Tuesday, August 13, 2013

Erwin Schrödinger and his cat in Google Doodle

Erwin Rudolf Josef Alexander Schrödinger was born on August 12th, 1887, i.e. 126 years and 1 day ago, in our then capital, namely Vienna, Austria-Hungary (where he also died in 1961), to a German-speaking botanist and a mostly British daughter of a chemist. He was their only child.

This background may explain some of this physicist's deep interest in the foundations of biology. However, he had some more unusual interests related to Eastern religions and pantheism – religious symbols often appeared in his work. In my opinion, this fact boils down to his family background, too. He was brought up in a Lutheran family but called himself an atheist. What he really meant by the word "atheist" was a "heretic" which is why his generalized "atheism" also allows the Eastern religions and similar things.

When he was in his 20s, he would study philosophy and experimental science and similar things in Vienna. During the First World War, right after he got habilitated in 1914, he was an officer in the Austrian fortress artillery. In 1920, he would become Max Wien's assistant and 1 year later, he was already a full professor in Breslau (now in Poland). In 1921, he went to Zürich. In 1927, after some of his famous years, he moved to Berlin to succeed Max Planck there.

In 1933, due to Erwin's peaceful opposition to the emerging institutionalized anti-Semitism in Germany, he moved to Oxford. However, the Britons were discriminating against women – at least when their number was greater than one. Schrödinger was living with his wife, with his mistress, and with his cat Milton. A year later, he would lecture at Princeton and hope that the New Jersey-based university wouldn't discriminate against households in which women were overrepresented. So no job worked over there, either. He delayed some visa paperwork and missed a job in Edinburgh as well which is why he took a position in Graz, Austria, in 1936. When Austria was absorbed by the Third Reich in 1939, he apologized for his previous opposition to Nazism – he would later apologize to Einstein for this apology. ;-)

In 1935, he proposed the "paradox" of his cat. In 1944, he was already intrigued by the research of life and proposed negentropy (the entropy that a living form may "export" to keep its entropy low) as well as a molecule that carries the gene. The latter proposal inspired James Watson to study genes and discover the DNA in 1953 according to Watson's own memoirs. However, Schrödinger wasn't really the first one to talk about the molecule of genes; it was H. J. Muller in the 1920s.

In the 1950s, he would move further towards consciousness and spiritualism but he also replaced his wife and mistress with assorted Irish women whom he made pregnant. He liked to be involved with the students. This whole life sounds dynamic, happy, and independent of conventions but Schrödinger did all these things despite his being a tuberculosis sufferer since the early 1920s – the disease finally killed him in 1961. His and his wife Annemarie Bertel's grave says\[

i \hbar \frac{\partial}{\partial t}\Psi = \hat H \Psi.

\] Guess whose equation it is. As a young scientist, he would study some ordinary classical questions in physics such as vibrations, electrical engineering, lightnings, radioactivity in the air, Brownian motion, and other things. Since 1921, he would work on the old Bohr model of the atom; he would write papers about color perception and colorimetry during the 1920s, too.

Most importantly, in January 1926 (months after the discovery of the matrix form of quantum mechanics), he would "derive" his equation and solved the hydrogen atom in the very same paper. It's a pretty difficult problem so his publishing the results in a single package seems rather impressive to me. Weeks later, he would also establish the basic quantum mechanical solutions for the harmonic oscillator, rigid rotors, diatomic molecules, and offered a new "derivation" of his equation. In the third paper in May 1926, he would demonstrate the equivalence of his equations to the Heisenberg equations (Dirac did a more comprehensible and universalist maneuver at roughly the same time) and treated the Stark effect. The fourth paper in this cool tetralogy would deal with time-dependent problems and scattering.

Rather soon, he would also started to say rubbish about quantum mechanics. Heisenberg originally said "I had no faith in a theory that ran completely counter to our Copenhagen conception." Needless to say, it was really the philosophical encapsulation that irritated Heisenberg – he saw why the equations were equivalent once the proof was given. But Heisenberg clearly rightfully kept his hostility towards the broader framework in which Schrödinger formulated his physics:
The more I think about the physical portion of Schrödinger's theory, the more repulsive I find it... What Schrödinger writes about the visualizability of his theory 'is probably not quite right,' in other words it's crap.
Heisenberg, writing to Pauli, 1926
While Schrödinger sort of understood that the interesting question is one about the eigenvalues of the Hamiltonians, he would misunderstand what quantum mechanics says in most of the other situations. So he would literally say that the wave function is an electron spread like cheese, and many other patently wrong things.

His misunderstanding didn't go away which is why he proposed his Schrödinger's cat experiment. He was convinced that the cat couldn't be in a superposition in any sense. It's clear by now – and it has arguably been clear since the mid 1920s – that the superpositions of quantum states are always equally allowed as the contributing ket vectors themselves. The superposition principle is essential and universally valid; in fact, contemporary experimenters are able to bring ever larger, pretty much macroscopic objects to generally superposed states. The superpositions usually can't be directly "perceived" as a possible answer to the measurement but quantum mechanics doesn't imply that they can.

Because of nothing else than the "visualizability", Schrödinger's equation became a more popular "picture" in which one may formulate quantum mechanics than the original matrix mechanics itself – I would say unfortunately (because it leads many people to the incorrect conclusion that the wave function is just another classical field and no "revolution" is needed) – but Schrödinger has never belonged to the group of founding fathers who correctly grasped the big picture and who could actively construct the right quantum mechanical explanation of any situation. So right after his constructive and impressive tetralogy of papers, he would become a chronic anti-quantum whiner.


  1. With two floozies at home he couldn't possibly get it right.

  2. Two floozies at home? Talk about superposition!

  3. "Weyl once said that Schrödinger did his great work during a late erotic outburst in his life, a striking example of the association in some people between sexual activity and scientific discovery, something Schrödinger himself was quite open about."

    from Ioan James "Remarkable physicists from Galileo to Yukawa".

  4. I’ve heard that too much sex can addle the brain.

  5. I think that people who have too much sex tend to become blasé with life and work. Example: Dominique Strauss-Khan.

  6. Nonsense. It is good (not only) for your brain. ;-) Look at this:

    Rutgers researchers Barry Komisaruk and Nan Wise Suggest Orgasms Better For Your Brain Than Crossword Puzzles ( http://www.huffingtonpost.com/2013/08/05/orgasms-good-for-you-study_n_3708222.html )

  7. Any sport is always good for your brain Honza ;-).

  8. Until the last angry judgement ("chronic"), I thought this article was quite nice and unbiased : ( .
    Sure, many of Schrodinger's beliefs (about anti-commuting variables, for e.g.), were weird, or nonsense. BUT, Schrodinger's picture makes the transition to QFT more intuitive.
    And, if not for Schrodinger's picture, many textbooks would probably not cover QM at all! (the authors wouldn't understand path integrals and matrix mechanics.)

    Also, Path Integrals become the most interesting after the Schrodinger Equation is derived.

    And Schrodinger's donkey helps people visualise state vectors (i.e. 1/sqrt2 |angry donkey> + 1/sqrt2 |angry monkey>).

    So, I don't think Schrodinger was all that bad . . . I would count him as a founding father of physics.

  9. Dear Dimension10,

    in a contrast with your claims, Schrodinger's picture is clearly the *least* natural picture in quantum field theory because unlike the Heisenberg, Dirac, and Feynman pictures, it doesn't allow the Lorentz invariance to be manifest.


  10. Well, I didn't; say the Schrodinger picture as it stands is natural. What I meant is that the Schrodinger Equation allows the transition to stuff like the Dirac Equation which makes Quantum Field Theory intuitive .

  11. The only problem is that the intuition that the picture encourages is completely wrong.

  12. Wait, the **Dirac Equation** gives wrong intuition???

  13. Sorry, you're confused about really basic QFT issues here.

    The Dirac equation isn't a Schrodinger's equation. It doesn't work as a description for one particle as it predicts negative probabilities and negative energies. Moreover, we know that the number of particles in the Universe is greater than one.

    For that reason, the Dirac equation has to be interpreted in the second-quantized form, as an equation for the Dirac field. And as an evolution equation for an operator (field), it is a Heisenberg equation of motion, not Schrodinger's equation, and it is indeed a basic example and confirmation of my assertion that natural, manifestly Lorentz-invariant etc. descriptions of QFT may appear in the Heisenberg picture but not in Schrodinger's picture.

  14. No, that's not what I mean...

    I in fact agree with that. BUT, what I'm saying is that,

    The *transition* to QFT, becomes rather intuitive when it is *compared* to the Schrodinger picture.

    The differences and stuff...

  15. Could you please be more specific?

    Your very suggestion that Dirac's equation in QFT is an equation for the wave function is one of the worst misconceptions or blunders that may indeed be mostly blamed on the ideology that the Schrodinger picture is the best one.

    The Dirac field in a QFT may be heuristically thought of as a wave function that was "quantized for the second time", this is why it's called "second quantization", but this analogy under the transition leads to a completely wrong physical interpretation of the objects.

    The right analogy between non-relativistic QM and QFT is one that carefully remembers which objects are wave functions and which objects are observables (operators) - and the Dirac field is simply not analogous to Schrodinger's PSI in this more important sense!

  16. I am certainly *not* saying that wavefuunctions are fields.

    Let me clarify...

    "Squaring" H Psi = i dpsi/dt, which is Schrodinger's general equation, and applying it to E^2=p^2 + m^2 , yields the Klein-Gordon Equation, . Then, that's for spin-0 fields.

    After, which, using Dirac's standard proof yields the Dirac Equation, after which one must realise that the psi is not a wavefunction, as you say .

    But, all this started out with H Psi = i d Psi/ d t . . .

  17. I don't know why you think it started with this simple equation by Schrodinger.

    If one is this vague and doesn't distinguish operators, wave functions, and c-number functions, all of this started by Maxwell's equations in the 19th century if not much earlier field equations in the previous centuries.

    The equations were gradually evolving a bit and the objects in them were changing the interpretation etc. but you surely know that Schrodinger wasn't the first one who introduced a heat-conduction-like or d'Alembert-like equation in physics, right?

  18. I'm quite sure I didn't say it resulted in the EFE... : )

    I am agree the Dirac Equation cannot be *derived* from the Schrod Eq. , but if you "square" the Schroudinger , and replace the Energy with the relativistic Energy , then you surely get the KG equatiyon?

    And letting the LHS be the square of a product of Dirac Matrices and \partial_\mu one surely obtains the Dirac Eq with a \pm on the RHS, and choosing it to be a + surely results in the Dirac Equation ? .

    And replacing the wavefunction with the field .

    Yes, that's not a derivation, but Schrodinger's Equation must have been the motivation, as seen above ^ .

  19. Be sure that I know all these manipulations and transformations allowing one to get from one equation to another etc. but it doesn't seem possible to me to understand why you think that any of those things would lead one to prefer Schrodinger's picture.

  20. Of course I'm sure that you know those manipulations : )

    I don't really *prefer* Schrodinger's picture, as opposed to path integrals and heisenberg but I just think it should get it's due credit for having had some use : ) .

  21. I'm sure old Erwin was the perfect gentleman and was simply giving all those lovely ladies a course of physics practicals, on the harmonic oscillator. His own personal one of course, but then that just showed how much he cared.

    Which reminds me. Here's an idea for a judiciously placed tattoo for the better educated and more socially adventurous swordsman: ẍ = -ω²x

    It could prove quite an icebreaker on those difficult occasions when one might be stuck for something to say by way of an introduction. Just whip in out to attract the curious and get the conversation rolling along nicely while keeping it focussed on the main thrust, so to speak. One would probably get fairly instant feedback on the chances of success that evening so it could save a lot of time and maybe a lot of money too. Of course, depending on the circumstances, some discretion might called for in order to reduce the risk of arrest.

    Worth a Nobel Prize for Literature, no?

  22. The reason you would prefer Schrödinger's picture is that it very simply guarantees unitary evolution. Unfortunately no one knows how to construct a Hamiltonian (and associated (Hilbert) state space) for even simpler processes such as in QED to give the correct time evolution.

  23. Dear James, what you write is complete nonsense showing that you don't understand the underlying linear algebra.

    The unitarity of the evolution is guaranteed by the Hermiticity of the Hamiltonian if there's one and this unitarity has nothing to do with pictures.

    In the Heisenberg picture, the operators L are changed to L+dt[H,L]/i*hbar which is exactly the formula for a unitary transformation of an operator L. When this evolution is integrated over some time (with a fixed hamiltonian), it becomes

    exp(H t / i hbar) L exp(-H t / i hbar),

    i.e. the standard conjugation by a unitary (evolution) operator.

    The unitarity in the Heisenberg picture is exactly as manifest as it is in Schrodinger's picture.

    It's also complete bullshit that we don't know the Hamiltonian for QED etc.

  24. "It may be done"


    I don't think you understand my point, nobody knows how to construct a continuous time evolution for simple QED interactions. In/Out states are about as good as we can calculate. If you claim to have a continuous time evolution model for a QED process you better publish it.

  25. Hi Dimension10,

    sorry for the off-topic, but you and your S-dual should be a bit careful at Stack Exchange. Such dualities are not exactly appreciated there, and they should by now means interact with each other. Having both following the popular-science proposal is a bit unwise, somebody has asked if they are the same in chat ... It could bring you into trouble :-/

  26. That explains it;

    I wass accidentally logged in to my S-dual (because the email associated with them are ssimilar, so I probably logged into my wrong account accidentally) and I realised that I was not following the proposal, and as I didn't know that I was logged into my S-dual, was surprised and followed the proposal...''

    Thanks for telling, unfollowed my S-dual from it. I had created that account just to propose that pop-sci proposal, as I didn''t want that to be attached to my normal account...

  27. My point being that the unitarity would be manifest in such a continuous time evolution model - rather than relying on renormalizing fudge factors. Sorry if I confused you.