There are two equivalent formulations of quantum mechanics: matrix mechanics, created by Werner Heisenberg in 1925, and wave mechanics, created by Erwin Schrödinger in 1926. But who proved they were equivalent, and in what year?
Also, can any of you recommend a good book on the history of quantum mechanics – particularly for someone like me who already is quite familiar with the physics?
The Age of Entanglement: When Quantum Physics Was Reborn, by Louisa Gilder goes over the creation of QM understanding almost paper by paper.
Thanks Exapno.
Regarding my question about the equivalence of wave mechanics and matrix mechanics, the wikipedia article on Carl Eckart (which unlike some of the others cites the original papers) says Schrodinger and Eckart independently proved their equivalence.
So I guess Schrödinger and Eckart are the real answers to my question, and the articles on Dirac and von Neumann are referring to their developing new approaches to quantum mechanics that encompass both the matrix and wave descriptions – e.g., Dirac’s bra-ket formalism, von Neumann’s axiomatic approach (observables are Hermitian operators, states are rays in a Hilbert space, etc.)
Anyway, even though I kind of answered my own question, I’d still be interested in any further suggestions of good books on the history of QM.
I really love to read and re-read “The Second Creation” by Crease and Mann. It covers a lot of stuff, from the luminiferous ether to the elecroweak unification. So there’s plenty of particle stuff in with the quantum stuff. But it tells a lot of great stories along the way about the scientists themselves and the ways the science happened. A lot of personality conflicts and real-world interruptions that make it such a zigzag path.
Everyone seems to think “Inward Bound” by Pais is great although I didn’t especially care for it.
One I did like was “Conceptual Developments of 20th Century Field Theory” by Cao. It also should win an award for long titles.
Although I can’t attest for the rigor of the paper*, this article states that Schrödinger’s equivalence proof was quite inadequate (from a mathematical perspective, at least). A valid proof of the equivalence of matrix and wave mechanics was eventually developed by the smartest man who ever lived, John von Neumann, about five years later.
Fucking von Neumann. Set theory, mathematical logic, operator theory and quantum mechanics, game theory and economics, the Manhattan Project, computer architecture, cellular automata, mergesort…
And here I am in my underwear not yet having eaten breakfast.
It’s interesting that when Dirac proposed this function (functional) mathematicians were outraged. Later when it turned out to be part of distribution theory (I think) they were duly impressed. (I think)
It’s worth mentioning that your namesake was no dummy, either. I remember taking a survey of algebra course in college, taught by a German professor. At the time I had no idea about how Germans write a double-S. I spent most of the semester wondering how it was that I’d never heard of this “Gaub” guy, despite the fact that he basically invented modern number theory.
Anyway, thanks for the link. I’ll defintely have a look at that article.
You think that’s frustrating? I can only imagine how Évariste Galois must make you feel. The guy got himself killed in a duel at the age of 20 and still somehow found time to invent his own branch of mathematics.
I’m going to stick my neck out and suggest that there really isn’t one.
There are plenty of pop science books that will skim through the history without engaging in the technical details at the level your question was pitched at. There are plenty of biographical works that follow individual careers through the events; these range from the fairly non-technical, but excellent (say, Cassidy’s Heisenberg book) to the thorough, but mediocre (Enz’s Pauli bio). There are the various memoirs. There are detailed reconstructions of bits of the story (such as Kuhn’s Black Body Theory …). There are fairly detailed overviews of the story as part of a much wider narrative of twentieth century physics (e.g. Inward Bound). Handy compilations of important papers, usually with good commentaries.
But beyond those substitutes you’re pretty much stuck. There is Mehra’s huge multi-volume affair, which does plod through everything, but is horrible and basically just amateurishly regurgitates its sources.
It seems an obvious gap in the literature, though a non-trivial one to fill. A good single volume The Origins of Quantum Mechanics, 1900-30 that doesn’t shy away from the technicalities and tries to synthesise the whole story.
Eh, he had one good idea. I can still aspire to that.
That’s a shame, bonzer. It seems like more than once I’ve read a textbook that started with “The history of quantum mechanics is a fascinating one, and one that every student ought to familiarize themselves with. Unfortunately, that is beyond the scope of this book. Anyway, here’s the Schrödinger equation. :p”
Although in fairness, the author usually doesn’t actually type “:p”.
Since we’re talking about the founders of quantum mechanics, here are a few tidbits about them I find interesting (some taken from wikipedia, so take with an appropriately large grain of salt):
Schrödinger and his wife had an “open” marriage (at some point she was actually involved with the eminent mathematician/physicist Hermann Weyl), for a while Schrödinger lived with both her and a second “wife” who was technically married to someone else.
When Heisenberg first discovered matrix mechanics, he didn’t know that the equations he’d written down described matrices. Amazing as it is to anyone studying physics today, at the time matrices weren’t widely studied by physicists, being largely the domain of pure mathematicians. It was Heisenberg’s boss, Max Born, who discovered the connection to matrices, and he and his student Pascual Jordan fleshed out the details.
Jordan, incidentally, was one of the most significant contributors to the early development of quantum mechanics not to win the Nobel Prize. (Apparently both Einstein and Wigner nominated him at various times.) It’s been speculated that he was passed over for the prize in part because he had been a member of the Nazi Party. After the war Jordan sought a recommendation from Born, and Born (who was of Jewish heritage and had lost family in the holocaust) basically told him to take a hike. Born eventually won the Nobel for work he did without Jordan.
Paul Dirac was a man of few words, who chose his words carefully. One of my favorite Dirac quotations concerns the difference between science and poetry:
“In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite.”
Pretty much all of what tim314 talks about is examined at length in Gilders’ book.
OK, I just read the paper you cite. Here’s what I make of it:
The author is responding to several other papers (recent papers by philosophers of science, not 1920’s era papers by physicists). As this author characterizes them, those papers are (1) arguing that Schrödinger’s proof and others prior to von Neumann weren’t rigorous, and (2) that this betrays some irrationality on the part of physicists for assuming the two theories had been proven equivalent. The author agrees with (1) but not with (2).
The author basically replies: Sure, Schrödinger’s paper doesn’t rigorously prove the equivalence of the two, and in fact this would have been impossible until the formalism was developed further and more experiments clarified the appropriate assumptions for the theory to make. Rather, he says Schrödinger mostly set out to prove that wave mechanics could duplicate the successes of matrix mechanics, particularly with regard to spectral lines where the matrix theory seemed to have an advantage. Of course, in hindsight this agreement between wave mechanics and matrix mechanics is understood to be a consequence of the equivalence of the two theories. The author claims that it is with this hindsight that the paper is seen as a “proof” of the equivalence of these theories. The author argues that in fact the paper does prove what Schrödinger wanted, which was just to prove that the two theories give the same results in some specific cases of interest.
Tim, I truly wish I had something intelligent to say in response to your precis and criticism. Alas, it is not be.
As an aside, Tim, you are living proof that someone can be extraordinarily smart yet still be a nice guy (with the measure being in the form of two linked questions: Would I like to go out for a beer with the person? Would there be a good chance that he/she would comment sagaciously on the physical nature and the physics of the head/liquid interface?)
Please don’t ever change!
Wow, thanks Karl! I think that’s the nicest thing anyone on this board has ever said about me. (Which is not to suggest that the rest of you have been a bunch of meanies or anything . . . )
Although the delta function is credited to Dirac, I have always believed that Oliver Heaviside was using something very like it in the 19th century. As a mathematician, I certainly feel a lot of sympathy for mathematicians who refused to believe anything “proved” using it until someone (Laurent Schwartz, to be precise) put it into a rigorous mathematical framework.
As for Galois, it is highly unfair to say that he had one good idea. First, it was so original that it basically took 50 years before mathematics had developed enough to be able to understand it. Groups had to be invented first. Since then it has blossomed into an amazingly beautiful theory, with ramifications in many areas of mathematics.
Incidentally, any mathematician with one good idea can be said to have had a successful career. As I look back on the 80 or so papers I have published, I realize that all but one of them consisted in extending someone else’s good idea just a bit further. The remaining paper had one new idea. It is staggering to imagine that Galois had one good idea at age 20 and we can only conjecture how many others he might have had had he lived.