Yes, you have read all those popular writings on quantum physics… Tons of them. … Right since your high-school days… And, you have watched all those YouTube videos on QM, featuring Dr. Quantum and whatnot. And so, you have always been able to rattle off a whole list of what all things are mysterious about QM. Not only that, you have always been convinced that your list is bigger than the others’.
You have also read or heard the Nobel laureates’ award ceremony lectures, even (auto)biographies. You have had all the avant garde professors at the world’s topmost universities reiterate precisely those same things again and again to you, sometimes with alternative formalisms—a few rare times, with self-invented formalisms that anyway always are completely equivalent to the existing QM. … You went to these professors in order to gain some insight into what might possibly help explain quantum mysteries, but, if you were persistent, instead came out almost becoming a wonderfully fast deduction-capable machine, able to address any entailments of any of those erudite formalisms, even to compare and contrast those entailments in any given situation. … Sometimes, you even attended those MOOC courses on the ‘net for the same purpose, and achieved it to varying degrees of success.
And, thus, finally, that sense that most everything (if not literally everything) about quantum mechanics is mysterious, is deepened in you. You can now intellectually appreciate that quantum mechanics is mysterious.
You believe that a respectable list of quantum mysteries would include, at the least, phenomena or features like the following: (i) the uncertainty principle, (ii) the inherent randomness, (iii) the wave-particle duality, (iv) the non-continuous nature of the “fabric” of “reality”, (v) many worlds, (vi) quantum entanglement, etc.
[If you work in quantum computing, your list should begin with (vi) above, and in any case, should necessarily include (ii). If you are a physicist trained at or working with CalTech (or perhaps even Cornell/Princeton/MIT), your list should emphatically begin with (iii), and accord it a subtly more exalted status. If you are an Indian physicist, you should believe that since (iii) doesn’t exist mathematically, it doesn’t exist physically, and hence, that the issue was resolved “long time ago.” If you are a layman, your list might appear in any random order, but what is more important, you would be equally convinced about each item in it.]
The reason I start with the (probable!) lists of quantum mysteries is that it’s been quite some time (certainly 30+ years) that I have thought that quantum mechanics cannot be mystical. And a fairly long time (certainly 20+ years) that QM absolutely is not as mysterious as it sounds. … I am sure you have noticed the difference between the last two sentences.
… With time, my list (of what is really mysterious about QM) has been growing shorter, and still shorter. (And my anger at philosophers and even physicists, greater and still greater.)
Finally, over the past three weeks, I realized that my list has now reached the stage where there is only one quantum mystery still left for me. And that real quantum mystery is—you could have predicted this if you know me well enough—none of the above.
What I wanted to blog about, today, was the one paper which I began reading, for the first time in my life, only in the last week of June. It made me realize the absolute shortness of my list. But, since I don’t have the time to write any more about it today (I have to run to college), let me just point out that paper and some helpful explanatory literature about it. (Given the author’s philosophy, reading the paper, in the sense of understanding it, does require a lot of ancillary explanatory material.)
The paper in question is: W. Heisenberg (1925) “Quantum-theoretical re-interpretation of kinematic and mechanical relations,” Z. Phys., vol. 33, pp. 879–893.
A few asides: I read the English translation of it; I don’t know German. This is the very first paper on QM. Heisenberg doesn’t even mention the word “arrays”; “set” is the nearest English equivalent of the word he uses.
And, among many things that are contrary to what everyone respectable (including Heisenberg himself) later on repeated to you, in this paper, Heisenberg actually talks about (and supplies the mathematics for) the electron only as a particle with a definite path (albeit not an a priori prescribed path as in Bohr’s circular or elliptical orbits).
Anyway, coming back to the helpful commentary (which is absolutely required for this paper), in the order of decreasing helpfulness to a general audience (though they all are helpful):
- Kevin McLeod, “A pseudo-history of quantum mechanics,” Class notes at the University of Wisconsin, Milwaukee
- J. G. de Swart (2010) “The parallel development of matrix and wave mechanics,” Bachelor’s thesis in physics and astronomy, University of Amsterdam
- William A. Fedak and Jeffrey J. Prentis (2009) “The 1925 Born and Jordan paper ‘On quantum mechanics’,” Am. J. Phys., vol. 77, No. 2, pp. 128–139
- Ian J. Aitchison, David A. MacManus and Thomas M. Snyder (2004) “Undertanding Heisenberg’s ‘magical’ paper of July 1925: A new look at the calculational details,” Am. J. Phys., Vol. 72, No. 11, pp. 1370–1379
- Michel Janssen (2009) “Van Vleck and Slater: Two Americans on the road to matrix mechanics.” Colloquium, Physics, St. Olaf College, Northfield, MN, October 7, 2009. (Slides available off the author’s Web site at Uni. of Minnesota.)
- Max Jammer (1966) “The Conceptual Development of Quantum Mechanics,” McGraw-Hill
- B. L. van der Waerden (1967) “Sources of Quantum Mechanics,” North-Holland
BTW, I only recently got my hands on the last two references, and now find how much of the reference material I had been missing on. Material like this is so wonderfully helpful and so easily available even in a third-class US university. (Internet follow-up folks, and Americans hungry for a second-hander’s kind of prestige, do notice this the next time you wish to harass me. (*)) I haven’t gone through anything else in these two books except for the portions related to Heisenberg’s first paper. But the reason I include them at the bottom of this references list is that they, IMO, serve to confound the issue more than illuminate it, as far as this paper is concerned. Jammer is so taken in by the later Copenhagen dogma that he inserts his own interpolations while explaining the very first paper on QM—the paper which began it all, and the paper which, IMO, is completely innocent of all the later murkiness. As to van der Waerden, even while editing a book that aimed to bring in English the original German papers on QM, he seems to have been unable to make up his mind whether his long introductory essay in this book was meant for the English-speaking people or the German-speaking ones.
In my (as you know, very limited) access, reading, and knowledge, the best material on Heisenberg’s first paper comes from two British sources: McLeod and Aitchinson et al. (German and American folks, what are you doing?) In the Aitchinson et al. paper, I just rapidly browsed through the anharmonic oscillator part of the calculations once, and then skipped it on my second reading. Even if this was the very first application of QM in its entire history, it still is just an application. Further, it’s a bit too complicated and, today, after some 87 years, it’s not so relevant for your first few readings of the paper. The main theoretical structure of QM comes earlier in the paper, and is far more interesting—and, illuminating. This is the part where my focus anyway was.
So, go through the paper and the materials, and try to form a guess as to what I might have thought of as being the only remaining (and real) quantum-theoretical/-mechanical/-physical mystery (at least in the essential terms, and from a conceptual angle).
The next time, I will tell you what that (IMO the only remaining) mystery of QM is (at least within the content and formalism of QM as it got developed until the first half of the last century). Also, next time, I will also try to note a few wonderful, salient, easy-to-misinterprete, and actually misinterpreted things, from Heisenberg’s paper.
For the time being, just one last bit: Don’t believe a word about how highly abstruse and abstract Heisenberg’s paper is. Go through it. If you go through the paper (with the help of the above explanatory material to help put it in some context and to help explain some maths), then the 23-year old Heisenberg comes across neither as a physicist with an absolutely-out-of-the-world kind of a genius, nor as a super-smart but crazy German scientist hell bent on destroying all certainty and all knowledge. Heisenberg instead comes across as a very simple and a very sincere sort of a person who is, in some way, urging his readership to (kindly) give his viewpoint their full attention and take it seriously, because it, he believes, has some definitive merits. True to his 23 years of age, and true to the (IMO the overall better culture of 1920s as compared to today’s), he at times even seems too much in awe of his established seniors when he mentions their work. But he also seems confident in directly jotting down his objections to their approach. If in this paper he doesn’t explain his mathematics or his leaps of faith via analogies, the omission wouldn’t be out of a desire to hide either of these behind the veil of the Kantian epistemology. The absence of explanations obviously are because the ideas are too new even to the author himself. … There is a certain flow to the writing (at least the English translation of it) of this paper, a certain kind of a naturalness (as seen from the author’s individual viewpoint), which is characteristic of any really original paper. And, as de Swart demonstrates, the essence of the paper is accessible to an undergraduate student, too. (… Weinberg, what exactly was your difficulty?)
And, once you finish this material, relax back a bit and try to think of (i) how much nonsense later on got injected into QM, and (ii) if you remove it all, then, what still might be left as a real quantum mechanical mystery to you.
* * * * * * * * * * * * * * *
A Song I Like:
[This song has excellence stamped all over it. And, it is rooted in the traditional Indian culture in an untranslatable sort of way. Which idiot said music is the universal language? You have to appreciate a Mozart only in his own settings. And, you have to appreciate this song also in its own settings—the settings that is as unfamiliar to today’s twitter-using women as it would be to a Westerner. And, though rooted in the traditional culture, the song doesn’t glorify any of those regressive customs. It simply assumes them, and then goes on to score one of the highest points ever reached, IMO, in music—at least in popular music. Shailendra’s lyrics, Sachin Dev Burman’s tune, and Asha Bhosale’s singing—the rendering of the emotion… All those reminiscences of the finer childhood moments spent at the parent’s place by a now-married daughter, the touch of a naturally felt love for it, that longing to once again visit a loving place after a long time, and even a sense of wistfulness for the years that have gone by never to come back again. It’s a blend of all such things (whether there right in the lyrics or not). And, everything here is just ultra-super-super-fine. … Soulful. … … And, you have to listen to it while being surrounded by the thick mist of the early monsoons, in India—while “saavan” still has not yet arrived… ]
(Hindi) “ab ke baras bhejo bhaiyyaa ko baabul…”
Singer: Asha Bhosale
Music: S. D. Burman
[Perhaps a minor editing is due(?)]