Schrödinger and Einstein

Schrödinger and Einstein helped invent quantum mechanics. But they didn’t really believe in its implications for the structure of reality, so in their later years they couldn’t get themselves to simply use it like most of their colleagues. Thus, they were largely sidelined. While others made rapid progress in atomic, nuclear and particle physics, they spent a lot of energy criticizing and analyzing quantum theory.

They also spent a lot of time on ‘unified field theories’: theories that sought to unify gravity and electromagnetism, without taking quantum mechanics into account.

After he finally found his equations describing gravity in November 1915, Einstein spent years working out their consequences. In 1917 he changed the equations, introducing the ‘cosmological constant’ Λ to keep the universe from expanding. Whoops.

In 1923, Einstein got excited about attempts to unify gravity and electromagnetism. He wrote to Niels Bohr:

I believe I have finally understood the connection between electricity and gravitation. Eddington has come closer to the truth than Weyl.

You see, Hermann Weyl and Arthur Eddington had both tried to develop unified field theories—theories that unified gravity and electromagnetism. Weyl had tried a gauge theory—indeed, he invented the term ‘gauge transformations’ at this time. In 1918 he asked Einstein to communicate a paper on it to the Berlin Academy. Einstein did, but pointed out a crushing physical objection to it in a footnote!

In 1921, Eddington tried a theory where the fundamental field was not the spacetime metric, but a torsion-free connection. He tried to show that both electromagnetism and gravity could be described by such a theory. But he didn’t even get as far as writing down field equations.

Einstein wrote three papers on Eddington’s ideas in 1923. He was so excited that he sent the first to the Berlin Academy from a ship sailing from Japan! He wrote down field equations and sought to connect them to Maxwell’s equations and general relativity. He was very optimistic at this time, concluding that

Eddington’s general idea in context with the Hamiltonian principle leads to a theory almost free of ambiguities; it does justice to our present knowledge about gravitation and electricity and unifies both kinds of fields in a truly accomplished manner.

Later he noticed the flaws in the theory. He had an elaborate approach to getting charged particles from singular solutions of the equation, though he wished they could be described by nonsingular solutions. He was stumped by the fact that the negatively and positively charged particles he knew—the electron and positron—had different masses. The same problem afflicted Dirac later, until the positron was discovered. But there were also problems even in getting Maxwell’s equations and general relativity from this framework, even approximately.

By the 1925 his enthusiasm had faded. He wrote to his friend Besso:

Regrettably, I had to throw away my work in the spirit of Eddington. Anyway, I now am convinced that, unfortunately, nothing can be made with the complex of ideas by Weyl–Eddington.

So, he started work on another unified field theory. And another.

And another.

Einstein worked obsessively on unified field theories until his death in 1955. He lost touch with his colleagues’ discoveries in particle physics. He had an assistant, Valentine Bargmann, try to teach him quantum field theory—but he lost interest in a month. All he wanted was a geometrical explanation of gravity and electromagnetism. He never succeeded in this quest.

But there’s more to this story!

The other side of the story is Schrödinger. In the 1940s, he too became obsessed with unified field theories. He and Einstein became good friends—but also competitors in their quest to unify the forces of nature.

But let’s back up a bit. In June 1935, after the famous Einstein-Podolsky-Rosen paper arguing that quantum mechanics was incomplete, Schrödinger wrote to Einstein:

I am very happy that in the paper just published in P.R. you have evidently caught dogmatic q.m. by the coat-tails.

Einstein replied:

You are the only person with whom I am actually willing to come to terms.

They bonded over their philosophical opposition to the Bohr–Heisenberg attitude to quantum mechanics. In November 1935, Schrödinger wrote his paper on ‘Schrödinger’s cat‘.

Schrödinger fled Austria after the Nazis took over. In 1940 he got a job at the brand-new Dublin Institute for Advanced Studies.

In 1943 he started writing about unified field theories, corresponding with Einstein. He worked on some theories very similar to those of Einstein and Straus, who were trying to unify gravity and electromagnetism in a theory involving a connection with torsion, whose Levi-Civita symbol was therefore non-symmetric. He wrote 8 papers on this subject.

Einstein even sent Schrödinger two of his unpublished papers on these ideas!

In late 1946, Schrödinger had a new insight. He was thrilled.

By 1947 Schrödinger thought he’d made a breakthrough. He presented a paper on January 27th at the Dublin Institute of Advanced Studies. He even called a press conference to announce his new theory!

He predicted that a rotating mass would generate a magnetic field.

The story of the great discovery was quickly telegraphed around the world, and the science editor of the New York Times interview Einstein to see what he thought.

Einstein was not impressed. In a carefully prepared statement he shot Schrödinger down:

Einstein was especially annoyed that Schrödinger had called a press conference to announce his new theory before there was any evidence supporting it.

Wise words. I wish people heeded them!

Schrödinger apologized in a letter to Einstein, claiming that he’d done the press conference just to get a pay raise. Einstein responded curtly, saying “your theory does not really differ from mine”.

They stopped writing to each other for 3 years.

I’d like to understand Schrödinger’s theory using the modern tools of differential geometry. I don’t think it’s promising. I just want to know what it actually says, and what it predicts! Go here for details:

• Schrödinger’s unified field theory, The n-Category Café, December 26, 2019.

For more on Schrödinger’s theory, try his book:

• Erwin Schrödinger, Space-Time Structure, Cambridge U. Press, Cambridge, 1950. Chapter XII: Generalizations of Einstein’s theory.

and his first paper on the theory:

• Erwin Schödinger, The final affine field laws I, Proceedings of the Royal Irish Academy A 51 (1945–1948), 163–171.

For a wonderfully detailed analysis of the history of unified field theories, including the work of Einstein and Schrödinger, read these:

• Hubert F. M. Goenner, On the history of unified field theories, Living Reviews in Relativity 7 (2004), article no. 2. On the history of unified field theories II (ca. 1930–ca. 1965), Living Reviews in Relativity 17 (2014), article no. 5.

especially Section 6 of the second paper. For more on the story of Einstein and Schrödinger, I recommend this wonderful book:

• Walter Moore, Schrödinger: Life and Thought, Cambridge U. Press, Cambridge, 1989.

This is where I got most of my quotes.