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 proton—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.

26 Responses to Schrödinger and Einstein

  1. nasosev says:

    “…by the fact that the negatively and positively charged particles he knew—the electron and positron—had different masses…”–I think you mean proton?

    • John Baez says:

      Yes, sorry, I meant “proton”. I’ll fix that.

      By the way, in some of his writings at that time he called it the “positive electron”. Maybe marveling over that made me write “positron”.

  2. J. F.G.H. says:

    Another character in this story is W. Heisenberg with his nonlinear spinor unified theory. Curiously, I found his equation in two (now three) differente moments of my life beyond academia: as a teenager in my second Enciclopedia (a gift after surgery of my parents), where a bad-typography let me asking about it for a decade; secondly, at my firts position as High School Teacher: it seems Heisenberg was somehow giving a talk there and there were a portrait of him and his nonlinear spinor equation. The third, internet of course, … Recently again, I reviewed in some talk I gave to my students about the-state-of-art of philosophy and Science, and the current view of the Universe (Multiverse is a problem, but it seems everyone is addopting it, so I focused on that concept in the talk, discussed the Tegmark’s classification and much more).

    • John Baez says:

      Heisenberg’s SU(2) theory is discussed quite nicely in this wonderful book, if I recall correctly:

      • Lochlainn O’Raifeartaigh, The Dawning of Gauge Theory, Princeton U. Press, Princeton, 1997.

      I don’t think most physicists take the multiverse seriously; some physicists have given up on figuring out the laws of our universe and have decided it’s easier to figure out the laws of all possible universes, and of course journalists find this much easier to talk about than actual physics, so it gets amplified. It’s very boring to me; let’s not talk about it! I should not have even replied to that part of your comment.

      • J. F.G.H. says:

        I agreee with you about the Multiverse issue. Indeed, when I gave my talk in interdisciplinary collaboration with the Philosophy department of my High School, I planned to show students the Multiverse is hard to validate because there is no unique definite of it (Tegmark’s classification shows that). However, turning to your main point…The depression in the theoretical community is mainly driven by a known fact: lifetime expections are low-end for discoveries, even if true there is new physics between the electroweak scale and the Planck scale, it is hardly to be shown in near future colliders, unless PeV tech arises soon…Cosmic rays and Ice-Cube suggests something happens in the PeV scale, and neutrinos are the king there. However, we are not going to have a PeV collider soon. Perhaps we will see VLHC and the Chinese Big Collider, but for many theorists, the real point is not having the opportunity to explore ideas there. Life expectation issue. The real hope, is Extrenomy: extreme astronomy likely will shed us better than colliders in the near future. After all, soon, every dark matter detector will approach and hit the neutrino floor (coherent neutrino-nuclei scattering will be detectable for near future DM detectors, specifically, solar neutrinos) so DM indirect searches will also become neutrino detector devices…

      • At least in some fields, a majority of physicists believe in the multiverse.

        Perhaps there are other universes in which that is not the case. :-)

      • John Baez says:

        At least in some fields, a majority of physicists believe in the multiverse.

        How would you characterize those fields? Would you say a majority of cosmologists believe in the multiverse, or just “theoretical cosmologists”, or just “string-theoretic theoretical cosmologists”, or what?

  3. J. F.G.H. says:

    Given the Einstein tensorial approach, as everybody knows, the real problem seems to be: there are many possible invariants (higher order in derivatives) to be included, and there are many possible generalizations of geometry. Finsler-Kagawuchi, Lanczos-Lovelock, teleparallelism, afine geometries, non-symmetric connections, Kaluza-Klein, now superstrings/M-theory,…What if the idea of geometry is wrong at some point? We know that Planck scale is very weird and no-smooth space-time (if any space-time at all!) exists at Planck temperature. In principle, similarly to the (to me unsolved) Hagedorn transition in superstrings/M-theory, at Planck temperature the own space-time melts and must be described by “something” is likely yet far beyond our empirical analysis (of course, some day, a very clever generation of physicists or a new genius will show us the way…), because the fundamental degrees of freedom of spacetime, take into account the discovery of black hole entropy by Hawking and Bekenstein, will rule at that temperature. Thus, space-time as we know is not eternal since, it can decay itself. Of course, quantum mechanics has to enter into the game somehow at some point, but the way in which it comes in is yet fully unveiled. Strings and branes captured only a very tiny fraction of it, like loop quantum gravity. Something is happening at planck length we can not imagine, unfortunately.

    • John Baez says:

      Personally I think it’s a bit bold to assume there’s nothing really mind-blowing to be found between the energies our current accelerators can probe, about 1013 eV, and the Planck scale, about 1028 eV. That’s 15 orders of magnitude.

      • nad says:

        Personally I think it’s a bit bold to assume there’s nothing really mind-blowing to be found between the energies our current accelerators can probe, about 1013 eV, and the Planck scale, about 1028 eV. That’s 15 orders of magnitude.

        I agree. Actually -I find- one should rather be more concerned about the opposite – namely that there are things to be found which might be mind-blowing in a rather figurative sense.

      • J. F.G.H. says:

        Yes, John. But people (physicists) focused on naturalness…And TeV gravity or so…The LHC data shows the MSSM is wrong (fortunately, at least for me, because the MSSM is too complicated!) and naturalness too. Where is the new physics scale is an enigma. We used to say new physics appeared at x10 scale factor, and it is not true (not under the previous mantras) anymore. I see dangerous the post-empirical “science” (a rebooted name for metascience or religious philosophy!) argument. Of course, the Multiverse can be OK (there are many planets, many galaxies, why not many Universes) but the point is empirical verification AND falsation…If not, a new age of technobabble and missguided Science could follow up. Frameworks? OK, I can live with them, but where is the limit of a framework or theory to be considered right? After all, the geocentric “framework” was kept for centuries until new data arised! Perhaps, we lived an era where 2 too big scientific revolutions (relativity and the quantum) were thought frequent and…The new revolutions could be centuries ahead…Or not…Of course, wars and pseudosciences can delay true scientific discoveries. Are we ready to find life or evidence of past life in other bodies of the solar system? And on exoplanets?

      • J. F.G.H. says:

        Neutrino data shows something happens at PeV scale or around, not below.

    • Blake Stacey says:

      I find enough strange things just from looking behind the sofa that I have to expect there are oddities in those 15 orders of magnitude.

      :-)

  4. “Schrödinger apologized in a letter to Einstein, claiming that he’d done the press conference just to get a pay raise. ”
    Oh dear.

    • John Baez says:

      This was probably false—a desperate excuse. If you read Walter Moore’s biography of Schrödinger you’ll see more about this episode. In the end Schrödinger filed all the documents about this in a file called “Die Einstein Schweinerei”. I guess “Schweinerei” would literally be translated “swinery”, but it means something like “awful mess”.

      • I now have Moore’s book and will get some more detail – it is clearly more complicated. One of my teachers, Joe Moyal, was asked by Dirac to visit Cambridge to explain his approach to quantum physics and some years later Joe crossed paths with Schrodinger (in Ireland I think). I have thus shaken hands with someone who has shaken hands with Dirac and Schrodinger!

      • I’ve heard “skulduggery” as a translation for “Schweinerei”, but that is not accurate. Having lived most of my life in Germany, but as a native speaker of (only) English, my own description would be “a bad situation intentionally provoked by someone who should have known better, usually to further their own personal gain, with ill consequences for others which are much greater than the gain produced”.

      • Wolfgang says:

        “Schweinerei” is an expression quite rich in connotations. As a native german I would understand it both as “awful mess” but also with an expression of malice if referring to someone’s actions. Thus, a messy place may be called like this, but also the action of someone which produced it, and even the ethical stance leading to this action, if it was done on purpose, especially if oneself is the victim of it (this would match “skulduggery”).

  5. Ishi Crew says:

    Schrodinger’s little book ‘what is life’ is a classic. You just need to read the first chapter, which explains QT (its an imagijnary diffusion ), and chapter 10 ‘mind and matter’. these are free online.

    alot of people seem to be into David Bohm–bohmian mechanics. eg the book by adam becker ‘what is real’. i’m agnostic.

    I think Van Kampen helped out Bohm. https://en.wikipedia.org/wiki/Nico_Van_Kampen

  6. Jim says:

    Regarding what the theory predicts, Coates R. Johnson explored this very issue in a slew of papers published in Physical Review D. Note one has to make some choices in regards to which quantities, exactly, should be identified with the electromagnetic field, electric charge, etc. Coates found that for certain choices he could derive a slightly modified Lorentz force equation, within the context of a post-Minkowskian approximation (see “Motion of particles in Einstein’s relativistic field theory II: application of general theory”, Physical Review D 4, 318). Of course the physical relevance of all this is very speculative. For what it’s worth, building on Coates’s work I obtained “Dark matter-like solutions to Einstein’s unified field equations” (Physical Review D 97, 044018, https://arxiv.org/abs/1802.04916).

  7. Paul Abbott says:

    You write that “Schrödinger and Einstein helped invent quantum mechanics. But they didn’t really believe in its implications for the structure of reality…”.

    I’m not convinced. For a fair and more balanced view, especially on Einstein’s position, “What Bell Did” by Tim Maudlin (https://arxiv.org/abs/1408.1826) is clear and unambiguous.

    So much press likes to point out Einstein’s failings, but Maudlin clearly sets the record straight.

    • John Baez says:

      That was my one-sentence explanation for why they spent so much time trying to unify classical electromagnetism and general relativity when other great physicists of their era (Pauli, Dirac, Heisenberg, etc.) were working on quantum field theory and fascinated by nucleons, mesons, neutrinos etc. It’s oversimplified—but Einstein and Schrödinger really did go in a different direction from the rest of the pack because of their reluctance to embrace quantum mechanics and especially quantum field theory.

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

    Before he came, he made sure that his unorthodox living arrangements wouldn’t be a problem. Schrödinger had a fascination, shall we say, for young girls, but also older women (not necessarily older than him, but women instead of girls), and when he moved to Dublin did so with his wife and mistress. His wife knew about his sex life and didn’t mind, as she had an interesting one of her own, her lover being none other than Hermann Weyl (whom she called Peter; his full name was Hermann Klaus Hugo Weyl).

    I mention this as it is another similarity shared by Schrödinger and Einstein, who apparently had many groupies and wasted no time cutting to the chase.

    Interesting that Einstein, Weyl, and Schrödinger were all interested in another sort of unification, so to speak.

    Eddington, by contrast, never married, and lived with his mother and sister. (Whether he was gay, I don’t know. I recently learned that “he never married” was a common euphemism for homosexuality in obituaries. (And it was decades after I watched western films on television that I realized that all the dancing girls in the saloons of the Old West were of course mostly prostitutes.) Of course, like Händel (also suspected by some of being gay), at that time and place he would have had to keep everything under wraps.

    • John Baez says:

      Thanks! This passage shows how Einstein had become quite alienated from quantum theory by 1927:

      Hendrik Anton Lorentz, President of the Solvay Scientific Committee, invited Einstein to deliver a plenary report at the congress. In a letter dated May 1, 1926, the great physicist agreed, emphasizing respect for his senior colleague: “If you want me to take up a report on quantum statistics, I will do it with pleasure, because if I’m not in a particularly difficult situation, then I can never say “no” to you” (Mehra-Rechenberg – 6, 2000, p. 234).

      However, after serious reflection, Einstein refused to give a report at the Fifth Solvay Congress. In a letter to Lorentz dated June 17, 1927, he admitted: “I remember that I promised you to prepare a report on quantum statistics for the Solvay Conference. After much hesitation, I came to the conclusion that I was not competent enough to prepare a report in a way that really corresponded to the state of things. The reason is that I am not able to actively participate in the modern development of quantum theory to the extent that it is necessary for the goal. Partly because my abilities are not enough to fully embrace the rapid development of the theory, but also because I do not share the purely statistical way of thinking on which it is based … Until the last moment I continued to hope that I could bring something to Brussels valuable. Now I have abandoned this hope. I ask you not to be angry with me because of this; it was not easy for me, although I tried my best” (Mehra – Rechenberg – 6, 2000, p. 241).

      • “I came to the conclusion that I was not competent enough to prepare a report in a way that really corresponded to the state of things. …Partly because my abilities are not enough to fully embrace the rapid development of the theory, but also because I do not share the purely statistical way of thinking on which it is based”

        This is the Dirty Harry equivalent of saying “A man’s gotta know his limitations”

        A really revealing quote indeed.

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