If you are a working/budding physicist, in all likelihood, you have been taught your quantum physics using books that mangle the historical order of development. Indeed, even McQuarrie’s book on quantum chemistry gives only a sketchy idea about the actual order in which the subject actually got developed. (IMO, the quantum chemistry books are better suited for a self-study of quantum physics. Among them, McQuarrie’s is the easiest to follow, though Levine’s has some topics better covered.)

The conceptual confusion that results out of abandoning the proper hierarchical order is just too huge. For instance, here is a quick question: Every one knows that Bohr’s model came on the scene before the real QM did. But the question is: When did the correspondence principle arrive? During those Bohr-Einstein debates? Or earlier?

Answer: Earlier. Right in 1913, when Bohr put forth his model. The Bohr-Einstein debates, in contrast, came much later, around the 1927 times, i.e., after all the essential principles of QM had already been discovered. And, BTW, it’s the complementarity principle which came during these latter times of the Bohr-Einstein debates.

Interesting? Ready for another question? Ok. Here we go.

Identify which development came first: (i) Dirac’s use of the Poisson brackets in quantum theory, (ii) The application of the matrix mechanics to the calculation of the hydrogen atom spectrum, (iii) The probability interpretation of the wave function?

If you are like 99% of others, you will say: In the order: (iii), (ii) and (i). The correct answer is: (i), (ii) and (iii), precisely in that order!

Don’t let yourself think that such questions are good for those fun quiz competitions or for the generally satisfying trivia. There is a very simple but very profound truth hidden in here: If Pauli could work out the hydrogen atom spectrum before anyone had even an inkling of a probability interpretation, what it obviously means is that there is some way that Pauli used, which is (implicitly or explicitly) more fundamental than some formal system that posits “probability currents” as the first axiom of QM.

More generally, if the historically less-progressed context (i.e. knowledge available by a certain year X) was factually enough (or sufficient) for someone to think of a great new idea, then, among all the conceivable or proposed ordering of topics or contexts that can be taken as foundational to explain that novel idea, the historically least progressed context is the only one that is necessary.

All the rest of the conceivable schemes are either after-thoughts, or organizational devices like mnemonics, or mere deductive tricks, or worse: mere cognitive burden on anyone who takes them seriously as a hierarchically proper scheme.

Having said that, now, pick up any of the introductory textbooks on quantum theory, carefully check out the order in which the topics are progressed in that book, and then ask yourself: How much of an unnecessary, useless cognitive burden is this particular author (i.e. an influential physicist) thrusting on your mind? How much lighter, better, would you feel if the order were something like the following? (The dates in parentheses follow the YYYY/MM format):

• Planck (1900/10): The quantization of energy of the electromagnetic oscillators in the walls of a light-radiating cavity
• Einstein(1905/06): The explanation of the photoelectric effect by quantizing the light radiation itself
• Einstein(1906/12): The first quantum theory of the specific heat of solids
• Bohr(1913/02–09): An explanation of the pattern of the discrete lines in the atomic spectra
• Bohr(1913/02–09): The correspondence principle
• Sommerfeld (1916–1920): Corrections to the Bohr model, introducing additional quantum numbers
• Compton (1923/05): A light scattering experiment, which confirms the quantum nature of light
• de Broglie (1923/09): The hypothesis of the matter waves, with a view to extend the wave-particle duality of light to matter as well
• Pauli (1925/01): The discovery of the exclusion principle, for the electrons in atoms
• Heisenberg (1925/06): The invention of the arrays of observables, to explain the atomic spectra
• Born and Jordon (1925/09): The first physical law stated using non-commuting symbols: $pq - qp = i\hbar I$
• Goudsmit and Uhlenbeck (1925/10): The experimental discovery of the electron spin
• Pauli (1925/11): The first success in applying the matrix mechanics to the line spectrum of hydrogen, including the Stark effect
• Dirac (1925/11): The identification of a Poisson brackets structure in Heisenberg’s analysis.
• Born, Jordon and Heisenberg (1925/11): The “three-man paper” on the mathematics of matrix mechanics submitted for publication (9 days after Dirac’s above paper)
• Schrodinger (1925/12): Formulation of the first ideas of his wave mechanics
• Schrodinger (1926/01): Successful application of his wave equation to the hydrogen atom
• Schrodinger (1926/03): Demonstration of the mathematical equivalence of the matrix mechanics and the wave mechanics
• Born (1926/07): The probability interpretation of the wave function
• Dirac (1926/09): The transformation theory—the wave and matrix mechanics as special cases
• Davisson and Germer (1927/01): Experimental confirmation of diffraction of electrons by a crystal lattice
• Heisenberg (1927/02): Formulation of the uncertainty principle
• Bohr (1927/09): Formulation of the complementarity principle and the Copenhagen interpretation
• Thomson (1927/11): Another experiment which confirms that matter diffracts
• Dirac (1930/05): Publication of the first edition of his book (having its “first chapter missing”)
• Dirac (1939): The third edition of his book introduces the bra-ket notation—the starting point for today’s “Alice and Bob”-obsessed idiots

As you probably know, I have been trying to follow the historical sequence in writing my book. So, in a way, I have been looking a bit carefully into the historical order in which things happened. Still, I had a few surprises in store even for me when I really sat down to compile the above list. Here they are: (i) Einstein’s 1906 paper (which I used to put somewhere in the late teens), and, (ii) Dirac’s 1925 paper.

I am sure that things like the following would come as surprises to many of you: (i) Dirac’s transformation theory being formulated before either the uncertainty principle or the complementarity principle was, (ii) Pauli working out the hydrogen atom line spectrum using the matrix mechanics barely within 2 months of the writing of Heisenberg’s first paper, and in fact before Heisenberg himself could succeed doing so, (iii) Born identifying the matrix nature of the Heisenberg’s non-commutative arrays and Jordon working out the derivations of the mathematics involved in it.

I also think that the help that was both required and received by Heisenberg, might have come as a surprise to many of you, esp. when contrasted with Schrodinger’s single-handed development of all the fundamentals of the wave mechanics—except, of course, the probability interpretation of the wave function, which was supplied by Born.

Most importantly, I think, quite a few must have been shocked to find that Dirac could work out his theory, even predict the existence of anti-matter, without explicitly using the bra-ket notation itself. It has become a fashion to explain this notation right in chapter 1 (though, thankfully, not right in the preface—not yet, anyway).

While writing on the heuristics that he follows while deciding whether a paper on the P-vs-NP issue is worth reading or not, Prof. Scott Aaronson has indicated that any paper not written in LaTeX is suspect.

I have a similar test for books, papers, tutorials etc. on quantum physics, especially the introductory or foundational ones. (Seriously. I have actually followed it over quite a few years in the recent past, and very successfully, too.)

I don’t take any paper/notes/tutorials/book on the foundations of quantum physics for a serious consideration (i.e., I don’t even browse or flip through its abstract) if it has “Alice” and “Bob” written anywhere within it.

Ditto, for any textbook on quantum physics, if it has those two words appearing within the first 90% of the real text matter.

So, hey physicists! Revise your books to follow the kind of an order I have given above!!

Why?

Because, I say so. That’s why.

* * * * *   * * * * *   * * * * *

No “A Song I Like” section, once again. I still go jobless. Keep that in mind.

[This is initial draft, published on September 26, 2012, 8:07 PM, IST. May be I will make some minor corrections/updates later on.]
[E&OE]

## 2 thoughts on “Hey physicists! Revise your books to follow this particular order!!”

1. From what I understand, the correct answer is (ii) (i) (iii). Heisenberg developed matrix mechanics and Pauli applied it to the hydrogen atom in 1925. The proofs of Heisenberg’s paper were sent by Born to Fowler in Cambridge who showed them to Dirac. Dirac then found that Poisson brackets could be applied to the same problem. Born’s probabilistic interpretation of the wavefunction came after Schrodinger published his paper in 1926.

Historically, the whole development happened so fast that I had to dig further to get it somewhat more straightened out. Conclusion? It really is a close call, and “the jury is still out”: whether (ii) (i) or (i) (ii).

When I wrote this post, I knew that Pauli had finished applying the matrix mechanics to the H atom (including the Stark effect) by “early November 1925” (re. Kumar’s book) but that a paper on it was published only later, in March 1926.

I also knew that Dirac had got the printer’s proof of Heisenberg’s first paper on 7th September; that he couldn’t make a head-way for weeks; and that his first paper containing the Poisson brackets idea was received by the Proc. Roy. Soc. on 7th November 1925.

Now, today, I have got to know the following two items additionally:

(1) In the further search following your comment today, I got to know that Pauli’s 1926 paper (the one applying matrix mechanics to H atom) itself, as published, carries a small note: “completed October 1925.” This note moves Pauli’s work further back in time, and, of course, works in favor of your position: (ii) then (i).

(2) Also, I got to know today, through Mehra’s book, that when Dirac used the Poisson brackets for the H atom calculations, he knew that Pauli had already succeeded working out the Balmer series using Heisenberg’s ideas, even though Dirac had no clue of the methods Pauli had used (because Pauli’s paper still had not been sent out for publication). That’s another evidence in favor of your position.

Yet, a point still remains: Wouldn’t Dirac have to first identify the Poisson brackets structure in Heisenberg’s ideas, before applying them in working out the H-spectrum calculations?

So, the issue still remains unsettled: When precisely did Dirac begin and finish his very first paper on this issue—the one that didn’t have application to the H spectrum calculations, the one that was received on 7th November? When was the work reported in it conceived and completed? Was this work, too, “completed in October”? If so, by what date within that same month? Or is it that Dirac really got the brackets idea only after October was already over?

It *is* a very, very close call. However, following a general remark in Mehra’s book concerning Dirac’s early work, I am now more inclined to think that your position seems more plausible. (BTW, I have read just a Google preview excerpt of Mehra’s book—don’t have access to his books yet.) But, still, as a final and formal statement, within the available evidence and strictly speaking, it still is an undecidable matter.

In quantum mechanics, *everything* is uncertain!

–Ajit
[E&OE]

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