Absolutely Random Notings on QM—Part 1: Bohr. And, a bad philosophy making its way into physics with his work, and his academic influence

TL;DR: Go—and keep—away.

I am still firming up my opinions. However, there is never a harm in launching yet another series of posts on a personal blog, is there? So here we go…

Quantum Mechanics began with Planck. But there was no theory of quanta in what Planck had offered.

What Planck had done was to postulate only the existence of the quanta of the energy, in the cavity radiation.

Einstein used this idea to predict the heat capacities of solids—a remarkable work, one that remains underappreciated in both text-books as well as popular science books on QM.

The first pretense at a quantum theory proper came from Bohr.

Bohr was thinking not about the cavity radiations, but about the spectra of the radiations emitted or absorbed by gases.

Matter, esp. gases, following Dalton, …, Einstein, and Perin, were made of distinct atoms. The properties of gases—especially the reason why they emitted or absorbed radiation only at certain distinct frequencies, but not at any other frequencies (including those continuous patches of frequencies in between the experimentally evident sharp peaks)—had to be explained in reference to what the atoms themselves were like. There was no other way out—not yet, not given the sound epistemology in physics of those days.

Thinking up a new universe still was not allowed back then in science let alone in physics. One still had to clearly think about explaining what was given in observations, what was in evidence. Effects still had be related back to causes; outward actions still had to be related back to the character/nature of the entities that thus acted.

The actor, unquestionably by now, was the atom. The effects were the discrete spectra. Not much else was known.

Those were the days were when the best hotels and restaurants in Berlin, London, and New York would have horse-driven buggies ushering in the socially important guests. Buggies still was the latest technology back then. Not many people thus ushered in are remembered today. But Bohr is.

If the atom was the actor, and the effects under study were the discrete spectra, then what was needed to be said, in theory, was something regarding the structure of the atom.

If an imagined entity sheer by its material/chemical type doesn’t do it, then it’s the structure—its shape and size—which must do it.

Back then, this still was regarded as one of the cardinal principles of science, unlike the mindless opposition to the science of Homeopathy today, esp. in the UK. But back then, it was known that one important reason that Calvin gets harassed by the school bully was that not just the sheer size of the latter’s matter but also that the structure of the latter was different. In other words: If you consumed alcohol, you simply didn’t take in so many atoms of carbon as in proportion to so many atoms of hydrogen, etc. You took in a structure, a configuration with which these atoms came in.

However, the trouble back then was, none had have the means to see the atoms.

If by structure you mean the geometrical shape and size, or some patterns of density, then clearly, there was no experimental observations pertaining to the same. The only relevant observation available to people back then was what had already been encapsulated in Rutherford’s model, viz., the incontestable idea that the atomic nucleus had to be massive and dense, occupying a very small space as compared to an atom taken as a whole; the electrons had to carry very little mass in comparison. (The contrast of Rutherford’s model of c. 1911 was to the earlier plum cake model by Thomson.)

Bohr would, therefore, have to start with Rutherford’s model of atoms, and invent some new ideas concerning it, and see if his model was consistent with the known results given by spectroscopic observations.

What Bohr offered was a model for the electrons contained in a nuclear atom.

However, even while differing from the Rutherford’s plum-cake model, Bohr’s model emphatically lacked a theory for the nature of the electrons themselves. This part has been kept underappreciated by the textbook authors and science teachers.

In particular, Bohr’s theory had absolutely no clue as to the process according to which the electrons could, and must, jump in between their stable orbits.

The meat of the matter was worse, far worse: Bohr had explicitly prohibited from pursuing any mechanism or explanation concerning the quantum jumps—an idea which he was the first to propose. [I don’t know of any one else originally but independently proposing the same idea.]

Bohr achieved this objective not through any deployment of the best possible levels of scientific reason but out of his philosophic convictions—the convictions of the more irrational kind. The quantum jumps were obviously not observable, according to him, only their effects were. So, strictly speaking, the quantum jumps couldn’t possibly be a part of his theory—plain and simple!

But then, Bohr in his philosophic enthusiasm didn’t stop just there. He went even further—much further. He fully deployed the powers of his explicit reasoning as well as the weight of his seniority in prohibiting the young physicists from even thinking of—let alone ideating or offering—any mechanism for such quantum jumps.

In other words, Bohr took special efforts to keep the young quantum enthusiasts absolutely and in principle clueless, as far as his quantum jumps were concerned.

Bohr’s theory, in a sense, was in line with the strictest demands of the philosophy of empiricism. Here is how Bohr’s application of this philosophy went:

  1. This electron—it can be measured!—at this energy level, now!
  2. [May be] The same electron, but this energy level, now!
  3. This energy difference, this frequency. Measured! [Thank you experimental spectroscopists; hats off to you, for, you leave Bohr alone!!]
  4. OK. Now, put the above three into a cohesive “theory.” And, BTW, don’t you ever even try to think about anything else!!

Continuing just a bit on the same lines, Bohr sure would have said (quoting Peikoff’s explanation of the philosophy of empiricism):

  1. [Looking at a tomato] We can only say this much in theory: “This, now, tomato!”
  2. Making a leeway for the most ambitious ones of the ilk: “This *red* tomato!!”

Going by his explicit philosophic convictions, it must have been a height of “speculation” for Bohr to mumble something—anything—about a thing like “orbit.” After all, even by just mentioning a word like “orbit,” Bohr was being absolutely philosophically inconsistent here. Dear reader, observe that the orbit itself never at all was an observable!

Bohr must have in his conscience convulsed at this fact; his own philosophy couldn’t possibly have, strictly speaking, permitted him to accommodate into his theory a non-measurable feature of a non-measurable entity—such as his orbits of his electrons. Only the allure of outwardly producing predictions that matched with the experiment might have quietened his conscience—and that too, temporarily. At least until he got a new stone-building housing an Institute for himself and/or a Physics Nobel, that is.

Possible. With Herr Herr Herr Doktor Doktor Doktor Professor Professors, anything is possible.

It is often remarked that the one curious feature of the Bohr theory was the fact that the stability of the electronic orbits was postulated in it, not explained.

That is, not explained in reference to any known physical principle. The analogy to the solar system indeed was just that: an analogy. It was not a reference to an established physical principle.

However, the basically marvelous feature of the Bohr theory was not that the orbits were stable (in violation of the known laws of electrodynamics). It was: there at all were any orbits in it, even if no experiment had ever given any evidence for the continuously or discontinuously subsequent positions electrons within an atom or of their motions.

So much for originator of the cult of sticking only to the “observables.”

What Sommerfeld did was to add footnotes to Bohr’s work.

Sommerfeld did this work admirably well.

However, what this instance in the history of physics clearly demonstrates is yet another principle from the epistemology of physics: how a man of otherwise enormous mathematical abilities and training (and an academically influential position, I might add), but having evidently no remarkable capacity for a very novel, breakthrough kind of conceptual thinking, just cannot but fall short of making any lasting contributions to physics.

“Math” by itself simply isn’t enough for physics.

What came to be known as the old quantum theory, thus, faced an impasse.

Under Bohr’s (and philosophers’) loving tutorship, the situation continued for a long time—for more than a decade!

A Song I Like:

(Marathi) “sakhi ga murali mohan mohi manaa…”
Music: Hridaynath Mangeshkar
Singer: Asha Bhosale
Lyrics: P. Savalaram

PS: Only typos and animals of the similar ilk remain to be corrected.



Off the blog. [“Matter” cannot act “where” it is not.]

I am going to go off the blogging activity in general, and this blog in most particular, for some time. [And, this time round, I will keep my promise.]

The reason is, I’ve just received the shipment of a book which I had ordered about a month ago. Though only about 300 pages in length, it’s going to take me weeks to complete. And, the book is gripping enough, and the issue important enough, that I am not going to let a mere blog or two—or the entire Internet—come in the way.

I had read it once, almost cover-to-cover, some 25 years ago, while I was a student in UAB.

Reading a book cover-to-cover—I mean: in-sequence, and by that I mean: starting from the front-cover and going through the pages in the same sequence as the one in which the book has been written, all the way to the back-cover—was quite odd a thing to have happened with me, at that time. It was quite unlike my usual habits whereby I am more or less always randomly jumping around in a book, even while reading one for the very first time.

But this book was different; it was extraordinarily engaging.

In fact, as I vividly remember, I had just idly picked up this book off a shelf from the Hill library of UAB, for a casual examination, had browsed it a bit, and then had began sampling some passage from nowhere in the middle of the book while standing in an library aisle. Then, some little time later, I was engrossed in reading it—with a folded elbow resting on the shelf, head turned down and resting against a shelf rack (due to a general weakness due to a physical hunger which I was ignoring [and I would have have to go home and cook something for myself; there was none to do that for me; and so, it was easy enough to ignore the hunger]). I don’t honestly remember how the pages turned. But I do remember that I must have already finished some 15-20 pages (all “in-the-order”!) before I even realized that I had been reading this book while still awkwardly resting against that shelf-rack. …

… I checked out the book, and once home [student dormitory], began reading it starting from the very first page. … I took time, days, perhaps weeks. But whatever the length of time that I did take, with this book, I didn’t have to jump around the pages.

The issue that the book dealt with was:

[Instantaneous] Action at a Distance.

The book in question was:

Hesse, Mary B. (1961) “Forces and Fields: The concept of Action at a Distance in the history of physics,” Philosophical Library, Edinburgh and New York.

It was the very first book I had found, I even today distinctly remember, in which someone—someone, anyone, other than me—had cared to think about the issues like the IAD, the concepts like fields and point particles—and had tried to trace their physical roots, to understand the physical origins behind these (and such) mathematical concepts. (And, had chosen to say “concepts” while meaning ones, rather than trying to hide behind poor substitute words like “ideas”, “experiences”, “issues”, “models”, etc.)

Twenty-five years later, I still remain hooked on to the topic. Despite having published a paper on IAD and diffusion [and yes, what the hell, I will say it: despite claiming a first in 200+ years in reference to this topic], I even today do find new things to think about, about this “kutty” [Original: IITM lingo; English translation: “small”] topic. And so, I keep returning to it and thinking about it. I still am able to gain new insights once in an odd while. … Indeed, my recent ‘net search on IAD (the one which led to Hesse and my buying the book) precisely was to see if someone had reported the conceptual [and of course, mathematical] observation which I have recently made, or not. [If too curious about it, the answer: looks like, none has.]

But now coming to Hesse’s writing style, let me quote a passage from one of her research papers. I ran into this paper only recently, last month (in July 2017), and it was while going through it that I happened [once again] to remember her book. Since I did have some money in hand, I did immediately decide to order my copy of this book.

Anyway, the paper I have in mind is this:

Hesse, Mary B. (1955) “Action at a Distance in Classical Physics,” Isis, Vol. 46, No. 4 (Dec., 1955), pp. 337–353, University of Chicago Press/The History of Science Society.

The paper (it has no abstract) begins thus:

The scholastic axiom that “matter cannot act where it is not” is one of the very general metaphysical principles found in science before the seventeenth century which retain their relevance for scientific theory even when the metaphysics itself has been discarded. Other such principles have been fruitful in the development of physics: for example, the “conservation of motion” stated by Descartes and Leibniz, which was generalized and given precision in the nineteenth century as the doctrine of the conservation of energy; …

Here is another passage, once again, from the same paper:

Now Faraday uses a terminology in speaking about the lines of force which is derived from the idea of a bundle of elastic strings stretched under tension from point to point of the field. Thus he speaks of “tension” and “the number of lines” cut by a body moving in the field. Remembering his discussion about contiguous particles of a dielectric medium, one must think of the strings as stretching from one particle of the medium to the next in a straight line, the distance between particles being so small that the line appears as a smooth curve. How seriously does he take this model? Certainly the bundle of elastic strings is nothing like those one can buy at the store. The “number of lines” does not refer to a definite number of discrete material entities, but to the amount of force exerted over a given area in the field. It would not make sense to assign points through which a line passes and points which are free from a line. The field of force is continuous.

See the flow of the writing? the authentic respect for the intellectual history, and yet, the overriding concern for having to reach a conclusion, a meaning? the appreciation for the subtle drama? the clarity of thought, of expression?

Well, these passages were from the paper, but the book itself, too, is similarly written.

Obviously, while I remain engaged in [re-]reading the book [after a gap of 25 years], don’t expect me to blog.

After all, even I cannot act “where” I am not.

A Song I Like:

[I thought a bit between this song and another song, one by R.D. Burman, Gulzar and Lata. In the end, it was this song which won out. As usual, in making my decision, the reference was exclusively made to the respective audio tracks. In fact, in the making of this decision, I happened to have also ignored even the excellent guitar pieces in this song, and the orchestration in general in both. The words and the tune were too well “fused” together in this song; that’s why. I do promise you to run the RD song once I return. In the meanwhile, I don’t at all mind keeping you guessing. Happy guessing!]

(Hindi) “bheegi bheegi…” [“bheege bheege lamhon kee bheegee bheegee yaadein…”]
Music and Lyrics: Kaushal S. Inamdar
Singer: Hamsika Iyer

[Minor additions/editing may follow tomorrow or so.]


QM: The physical view it takes—1

So, what exactly is quantum physics like? What is the QM theory all about?

You can approach this question at many levels and from many angles. However, if an engineer were to ask me this question (i.e., an engineer with sufficiently good grasp of mathematics such as differential equations and linear algebra), today, I would answer it in the following way. (I mean only the non-relativistic QM here; relativistic QM is totally beyond me, at least as of today):

Each physics theory takes a certain physical view of the universe, and unless that view can be spelt out in a brief and illuminating manner, anything else that you talk about it (e.g. the maths of the theory) tends to become floating, even meaningless.

So, when we speak of QM, we have to look for a physical view that is at once both sufficiently accurate and highly meaningful intuitively.

But what do I mean by a physical view? Let me spell it out first in the context of classical mechanics so that you get a sense of that term.

Personally, I like to think of separate stages even within classical mechanics.

Consider first the Newtonian mechanics. We can say that the Newtonian mechanics is all about matter and motion. (Maxwell it was, I think, who characterized it in this beautifully illuminating a way.) Newton’s original mechanics was all about the classical bodies. These were primarily discrete—not quite point particles, but finite ones, with each body confined to a finite and isolated region of space. They had no electrical attributes or features (such as charge, current, or magnetic field strength). But they did possess certain dynamical properties, e.g., location, size, density, mass, speed, and most importantly, momentum—which was, using modern terminology, a vector quantity. The continuum (e.g. a fluid) was seen as an extension of the idea of the discrete bodies, and could be studied by regarding an infinitesimal part of the continuum as if it were a discrete body. The freshly invented tools of calculus allowed Newton to take the transition from the discrete bodies (billiard balls) to both: the point-particles (via the shells-argument) as well as to the continuum (e.g. the drag force on a submerged body.)

The next stage was the Euler-Lagrange mechanics. This stage represents no new physics—only a new physical view. The E-L mechanics essentially was about the same kind of physical bodies, but now a number (often somewhat wrongly called a scalar) called energy being taken as the truly fundamental dynamical attribute. The maths involved the so-called variations in a global integral expression involving an energy-function (or other expressions similar to energy), but the crucial dynamic variable in the end would be a mere number; the number would be the outcome of evaluating a definite integral. (Historically, the formalism was developed and applied decades before the term energy could be rigorously isolated, and so, the original writings don’t use the expression “energy-function.” In fact, even today, the general practice is to put the theory using only the mathematical and abstract terms of the “Lagrangian” or the “Hamiltonian.”) While Newton’s own mechanics was necessarily about two (or more) discrete bodies locally interacting with each other (think collisions, friction), the Euler-Lagrange mechanics now was about one discrete body interacting with a global field. This global field could be taken to be mass-less. The idea of a global something (it only later on came to be called a field) was already a sharp departure from the original Newtonian mechanics. The motion of the massive body could be predicted using this kind of a formalism—a formalism that probed certain hypothetical variations in the global field (or, more accurately, in the interactions that the global field had with the given body). The body itself was, however, exactly as in the original Newtonian mechanics: discrete (or spread over definite and delimited region of space), massive, and without any electrical attributes or features.

The next stage, that of the classical electrodynamics, was about the Newtonian massive bodies but now these were also seen as endowed with the electrical attributes in addition to the older dynamical attributes of momentum or energy. The global field now became more complicated than the older gravitational field. The magnetic features, initially regarded as attributes primarily different from the electrical ones, later on came to be understood as a mere consequence of the electrical ones. The field concept was now firmly entrenched in physics, even though not always very well understood for what it actually was: as a mathematical abstraction. Hence the proliferation in the number of physical aethers. People rightly sought the physical referents for the mathematical abstraction of the field, but they wrongly made hasty concretizations, and that’s how there was a number of aethers: an aether of light, an aether of heat, an aether of EM, and so on. Eventually, when the contradictions inherent in the hasty concretizations became apparent, people threw the baby with the water, and it was not long before Einstein (and perhaps Poincare before him) would wrongly declare the universe to be devoid of any form of aether.

I need to check the original writings by Newton, but from whatever I gather (or compile, perhaps erroneously), I think that Newton had no idea of the field. He did originate the idea of the universal gravitation, but not that of the field of gravity. I think he would have always taken gravity to be a force that was directly operating between two discrete massive bodies, in isolation to anything else—i.e., without anything intervening between them (including any kind of a field). Gravity, a force (instantaneously) operating at a distance, would be regarded as a mere extension of the idea of the force by the direct physical contact. Gravity thus would be an effect of some sort of a stretched spring to Newton, a linear element that existed and operated between only two bodies at its two ends. (The idea of a linear element would become explicit in the lines of force in Faraday’s theorization.) It was just that with gravity, the line-like spring was to be taken as invisible. I don’t know, but that seems like a reasonable implicit view that Newton must have adopted. Thus, the idea of the field, even in its most rudimentary form, probably began only with the advent of the Euler-Lagrange mechanics. It anyway reached its full development in Maxwell’s synthesis of electricity and magnetism into electromagnetism. Remove the notion of the field from Maxwell’s theory, and it is impossible for the theory to even get going. Maxwellian EM cannot at all operate without having a field as an intermediate agency transmitting forces between the interacting massive bodies. On the other hand, Newtonian gravity (at least in its original form and at least for simpler problems) can. In Maxwellian EM, if two bodies suddenly change their relative positions, the rest of the universe comes to feel the change because the field which connects them all has changed. In Newtonian gravity, if two bodies suddenly change their relative positions, each of the other bodies in the universe comes to feel it only because its distances from the two bodies have changed—not because there is a field to mediate that change. Thus, there occurs a very definite change in the underlying physical view in this progression from Newton’s mechanics to Euler-Lagrange-Hamilton’s to Maxwell’s.

So, that’s what I mean by the term: a physical view. It is a view of what kind of objects and interactions are first assumed to exist in the universe, before a physics theory can even begin to describe them—i.e., before any postulates can even begin to be formulated. Let me hasten to add that it is a physical view, and not a philosophical view, even though physicists, and worse, mathematicians, often do confuse the issue and call it a (mere) philosophical discussion (if not a digression). (What better can you expect from mathematicians anyway? Or even from physicists?)

Now, what about quantum mechanics? What kind of objects does it deal with, and what kind of a physical view is required in order to appreciate the theory best?

What kind of objects does QM deal with?

QM once again deals with bodies that do have electromagnetic attributes or features—not just the dynamical ones. However, it now seeks to understand and explain how these features come to operate so that certain experimentally observed phenomena such as the cavity radiation and the gas spectra (i.e., the atomic absorption- and emission-spectra) can be predicted with a quantitative accuracy. In the process, QM keeps the idea of the field more or less intact. (No, strictly speaking it doesn’t, but that’s what physicists think anyway). However, the development of the theory was such that it had to bring the idea of the spatially delimited massive body, occupying a definite place and traveling via definite paths, into question. (In fact, quantum physicists went overboard and threw it out quite gleefully, without a thought.) So, that is the kind of “objects” it must assume before its theorization can at all begin. Physicists didn’t exactly understand what they were dealing with, and that’s how arose all its mysteries.

Now, how about its physical view?

In my (by now revised) opinion, quantum mechanics basically is all about the electronic orbitals and their evolutions (i.e., changes in the orbitals, with time).

(I am deliberately using the term “electronic” orbital, and not “atomic” orbital. When you say “atom,” you must mean something that is localized—else, you couldn’t possibly distinguish this object from that at the gross scale. But not so when it is the electronic orbitals. The atomic nucleus, at least in the non-relativistic QM, can be taken to be a localized and discrete “particle,” but the orbitals cannot be. Since the orbitals are necessarily global, since they are necessarily spread everywhere, there is no point in associating something local with them, something like the atom. Hence the usage: electronic orbitals, not atomic orbitals.)

The electronic orbital is a field whose governing equation is the second-order linear PDE that is Schrodinger’s equation, and the problems in the theory involve the usual kind of IVBV problems. But a further complexity arises in QM, because the real-valued orbital density isn’t the primary unknown in Schrodinger’s equation; the primary unknown is the complex-valued wavefunction.

The Schrodinger equation itself is basically like the diffusion equation, but since the primary unknown is complex-valued, it ends up showing some of the features of the wave equation. (That’s one reason. The other reason is, the presence of the potential term. But then, the potential here is the electric potential, and so, once again, indirectly, it has got to do with the complex nature of the wavefunction.) Hence the name “wave equation,” and the term “wavefunction.” (The “wavefunction” could very well have been called the “diffusionfunction,” but Schrodinger chose to call it the wavefunction, anyway.) Check it out:

Here is the diffusion equation:

\dfrac{\partial}{\partial t} \phi = D \nabla^2 \phi
Here is the Schrodinger equation:
\dfrac{\partial}{\partial t} \Psi = \dfrac{i\hbar}{2\mu} \nabla^2 \Psi + V \Psi

You can always work with two coupled real-valued equations instead of the single, complex-valued, Schrodinger’s equation, but it is mathematically more convenient to deal with it in the complex-valued form. If you were instead to work with the two coupled real-valued  equations, they would still end up giving you exactly the same results as the Schrodinger equation. You will still get the Maxwellian EM after conducting suitable grossing out processes. Yes, Schrodinger’s equation must give rise to the Maxwell’s equations. The two coupled real-valued equations would give you that (and also everything else that the complex-valued Schrodinger’s equation does). Now, Maxwell’s equations do have an inherent  coupling between the electric and magnetic fields. This, incidentally, is the simplest way to understand why the wavefunction must be complex-valued. [From now on, don’t entertain the descriptions like: “Why do the amplitudes have to be complex? I don’t know. No one knows. No one can know.” etc.]

But yes, speaking in overall terms, QM is, basically, all about the electronic orbitals and the changes in them. That is the physical view QM takes.

Hold that line in your mind any time you hit QM, and it will save you a lot of trouble.

When it comes to the basics or the core (or the “heart”) of QM, physicists will never give you the above answer. They will give you a lot many other answers, but never this one. For instance, Richard Feynman thought that the wave-particle duality (as illustrated by the single-particle double-slit interference arrangement) was the real key to understanding the QM theory. Bohr and Heisenberg instead believed that the primacy of the observables and the principle of the uncertainty formed the necessary key. Einstein believed that entanglement was the key—and therefore spent his time using this feature of the QM to deny completeness to the QM theory. (He was right; QM is not complete. He was not on the target, however; entanglement is merely an outcome, not a primary feature of the QM theory.)

They were all (at least partly) correct, but none of their approaches is truly illuminating—not to an engineer anyway.

They were correct in the sense, these indeed are valid features of QM—and they do form some of the most mystifying aspects of the theory. But they are mystifying only to an intuition that is developed in the classical mechanical mould. In any case, don’t mistake these mystifying features for the basic nature of the core of the theory. Discussions couched in terms of the more mysterious-appearing features in fact have come to complicate the quantum story unnecessarily; not helped simplify it. The actual nature of the theory is much more simple than what physicists have told you.

Just the way the field in the EM theory is not exactly the same kind of a continuum as in the original Newtonian mechanics (e.g., in EM it is mass-less, unlike water), similarly, neither the field nor the massive object of the QM is exactly as in their classical EM descriptions. It can’t be expected to be.

QM is about some new kinds of the ultimate theoretical objects (or building blocks) that especially (but not exclusively) make their peculiarities felt at the microscopic (or atomic) scale. These theoretical objects carry certain properties such that the theoretical objects go on to constitute the observed classical bodies, and their interactions go on to produce the observed classical EM phenomena. However, the new theoretical objects are such that they themselves do not (and cannot be expected to) possess all the features of the classical objects. These new theoretical objects are to be taken as more fundamental than the objects theorized in the classical mechanics. (The physical entities in the classical mechanics are: the classical massive objects and the classical EM field).

Now, this description is quite handful; it’s not easy to keep in mind. One needs a simpler view so that it can be held and recalled easily. And that simpler view is what I’ve told you already:

To repeat: QM is all about the electronic orbital and the changes it undergoes over time.

Today, most any physics professor would find this view objectionable. He would feel that it is not even a physics-based view, it is a chemistry-based one, even if the unsteady or the transient aspect is present in the formulation. He would feel that the unsteady aspect in the formulation is artificial; it is more or less slapped externally on to the picture of the steady-state orbitals given in the chemistry textbooks, almost as an afterthought of sorts. In any case, it is not physics—that’s what he would be sure of. By that, he would also be sure to mean that this view is not sufficiently mathematical. He might even find it amusing that a physical view of QM can be this intuitively understandable. And then, if you ask him for a sufficiently physics-like view of QM, he would tell you that a certain set of postulates is what constitutes the real core of the QM theory.

Well, the QM postulates indeed are the starting points of QM theory. But they are too abstract to give you an overall feel for what the theory is about. I assert that keeping the orbitals always at the back of your mind helps give you that necessary physical feel.

OK, so, keeping orbitals at the back of the mind, how do we now explain the wave-particle duality in the single-photon double-slit interference experiment?

Let me stop here for this post; I will open my next post on this topic precisely with that question.

A Song I Like:

(Hindi) “ik ajeeb udaasi hai, meraa man_ banawaasi hai…”
Music: Salil Chowdhury
Singer: Sayontoni Mazumdar
Lyrics: (??)

[No, you (very probably) never heard this song before. It comes not from a regular film, but supposedly from a tele-film that goes by the name “Vijaya,” which was produced/directed by one Krishna Raaghav. (I haven’t seen it, but gather that it was based on a novel of the same name by Sharat Chandra Chattopadhyaya. (Bongs, I think, over-estimate this novelist. His other novel is Devadaas. Yes, Devadaas. … Now you know. About the Chattopadhyaya.)) Anyway, as to this song itself, well, Salil-daa’s stamp is absolutely unmistakable. (If the Marathi listener feels that the flute piece appearing at the very beginning somehow sounds familiar, and then recalls the flute in Hridayanath Mangeshkar’s “mogaraa phulalaa,” then I want to point out that it was Hridayanath who once assisted Salil-daa, not the other way around.) IMO, this song is just great. The tune may perhaps sound like the usual ghazal-like tune, but the orchestration—it’s just extraordinary, sensitive, and overall, absolutely superb. This song in fact is one of Salil-daa’s all-time bests, IMO. … I don’t know who penned the lyrics, but they too are great. … Hint: Listen to this song on high-quality head-phones, not on the loud-speakers, and only when you are all alone, all by yourself—and especially as you are nursing your favorite Sundowner—and especially during the times when you are going jobless. … Try it, some such a time…. Take care, and bye for now]


A bit about my trade…

Even while enjoying my writer’s block, I still won’t disappoint you. … My browsing has yielded some material, and I am going to share it with you.

It all began with googling for some notes on CFD. One thing led to another, and soon enough, I was at this page [^] maintained by Prof. Praveen Chandrashekhar of TIFR Bangalore.

Do go through the aforementioned link; highly recommended. It tells you about the nature of my trade [CFD]…

As that page notes, this article had first appeared in the AIAA Student Journal. Looking at the particulars of the anachronisms, I wanted to know the precise date of the writing. Googling on the title of the article led me to a PDF document which was hidden under a “webpage-old” sub-directory, for the web pages for the ME608 course offered by Prof. Jayathi Murthy at Purdue [^]. At the bottom of this PDF document is a note that the AIAA article had appeared in the Summer of 1985. … Hmm…. Sounds right.

If you enjoy your writer’s block [the way I do], one sure way to continue having it intact is to continue googling. You are guaranteed never to come out it. I mean to say, at least as far as I know, there is no equivalent of Godwin’s law [^] on the browsing side.

Anyway, so, what I next googled on was: “wind tunnels.” I was expecting to see the Wright brothers as the inventors of the idea. Well, I was proved wrong. The history section on the Wiki page [^] mentions Benjamin Robins and his “whirling arm” apparatus to determine drag. The reference for this fact goes to a book bearing the title “Mathematical Tracts of the late Benjamin Robins, Esq,” published, I gathered, in 1761. The description of the reference adds the sub-title (or the chapter title): “An account of the experiments, relating to the resistance of the air, exhibited at different times before the Royal Society, in the year 1746.” [The emphasis in the italics is mine, of course! [Couldn’t you have just guessed it?]]

Since I didn’t know anything about the “whirling arm,” and since the Wiki article didn’t explain it either, a continuation of googling was entirely in order. [The other reason was what I’ve told you already: I was enjoying my writer’s block, and didn’t want it to go away—not so soon, anyway.] The fallout of the search was one k-12 level page maintained by NASA [^]. Typical of the government-run NASA, there was no diagram to illustrate the text. … So I quickly closed the tab, came back to the next entries in the search results, and landed on this blog post [^] by “Gina.” The name of the blog was “Fluids in motion.”

… Interesting…. You know, I knew about, you know, “Fuck Yeah Fluid Dynamics” [^] (which is a major time- and bandwidth-sink) but not about “Fluids in motion.” So I had to browse the new blog, too. [As to the FYFD, I only today discovered the origin of the peculiar name; it is given in the Science mag story here [^].]

Anyway, coming back to Gina’s blog, I then clicked on the “fluids” category, and landed here [^]… Turns out that Gina’s is a less demanding on the bandwidth, as compared to FYFD. [… I happen to have nearly exhausted my monthly data limit of 10 GB, and the monthly renewal is on the 5th June. …. Sigh!…]

Anyway, so here I was, at Gina’s blog, and the first post in the “fluids” category was on “murmuration of starlings,” [^]. There was a link to a video… Video… Video? … Intermediate Conclusion: Writer’s blocks are costly. … Soon after, a quiet temptation thought: I must get to know what the phrase “murmuration of starlings” means. … A weighing in of the options, and the final conclusion: what the hell! [what else], I will buy an extra 1 or 2 GB add-on pack, but I gotta see that video. [Writer’s block, I told you, is enjoyable.] … Anyway, go, watch that video. It’s awesome. Also, Gina’s book “Modeling Ships and Space Craft.” It too seems to be awesome: [^] and [^].

The only way to avoid further spending on the bandwidth was to get out of my writer’s block. Somehow.

So, I browsed a bit on the term [^], and took the links on the first page of this search. To my dismay, I found that not even a single piece was helpful to me, because none was relevant to my situation: every piece of advice there was obviously written only after assuming that you are not enjoying your writer’s block. But what if you do? …

Anyway, I had to avoid any further expenditure on the bandwidth—my expenditure—and so, I had to get out of my writer’s block.

So, I wrote something—this post!

[Blogging will continue to remain sparse. … Humor apart, I am in the middle of writing some C++ code, and it is enjoyable but demanding on my time. I will remain busy with this code until at least the middle of June. So, expect the next post only around that time.]

[May be one more editing pass tomorrow… Done.]



The anti-, an anti-anti-, my negativism, and miscellaneous


A better title could very well have been “What I am up against.” However, that title, I thought, would be misleading. … I really am up against many things which I am going to touch on, in this post. But the point is, these are not the only things that I am up against, and so, that title would therefore be too general.

Part I: The Anti-

First, of course, comes the anti.

I stumbled across W. E. Lamb, Jr.’s excellent paper: “Anti-photon” (1995) Appl. Phys. B, vol. 60, p. 77–84. Here is the abstract:

“It should be apparent from the title of this article that the author does not like the use of the word “photon”, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the “aether” or “vacuum” to stand for empty space, even if no such thing existed. There are very good substitute words for “photon”, (e.g., “radiation” or “light”), and for “photonics” (e.g., “optics” or “quantum optics”). Similar objections are possible to use of the word “phonon”, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.”

BTW, in case you don’t know, W. E. Lamb, Jr., was an American, who received a Nobel in physics, for his work related to the fine structure of hydrogen [^].

So, that’s the first bit of what I am up against.

Also in case you didn’t notice, the initials are important; this isn’t (Sir) Horace Lamb (who, in case you don’t know, was that late 19th–early 20th century British guy who wrote books on hydrodynamics and acoustics that people like me still occasionally refer to [^]. (Lamb and Love continue to remain in circulation (even if a low circulation) among mechanicians even today. (Love, who? … That’s an exercise left for the reader…)))

Oh, BTW, talking of very good books that now have come in the public domain, and (the preparation required for) QM, and all the anti- and un- things, note that Professor Howard Georgi [^]’s excellent book on waves has by now come in the public domain [^].

(Even if only parenthetically, I have to note: I am anti-diversity, too. … This anti thing simply doesn’t leave me alone, though I will try to minimize its usage. Starting right now. … Georgi was born in California. He also maintains a page about women in physics [^].)

… Ummm, I’d better wrap up this part, and so…

… All in all, you can see that I don’t seem to be taking my opposition very seriously, though I admit I should start doing so some day. But the paper is great. (We were talking about the anti-photon paper, remember?) Here is an excerpt in case I haven’t already succeeded in persuading you to go through it, immediately:

“During my eight years in Berkeley, I had just one conversation with Lewis, in 1937, when he called me into his office to give some advice. It was: “When a theorist does not know what to do next, he is useless. An experimental scientist can always go into his laboratory and “polish up the brass”.”

This is the same Lewis who coined the word “photon.” … Now it convinces you to go through the paper, doesn’t it? (The paper is by Lamb; W. E. Lamb.)

[… On a more serious note, this paper has very good notings regarding the history of the idea of the photon.]

Part II: The Anti- Equals the Anti-Anti-

There is no typo here.

Even as I was recoiling off the glow (I won’t use “radiation” or “light”) of [the physics Nobel laureate] Lamb’s reputation, I began wondering precisely how I would counter his anti-photon argument. I even thought of doing a blog post about it. (After all, recently, Roger Schlafly has been hinting at that same idea, too. [May be TBD: insert links])

However, a better sense prevailed, and I did a Google search. I found a good blog post that gives a good rejoinder to the anti-photon arguments. The post is written in simple enough language that any one could understand. … But should I recommend it to you?… The thing is: It comes from a physicist who is reputed to have attempted teaching quantum physics to dogs. Or, at least, teaching people how to teach quantum physics, to dogs.

But of course, in physics, personalities don’t count, and neither do, you know, sort of like, “insults.” [I am also anti-animal rights, BTW [though all in favor of dogs].] And so, let me lead you to the relevant post.

The quantum physics-loving folks would have guessed the man by now (and every one, the fact that the author must be a man, not a woman). So the only remaining part would be which post by Chad Orzel. Here it is [^]. Once you finish reading it (including the comments on the post), then, also go through these couple of others posts by him touching on the same topic [^] [^] (and their blog comments). And, a great post (at wired.com!) by Rhett Allain [^] on the anti-photon side, to which Orzel makes a reference.

Orzel’s basic argument is that anti-bunching equals anti-anti-photon.

That explains the second part of the title.

But, before wrapping up this part, just a word on the PhD guides on the “polishing brass” side, and Indians. The anti-bunching experiments were done by Leonard Mandel [^], who among other things also guided Rupamanjari Ghosh’s PhD thesis. … Rupa…, who? I will save you the trouble of googling; see here: [^ (I am anti-government in education and science, too)] and here [^ (oh well, this post is getting just too long)].

Part III: My Negativism

Roger Schlafly has just recently written an interestingly long post on quantum entanglement. (Very long, by his standards.) In that post [^], he identifies himself as a logical positivist. This isn’t the first time that he has attributed logical positivism to his intellectual positions. Schlafly’s recent post is written, as usual, with good/great clarity

Now consider the premises, this time three, instead of the usual two: (i) Schlafly identifies himself as a logical positivist, (ii) I don’t agree with some part of his positions, and (iii) logic is logic—it cares for completeness.

Ergo, I must be a logical negativist.

That explains the third part of the title.

Some day I plan to write a post on the triplet and singlet states, and quantum entanglement.

Some still later day, I plan to explain how QM is incomplete, by pointing out how it can be made complete. … That is too big a goal to keep, you say?

Well, I do plan to at least explain in simpler terms the phenomenon of quantum entanglement, but only in reference to the text-book treatments. … That should be doable, what say?

… Don’t hold me responsible etc. on this promise; I am careless etc.; and so,  it might very well be in mid-2016 when I might actually deliver on it. … So, for the time being, make do with my logical negativism.

Part IV: Miscellaneous

M1: The preface to Georgi’s book notes the help he received while writing the book inter alia from (the same) Griffiths (as the one who has written very popular undergraduate text-books on electrodynamics and QM). (Griffiths studied at Harvard where Georgi has been a professor, though chances are they were contemporaries.) (No, this Griffiths isn’t the same as the Griffiths of fracture mechanics [^].) (Yes, this Georgi is the same as the one who has advocated the unparticle mechanics [^]. (But why didn’t he use the anti- prefix here?))

M2: The most succinct (and as far as I can make out, correct) treatment of the meaning of “hidden variables” has been not in the recent Internet writings on Bell’s inequalities but in Griffith’s undergraduate text-book on QM.

Why I mention this bit… That’s because, recently, the MIT professor Scott Aaronson had a field day about hidden variables (notably with Travis Norsen) [^], though since then he seems to have moved on to some other things related to theoretical computational complexity, e.g. this graph isomorphism-related thingie [^].

But, no, if you want to know about the so-called hidden variables well (and don’t have my “approach” or at least my “confidence”), then don’t look up the material on the ‘net or blog posts, esp. those by CS folks or complexity theorists. Instead, hit Griffith’s (text-)book.

M3: However, I am unhappy about Griffith’s treatment of the quantum postulates—he (like QChem and most all UG QM books) has only the usual \Psi and doesn’t include the spinor function right while discussing the state definition. Indeed, he continues implicitly treating the two in a somewhat disjoint manner even afterwards (exactly like all UG text-books do). Separable doesn’t mean disjointed.

I am also unhappy about Griffith’s (and every other QM text-book’s) treatment of the basic ideas of identical particles and their states—the treatments are just not conceptually clarifying enough. … May I assist you rewriting this topic, Professor Griffiths? … Oh well… Before I actually make that offer to him, I will try my hand at the task, at this blog…. Sometime in/after mid-2016. (Hopefully earlier.)

But, yes, if you ask me, it’s only the spin and identical particles that still remain truly nebulous topics for the student, today. With single-particle interference experiments and the ubiquity of simulations, one wouldn’t think that people would have too much difficulty with wave-particle duality or interference etc.

Contrast staring at one or two manually drawn static graphs in a book/paper, and imagining how things would change with time, under different governing equations and different boundary conditions, vs. going through simulations on your smartphone, adjusting FPS, changing boundary conditions with the flick of a button… Students (like me) must be having it exponentially easier to learn QM these days, as compared to those hapless 20th century guys.

The points where today’s students are likely to falter would be a bit more advanced ones, like angular momentum. In fact, today’s students don’t know angular momentum well even in the classical mechanics settings. (Ask yourself: how clear and confident are you about, say, Coriolis forces, say, as covered in Shames, or in Timoshenko and Young?).

So, to wrap up, it has to be identical particles and spin that still remain the really difficult topics. Now, it so happens that it is these concepts that underlie popular expositions of entanglement. Little surprise that people never get the confidence that they would be able to deal with entanglement right.

(Focusing on “just” two states of the spin up- and down-, and therefore treating the phenomenon via an abstract two component vector, and then thinking that starting a discussion with this “simple” vector, is a very bad idea, epistemologically speaking. … Yes, I am anti-Susskind’s “theoretical minimum,” too. And yes, Griffiths is right in choosing the traditional way (of the sequence in which to present the QM spin). It’s just that he needs to explain it in (even) better manner, that’s all….)

M4: The day before yesterday was the first time this year that I happened to finally sense that wonderful winter-time air of Pune’s, while returning in the evening from our college. (Monday was a working day for us; no continuous 9-day patch of a vacation.)

It still doesn’t feel like the Diwali air this year in Pune, but it’s getting close: I spotted some nice fog/mist on the nearby nallah (i.e. a small stream) and a nearby canal, a couple of times. …

This has been a year of (heavy) drought. And anyway, these days, there is virtually no difference between the Diwali days and the rest of the year. … Shopping malls are fully Diwali-like at any time of the year for those who have the money, and most women—whether working or otherwise—these days outsource their (Marathi) “chakalee”-making anyway—even during Diwali. So, there isn’t much of a difference between the Diwali days and the other days. Except for the weather. Weather still continues to change in a distinctly perceptible way sometime around Diwali. … So, that’s about all what Diwali means to me, this year.

And, of course, some memories of the magical Diwalis that I have spent in my childhood… Many of these were spent (at least for the (Marathi) “bhau-beej” day and a couple of days more) at my maternal uncle’s place (a very small town, a sub taluka-level place). … As far as I am concerned, those Diwali’s are still real; they would easily remain that way throughout my life.

PS: Having written the post, I just stepped into the kitchen to make me a cup of tea, and that’s when father told me that home-made (Marathi) “chakalee”s had arrived from our family friends just last evening; I didn’t know about it.

Instantaneously, my song-selection collapsed into an anti-previously measured state. (It happens. Real life is more weird than QM.)


Happy Diwali!

PS (also) to Epilogue:

Excuse me for a couple of weeks now. I will continue studying QM (from text-books), but I will also have to be taking out my notes for an undergraduate course on CFD (computational fluid dynamics, in case you didn’t know) that I should be teaching the next semester—which begins right in mid-December. (In India, we don’t always follow the Christmas–New Year’s–Next Term sequence.) I anyway will also be traveling a bit (just short distances like Mumbai and Nasik or so) over the next couple of weeks. So, I don’t think I will have the time to write a post. (That, in fact, was the reason why I threw in a lot of stuff right in this post.)

… So, there… Take care, and best wishes, once again, for a bright and happy Diwali (and to those of you who start a new year in Diwali, best wishes for a happy and prosperous new year too.)

A Song I Like

(Marathi) “tabakaamadhye ithe tevatee…”  (search on the transcriptionally incorrect “divya divyanchi jyot”)
Singer: Asha Bhosale
Lyrics: Ravindra Bhat
Music: Sudhir Phadake

[PS: I kept on adding material after publication of post, and now it has become some 1.5 times the original one. Sorry about that (though I did all the revisions right within 18 hours of publication), but now I am going stop editing any further. Put up with my grammatical mistakes and awkward constructions, as usual. And, if in doubt, ask me! Bye for now.]


Mathematics—Historic, Contemporary, and Its Relation to Physics

The title of this post does look very ambitious, but in fact the post itself isn’t. I mean, I am not going to even attempt to integrate these diverse threads at all. Instead, I am going to either just jot down a few links, or copy-paste my replies (with a bit editing) that I had made at some other blogs.


1. About (not so) ancient mathematics:

1.1 Concerning calculus: It was something of a goose-bumps moment for me to realize that the historic Indians had very definitely gotten to that branch of mathematics which is known as calculus. You have to understand the context behind it.

Some three centuries ago, there were priority battles concerning invention of calculus (started by Newton, and joined by Liebniz and his supporters). Echoes of these arguments could still be heard in popular science writings as recently as when I was a young man, about three decades ago.

Against this backdrop, it was particularly wonderful that an Indian mathematician as early as some eight centuries ago had gotten to the basic idea of calculus.

The issue was highlighted by Prof. Abinandanan at the blog nanpolitan, here [^]. It was based on an article by Prof. Biman Nath that had appeared in the magazine Frontline [^]. My replies can be found at Abi’s post. I am copy-pasting my replies here. I am also taking the opportunity to rectify a mistake—somehow, I thought that Nath’s article appeared in the Hindu newspaper, and not in the Frontline magazine. My comment (now edited just so slightly):

A few comments:

0. Based on my earlier readings of the subject matter (and I have never been too interested in the topic, and so, it was generally pretty much a casual reading), I used to believe that the Indians had not reached that certain abstract point which would allow us to say that they had got to calculus. They had something of a pre-calculus, I thought.

Based (purely) on Prof. Nath’s article, I have now changed my opinion.

Here are a few points to note:

1. How “jyaa” turned to “sine” makes for a fascinating story. Thanks for its inclusion, Prof. Nath.

2. Aaryabhata didn’t have calculus. Neither did Bramhagupta [my spelling is correct]. But if you wonder why the latter might have laid such an emphasis on the zero about the same time that he tried taking Aaryabhata’s invention further, chances are, there might have been some churning in Bramhagupta’s mind regarding the abstraction of the infinitesimal, though, with the evidence available, he didn’t reach it.

3. Bhaaskara II, if the evidence in the article is correct, clearly did reach calculus. No doubt about it.

He did not only reach a more abstract level, he even finished the concept by giving it a name: “taatkaalik.” Epistemologically speaking, the concept formation was complete.

I wonder why Prof. Nath, writing for the Frontline, didn’t allocate a separate section to Bhaaskara II. The “giant leap” richly deserved it.

And, he even got to the max-min problem by setting the derivative to zero. IMO, this is a second giant leap. Conceptually, it is so distinctive to calculus that even just a fleeting mention of it would be enough to permanently settle the issue.

You can say that Aaryabhata and Bramhagupta had some definite anticipation of calculus. And you can’t possible much more further about Archimedes’ method of exhaustion either. But, as a sum total, I think, they still missed calculus per say.

But with this double whammy (or, more accurately, the one-two punch), Bhaaskara II clearly had got the calculus.

Yes, it would have been nice if he could have left for the posterity a mention of the limit. But writing down the process of reaching the invention has always been so unlike the ancient Indians. Philosophically, the atmosphere would generally be antithetical to such an idea; the scientist, esp. the mathematician, may then be excused.

But then, if mathematicians had already been playing with infinite series with ease, and were already performing the calculus of finite differences in the context of these infinite series, even explicitly composing verses about their results, then they can be excused for not having conceptualized limits.

After all, even Newton initially worked only with the fluxion and Leibniz with the infinitesimal. The modern epsilon-delta definition still was some one–two centuries (in the three–four centuries of modern science) in the coming.

But when you explicitly say “instantaneous,” (i.e. after spelling out the correct thought process leading to it), there is no way one can say that some distance had yet to be travelled to reach calculus. The destination was already there.

And as if to remove any doubt still lingering, when it comes to the min-max condition, no amount of merely geometric thinking would get you there. Reaching of that conclusion means that the train had not already left the first station after entering the calculus territory, but also that it had in fact gone past the second or the third station as well. Complete with an application from astronomy—the first branch of physics.

I would like to know if there are any counter-arguments to the new view I now take of this matter, as spelt out above.

4. Maadhava missed it. The 1/4 vs. 1/6 is not hair-splitting. It is a very direct indication of the fact that either Maadhava did a “typo” (not at all possible, considering that these were verses to be by-hearted by repetition by the student body), or, obviously, he missed the idea of the repeated integration (which in turn requires considering a progressively greater domain even if only infinitesimally). Now this latter idea is at the very basis of the modern Taylor series. If Maadhava were to perform that repeated integration (and he would be a capable mathematical technician to be able to do that should the idea have struck him), then he would surely get 1/6. He would get that number, even if he were not to know anything about the factorial idea. And, if he could not get to 1/6, it’s impossible that he would get the idea of the entire infinite series i.e. the Taylor series, right.

5. Going by the content of the article, Prof. Nath’s conclusion in the last paragraph is, as indicated above, in part, non-sequitur.

6. But yes, I, too, very eagerly look forward to what Prof. Nath has to say subsequently on this and related issues.

But as far as the issues such as the existence of progress only in fits here and there, and indeed the absence of a generally monotonously increasing build-up of knowledge (observe the partial regression in Bramhagupta from Aaryabhat, or in Maadhav from Bhaaskar II), I think that philosophy as the fundamental factor in human condition, is relevant.

7. And, oh, BTW, is “Matteo Ricci” a corrupt form of the original “Mahadeva Rishi” [or “Maadhav Rishi”] or some such a thing? … May Internet battles ensue!

1.2 Concerning “vimaan-shaastra” and estimating \pi: Once again, this was a comment that I made at Abi’s blog, in response to his post on the claims concerning “vimaan-shaastra” and all, here[^]. Go through that post, to know the context in which I wrote the following comment (reproduced here with a bit of copy-editing):

I tend not to out of hand dismiss claims about the ancient Indian tradition. However, this one about the “Vimaan”s and all does seem to exceed even my limits.

But, still, I do believe that it can also be very easy to dismiss such claims without giving them due consideration. Yes, so many of them are ridiculous. But not all. Indeed, as a less noted fact, some of the defenders themselves do contradict each other, but never do notice this fact.

Let me give you an example. I am unlike some who would accept a claim only if there is a direct archaeological evidence for it. IMO, theirs is a materialistic position, and materialism is a false premise; it’s the body of the mind-body dichotomy (in Ayn Rand’s sense of the terms). And, so, I am willing to consider the astronomical references contained in the ancient verses as an evidence. So, in that sense, I don’t dismiss a 10,000+ old history of India; I don’t mindlessly accept 600 BC or so as the starting point of civilization and culture, a date so convenient to the missionaries of the Abrahamic traditions. IMO, not every influential commentator to come from the folds of the Western culture can be safely assumed to have attained the levels obtained by the best among the Greek or enlightenment thinkers.

And, so, I am OK if someone shows, based on the astronomical methods, the existence of the Indian culture, say, 5000+ years ago.

Yet, there are two notable facts here. (i) The findings of different proponents of this astronomical method of dating of the past events (say the dates of events mentioned in RaamaayaNa or Mahaabhaarata) don’t always agree with each other. And, more worrisome is the fact that (ii) despite Internet, they never even notice each other, let alone debate the soundness of their own approaches. All that they—and their supporters—do is to pick out Internet (or TED etc.) battles against the materialists.

A far deeper thinking is required to even just approach these (and such) issues. But the proponents don’t show the required maturity.

It is far too easy to jump to conclusions and blindly assert that there were material “Vimaana”s; that “puShpak” etc. were neither a valid description of a spiritual/psychic phenomenon nor a result of a vivid poetic imagination. It is much more difficult, comparatively speaking, to think of a later date insertion into a text. It is most difficult to be judicious in ascertaining which part of which verse of which book, can be reliably taken as of ancient origin, which one is a later-date interpolation or commentary, and which one is a mischievous recent insertion.

Earlier (i.e. decades earlier, while a school-boy or an undergrad in college etc.), I tended to think the very last possibility as not at all possible. Enough people couldn’t possibly have had enough mastery of Sanskrit, practically speaking, to fool enough honest Sanskrit-knowing people, I thought.

Over the decades, guess, I have become wiser. Not only have I understood the possibilities of the human nature better on the up side, but also on the down side. For instance, one of my colleagues, an engineer, an IITian who lived abroad, could himself compose poetry in Sanskrit very easily, I learnt. No, he wouldn’t do a forgery, sure. But could one say the same for every one who had a mastery of Sanskrit, without being too naive?

And, while on this topic, if someone knows the exact reference from which this verse quoted on Ramesh Raskar’s earlier page comes, and drops a line to me, I would be grateful. http://www.cs.unc.edu/~raskar/ . As usual, when I first read it, I was impressed a great deal. Until, of course, other possibilities struck me later. (It took years for me to think of these other possibilities.)

BTW, Abi also had a follow-up post containing further links about this issue of “vimaan-shaastra” [^].

But, in case you missed it, I do want to highlight my question again: Do you know the reference from which this verse quoted by Ramesh Raskar (now a professor at MIT Media Lab) comes? If yes, please do drop me a line.


2. An inspiring tale of a contemporary mathematician:

Here is an inspiring story of a Chinese-born mathematician who beat all the odds to achieve absolutely first-rank success.

I can’t resist the temptation to insert my trailer: As a boy, Yitang Zhang could not even attend school because he was forced into manual labor on vegetable-growing farms—he lived in the Communist China. As a young PhD graduate, he could not get a proper academic job in the USA—even if he got his PhD there. He then worked as an accountant of sorts, and still went on to solve one of mathematics’ most difficult problems.

Alec Wilkinson writes insightfully, beautifully, and with an authentic kind of admiration for man the heroic, for The New Yorker, here [^]. (H/T to Prof. Phanish Suryanarayana of GeorgiaTech, who highlighted this article at iMechanica [^].)


3. FQXi Essay Contest 2015:

(Hindi) “Picture abhi baaki nahin hai, dost! Picture to khatam ho gai” … Or, welcome back to the “everyday” reality of the modern day—modern day physics, modern day mathematics, and modern day questions concerning the relation between the two.

In other words, they still don’t get it—the relation between mathematics and physics. That’s why FQXi [^] has got an essay contest about it. They even call it “mysterious.” More details here [^]. (H/T to Roger Schlafly [^].)

Though this last link looks like a Web page of some government lab (American government, not Indian), do check out the second section on that same page: “II Evaluation Criteria.” The main problem description appears in this section. Let me quote the main problem description right in this post:

The theme for this Essay Contest is: “Trick or Truth: the Mysterious Connection Between Physics and Mathematics”.

In many ways, physics has developed hand-in-hand with mathematics. It seems almost impossible to imagine physics without a mathematical framework; at the same time, questions in physics have inspired so many discoveries in mathematics. But does physics simply wear mathematics like a costume, or is math a fundamental part of physical reality?

Why does mathematics seem so “unreasonably” effective in fundamental physics, especially compared to math’s impact in other scientific disciplines? Or does it? How deeply does mathematics inform physics, and physics mathematics? What are the tensions between them — the subtleties, ambiguities, hidden assumptions, or even contradictions and paradoxes at the intersection of formal mathematics and the physics of the real world?

This essay contest will probe the mysterious relationship between physics and mathematics.

Further, this section actually carries a bunch of thought-provocative questions to get you going in your essay writing. … And, yes, the important dates are here [^].

Now, my answers to a few questions about the contest:

Is this issue interesting enough? Yes.

Will I write an essay? No.

Why? Because I haven’t yet put my thoughts in a sufficiently coherent form.

However, I notice that the contest announcement itself includes so many questions that are worth attempting. And so, I will think of jotting down my answers to these questions, even if in a bit of a hurry.

However, I will neither further forge the answers together in a single coherent essay, nor will I participate in the contest.

And even if I were to participate… Well, let me put it this way. Going by Max Tegmark’s and others’ inclinations, I (sort of) “know” that anyone with my kind of answers would stand a very slim chance of actually landing the prize. … That’s another important reason for me not even to try.

But, yes, at least this time round, many of the detailed questions themselves are both valid and interesting. And so, it should be worth your while addressing them (or at least knowing what you think of them for your answers). …

As far as I am concerned, the only issue is time. … Given my habits, writing about such things—the deep and philosophical, and therefore fascinating things, the things that are interesting by themselves—have a way of totally getting out of control. That is, even if you know you aren’t going to interact with anyone else. And, mandatory interaction, incidentally, is another FQXi requirement that discourages me from participating.

So, as the bottom-line: no definitive promises, but let me see if I can write a post or a document by just straight-forwardly jotting down my answers to those detailed questions, without bothering to explain myself much, and without bothering to tie my answers together into a coherent whole.

Ok. Enough is enough. Bye for now.

[May be I will come back and add the “A Song I Like” section or so. Not sure. May be I will; may be I won’t. Bye.]



Free books on the nature of mathematics

Just passing along a quick tip, in case you didn’t know about it:

Early editions of quite a few wonderful books concerning history and nature of mathematics have now become available for free downloading at archive.org. (I hope they have checked the copyrights and all):

Books by Prof. Morris Kline:

  1. Mathematics in Western Culture (1954) [^]
  2. Mathematics and the Search for Knowledge (1985) [^]
  3. Mathematics and the Physical World (1959) [^] (I began Kline’s books with this one.)

Of course, Kline’s 3-volume book, “Mathematical Thought from Ancient to Modern Times,” is the most comprehensive and detailed one. However, it is not yet available off archive.org. But that hardly matters, because the book is in print, and a pretty inexpensive (Rs. ~1600) paperback is available at Amazon [^]. The Kindle edition is just Rs. 400.

(No, I don’t have Kindle. Neither do I plan to buy one. I will probably not use it even if someone gives it to me for free. I am sure I will find someone else to pass it on for free, again! … I don’t have any use for Kindle. I am old enough to like my books only the old-fashioned way—the fresh smell of the paper and the ink included. Or, the crispiness of the fading pages of an old one. And, I like my books better in the paperback format, not hard-cover. Easy to hold while comfortably reclining in my chair or while lying over a sofa or a bed.)

Anyway, back to archive.org.

Prof. G. H. Hardy’s “A Mathematician’s Apology,” too, has become available for free downloading [^]. It’s been more than two decades since I first read it. … Would love to find time to go through it again.

Anyway, enjoy! (And let me know if you run into some other interesting books at archive.org.)

* * * * *   * * * * *   * * * * *

A Song I Like:
(Hindi) “chain se hum ko kabhie…”
Music: O. P. Nayyar
Singer: Asha Bhosale
Lyrics: S. H. Bihari

Incidentally, I have often thought that this song was ideally suited for a saxophone, i.e., apart from Asha’s voice. Not just any instrument, but, specifically, only a saxophone. … Today I searched for, and heard for the first time, a sax rendering—the one by Babbu Khan. It’s pretty good, though I had a bit of a feeling that someone could do better, probably, a lot better. Manohari Singh? Did he ever play this song on a sax?

As to the other instruments, though I often do like to listen to a flute (I mean the Indian flute (“baansuri”)), this song simply is not at all suited to one. For instance, just listen to Shridhar Kenkare’s rendering. The entire (Hindi) “dard” gets lost, and then, worse: that sweetness oozing out in its place, is just plain irritating. At least to me. On the other hand, also locate on the ‘net a violin version of this song, and listen to it. It’s pathetic. … Enough for today. I have lost the patience to try out any piano version, though I bet it would sound bad, too.

Sax. This masterpiece is meant for the sax. And, of course, Asha.



The Fall of the Berlin Wall—It happened 25 years ago!

[See an important update near the bottom of this post. 2014.11.12.]

The Berlin Wall got demolished right on this day, 25 years ago.

A young Indian engineer from Pune had liked the event. [Guess who.] …

* * * * *   * * * * *   * * * * * 

With progressing age, they say, even distantly past events begin to look like they happened just yesterday. A lot of sense there is, in it. This event—the Fall of the Berlin Wall—does look like it happened, well, not exactly yesterday, but, say, something like just a few years ago or so. … Certainly not as long as twenty-five years ago!

But, of course, 25 years is a long time, if you sit and think about it.

Chances are, you might be reading this post on your iPad or even a nice and slim smart phone. …

Going back in time to 1989, the telephone hand-sets in India in those days still were those big black behemoths sitting at one place permanently (and, at offices, they were often put inside a transparent perspex box, complete with a lock and a key). The hand-sets would come equipped with those mechanical dials (from which the word “dialing” comes). They were manufactured by the state-owned industrial unit. Was it the TCI? I no longer remember the name, but I do distinctly remember that they had their main factory and head office, of all places, in Bengaluru—which, of course, was Bangalore back then! [You would know about that, wouldn’t you?] And, of course, not just the Planning Commission but also the Bangaloreans themselves would tell you, with a quietly satisfying kind of anticipation, that there was a “natural” limit as to how big their city could grow, because there was only one dam for the water supply to the entire city. Acute water shortage implied that the city would remain small, and not get out of control as had happened to Bombay or Calcutta. [Kanpur, Ahmedabad or Nagpur would not be on their radar, but they would ask with a bit of concern whether Pune, too, had a similar natural limit or not. I am talking about Bangaloreans of those days.]

In 1989, there were no STD/ISD/PCO booths (which came to life only in the early 1990s, spread everywhere before the turn of the millennium, and now already are on their way to extinction.) So, in 1989, to call someone from a different town, you would have to book a Trunk Call with the telephone company P&T department, an hour or two in advance. Sometimes it wouldn’t go through for ten hours or even more. [Once my colleague had booked a Trunk Call to Jamshedpur on a Monday morning, and had gotten it through it only on the Thursday afternoon. In short, he could have taken a train to physically visit the town and even return back, faster than a mere telephone call would go through. And, no, this is not a made-up example; it actually happened.]

… Sure, by the time it was 1989, the Ind-Suzukis and the Yamahas and the Maruti 800s had already arrived on the scene, but the days of the Hamara Bajaj scooters commanding a hefty premium still belonged to a very recent past—the marriages in which a Bajaj Chetak was “gifted” to the groom, had still not had produced school-going kids. There still was only one TV channel, and it belonged to the state. Its opening visual was static, and as far inducing a mental trance is concerned, the only music to surpass it was the opening music of the state-owned All India Radio (which would instantly put you to sleep, any time you heard it). The news never broke, but the atmosphere was such that people were content and not really bothered about what was happening elsewhere in the world—none of their life’s concerns involved anything that happened in the other parts of  the world. Pune was the fifth or sixth most industrialized town, but even then, most of the “normal” kind of young engineers working even in private industries in Pune, in 1989, would find it neither possible nor necessary to keep up with even the major events occurring elsewhere in the world. … But then, the habits of this young engineer—the one who really appreciated the fall of the Berlin Wall—were, back then, a bit different.

Even as a school-going child growing up in the rural parts of India (of even earlier times), he had always had a voracious appetite for reading “in general.” Anything on the non-fiction side other than the prescribed text-books would instantly qualify as being sufficiently gripping. (Sometimes, works of fiction would be attractive, too, especially if no non-fiction was at all available!) He had therefore already gotten to know about the Berlin Wall right while in his early secondary school (say, around the 5th, 6th or, at the most, 7th standard)—even if his reading was entirely limited only to Marathi. … The Berlin Wall, and in Marathi? How come?

Well, it would so happen that for the want of original stories that are sufficiently dramatic, Marathi magazines like “Amrut” and “Navneet” would regularly lift material from the likes of “Reader’s Digest,” translate them, and run them. After all, if catching the potential buyer’s attention is your objective, there are limits as to how many times you can possibly run the same story about Shivaji’s escape from Agra. Stories from the second world war were readily available, and would be run. The stories like those about the daring escapes from East Germany apparently fell in the same category, and fit the bill. And, so long as the existential conditions in the East Germany were not highlighted, so long as the communism was not depicted in a critical light, they would pose no problem. [Indeed, this state would continue even during the Emergency time Censors.] So, the Marathi magazines could, and did, run the daring escape stories involving the Berlin Wall too. And it was thus that this young engineer had gotten to know about the Berlin Wall for quite some time by the time the circumstances were ripe for it to be felled.

Yet, come to think of it, despite the eternally existing Censor and the relatively brief Emergency, India in those days perhaps was less restrictive than what otherwise might be imagined today. I mean to say, consider the case of an extremist for liberty, like Ayn Rand.

Sure enough, the English-reading and -writing intellectuals in India would regularly look down on Ayn Rand those days, but, really speaking, for the most part, they actually did not even openly criticize her. Doing so would have granted her a certain kind of visibility (I mean, a respectable kind of a visibility), a potential result they either directly detested, or, indirectly, they “took it in” from their British and American intellectual counterparts that talking about Ayn Rand was just not a “done thing.” And so, they simply shunned her completely. … When it came to anything Capitalistic and/or American, their favourite sport was to erect a straw-man, attack it, and then quickly submerge the whole thing in “a sticky puddle of stale syrup—of benevolent bromides and apologetic generalities about brother love, global progress,” and, by the time it was 1989, about the extraordinary flexibility and generality of the Soviet Model as evidenced by “Perestroika” and “Glasnost.” That’s what the English-writing intellectuals in India were like, in 1989. [As to the quoted words: go look up their source.]

As to the informal college culture, there were stories still floating in the air, even in 1989, about how Ayn Rand had in her later life been deserted by all her followers fans, and had gone mad, and had to die alone in a mental asylum—and how it was the work of poetic justice, given her “philosophy.” It was a story often circulated even on the campuses of the leading engineering schools—not just COEP but also IITs [you know, those MIT + Harvard Combo-Packs?] However, to be fair, sure, by the time it was 1989, the trend had already gone past its peak at the e-schools. I remember being told in 1989 that some medicine (and management) school folks were repeating the story even in the late 1980s, but in e-schools, I knew, such story-tellers were getting to be rarer birds.

But, of course, I am writing about how India perhaps was not so restrictive a place in those days… So, let me tell, despite the above-mentioned indicators, it also is a fact that Ayn Rand’s books had been freely available, if not on the respectable book-shelves then at least on the foot-paths, at least in the main 8–10 cities in India. On the foot-paths, they would be randomly arranged side-by-side with those by, say, Alistair McLean, Irving Wallace, Harold Robbins, Lee Iacocca, and, of course, Dale Carnegie. …

…Talking about the books on foot-paths of Pune, in 1989, Deepak Chopra, Paulo Coelho and Harry Potter had yet to come to the scene, and Yogonanda, Shri Shri Ravi Shankar, Vastu-Shaastra, etc. were all complete unknowns (though Rajneesh was not). Danielle Steele had just begun making an appearance, and The Zen and the Art of Motorcycle (Something) had already begun receding. The books on how to make a killing on the stock market had yet to come, prosper, and disappear (all of which happened within a decade or so spread over the 1990s and the early naughties)…

…About the only English books to have more or less bucked all the passing trends over all the last 25 years, and have consistently remained visible on the Pune foot-paths (though with a considerably shrunken total space for these sellers), have been those bearing the following words in large thick fonts: Pyramid, Bermuda Triangle, Hypnotism, Dale Carnegie, Cheiro, Ayn Rand, and of course, Einstein. And, now that I recall it a bit better, by the time it was 1989, the sales of Ayn Rand’s books had already migrated from the foot-paths to the railway-station book-sellers (of the main 8–10 cities in India), to a few avant garde English book sellers in Pune those days—notably, the Manneys in the Camp, and the Popular at Deccan Gymkhana. [The first was still in existence; the second had not yet started selling toys and gifts etc.]

Anyway, coming back to this engineer from Pune (remember the one who was young in 1989?), having gone through the Ayn Rand paperbacks in college, and now as a young working engineer sincerely reading through India Today, Business India, Business World, Technocrat, etc., even Outlook (and even Frontline), the Fall of the Berlin Wall was, to him, a more or less an anticipated event.

When the event actually took place in 1989, it decidedly was a piece of drama to many people in his circle of family, friends and colleagues. A large number of mostly white people (/Europeans) seemingly randomly coming together on streets and tearing down an existing concrete structure, was a very odd sight to behold, and therefore, rather dramatic in nature, to them.

To this young engineer, it was dramatic, and more than that: it was a piece of history unfolding right in front of his eyes. If he could believe in God, he would have also seen it as the coming true of a deeply prayed for wish that was so late in being granted from the heavens. But, the way it happened, he didn’t think in these terms. It was simply a very welcome event to him. Actually, it was even more welcome to him than it would otherwise have been, because it had happened on the backdrop of another set of the then recent events: the Tiananmen Square Protests, and the slightly earlier “Handover” of Hong Kong. The Fall of the Berlin Wall was a moment to cherish, to him. It was an event he liked.


* * * * *   * * * * *   * * * * *

Update on 2014.11.12 begins:

1. Over the past couple of days after publishing this post, I thought about it a bit, and tried to recall the precise time when I must have read that story about the escape from the East Germany, in some Marathi magazine. The story I had in mind was the one in which they had used a home-made hot air balloon. I was sure that the very first time I read it was in Marathi—in either “Amrut” or “Navneet” or some magazine like that, but certainly not in the government-run Marathi magazine for kids by the title: “Kishor”. I was sure of that.

After doing a Google search after writing the post, I now realize that this escape had occurred only in September 1979, and by that time, I was already in the first year of engineering at COEP. So, a conservative estimate is that I read about it when I was in second or third year of engineering—not in the early secondary school, as I wrote above.

I regret this mistake.

But, of course, as far as reading non-fiction goes, there was something to what I wrote. I had already begun trying to read the Marathi non-fiction magazine for the mature adult, viz. “Kirloskar,” right while I was in my primary school. I remember going through their coverage of  the Apollo 11 story in the same month that the magazine arrived. (Of course, I could do it only with a lot of help from my parents, but the point is, they were initially astonished to find that I was already through a few paragraphs on my own, though stumbling over unknown words). Now, I of course do remember reading the same story again (perhaps a few times over again), later on in secondary school, though I am sure I don’t mix up these subsequent readings from the first. And, I certainly was reading “Kirloskar” completely on my own way before my 7th standard—that too, I remember. So, certainly, I was reading “Amrut,” too (which relatively carried a much more light writing), by that time.

2. Next, another point. Could they have allowed the escape story to run during the Emergency times? (By “they”, I mean: the Censor Board itself, directly, or the plain editorial sense in the presence of a heavy censoring during the Emergency, indirectly.)

On second thoughts, thinking more carefully and deeply on this point, I think not.

Yes, it is true that Marathi magazines would often run the second world war stories. In fact, for a chapter in our government-written text-book in high-school, we had a certain II WW story. The chapter, of the title (Marathi) “swaadheen ki daivaadheen?,” was an excerpt from a book of the same title. This book was about the experience of an Indian soldier on the Italian/Austrian battle-front, I think. [Major R. G. Salvi, a search now lets me recall.] Now, not just this book, but also this chapter (the excerpt) had mentioned “fascists” as enemies. … But doing so would be fine by the communists, I guess. The real issue is: Could they have included a story depicting communists as an enemy? On that count, I think, not. After all, those were the days of Marathi and Hindi magazines like “Soviet Desh/Nari/etc” being made available at throw-away subscription rates, and of rave reviews in the local press of a book of the title “Malayaa Jhemalyaa” or something like that. The quoted word is the title of a Russian book—an autobiography, perhaps Brezhnev’s. I have read these words only in Marathi, and so don’t know their proper English transcription or the Russian spelling. No, not every major newspaper ran reviews of the book; sure, their appearance was a bit rare. But they were there—and without fail, they were either rave or deeply appreciative.

So, it would anyway have to be some time after Emergency so that stories concerning successful escapes from a communist country could get published in Marathi magazines like “Amrut” (I mean to say, even if that hot-air balloon escape were to occur much before the Emergency, which it did not.) Yet, in my writing above, I indicated that they could have run the story during Emergency. On more careful thinking as outlined above, now I think not.

I regret also this mistake.

I will let the original post remain as is, so that I remember this lesson to better check back the facts before writing even an utterly informal post.

It is true that with progressing age, not only does the recall become more hazy but also that there is this tendency whereby the past begins to get seen, at times, with “rosy-tinted glasses.” But then, the way I think about it, the necessary corrections, too, are easily possible. Perhaps progressively more easily, if you are like me.

[And, of course, that young engineer (mentioned in the main text of the post above) was me (or should it be an “I” here)?]

Update on 2014.11.12 over.

* * * * *   * * * * *   * * * * *

No “A Song I Like” section for this time round, but instead, do go, watch the video they at Google Doodle have put out [^]. It’s a short and simple one. As to the piece of the music that goes with it, while it is too short for me to know what to make of it, at least it sounds easy on the ears, even melodious. … Perhaps, the whole piece could be more interesting, or even actually likeable.

* * * * *   * * * * *   * * * * *

As usual, a minor editing would be due, though I am not if I am going to come back and do that. The academic terms are over, and so, it’s time to pick up the pieces of thought about research that, as of today, are all scattered in the mind, gather them together and arrange them in some order, and then think if anything could be practically done on the research side with them. … More, later.



A welcome development about QM that I got to know of, recently

This post shall be brief. I promise. (And, it will be easy enough to keep my promise. … Read on to know why…)

First, I refer you to my last blog post about QM, namely, “The mysterious quantum mystery” [^].

In that post, I had talked about Heisenberg’s first paper, and then had asked you:

“…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.”

As you know, in that post, as most times, I find the quantum mechanics folks to be an odd mixture of the dogmatic and the hilarious. (And regardless of their relative percentages in the mixture, most often, the first is the direct cause of the second.)

In contrast, in this post, I am going to briefly mention a certain development concerning the presentation of quantum mechanics which is only too welcome. … IMO, it is a wonderful development, and one that is truly worthy of respect.

OK, let me not stretch your patience any further.

I am talking about a new book on QM—at least one that was new to me until a few days after my last post on QM (i.e. until about 28th/29th of July).

The book in question is:

Longair, M. S. (2013) “Quantum Concepts in Physics: An Alternative Approach to the Understanding of Quantum Mechanics,” Cambridge: Cambridge University Press.

The best way in which, IMO, I might introduce this book to you is to say that this is the book that I both did not expect to find, and yet, curiously, was always looking for, for many, many years—certainly, for more than two decades.

The second-best way to introduce this book to you, is to say: (i) that this book is written in the style of a typical university text-book on a topic other than quantum mechanics, topic like, say, fluid mechanics or heat transfer; (ii) that it is (or at least should be) understandable to an undergraduate (or at least the beginning post-graduate) student of physics (if not also of engineering/technology/applied sciences); and, most importantly, (iii) that it presents quantum mechanics in the historical order of development.

The third-best way to introduce the book to you is to ask you to go and notice the official blurb at the publisher’s site [^].

A bad way to introduce the book to you is to ask you to go and read a very expected kind of a customer reaction (but a well-meaning one) which the book has already generated at Amazon—I mean the closing sentence in this review [^]. Don’t believe it.

Instead, do what I did. Buy the book. Immediately.

I have not yet read even 10% of this book. But, I, as usual, have randomly browsed all through the text. … It’s a great book.

I will certainly have occasion to write more about it some time in future—by way of both: a review, and some occasional reference in connection with my own thoughts.

And, for those of you who do buy books on QM but still are not yet sure if you should really buy this one or not: Note the Wiki page on the author. In short: the author is an FRS guy who (very recently) retired as the Director of Development at the Cavendish Laboratory (i.e. the physics department of the University of Cambridge) [^].

I hope that if you read this book, you will come to concur with me that this book probably provides a better introduction to the author than any other of his credentials (CBE, FRS, FRSE, Cambridge…)

* * * * *   * * * * *   * * * * *

One question you would be dying to ask me at this stage (if you know me) would be: “Does it mean you won’t be writing your book, Ajit?”

You could have predicted the answer I would give (that is, if you know me really well). Anyway, let me give you my answer without letting you get anywhere near the process of death. The answer is: “No. It simply means that I now have a great reference to fall back on, in the writing of my own book. It should help hasten up—rather than kill—the process of writing and finishing of my own book.”

Ok, more, later.

* * * * *   * * * * *   * * * * *

A Song I Like:

(Marathi) “roop paahataa lochani, sukh aale vo saajaNi…”
Lyrics: Sant Dynaaneshwar
Singer (of the version I like): Asha Bhosale
Music (of the version I like): C. Ramchandra


The mysterious quantum mystery…

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
Lyrics: Shailendra


[Perhaps a minor editing is due(?)]