interesting post, and a really good summary. Yes, we think the manuscript was likely written in January 1931. We did speculate about the role of Mach’s principle in Einstein’s deliberations, but we couldn’t agree amongst ourselves what Einstein’s view of the principle likely was in 1931, so i left it out. However, I will be very interested to see what the referees say on this.

Thanks! May be this book can help: Barbour, Julian, B. and Herbert Pfister (editors), Mach’s Principle: From Newton’s Bucket to Quantum Gravity, Einstein Studies series (edited by Don Howard and John Stachel), Birkhäuser, Boston, 1995.

You will find in this book many original excerpts, for instance, “Mach’s Principle and the Creation of Matter” by Fred Hoyle, and scholarly papers on Mach’s principle and Einstein’s theory of relativity.

Einstein wrote travel diaries (November 1930 – January 1931)! The travel diaries are in the Einstein Archives. Maybe Einstein wrote something about Mach’s principle and a steady state model in his travel diaries!

You can consult John Stachel.