A list of books for understanding the non-relativistic QM

TL;DR: NFY (Not for you).


In this post, I will list those books which have been actually helpful to me during my self-studies of QM.

But before coming to the list, let me first note down a few points which would be important for engineers who wish to study QM on their own. After all, my blog is regularly visited by engineers too. That’s what the data about the visit patterns to various posts says.

Others (e.g. physicists) may perhaps skip over the note in the next section, and instead jump directly over to the list itself. However, even if the note for engineers is too long, perhaps, physicists should go through it too. If they did, they sure would come to know a bit more about the kind of background from which the engineers come.


I. A note for engineers who wish to study QM on their own:

The point is this: QM is vast, even if its postulates are just a few. So, it takes a prolonged, sustained effort to learn it.

For the same reason (of vastness), learning QM also involves your having to side-by-side learn an entirely new approach to learning itself. (If you have been a good student of engineering, chances are pretty good that you already have some first-hand idea about this meta-learning thing. But the point is, if you wish to understand QM, you have to put it to use once again afresh!)

In terms of vastness, QM is, in some sense, comparable to this cluster of subjects spanning engineering and physics: engineering thermodynamics, statistical mechanics, kinetics, fluid mechanics, and heat- and mass-transfer.

I.1 Thermodynamics as a science that is hard to get right:

The four laws of thermodynamics (including the zeroth and the third) are easy enough to grasp—I mean, in the simpler settings. But when it comes to this subject (as also for the Newtonian mechanics, i.e., from the particle to the continuum mechanics), God lies not in the postulates but in their applications.

The statement of the first law of thermodynamics remains the same simple one. But complexity begins to creep in as soon as you begin to dig just a little bit deeper with it. Entire categories of new considerations enter the picture, and the meaning of the same postulates gets both enriched and deepened with them. For instance, consider the distinction of the open vs. the closed vs. the isolated systems, and the corresponding changes that have to be made even to the mathematical statements of the law. That’s just for the starters. The complexity keeps increasing: studies of different processes like adiabatic vs. isochoric vs. polytropic vs. isentropic etc., and understanding the nature of these idealizations and their relevance in diverse practical applications such as: steam power (important even today, specifically, in the nuclear power plants), IC engines, jet turbines, refrigeration and air-conditioning, furnaces, boilers, process equipment, etc.; phase transitions, material properties and their variations; empirical charts….

Then there is another point. To really understand thermodynamics well, you have to learn a lot of other subjects too. You have to go further and study some different but complementary sciences like heat and mass transfer, to begin with. And to do that well, you need to study fluid dynamics first. Kinetics is practically important too; think of process engineering and cost of energy. Ideas from statistical mechanics are important from the viewpoint of developing a fundamental understanding. And then, you have to augment all this study with all the empirical studies of the irreversible processes (think: the boiling heat transfer process). It’s only when you study such an entire gamut of topics and subjects that you can truly come to say that you now have some realistic understanding of the subject matter that is thermodynamics.

Developing understanding of the aforementioned vast cluster of subjects (of thermal sciences) is difficult; it requires a sustained effort spanning over years. Mistakes are not only very easily possible; in engineering schools, they are routine. Let me illustrate this point with just one example from thermodynamics.

Consider some point that is somewhat nutty to get right. For instance, consider the fact that no work is done during the free expansion of a gas. If you are such a genius that you could correctly get this point right on your very first reading, then hats off to you. Personally, I could not. Neither do I know of even a single engineer who could. We all had summarily stumbled on some fine points like this.

You see, what happens here is that thermodynamics and statistical mechanics involve entirely different ways of thinking, but they both are being introduced almost at the same time during your UG studies. Therefore, it is easy enough to mix up the some disparate metaphors coming from these two entirely different paradigms.

Coming to the specific example of the free expansion, initially, it is easy enough for you to think that since momentum is being carried by all those gas molecules escaping the chamber during the free expansion process, there must be a leakage of work associated with it. Further, since the molecules were already moving in a random manner, there must be an accompanying leakage of the heat too. Both turn out to be wrong ways of thinking about the process! Intuitions about thermodynamics develop only slowly. You think that you understood what the basic idea of a system and an environment is like, but the example of the free expansion serves to expose the holes in your understanding. And then, it’s not just thermo and stat mech. You have to learn how to separate both from kinetics (and they all, from the two other, closely related, thermal sciences: fluid mechanics, and heat and mass transfer).

But before you can learn to separate out the unique perspectives of these subject matters, you first have to learn their contents! But the way the university education happens, you also get exposed to them more or less simultaneously! (4 years is as nothing in a career that might span over 30 to 40 years.)

Since you are learning a lot many different paradigms at the same time, it is easy enough to naively transfer your fledgling understanding of one aspect of one paradigm (say, that of the particle or statistical mechanics) and naively insert it, in an invalid manner, into another paradigm which you are still just learning to use at roughly the same time (thermodynamics). This is what happens in the case of the free expansion of gases. Or, of throttling. Or, of the difference between the two… It is a rare student who can correctly answer all the questions on this topic, during his oral examination.

Now, here is the ultimate point: Postulates-wise, thermodynamics is independent of the rest of the subjects from the aforementioned cluster of subjects. So, in theory, you should be able to “get” thermodynamics—its postulates, in all their generality—even without ever having learnt these other subjects.

Yet, paradoxically enough, we find that complicated concepts and processes also become easier to understand when they are approached using many different conceptual pathways. A good example here would be the concept of entropy.

When you are a XII standard student (or even during your first couple of years in engineering), you are, more or less, just getting your feet wet with the idea of the differentials. As it so happens, before you run into the concept of entropy, virtually every physics concept was such that it was a ratio of two differentials. For instance, the instantaneous velocity is the ratio of d(displacement) over d(time). But the definition of entropy involves a more creative way of using the calculus: it has a differential (and that too an inexact differential), but only in the numerator. The denominator is a “plain-vanilla” variable. You have already learnt the maths used in dealing with the rates of changes—i.e. the calculus. But that doesn’t mean that you have an already learnt physical imagination with you which would let you handle this kind of a definition—one that involves a ratio of a differential quantity to an ordinary variable. … “Why should only one thing change even as the other thing remains steadfastly constant?” you may wonder. “And if it is anyway going to stay constant, then is it even significant? (Isn’t the derivative of a constant the zero?) So, why not just throw the constant variable out of the consideration?” You see, one major reason you can’t deal with the definition of entropy is simply because you can’t deal with the way its maths comes arranged. Understanding entropy in a purely thermodynamic—i.e. continuum—context can get confusing, to say the least. But then, just throw in a simple insight from Boltzmann’s theory, and suddenly, the bulb gets lit up!

So, paradoxically enough, even if multiple paradigms mean more work and even more possibilities of confusion, in some ways, having multiple approaches also does help.

When a subject is vast, and therefore involves multiple paradigms, people regularly fail to get certain complex ideas right. That happens even to very smart people. For instance, consider Maxwell’s daemon. Not many people could figure out how to deal with it correctly, for such a long time.

…All in all, it is only some time later, when you have already studied all these topics—thermodynamics, kinetics, statistical mechanics, fluid mechanics, heat and mass transfer—that finally things begin to fall in place (if they at all do, at any point of time!). But getting there involves hard effort that goes on for years: it involves learning all these topics individually, and then, also integrating them all together.

In other words, there is no short-cut to understanding thermodynamics. It seems easy enough to think that you’ve understood the 4 laws the first time you ran into them. But the huge gaps in your understanding begin to become apparent only when it comes to applying them to a wide variety of situations.

I.2 QM is vast, and requires multiple passes of studies:

Something similar happens also with QM. It too has relatively few postulates (3 to 6 in number, depending on which author you consult) but a vast scope of applicability. It is easy enough to develop a feeling that you have understood the postulates right. But, exactly as in the case of thermodynamics (or Newtonian mechanics), once again, the God lies not in the postulates but rather in their applications. And in case of QM, you have to hasten to add: the God also lies in the very meaning of these postulates—not just their applications. QM carries a one-two punch.

Similar to the case of thermodynamics and the related cluster of subjects, it is not possible to “get” QM in the first go. If you think you did, chances are that you have a superhuman intelligence. Or, far, far more likely, the plain fact of the matter is that you simply didn’t get the subject matter right—not in its full generality. (Which is what typically happens to the CS guys who think that they have mastered QM, even if the only “QM” they ever learnt was that of two-state systems in a finite-dimensional Hilbert space, and without ever acquiring even an inkling of ideas like radiation-matter interactions, transition rates, or the average decoherence times.)

The only way out, the only way that works in properly studying QM is this: Begin studying QM at a simpler level, finish developing as much understanding about its entire scope as possible (as happens in the typical Modern Physics courses), and then come to studying the same set of topics once again in a next iteration, but now to a greater depth. And, you have to keep repeating this process some 4–5 times. Often times, you have to come back from iteration n+2 to n.

As someone remarked at some forum (at Physics StackExchange or Quora or so), to learn QM, you have to give it “multiple passes.” Only then can you succeed understanding it. The idea of multiple passes has several implications. Let me mention only two of them. Both are specific to QM (and not to thermodynamics).

First, you have to develop the art of being able to hold some not-fully-satisfactory islands of understanding, with all the accompanying ambiguities, for extended periods of time (which usually runs into years!). You have to learn how to give a second or a third pass even when some of the things right from the first pass are still nowhere near getting clarified. You have to learn a lot of maths on the fly too. However, if you ask me, that’s a relatively easier task. The really difficult part is that you have to know (or learn!) how to keep forging ahead, even if at the same time, you carry a big set of nagging doubts that no one seems to know (or even care) about. (To make the matters worse, professional physicists, mathematicians and philosophers proudly keep telling you that these doubts will remain just as they are for the rest of your life.) You have to learn how to shove these ambiguous and un-clarified matters to some place near the back of your mind, you have to learn how to ignore them for a while, and still find the mental energy to once again begin right from the beginning, for your next pass: Planck and his cavity radiation, Einstein, blah blah blah blah blah!

Second, for the same reason (i.e. the necessity of multiple passes and the nature of QM), you also have to learn how to unlearn certain half-baked ideas and replace them later on with better ones. For a good example, go through Dan Styer’s paper on misconceptions about QM (listed near the end of this post).

Thus, two seemingly contradictory skills come into the play: You have to learn how to hold ambiguities without letting them affect your studies. At the same time, you also have to learn how not to hold on to them forever, or how to unlearn them, when the time to do becomes ripe.

Thus, learning QM does not involve just learning of new contents. You also have learn this art of building a sufficiently “temporary” but very complex conceptual structure in your mind—a structure that, despite all its complexity, still is resilient. You have to learn the art of holding such a framework together over a period of years, even as some parts of it are still getting replaced in your subsequent passes.

And, you have to compensate for all the failings of your teachers too (who themselves were told, effectively, to “shut up and calculate!”) Properly learning QM is a demanding enterprise.


II. The list:

Now, with that long a preface, let me come to listing all the main books that I found especially helpful during my various passes. Please remember, I am still learning QM. I still don’t understand the second half of most any UG book on QM. This is a factual statement. I am not ashamed of it. It’s just that the first half itself managed to keep me so busy for so long that I could not come to studying, in an in-depth manner, the second half. (By the second half, I mean things like: the QM of molecules and binding, of their spectra, QM of solids, QM of complicated light-matter interactions, computational techniques like DFT, etc.) … OK. So, without any further ado, let me jot down the actual list.  I will subdivide it in several sub-sections


II.0. Junior-college (American high-school) level:

Obvious:

  • Resnick and Halliday.
  • Thomas and Finney. Also, Allan Jeffrey

II.1. Initial, college physics level:

  • “Modern physics” by Beiser, or equivalent
  • Optional but truly helpful: “Physical chemistry” by Atkins, or equivalent, i.e., only the parts relevant to QM. (I know engineers often tend to ignore the chemistry books, but they should not. In my experience, often times, chemistry books do a superior job of explaining physics. Physics, to paraphrase a witticism, is far too important to be left to the physicists!)

II.2. Preparatory material for some select topics:

  • “Physics of waves” by Howard Georgi. Excellence written all over, but precisely for the same reason, take care to avoid the temptation to get stuck in it!
  • Maths: No particular book, but a representative one would be Kreyszig, i.e., with Thomas and Finney or Allan Jeffrey still within easy reach.
    • There are a few things you have to relearn, if necessary. These include: the idea of the limits of sequences and series. (Yes, go through this simple a topic too, once again. I mean it!). Then, the limits of functions.
      Also try to relearn curve-tracing.
    • Unlearn (or throw away) all the accounts of complex numbers which remain stuck at the level of how \sqrt{-1} was stupefying, and how, when you have complex numbers, any arbitrary equation magically comes to have roots, etc. Unlearn all that talk. Instead, focus on the similarities of complex numbers to both the real numbers and vectors, and also their differences from each. Unlike what mathematicians love to tell you, complex numbers are not just another kind of numbers. They don’t represent just the next step in the logic of how the idea of numbers gets generalized as go from integers to real numbers. The reason is this: Unlike the integers, rationals, irrationals and reals, complex numbers take birth as composite numbers (as a pair of numbers that is ordered too), and they remain that way until the end of their life. Get that part right, and ignore all the mathematicians’ loose talk about it.
      Study complex numbers in a way that, eventually, you should find yourself being comfortable with the two equivalent ways of modeling physical phenomena: as a set of two coupled real-valued differential equations, and as a single but complex-valued differential equation.
    • Also try to become proficient with the two main expansions: the Taylor, and the Fourier.
    • Also develop a habit of quickly substituting truncated expansions (i.e., either a polynomial, or a sum complex exponentials having just a few initial harmonics, not an entire infinity of them) into any “arbitrary” function as an ansatz, and see how the proposed theory pans out with these. The goal is to become comfortable, at the same time, with a habit of tracing conceptual pathways to the meaning of maths as well as with the computational techniques of FDM, FEM, and FFT.
    • The finite differences approximation: Also, learn the art of quickly substituting the finite differences (\Delta‘s) in place of the differential quantities (d or \partial) in a differential equation, and seeing how it pans out. The idea here is not just the computational modeling. The point is: Every differential equation has been derived in reference to an elemental volume which was then taken to a vanishingly small size. The variation of quantities of interest across such (infinitesimally small) volume are always represented using the Taylor series expansion.
      (That’s correct! It is true that the derivations using the variational approach don’t refer to the Taylor expansion. But they also don’t use infinitesimal volumes; they refer to finite or infinite domains. It is the variation in functions which is taken to the vanishingly small limit in their case. In any case, if your derivation has an infinitesimall small element, bingo, you are going to use the Taylor series.)
      Now, coming back to why you must learn develop the habit of having a finite differences approximation in place of a differential equation. The thing is this: By doing so, you are unpacking the derivation; you are traversing the analysis in the reverse direction, you are by the logic of the procedure forced to look for the physical (or at least lower-level, less abstract) referents of a mathematical relation/idea/concept.
      While thus going back and forth between the finite differences and the differentials, also learn the art of tracing how the limiting process proceeds in each such a case. This part is not at all as obvious as you might think. It took me years and years to figure out that there can be infinitesimals within infinitesimals. (In fact, I have blogged about it several years ago here. More recently, I wrote a PDF document about how many numbers are there in the real number system, which discusses the same idea, from a different angle. In any case, if you were not shocked by the fact that there can be an infinity of infinitesimals within any infinitesimal, either think sufficiently long about it—or quit studying foundations of QM.)

II.3. Quantum chemistry level (mostly concerned with only the TISE, not TDSE):

  • Optional: “QM: a conceptual approach” by Hameka. A fairly well-written book. You can pick it up for some serious reading, but also try to finish it as fast as you can, because you are going to relean the same stuff once again through the next book in the sequence. But yes, you can pick it up; it’s only about 200 pages.
  • “Quantum chemistry” by McQuarrie. Never commit the sin of bypassing this excellent book.
    Summarily ignore your friend (who might have advised you Feynman vol. 3 or Susskind’s theoretical minimum or something similar). Instead, follow my advice!
    A suggestion: Once you finish reading through this particular book, take a small (40 page) notebook, and write down (in the long hand) just the titles of the sections of each chapter of this book, followed by a listing of the important concepts / equations / proofs introduced in it. … You see, the section titles of this book themselves are complete sentences that encapsulate very neat nuggets. Here are a couple of examples: “5.6: The harmonic oscillator accounts for the infrared spectrum of a diatomic molecule.” Yes, that’s a section title! Here is another: “6.2: If a Hamiltonian is separable, then its eigenfunctions are products of simpler eigenfunctions.” See why I recommend this book? And this (40 page notebook) way of studying it?
  • “Quantum physics of atoms, molecules, solids, nuclei, and particles” (yes, that’s the title of this single volume!) by Eisberg and Resnick. This Resnick is the same one as that of Resnick and Halliday. Going through the same topics via yet another thick book (almost 850 pages) can get exasperating, at least at times. But guess if you show some patience here, it should simplify things later. …. Confession: I was too busy with teaching and learning engineering topics like FEM, CFD, and also with many other things in between. So, I could not find the time to read this book the way I would have liked to. But from whatever I did read (and I did go over a fairly good portion of it), I can tell you that not finishing this book was a mistake on my part. Don’t repeat my mistake. Further, I do keep going back to it, and may be as a result, I would one day have finished it! One more point. This book is more than quantum chemistry; it does discuss the time-dependent parts too. The only reason I include it in this sub-section (chemistry) rather than the next (physics) is because the emphasis here is much more on TISE than TDSE.

II.4. Quantum physics level (includes TDSE):

  • “Quantum physics” by Alastair I. M. Rae. Hands down, the best book in its class. To my mind, it easily beats all of the following: Griffiths, Gasiorowicz, Feynman, Susskind, … .
    Oh, BTW, this is the only book I have ever come across which does not put scare-quotes around the word “derivation,” while describing the original development of the Schrodinger equation. In fact, this text goes one step ahead and explicitly notes the right idea, viz., that Schrodinger’s development is a derivation, but it is an inductive derivation, not deductive. (… Oh God, these modern American professors of physics!)
    But even leaving this one (arguably “small”) detail aside, the book has excellence written all over it. Far better than the competition.
    Another attraction: The author touches upon all the standard topics within just about 225 pages. (He also has further 3 chapters, one each on relativity and QM, quantum information, and conceptual problems with QM. However, I have mostly ignored these.) When a book is of manageable size, it by itself is an overload reducer. (This post is not a portion from a text-book!)
    The only “drawback” of this book is that, like many British authors, Rae has a tendency to seamlessly bunch together a lot of different points into a single, bigger, paragraph. He does not isolate the points sufficiently well. So, you have to write a lot of margin notes identifying those distinct, sub-paragraph level, points. (But one advantage here is that this procedure is very effective in keeping you glued to the book!)
  • “Quantum physics” by Griffiths. Oh yes, Griffiths is on my list too. It’s just that I find it far better to go through Rae first, and only then come to going through Griffiths.
  • … Also, avoid the temptation to read both these books side-by-side. You will soon find that you can’t do that. And so, driven by what other people say, you will soon end up ditching Rae—which would be a grave mistake. Since you can keep going through only one of them, you have to jettison the other. Here, I would advise you to first complete Rae. It’s indispensable. Griffiths is good too. But it is not indispensable. And as always, if you find the time and the inclination, you can always come back to Griffiths.

II.5. Side reading:

Starting sometime after finishing the initial UG quantum chemistry level books, but preferably after the quantum physics books, use the following two:

  • “Foundations of quantum mechanics” by Travis Norsen. Very, very good. See my “review” here [^]
  • “Foundations of quantum mechanics: from photons to quantum computers” by Reinhold Blumel.
    Just because people don’t rave a lot about this book doesn’t mean that it is average. This book is peculiar. It does look very average if you flip through all its pages within, say, 2–3 minutes. But it turns out to be an extraordinarily well written book once you begin to actually read through its contents. The coverage here is concise, accurate, fairly comprehensive, and, as a distinctive feature, it also is fairly up-to-date.
    Unlike the other text-books, Blumel gives you a good background in the specifics of the modern topics as well. So, once you complete this book, you should find it easy (to very easy) to understand today’s pop-sci articles, say those on quantum computers. To my knowledge, this is the only text-book which does this job (of introducing you to the topics that are relevant to today’s research), and it does this job exceedingly well.
  • Use Blumel to understand the specifics, and use Norsen to understand their conceptual and the philosophical underpinnings.

II.Appendix: Miscellaneous—no levels specified; figure out as you go along:

  • “Schrodinger’s cat” by John Gribbin. Unquestionably, the best pop-sci book on QM. Lights your fire.
  • “Quantum” by Manjit Kumar. Helps keep the fire going.
  • Kreyszig or equivalent. You need to master the basic ideas of the Fourier theory, and of solutions of PDEs via the separation ansatz.
  • However, for many other topics like spherical harmonics or calculus of variations, you have to go hunting for explanations in some additional books. I “learnt” the spherical harmonics mostly through some online notes (esp. those by Michael Fowler of Univ. of Virginia) and QM textbooks, but I guess that a neat exposition of the topic, couched in contexts other than QM, would have been helpful. May be there is some ancient acoustics book that is really helpful. Anyway, I didn’t pursue this topic to any great depth (in fact I more or less skipped over it) because as it so happens, analytical methods fall short for anything more complex than the hydrogenic atoms.
  • As to the variational calculus, avoid all the physics and maths books like a plague! Instead, learn the topic through the FEM books. Introductory FEM books have become vastly (i.e. categorically) better over the course of my generation. Today’s FEM text-books do provide a clear evidence that the authors themselves know what they are talking about! Among these books, just for learning the variational calculus aspects, I would advise going through Seshu or Fish and Belytschko first, and then through the relevant chapter from Reddy‘s book on FEM. In any case, avoid Bathe, Zienkiewicz, etc.; they are too heavily engineering-oriented, and often, in general, un-necessarily heavy-duty (though not as heavy-duty as Lancosz). Not very suitable for learning the basics of CoV as is required in the UG QM. A good supplementary book covering CoV is noted next.
  • “From calculus to chaos: an introduction to dynamics” by David Acheson. A gem of a book. Small (just about 260 pages, including program listings—and just about 190 pages if you ignore them.) Excellent, even if, somehow, it does not appear on people’s lists. But if you ask me, this book is a must read for any one who has anything to do with physics or engineering. Useful chapters exist also on variational calculus and chaos. Comes with easy to understand QBasic programs (and their updated versions, ready to run on today’s computers, are available via the author’s Web site). Wish it also had chapters, say one each, on the mechanics of materials, and on fracture mechanics.
  • Linear algebra. Here, keep your focus on understanding just the two concepts: (i) vector spaces, and (ii) eigen-vectors and -values. Don’t worry about other topics (like LU decomposition or the power method). If you understand these two topics right, the rest will follow “automatically,” more or less. To learn these two topics, however, don’t refer to text-books (not even those by Gilbert Strang or so). Instead, google on the online tutorials on computer games programming. This way, you will come to develop a far better (even robust) understanding of these concepts. … Yes, that’s right. One or two games programmers, I very definitely remember, actually did a much superior job of explaining these ideas (with all their complexity) than what any textbook by any university professor does. (iii) Oh yes, BTW, there is yet another concept which you should learn: “tensor product”. For this topic, I recommend Prof. Zhigang Suo‘s notes on linear algebra, available off iMechanica. These notes are a work in progress, but they are already excellent even in their present form.
  • Probability. Contrary to a wide-spread impression (and to what one group of QM interpreters say), you actually don’t need much of statistics or probability in order to get the essence of QM right. Whatever you need has already been taught to you in your UG engineering/physics courses.Personally, though I haven’t yet gone through them, the two books on my radar (more from the data science angle) are: “Elementary probability” by Stirzaker, and “All of statistics” by Wasserman. But, frankly speaking, as far as QM itself is concerned, your intuitive understanding of probability as developed through your routine UG courses should be enough, IMHO.
  • As to AJP type of articles, go through Dan Styer‘s paper on the nine formulations (doi:10.1119/1.1445404). But treat his paper on the common misconceptions (10.1119/1.18288) with a bit of caution; some of the ideas he lists as “misconceptions” are not necessarily so.
  • arXiv tutorials/articles: Sometime after finishing quantum chemistry and before beginning quantum physics, go through the tutorial on QM by Bram Gaasbeek [^]. Neat, small, and really helpful for self-studies of QM. (It was written when the author was still a student himself.) Also, see the article on the postulates by Dorabantu [^]. Definitely helpful. Finally, let me pick up just one more arXiv article: “Entanglement isn’t just for spin” by Dan Schroeder [^]. Comes with neat visualizations, and helps demystify entanglement.
  • Computational physics: Several good resources are available. One easy to recommend text-book is the one by Landau, Perez and Bordeianu. Among the online resources, the best collection I found was the one by Ian Cooper (of Univ. of Sydney) [^]. He has only MatLab scripts, not Python, but they all are very well documented (in an exemplary manner) via accompanying PDF files. It should be easy to port these programs to the Python eco-system.

Yes, we (finally) are near the end of this post, so let me add the mandatory catch-all clauses: This list is by no means comprehensive! This list supersedes any other list I may have put out in the past. This list may undergo changes in future.

Done.

OK. A couple of last minute addenda: For contrast, see the article “What is the best textbook for self-studying quantum mechanics?” which has appeared, of all places, on the Forbes!  [^]. (Looks like the QC-related hype has found its way into the business circles as well!) Also see the list at BookScrolling.com: “The best books to learn about quantum physics” [^].

OK. Now, I am really done.


A song I like:
(Marathi) “kiteedaa navyaane tulaa aaThavaave”
Music: Mandar Apte
Singer: Mandar Apte. Also, a separate female version by Arya Ambekar
Lyrics: Devayani Karve-Kothari

[Arya Ambekar’s version is great too, but somehow, I like Mandar Apte’s version better. Of course, I do often listen to both the versions. Excellent.]


[Almost 5000 More than 5,500 words! Give me a longer break for this time around, a much longer one, in fact… In the meanwhile, take care and bye until then…]

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Would it happen to me, too? …Also, other interesting stories / links

1. Would it happen to me, too?

“My Grandfather Thought He Solved a Cosmic Mystery,”

reports Veronique Greenwood for The Atlantic [^] [h/t the CalTech physicist Sean Carroll’s twitter feed]. The story has the subtitle:

“His career as an eminent physicist was derailed by an obsession. Was he a genius or a crackpot?”

If you visit the URL for this story, the actual HTML page which loads into your browser has another title, similar to the one above:

“Science Is Full of Mavericks Like My Grandfather. But Was His Physics Theory Right?”

Hmmm…. I immediately got interested. After all, I do work also on foundations of quantum mechanics. … “Will it happpen to me, too?” I thought.

At this point, you should really go through Greenwood’s article, and continue reading here only after you have finished reading it.


Any one who has worked on any conceptually new approach would find something in Greenwood’s article that resonates with him.

As to me, well, right at the time that attempts were being made to find examiners for my PhD, my guide (and even I) had heard a lot of people say very similar things as Greenwood now reports: “I don’t understand what you are saying, so please excuse me.” This, when I thought that my argument should be accessible even to an undergraduate in engineering!

And now that I continue working on the foundations of QM, having developed a further, completely new (and more comprehensive) approach, naturally, Greenwood’s article got me thinking: “Would it happen to me, too? Once again? What if it does?”


…Naah, it wouldn’t happen to me—that was my conclusion. Not even if I continue talking about, you know, QM!


But why wouldn’t something similar happen to me? Especially given the fact that a good part of it has already happened to me in the past?

The reason, in essence, is simple.

I am not just a physicist—not primarily, anyway. I am primarily an engineer, a computational modeller. That’s why, things are going to work out in a different way for me.

As to my past experience: Well, I still earned my PhD degree. And with it, the most critical part of the battle is already behind me. There is a lot of resistance to your acceptance before you have a PhD. Things do become a lot easier once you have gone successfully past it. That’s another reason why things are going to work out in a different way now. … Let me explain in detail.


I mean to say, suppose that I have a brand-new approach for resolving all the essential quantum mechanical riddles. [I think I actually do!]

Suppose that I try to arrange for a seminar to be delivered by me to a few physics professors and students, say at an IIT, IISER, or so. [I actually did!]

Suppose that they don’t respond very favorably or very enthusiastically. Suppose they are outright skeptical when I say that in principle, it is possible to think of a classical mechanically functioning analog simulator which essentially exhibits all the essential quantum mechanical features. Suppose that they get stuck right at that point—may be because they honestly and sincerely believe that no classical system can ever simulate the very quantum-ness of QM. And so, short of calling me a crack-pot or so, they just directly (almost sternly) issue the warning that there are a lot of arguments against a classical system reproducing the quantum features. [That’s what has actually happened; that’s what one of the physics professors I contacted wrote back to me.]

Suppose, then, that I send an abstract to an international conference or so. [This too has actually happend, too, recently.]

Suppose that, in the near future, the conference organizers too decline my submission. [In actual reality, I still don’t know anything about the status of my submission. It was in my routine searches that I came across this conference, and noticed that I did have about 4–5 hours’ time to meet the abstracts submissions deadline. I managed to submit my abstract within time. But since then, the conference Web site has not got updated. There is no indication from the organizers as to when the acceptance or rejection of the submitted abstracts would be communicated to the authors. An enquiry email I wrote to the organizers has gone unanswered for more than a week by now. Thus, the matter is still open. But, just for the sake of the argument, suppose that they end up rejecting my abstract. Suppose that’s what actually happens.]

So what?

Since I am not a physicist “proper”, it wouldn’t affect me the way it might have, if I were to be one.

… And, that way, I could even say that I am far too smart to let something like that (I mean some deep disappointment or something like that) happen to me! … No, seriously! Let me show you how.

Suppose that the abstract I sent to an upcoming conference was written in theoretical/conceptual terms. [In actual reality, it was.]

Suppose now that it therefore gets rejected.

So what?

I would simply build a computational model based on my ideas. … Here, remember, I have already begun “talking things” about it [^]. No one has come up with a strong objection so far. (May be because they know the sort of a guy I am.)

So, if my proposed abstract gets rejected, what I would do is to simply go ahead and perform a computer simulation of a classical system of this sort (one which, in turn, simulates the QM phenomena). I might even publish a paper or two about it—putting the whole thing in purely classical terms, so that I manage to get it published. (Before doing that, I might even discuss the technical issues involved on blogs, possibly even at iMechanica!)

After such a paper (ostensibly only on the classical mechanics) gets accepted and published, I will simply write a blog post, either here or at iMechanica, noting how that system actually simulates the so-and-so quantum mechanical feature. … Then, I would perform another simulation—say using DFT. (And it is mainly for DFT that I would need help from iMechanicians or so.) After it too gets accepted and published, I will write yet another blog post, explaining how it does show some quantum mechanical-ness. … Who knows such a sequence could continue…

But such a series (of the simulations) wouldn’t be very long, either! The thing is this.

If your idea does indeed simplify certain matters, then you don’t have to argue a lot about it—people can see its truth real fast. Especially if it has to do with “hard” sciences like engineering—even physics!

If your basic idea itself isn’t so good, then, putting it in the engineering terms makes it more likely that even if you fail to get the weakness of your theory, someone else would. All in all, well and good for you.

As to the other possibility, namely, if your idea is good, but, despite putting it in the simpler terms (say in engineering or simulation terms), people still fail to see it, then, well, so long as your job (or money-making potential) itself is not endangered, then I think that it is a good policy to leave the mankind to its own follies. It is not your job to save the world, said Ayn Rand. Here, I believe her. (In fact, I believed in this insight even before I had ever run into Ayn Rand.)


As to the philosophic issues such as those involved in the foundations of QM—well, these are best tackled philosophically, not physics-wise. I wouldn’t use a physics-based argument to take a philosophic argument forward. Neither would I use a philosophical argument to take a physics-argument forward. The concerns and the methods of each are distinctly different, I have come to learn over a period of years.

Yes, you can use a physics situation as being illustrative of a philosophic point. But an illustration is not an argument; it is merely a device to make understanding easier. Similarly, you could try to invoke a philosophic point (say an epistemological point) to win a physics-based argument. But your effort would be futile. Philosophic ideas are so abstract that they can often be made to fit several different, competing, physics-related arguments. I would try to avoid both these errors.

But yes, as a matter of fact, certain issues that can only be described as philosophic ones, do happen to get involved when it comes to the area of the foundations of QM.

Now, here, given the nature of philosophy, and of its typical practitioners today (including those physicists who do dabble in philosophy), even if I become satisfied that I have resolved all the essential QM riddles, I still wouldn’t expect these philosophers to accept my ideas—not immediately anyway. In fact, as I anticipate things, philosophers, taken as a group, would never come to accept my position, I think. Such an happenstance is not necessarily to be ascribed to the personal failings of the individual philosophers (even if a lot of them actually do happen to be world-class stupid). That’s just how philosophy (as a discipline of studies) itself is like. A philosophy is a comprehensive view of existence—whether realistic or otherwise. That’s why it’s futile to expect that all of the philosophers would come to agree with you!

But yes, I would expect them to get the essence of my argument. And, many of them would, actually, get my argument, its logic—this part, I am quite sure of. But just the fact that they do understand my argument would not necessarily lead them to accept my positions, especially the idea that all the QM riddles are thereby resolved. That’s what I think.


Similarly, there also are a lot of mathematicians who dabble in the area of foundations of QM. What I said for philosophers also applies more or less equally well to them. They too would get my ideas immediately. But they too wouldn’t, therefore, come to accept my positions. Not immediately anyway. And in all probability, never ever in my lifetime or theirs.


So, there. Since I don’t expect an overwhelming acceptance of my ideas in the first place, there isn’t going to be any great disappointment either. The very expectations do differ.

Further, I must say this: I would never ever be able to rely on a purely abstract argument. That would feel like too dicey or flimsy to me. I would have to offer my arguments in terms of physically existing things, even if of a brand new kind. And, machines built out of them. At least, some working simulations. I would have to have these. I would not be able to rest on an abstract argument alone. To be satisfactory to me, I would have to actually build a machine—a soft machine—that works. And, doing just this part itself is going to be far more than enough to keep me happy. They don’t have to accept the conceptual arguments or the theory that goes with the design of such (soft) machines. It is enough that I play with my toys. And that’s another reason why I am not likely to derive a very deep sense of disenchantment or disappointment.


But if you ask me, the way I really, really like think about it is this:

If they decline my submission to the conference, I will write a paper about it, and send it, may be, to Sean Carroll or Sabine Hosenfelder or so. … The way I imagine things, he is then going to immediately translate my paper into German, add his own name to ensure its timely publication, and … . OK, you get the idea.

[In the interests of making this post completely idiot-proof, let me add: Here, in this sub-section, I was just kidding.]


2. The problem with the Many Worlds:

“Why the Many Worlds interpretation has many problems.”

Philip Ball argues in an article for the Quanta Mag [^] to the effect that many worlds means no world at all.

No, this is not exactly what he says. But what he says is clear enough that it is this conclusion which becomes inescapable.

As to what he actually says: Well, here is a passage, for instance:

“My own view is that the problems with the MWI are overwhelming—not because they show it must be wrong, but because they render it incoherent. It simply cannot be articulated meaningfully.”

In other words, Ball’s actual position is on the epistemic side, not on the ontic. However, his arguments are clear enough (and they often enough touch on issues that are fundamental enough) that the ontological implications of what he actually says, also become inescapable. OK, sometimes, the article unnecessarily takes detours into non-essentials, even into something like polemics. Still, overall, the write up is very good. Recommended very strongly.

Homework for you: If the Many Worlds idea is that bad, then explain why it might be that many otherwise reasonable people (for instance, Sean Carroll) do find the Many Worlds approach attractive. [No cheating. Think on your own and write. But if cheating is what you must do, then check out my past comment at some blog—I no longer remember where I wrote it, but probably it was on Roger Schlafly’s blog. My comment had tackled precisely this latter issue, in essential terms. Hints for your search: My comment had spoken about data structures like call-stacks and trees, and their unfolding.]


3. QM as an embarrassment to science:

“Why quantum mechanics is an “embarrassment” to science”

Brad Plumer in his brief note at the Washington Post [^] provides a link to a video by Sean Carroll.

Carroll is an effective communicator.

[Yes, he is the same one who I imagine is going to translate my article into German and… [Once again, to make this post idiot-proof: I was just kidding.]]


4. Growing younger…

I happened to take up a re-reading of David Ruelle’s book: “Chance and Chaos”. The last time I read it was in the early 1990s.

I felt younger! … May be if something strikes me while I am going through it after a gap of decades, I will come back and note it here.


5. Good introductory resources on nonlinear dynamics, catastrophe theory, and chaos theory:

If you are interested in the area of nonlinear dynamics, catastrophe theory and chaos theory, here are a few great resources:

  • For a long time, the best introduction to the topic was a brief write-up by Prof. Harrison of UToronto; it still remains one of the best [^].
  • Prof. Zeeman’s 1976 article for SciAm on the catastrophe theory is a classic. Prof. Zhigang Suo (of Harvard) has written a blog post of title “Recipe for catastrophe”at iMechanica [^], in which he helpfully provides a copy of Zeeman’s article. I have strongly recommended Zeeman’s write-up before, and I strongly recommend it once again. Go through it even if only to learn how to write for the layman and still not lose precision or quality.
  • As to a more recent introductory expositions, do see Prof. Geoff Boeing’s blog post: “Chaos theory and the logistic map” [^]. Boeing is a professor of urban planning, and not of engineering, physics, CS, or maths. But it is he who gives the clearest idea about the distinction between randomness and chaos that I have ever run into. (However, I only later gathered that he does have a UG in CS, and a PG in Information Management.) Easy to understand. Well ordered. Overall, very highly recommended.

Apart from it all:

Happy Diwali!


A song I like:

(Hindi) “tere humsafar geet hai tere…”
Music: R. D. Burman
Singers: Kishore Kumar, Mukesh, Asha Bhosale
Lyrics: Majrooh Sultanpuri

[Has this song been lifted from some Western song? At least inspired from one?

Here are the reasons for this suspicion: (1) It has a Western-sounding tune. It doesn’t sound Indian. There is no obvious basis either in the “raag-daari,” or in the Indian folk music. (ii) There are (beautiful) changes in the chords here. But there is no concept of chords in the traditional Indian music—basically, there is no concept of harmony in it, only of melody. (iii) Presence of “yoddling” (if that’s the right word for it). That too, by a female singer. That too, in the early 1970’s! Despite all  the “taan”s and “firat”s and all that, this sort of a thing (let’s call it yoddling) has never been a part of the traditional Indian music.

Chances are good that some of the notes were (perhaps very subconsciously) inspired from a Western tune. For instance, I can faintly hear “jingle bells” in the refrain. … But the question is: is there a more direct correspondence to a Western tune, or not.

And, if it was not lifted or inspired from a Western song, then it’s nothing but a work of an absolute genius. RD anyway was one—whether this particular song was inspired from some other song, or not.

But yes, I liked this song a great deal as a school-boy. It happened to strike me once again only recently (within the last couple of weeks or so). I found that I still love it just as much, if not more.]


[As usual, may be I will come back tomorrow or so, and edit/streamline this post a bit. One update done on 2018.11.04 08:26 IST. A second update done on 2018.11.04 21:01 IST. I will now leave this post in whatever shape it is in. Got to move on to trying out a few things in Python and all. Will keep you informed, probably after Diwali. In the meanwhile, take care and bye for now…]

Blog-Filling—Part 3

Note: A long Update was added on 23 November 2017, at the end of the post.


Today I got just a little bit of respite from what has been a very tight schedule, which has been running into my weekends, too.

But at least for today, I do have a bit of a respite. So, I could at least think of posting something.

But for precisely the same reason, I don’t have any blogging material ready in the mind. So, I will just note something interesting that passed by me recently:

  1. Catastrophe Theory: Check out Prof. Zhigang Suo’s recent blog post at iMechanica on catastrophe theory, here [^]; it’s marked by Suo’s trademark simplicity. He also helpfully provides a copy of Zeeman’s 1976 SciAm article, too. Regular readers of this blog will know that I am a big fan of the catastrophe theory; see, for instance, my last post mentioning the topic, here [^].
  2. Computational Science and Engineering, and Python: If you are into computational science and engineering (which is The Proper And The Only Proper long-form of “CSE”), and wish to have fun with Python, then check out Prof. Hans Petter Langtangen’s excellent books, all under Open Source. Especially recommended is his “Finite Difference Computing with PDEs—A Modern Software Approach” [^]. What impressed me immediately was the way the author begins this book with the wave equation, and not with the diffusion or potential equation as is the routine practice in the FDM (or CSE) books. He also provides the detailed mathematical reason for his unusual choice of ordering the material, but apart from his reason(s), let me add in a comment here: wave \Rightarrow diffusion \Rightarrow potential (Poisson-Laplace) precisely was the historical order in which the maths of PDEs (by which I mean both the formulations of the equations and the techniques for their solutions) got developed—even though the modern trend is to reverse this order in the name of “simplicity.” The book comes with Python scripts; you don’t have to copy-paste code from the PDF (and then keep correcting the errors of characters or indentations). And, the book covers nonlinearity too.
  3. Good Notes/Teachings/Explanations of UG Quantum Physics: I ran across Dan Schroeder’s “Entanglement isn’t just for spin.” Very true. And it needed to be said [^]. BTW, if you want a more gentle introduction to the UG-level QM than is presented in Allan Adam (et al)’s MIT OCW 8.04–8.06 [^], then make sure to check out Schroeder’s course at Weber [^] too. … Personally, though, I keep on fantasizing about going through all the videos of Adam’s course and taking out notes and posting them at my Web site. [… sigh]
  4. The Supposed Spirituality of the “Quantum Information” Stored in the “Protein-Based Micro-Tubules”: OTOH, if you are more into philosophy of quantum mechanics, then do check out Roger Schlafly’s latest post, not to mention my comment on it, here [^].

The point no. 4. above was added in lieu of the usual “A Song I Like” section. The reason is, though I could squeeze in the time to write this post, I still remain far too rushed to think of a song—and to think/check if I have already run it here or not. But I will try add one later on, either to this post, or, if there is a big delay, then as the next “blog filler” post, the next time round.

[Update on 23 Nov. 2017 09:25 AM IST: Added the Song I Like section; see below]

OK, that’s it! … Will catch you at some indefinite time in future here, bye for now and take care…


A Song I Like:

(Western, Instrumental) “Theme from ‘Come September'”
Credits: Bobby Darin (?) [+ Billy Vaughn (?)]

[I grew up in what were absolutely rural areas in Maharashtra, India. All my initial years till my 9th standard were limited, at its upper end in the continuum of urbanity, to Shirpur, which still is only a taluka place. And, back then, it was a decidedly far more of a backward + adivasi region. The population of the main town itself hadn’t reached more than 15,000 or so by the time I left it in my X standard; the town didn’t have a single traffic light; most of the houses including the one we lived in) were load-bearing structures, not RCC; all the roads in the town were of single lanes; etc.

Even that being the case, I happened to listen to this song—a Western song—right when I was in Shirpur, in my 2nd/3rd standard. I first heard the song at my Mama’s place (an engineer, he was back then posted in the “big city” of the nearby Jalgaon, a district place).

As to this song, as soon as I listened to it, I was “into it.” I remained so for all the days of that vacation at Mama’s place. Yes, it was a 45 RPM record, and the permission to put the record on the player and even to play it, entirely on my own, was hard won after a determined and tedious effort to show all the elders that I was able to put the pin on to the record very carefully. And, every one in the house was an elder to me: my siblings, cousins, uncle, his wife, not to mention my parents (who were the last ones to be satisfied). But once the recognition arrived, I used it to the hilt; I must have ended up playing this record for at least 5 times for every remaining day of the vacation back then.

As far as I am concerned, I am entirely positive that appreciation for a certain style or kind of music isn’t determined by your environment or the specific culture in which you grow up.

As far as songs like these are concerned, today I am able to discern that what I had immediately though indirectly grasped, even as a 6–7 year old child, was what I today would describe as a certain kind of an “epistemological cleanliness.” There was a clear adherence to certain definitive, delimited kind of specifics, whether in terms of tones or rhythm. Now, it sure did help that this tune was happy. But frankly, I am certain, I would’ve liked a “clean” song like this one—one with very definite “separations”/”delineations” in its phrases, in its parts—even if the song itself weren’t to be so directly evocative of such frankly happy a mood. Indian music, in contrast, tends to keep “continuity” for its own sake, even when it’s not called for, and the certain downside of that style is that it leads to a badly mixed up “curry” of indefinitely stretched out weilings, even noise, very proudly passing as “music”. (In evidence: pick up any traditional “royal palace”/”kothaa” music.) … Yes, of course, there is a symmetrical downside to the specific “separated” style carried by the Western music too; the specific style of noise it can easily slip into is a disjointed kind of a noise. (In evidence, I offer 90% of Western classical music, and 99.99% of Western popular “music”. As to which 90%, well, we have to meet in person, and listen to select pieces of music on the fly.)

Anyway, coming back to the present song, today I searched for the original soundtrack of “Come September”, and got, say, this one [^]. However, I am not too sure that the version I heard back then was this one. Chances are much brighter that the version I first listened to was Billy Vaughn’s, as in here [^].

… A wonderful tune, and, as an added bonus, it never does fail to take me back to my “salad days.” …

… Oh yes, as another fond memory: that vacation also was the very first time that I came to wear a T-shirt; my Mama had gifted it to me in that vacation. The actual choice to buy a T-shirt rather than a shirt (+shorts, of course) was that of my cousin sister (who unfortunately is no more). But I distinctly remember she being surprised to learn that I was in no mood to have a T-shirt when I didn’t know what the word meant… I also distinctly remember her assuring me using sweet tones that a T-shirt would look good on me! … You see, in rural India, at least back then, T-shirts weren’t heard of; for years later on, may be until I went to Nasik in my 10th standard, it would be the only T-shirt I had ever worn. … But, anyway, as far as T-shirts go… well, as you know, I was into software engineering, and so….

Bye [really] for now and take care…]

 

A prediction. Also, a couple of wishes…

The Prediction:

While the week of the Nobel prizes always has a way to generate a sense of suspense, of excitement, and even of wonderment, as far as I am concerned, the one prize that does that in the real sense to me is, of course, the Physics Nobel. … Nothing compares to it. Chemistry can come close, but not always. [And, Mr. Nobel was a good guy; he instituted no prize for maths! [LOL!]]. …

The Physics Nobel is the King of all awards in all fields, as far as I am concerned.

That’s why, this year, I have this feeling of missing something. … The reason is, this year’s Physics Nobel is already “known”; it will go to Kip Thorne and pals.

[I will not eat crow even if they don’t get it. [… Unless, of course, you know a delicious recipe or two for the same, and also demonstrate it to me, complete with you sampling it first.]]

But yes, Kip Thorne richly deserves it, and he will get it. That’s the prediction. I wanted to slip it in even if only few hours before the announcement arrives.

I will update this post later right today/tonight, after the Physics Nobel is actually announced.


Now let me come to the couple of wishes, as mentioned in the title. I will try to be brief. [Have been too busy these days… OK. Will let you know. We are going in for accreditation, and so, it’s been all heavy documentation-related work for the past few months. Despite all that hard-work, we still have managed to slip a bit on the progress, and so, currently, we are working on all week-ends and on most public holidays, too. [Yes, we came to work yesterday.] So, it’s only somehow that I manage to find some time to slip in this post—which is written absolutely on the fly, with no second thoughts or re-reading before posting. … So excuse me if there is a bit of lack of balance in the presentation, and of course, typos etc.]


Wish # 1:

The first wish is that a Physics Nobel should go, in a combined way, to what actually are two separate, but very intimately related, and two most significant advances in the physical understanding of man: (i) chaos theory (including fractals) and (ii)catastrophe theory.

If you don’t like the idea of two ideas being given a single Nobel, then, well, let me put it this way: the Nobel should be given for achieving the most significant advancements in the field of the differential nonlinearities, for a very substantial progress in the physical understanding of the behaviour of nonlinear physical systems, forging pathways for predictive capacity.

Let me emphasize, this has been one of the most significant advances in physics in the last century. No, saying so is emphatically not a hyperbole.

And, yes, it’s an advance in physics, primarily, and then, also in maths—but only secondarily.

… It’s unfortunate that an advancement which has been this remarkable never did register as such with most of the S&T “manpower”, esp., engineers and practical designers. It’s also unfortunate that the twin advancement arrived on the scene at the time of bad cultural (even epistemological) trends, and so, the advancements got embedded in a fabric of hyperbole, even nonsense.

But regardless of the cultural tones in which the popular presentations of these advancements (esp. of the chaos theory) got couched, taken as a science, the studies of nonlinearity in the physical systems has been a very, very, original, and a very, very creative, advancement. It needs to be recognized as such.

That way, I don’t much care for what it helped produce on the maths side of it. But yes, even a not very extraordinarily talented undergraduate in CS (one with a special interest in deterministic methods in cryptography) would be able to tell you how much light got shone on their discipline because of the catastrophe and chaos theories.

The catastrophe theory has been simply marvellous in one crucial aspect: it actually pushed the boundaries of what is understood by the term: mathematics. The theory has been daring enough to propose, literally for the first time in the entire history of mankind, a well-refined qualitative approach to an infinity of quantitative processes taken as a group.

The distinction between the qualitative and the quantitative had kept philosophers (and laymen) pre-occupied for millenia. But the nonlinear theory has been the first theoretical approach that tells you how to spot and isolate the objective bases for distinguishing what we consider as the qualitative changes.

Remove the understanding given by the nonlinear theory—by the catastrophe-theoretical approach—and, once in the domain of the linear theory, the differences in kind immediately begin to appear as more or less completely arbitrary. There is no place in theory for them—the qualitative distinctions are external to the theory because a linear system always behaves exactly the same with any quantitative changes made, at any scale, to any of the controlling parameters. Since in the linear theory the qualitative changes are not produced from within the theory itself, such distinctions must be imported into it out of some considerations that are in principle external to the theory.

People often confuse such imports with “applications.” No, when it comes to the linear theory, it’s not the considerations of applications which can be said to be driving any divisions of qualitative changes. The qualitative distinctions are basically arbitrary in a linear theory. It is important to realize that that usual question: “Now where do we draw the line?” is basically absolutely superfluous once you are within the domain of the linear systems. There are no objective grounds on the basis of which such distinctions can be made.

Studies of the nonlinear phenomena sure do precede the catastrophe and the chaos theories. Even in the times before these two theories came on the scene, applied physicists would think of certain ideas such as differences of regimes, esp. in the areas like fluid dynamics.

But to understand the illuminating power of the nonlinear theory, just catch hold of an industrial CFD guy (or a good professor of fluid dynamics from a good university [not, you know, from SPPU or similar universities]), and ask him whether there can be any deeper theoretical significance to the procedure of the Buckingham Pi Theorem, to the necessity, in his art (or science) of having to use so many dimensionless numbers. (Every mechanical/allied engineering undergraduate has at least once in life cursed the sheer number of them.) The competent CFD guy (or the good professor) would easily be at a loss. Then, toss a good book on the Catastrophe Theory to him, leave him alone for a couple of weeks or may be a month, return, and raise the same question again. He now may or may not have a very good, “flowy” sort of a verbal answer ready for you. But one look at his face would tell you that it has now begun to reflect a qualitatively different depth of physical understanding even as he tries to tackle that question in his own way. That difference arises only because of the Catastrophe Theory.

As to the Chaos Theory (and I club the fractal theory right in it), more number of people are likely to know about it, and so, I don’t have to wax a lot (whether eloquently or incompetently). But let me tell you one thing.

Feigenbaum’s discovery of the universal constant remains, to my mind, one of the most ingenious advancements in the entire history of physics, even of science. Especially, given the experimental equipment with which he made that discovery—a handheld HP Calculator (not a computer) in the seventies (or may be in the sixties)! … And yes, getting to that universal constant was, if you ask me, an act of discovery, and not of invention. (Invention was very intimately involved in the process; but the overall act and the end-product was one of discovery.)

So, here is a wish that these fundamental studies of the nonlinear systems get their due—the recognition they so well deserve—in the form of a Physics Nobel.

…And, as always, the sooner the better!


Wish # 2:

The second wish I want to put up here is this: I wish there was some commercial/applied artist, well-conversant with the “art” of supplying illustrations for a physics book, who also was available for a long-term project I have in mind.

To share a bit: Years ago (actually, almost two decades ago, in 1998 to be precise), I had made a suggestion that novels by Ayn Rand be put in the form of comics. As far as I was concerned, the idea was novel (i.e. new). I didn’t know at that time that a comics-book version of The Fountainhead had already been conceived of by none other than Ayn Rand herself, and it, in fact, had also been executed. In short, there was a comics-book version of The Fountainhead. … These days, I gather, they are doing something similar for Atlas Shrugged.

If you think about it, my idea was not at all a leap of imagination. Newspapers (even those in India) have been carrying comic strips for decades (right since before my own childhood), and Amar Chitrakatha was coming of age just when I was. (It was founded in 1967 by Mr. Pai.)

Similarly, conceiving of a comics-like book for physics is not at all a very creative act of imagination. In fact, it is not even original. Everyone knows those books by that Japanese linguistics group, the books on topics like the Fourier theory.

So, no claim of originality here.

It’s just that for my new theory of QM, I find that the format of a comics-book would be most suitable. (And what the hell if physicists don’t take me seriously because I put it in this form first. Who cares what they think anyway!)

Indeed, I would even like to write/produce some comics books on maths topics, too. Topics like grads, divs, curls, tensors, etc., eventually. … Guess I will save that part for keeping me preoccupied during my retirement. BTW, my retirement is not all that far away; it’s going to be here pretty soon, right within just five years from now. (Do one thing: Check out what I was writing, say in 2012 on this blog.)

But the one thing I would like write/produce right in the more immediate future is: the comics book on QM, putting forth my new approach.

So, in the closing, here is a request. If you know some artist (or an engineer/physicist with fairly good sketching/computer-drawing skills), and has time at hand, and has the capacity to stay put in a sizeable project, and won’t ask money for it (a fair share in the royalty is a given—provided we manage to find a publisher first, that is), then please do bring this post to his notice.

 


A Song I Like:

And, finally, here is the Marathi song I had promised you the last time round. It’s a fusion of what to my mind is one of the best tunes Shrinivas Khale ever produced, and the best justice to the words and the tunes by the singer. Imagine any one else in her place, and you will immediately come to know what I mean. … Pushpa Pagdhare easily takes this song to the levels of the very best by the best, including Lata Mangeshkar. [Oh yes, BTW, congrats are due to the selection committe of this year’s Lata Mangeshkar award, for selecting Pushpa Pagdhare.]

(Marathi) “yeuni swapnaat maajhyaa…”
Singer: Pushpa Pagdhare
Music: Shrinivas Khale
Lyrics: Devakinandan Saraswat

[PS: Note: I am going to come back and add an update once this year’s Physics Nobel is announced. At that time (or tonight) I will also try to streamline this post.

Then, I will be gone off the blogging for yet another couple of weeks or so—unless it’s a small little “kutty” post of the “Blog-Filler” kind or two.]