Absolutely Random Notings on QM—Part 3: Links to some (really) interesting material, with my comments

The “pride of place” for this post goes to a link to this book:

Norsen, Travis (2017) “Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory,” Springer

This book is (i) the best supplementary book for a self-study of QM, and simultaneously, also (ii) the best text-book on a supplementary course on QM, both at the better-prepared UG / beginning PG level.

A bit expensive though, but extensive preview is available on Google books, here [^]. (I plan to buy it once I land a job.)

I was interested in the material from the first three chapters only, more or less. It was a delight even just browsing through these chapters. I intend to read it more carefully soon enough. But even on the first, rapid browsing, I noticed that several pieces of understanding that I had so painstakingly come to develop (over a period of years) are given quite straight-forwardly here, as if they were a matter of well known facts—even if other QM text-books only cursorily mention them, if at all.

For instance, see the explanation of entanglement here. Norsen begins by identifying that there is a single wavefunction, always—even for a multi-particle system. Then after some explanation, he states: “But, as usual in quantum mechanics, these states do not exhaust the possibilities—instead, they merely form a basis for the space of all possible wave functions. …”… Note the emphasis on the word “basis” which Norsen helpfully puts.

Putting this point (which Norsen discusses with a concrete example), but in my words: There is always a single wavefunction, and for a multi-particle system, its basis is bigger; it consists of the components of the tensor product (formed from the components of the basis of the constituent systems). Sometimes, the single wavefunction for the multi-particle system can be expressed as a result of a single tensor-product (in which case it’s a separable state), and at all other times, only as an algebraic sum of the results of many such tensor-products (in which case they all are entangled states).

Notice how there is no false start of going from two separate systems, and then attempting to forge a single system out of them. Notice how, therefore, there is no hand-waving at one electron being in one galaxy, and another electron in another galaxy, and so on, as if to apologize for the very idea of the separable states. Norsen achieves the correct effect by beginning on the right note: the emphasis on the single wavefunction for the system as a whole to begin with, and then clarifying, at the right place, that what the tensor product gives you is only the basis set for the composite wavefunction.

There are many neat passages like this in the text.

I was about to say that Norsen’s book is the Resnick and Halliday of QM, but then came to hesitate saying so, because I noticed something odd even if my browsing of the book was rapid and brief.

Then I ran into

Ian Durham’s review of Norsen’s book, at the FQXi blog,

which is our link # 2 for this post [^].

Durham helpfully brings out the following two points (which I then verified during a second visit to Norsen’s book): (i) Norsen’s book is not exactly at the UG level, and (ii) the book is a bit partial to Bell’s characterization of the quantum riddles as well as to the Bohmian approach for their resolution.

The second point—viz., Norsen’s fascination for / inclination towards Bell and Bohm (B&B for short)—becomes important only because the book is, otherwise, so good: it carries so many points that are not even passingly mentioned in other QM books, is well written (in a conversational style, as if a speech-to-text translator were skillfully employed), easy to understand, thorough, and overall (though I haven’t read even 25% of it, from whatever I have browsed), it otherwise seems fairly well balanced.

It is precisely because of these virtues that you might come out giving more weightage to the B&B company than is actually due to them.

Keep that warning somewhere at the back of your mind, but do go through the book anyway. It’s excellent.

At Amazon, it has got 5 reader reviews, all with 5 stars. If I were to bother doing a review there, I too perhaps would give it 5 stars—despite its shortcomings/weaknesses. OK. At least 4 stars. But mostly 5 though. … I am in an indeterminate state of their superposition.

… But mark my words. This book will have come to shape (or at least to influence) every good exposition of (i.e. introduction to) the area of the Foundations of QM, in the years to come. [I say that, because I honestly don’t expect a better book on this topic to arrive on the scene all that soon.]

Which brings us to someone who wouldn’t assign the $|4\rangle + |5\rangle$ stars to this book. Namely, Lubos Motl.

If Norsen has moved in the Objectivist circles, and is partial to the B&B company, Motl has worked in the string theory, and is not just partial to it but even today defends it very vigorously—and oddly enough, also looks at that “supersymmetric world from a conservative viewpoint.” More relevant to us: Motl is not partial to the Copenhagen interpretation; he is all the way into it. … Anyway, being merely partial is something you wouldn’t expect from Motl, would you?

But, of course, Motl also has a very strong grasp of QM, and he displays it well (even powerfully) when he writes a post of the title:

“Postulates of quantum mechanics almost directly follow from experiments.” [^]

Err… Why “almost,” Lubos? 🙂

… Anyway, go through Motl’s post, even if you don’t like the author’s style or some of his expressions. It has a lot of educational material packed in it. Chances are, going through Motl’s posts (like the present one) will come to improve your understanding—even if you don’t share his position.

As to me: No, speaking from the new understanding which I have come to develop regarding the foundations of QM [^] and [^], I don’t think that all of Motl’s objections would carry. Even then, just for the sake of witnessing the tight weaving-in of the arguments, do go through Motl’s post.

Finally, a post at the SciAm blog:

“Coming to grips with the implications of quantum mechanics,” by Bernardo Kastrup, Henry P. Stapp, and Menas C. Kafatos, [^].

The authors say:

“… Taken together, these experiments [which validate the maths of QM] indicate that the everyday world we perceive does not exist until observed, which in turn suggests—as we shall argue in this essay—a primary role for mind in nature.”

No, it didn’t give me shivers or something. Hey, this is QM and its foundations, right? I am quite used to reading such declarations.

Except that, as I noted a few years ago on Scott Aaronson’s blog [I need to dig up and insert the link here], and then, recently, also at

Roger Schlafly’s blog [^],

you don’t need QM in order to commit the error of inserting consciousness into a physical theory. You can accomplish exactly the same thing also by using just the Newtonian particle mechanics in your philosophical arguments. Really.

Yes, I need to take that reply (at Schlafly’s blog), edit it a bit and post it as a separate entry at this blog. … Some other time.

For now, I have to run. I have to continue working on my approach so that I am able to answer the questions raised and discussed by people such as those mentioned in the links. But before that, let me jot down a general update.

A general update:

Oh, BTW, I have taken my previous QM-related post off the top spot.

That doesn’t mean anything. In particular, it doesn’t mean that after reading into materials such as that mentioned here, I have found some error in my approach or something like that. No. Not at all.

All it means is that I made it once again an ordinary post, not a sticky post. I am thinking of altering the layout of this blog, by creating a page that highlights that post, as well as some other posts.

But coming back to my approach: As a matter of fact, I have also written emails to a couple of physicists, one from IIT Bombay, and another from IISER Pune. However, things have not worked out yet—things like arranging for an informal seminar to be delivered by me to their students, or collaborating on some QM-related simulations together. (I could do the simulations on my own, but for the seminar, I would need an audience! One of them did reply, but we still have to shake our hands in the second round.)

In the meanwhile, I go jobless, but I keep myself busy. I am preparing a shortish set of write-ups / notes which could be used as a background material when (at some vague time in future) I go and talk to some students, say at IIT Bombay/IISER Pune. It won’t be comprehensive. It will be a little more than just a white-paper, but you couldn’t possibly call it even just the preliminary notes for my new approach. Such preliminary notes would come out only after I deliver a seminar or two, to physics professors + students.

At the time of delivering my proposed seminar, links like those I have given above, esp. Travis Norsen’s book, also should prove a lot useful.

But no, I haven’t seen something like my approach being covered anywhere, so far, not even Norsen’s book. There was a vague mention of just a preliminary part of it somewhere on Roger Schlafly’s blog several years ago, only once or so, but I can definitely say that I had already had grasped even that point on my own before Schlafly’s post came. And, as far as I know, Schlafly hasn’t come to pursue that thread at all, any time later…

But speaking overall, at least as of today, I think I am the only one who has pursued this (my) line of thought to the extent I have [^].

So, there. Bye for now.

I Song I Like:
(Hindi) “suno gajar kya gaaye…”
Singer: Geeta Dutt
Music: S. D. Burman
Lyrics: Sahir Ludhianvi
[There are two Geeta’s here, and both are very fascinating: Geeta Dutt in the audio, and Geeta Bali in the video. Go watch it; even the video is recommended.]

As usual, some editing after even posting, would be inevitable.

Some updates made and some streamlining done on 30 July 2018, 09:10 hrs IST.

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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]

[E&OE]

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What mental imagery for “QM” do I carry?—part 2

This post continues from my last post, here [^].

So, what’s the mental imagery that rushes to my mind when I think of the idea/concept: “Quantum Mechanics”?

Since I have thought about this topic for such a long time (certainly for more than two decades), as far as I am concerned, the picture has no problem immediately jumping to the surface of my mind. However, to write it down is going to take a lot of words, and so, it may not look like a readily available image to you. In any case, since the imagery is a bit complex, brace yourself for yet another long post. Certainly more than a thousand words!

Keep a fresh paper and a few color sketch-pens ready to draw the diagram as we go along.

What I imagine is basically a fake quantum system, because I don’t want my picture to be complicated by a lot of what I regard are the inessential details.

I basically imagine a two-atom system with a bond, in which the nuclei are, in the first stage at least, taken to be fixed in space. Thus, the entire quantum universe consists of only these particles: two positively charged massive nuclei (say two protons), two (or more) negatively charged lighter electrons, and a bunch of massless photons to establish the bond.

In the first version of my imagery, the system is in the time-independent ground state of the molecule. I then add an imagination of a time evolution from this ground state to an excited state, and then, the subsequent collapse back to the ground state. Thus, it’s not a single picture but a series of them.

For the static version of the ground state, using a blue sketch pen, put two blue dots some sizable distance apart near the center of a piece of paper. These blue dots—the nuclei—don’t move.

For the two electrons, take a red sketch pen and make a lot of red dots (of equal sizes) around the two blue dots. The local density of the red dots should be higher near the nuclei, and it should drop off to a negligible density near the edges of the paper. I declare myself that as the paper extends to the (other) end of the universe—and note, not “to” infinity—the dots go on decreasing in density. Yes, I believe in a spatially cyclic—closed and finite—universe. It’s my mental imagery, remember? [There are a lot of trees still left in the world, and new ones are always being planted. So, help yourself with another piece of paper, to draw your imagery. Here, we are concerned only with mine.]

I then take a sketch pen of any faint color, say grey, and add a lot of more dots. These are the virtual photons.

The classes of elementary particles in my mental quantum universe is thus exactly three: nuclei, electrons, and photons, that’s all. I could complicate it more, later. But before I could complicate it further, I know, I would have to get at least this version of the imagery right. And, I remain stuck up right there. That’s why, I regard mass of the massive particles (protons and electrons) as their intrinsic property—a possible compromise from the best possible quantum picture. It actually is a leftover from the Newtonian universe, but it’s OK by me.

The red dots together represent the specific position that any one of the two electrons is likely to occupy. In particular, although there are numerous red dots (and in the continuum limit an infinite number of these), at any given instant, a given electron is found only at one of these dots—the rest are indicative but unoccupied positions.

Note, in my picture, it does not matter which dot corresponds to which electron, even if I know that the electrons always are two separate (and spatially distinguished) entities. The specific positions of the red dots are immaterial; their local density taken together, however, does matter.

This point about the dots and their density has been implicitly well-understood by me, and so it doesn’t find too prominent a place in my imagery, but perhaps it is necessary to spell it out in greater detail. Here is a visualization aid for getting the density of the dots right. Write a Python + matplotlib program to draw such dots. Here is the algorithm. Say, divide the drawing surface (say of 15 X 15 cm extent) into a finite number of square cells (say 1 cm square each). Assume any suitable nonuniform distribution for the electron cloud. Remember, this is all a fake distribution. So anything convenient to you is OK. For instance, the distribution obtained by superposing two Gaussian distributions each of which is centered around one of the two nuclei. Or, the sinc function. Etc. Now, for any cell, you can use the assumed distribution to find out the local density of dots contained in it. In fact, you don’t even have to use the idea of cells; directly using the discrete space of pixels is enough: using a pseudo random number generator, write a program to light up a pixel with a dot such that the probability of its being lit up is proportional to the local distribution density there. Or, you may use the idea of cells thus: find out the density at each of the four corners of a given cell using the analytical expression for the assumed distribution, and then, using the simplest approximate bi-linear interpolation, determine the interpolated density, and then use it to probabilistically to light up the pixels. Finally, another method is to use the strength at the corners of the cell to first decide the number of pixels to light up in a cell, and then randomize the x- and y-coordinates (rather than the lighting up amplitude) for deciding the places where this precise number of dots will get lit up.

Repeat the selected algorithm over time, so that while the density of dots per cell remains constant, due to the changes in the specific random numbers generated, the specific pixels being lit up goes on changing. That’s what I mean by a distribution of dots that is proportional to probability. A specific realization of probabilities isn’t important; that’ the point.

It’s understood that the local density of dots gives you only the probability of finding an electron over that local volume. So, what I do is: I make any two red dots slightly brighter (or bigger, or highlighted via any other means, e.g., via encircling) than the other dots. That’s where the two electrons actually are, at any given instant of time, in my imagery. In the next instant, of course, they occupy some other instantaneous position of some other dot.

Now, an important question: How do the highlighted dots—the positions where the electrons really are—move?

In my imagery, they always move to one of the adjacent instantaneous positions for the neighboring un-highlighted dots. A highlighted dot (the actual position of the electron) never jumps over any one of the un-highlighted dots lying closest to it in its local neighborhood. In other words, IAD (instantaneous action at a distance) summarily goes out for a toss, in my imagery.

Hmmm… But how do the real electrons actually move, even if they move only in their local neighborhood over any given slice of time? … Enter those grey photons. Do I need to say more? Perhaps I do. After all, it’s my imagery.

Before going on to telling you a bit more about the photons themselves, I have to modify my imagery a bit. I now imagine that the edges of the paper represent a virtual end of the universe, and so, I apply a zero density Dirichlet condition on these edges. The sandbox is the universe, in short.

Next, I apply a conservation principle also to the number of photons. Yes, your friendly Nobel laureates go for a toss in my imagery. In my imagery, this happens mostly silently. However, I now recognize that in your imagery of my imagery, they perhaps don’t go out equally silently. They perhaps go out screaming “shame,” “shame,” “ignorance,” “ignorance,” etc. And, along with them go also your not so friendly physics professors at IISc Bangalore, not to mention those at the five old IITs (and all the new ones). (It’s my imagery, remember?) The total number of the small grey dots thus always remains constant.

Another thing. Photons can pass through each other; electrons and protons don’t. All the elementary particles—the nuclei, electrons and photons—are spatially definite; every particle of each kind is confined to a region of space. Which means, I can always point out to some region of paper and say: this given dot does not exist there—a given dot is not spread out everywhere. The existence condition acquires different binary values at a given position. If the particle exists here, it does not exist there. Vice versa.

This requirement does not rule out the possibility that the same place may be occupied by two particles. But, this provision is currently made only for the photons.

[In my current research (i.e. idle arm-chair thinking), I am re-examining this aspect—I am wondering if I can allow two electrons, or one electron and one proton, to occupy the same region of space or not. I am not throwing out the possibility out of the hand. But, the imagery as of now does not allow this possibility. BTW, I have a very, very good logic (very, very good, even to my unsatisfiable self) to think why photons should overlap but not protons or electrons, though I am sure I will keep re-examining the issue. And, no, I am not going to disclose the reasons either way—not until I write a paper on the topic. [evil grin.]]

What exactly are these photons like? Do they have a structure? Yes, or no? What is the difference between these greylings that are the virtual photons and the real photons?

Patience, people, patience. I certainly know the answers; it’s just that I don’t feel like jotting them down here and now, that’s all. [Yawn. Then, an evil grin.]

Do you still want me to narrate how the system evolves? Yes? No? [The evil grin is repeated; then, after a while, it is suppressed.]

OK. Let me be less evil. … You were asking for the difference between the virtual and the real photons, na? OK. Here is my (partial) answer: The similarity between the virtual photons and the real photons is that they both are real. They both exist in spatially delimited sense. The difference between them is that the virtual photons are incapable of altering a given eigen-state; instead, they help bring it into being in the first place. The real photons, in contrast, are those that are capable of changing the eigen-states. To see how, you have to expand the details of this simple imagery a bit more. However, the picture then becomes too complicated. In any case, these additional details is what I myself don’t recollect right in the first second; they come to me only in, say, the 3rd or the 5th second.

So, the rest of the QM is just details, maths, and applications, as far as I am concerned. The real quantum story ends here.

QM is, first and foremost, a theory of sequences of stable configurations of elementary building blocks of matter, and of the passage of matter through these various configurations. To my mind, QM is just that.

It’s, thus, the most elementary materials science. Even chemistry, if you wish. That’s what QM is to me. The mechanics part is only for calculations. QM becomes a branch of physics only because physics is able to supply the principles that allow you to perform the calculations.

But the real QM is only about configuration of matter.

A few remaining notes.

This picture of mine is both in accord with the established axioms of the mainstream theory, as well as at odds with the non-axiomatic but routine assumptions made in the theory.

Pick up any good introductory text on QChem or QM (McQuarrie’s or Levins, or Griffith’s are enough). Go through the list of axioms.

The picture I have here is not in conflict with any of these—the mainstream axioms themselves. Not in the basic sense of the terms they use, anyway. (Challenge for you: Show me one place in one axiom where there is a conflict.)

Yet, my picture also gloatingly insults many of the most mystically revered pillars of QM. These are the suppositions built, not by science popularizers, but by both the ordinary professors and the Nobel laureates of physics alike, including Feynman. Go through the above description once again, and find all of the points where I happily depart from this part of the mainstream tradition. Here is a partial list: spatially delimited elementary particles, specific locations and paths for particles, conservation of photons. … And, at least two more. Find them out. If you really know your Feynman, Dirac, Shankar, or even just Griffiths, you should have no difficulty completing this exercise.

* * * * *   * * * * *   * * * * *

A [Video of a] Song I Like

I am going to make an exception to my usual rules for this section, this time round. (i) I am going to repeat a song in this section—something I haven’t done so far, and, for that reason, (ii) I am going to make a reference to a video—not just the audio—of that song.

I have in mind, a YouTube video officially uploaded by Saregama, i.e., the recording/publishing company.

However, the thing is, as far as I know, the credits as noted by Saregama are wrong. The song, the music, and in fact even the choreography of the dance in the video—they all come from a single man who is not even passingly mentioned by Saregama, viz., the Nobel laureate Gurudeb Robindranath Thakur [hey Bongs, did I get that spelling right?]. Salil Chaudhary merely conducted the music; Hemant Mukherjee/Mukhopadhyaya [i.e. the Hindi film music composer and singer Hemant Kumar] merely sang the piece. [That is, as far as I know. If I am mistaken about any of these aspects, please do correct me.]

One more comment.

This is one dance you can never imagine as originating in any other land, and at any other time. It had to be in India, specifically, in British India, specifically in Bengal, and specifically after the Enlightenment spirit brought by the British had been readily integrated into the local culture by men who also were well-steeped in the best traditions of the ancient Indian culture. This instance of music and dance is a product of someone who was at the cross-roads of those two cultures. He was educated in the Western Enlightenment ideas, and yet he remained recognizably Indian in his soul. Ravindranath Tagore.

As far as the music part is concerned, you can detect a faint Western influence here: the idea of building a piece of music using a progression of chords subtly does find its way here. Thus, though the music is on the whole Indian, you can still detect a faint shade of the Western influence.

Yet, the dance movements here are very emphatically only Indian. The bodily movements are just too supple, just too fluid, either for the West, or for that matter, even for the rest of the East. They obviously are steeped into the traditional Indian culture. Yet, the movements here are too innovative to be merely “traditional;” compare them, after you watch the video, with any BharatnaaTyam or Kathak you saw recently.

The facial expressions of the dancers are only a bit reserved, not too much. These obviously come from the Indian “abhinaya” tradition. Yet, the expressions here drop out that overly dramatic part in the traditional “abhinaya.” The expressions here are, in fact, informal enough to be almost immediately recognizable even to the layman; they are almost of the simple, homely, kind. It’s this part that, by way of an example, serves to highlight the importance of facial expressions in dance. Compare the dancers here with any severely stern-faced, or at least unnecessarily formal-faced Western dancer—which means, most any Western dancer. In any tradition. Ballet, or otherwise. [And no, the expressions here aren’t mindless as in Gypsy or carnival traditions anywhere.]

To say that the dance here, overall, is graceful etc., is a complete waste of words; I have no desire to rush into the category of the eloquent dumb; not so soon anyway. So, let me point out the video to you. Except for just one more noting. Please allow me that.

All the dancers here—including the lead female—have a wheatish, nay, dark wheatish complexion. It’s beautiful.

To reveal a bit about me (it’s not at all a secret; all my friends have always known it): Keeping all other things constant or irrelevant, throughout my life, I have always found the dark wheatish complexion to be the most beautiful one. Even rivetingly so. Not as black as some of the Africans go, but a definitely dark tone, nevertheless. I have never had a fascination for the fair skin. A fair-skinned girl had to be exceptionally beautiful otherwise—in the structure of her face and body—before I could come involuntarily to describe her as being beautiful. Otherwise, using that adjective has been instinctively impossible for me. (No, I have never found either Aishwarya Rai or Madhuri Dixit very beautiful. They are OK, certainly not bad; the first one is passable as above average; the second one as much above average. But neither is ravishingly beautiful. Beauty, to me, is, say, Nandita Das, esp. her younger self. Also, the younger Sonali Kulkarni (the senior one, of course; realize, she alone has a dark complexion among the two).)

In this regard, my tastes have been so much at odds at the prevailing cultural norms in India that I have always felt being more than a bit out of place about it. [In my college days, I had to defend myself against the charge that I was being a maverick just for the heck of being one. At 50+, hopefully, no one levels that charge once again at me.]

It therefore was a very delightful surprise to me when I heard it from a highly respected Sanskrit scholar in Pune (himself a fair-skinned one, in fact, he was born in the Konkanastha Brahmin caste) that the standard of beauty in the ancient India has always included a dark skin tone. Also, relatively fuller (though not very thick) lips. Neither the fair skin, nor the European-thin lips. Rama was wheatish, and KrishNa was relatively even darker in skin color. Also, women like RukmiNi. She was dark-skinned, and was considered very beautiful. Sita was wheatish, too; she too was regarded as beautiful. But it’s the Sanskrit literature preexisting before all these Gods’ times which informs us that the standards were neither compromised nor even slightly modified for these Gods; instead, the existing standards of beauty themselves were merely applied while describing them. Indeed, Sita was regarded more as a smart or sharp-looking than as being very beautiful, whereas RukmiNi was regarded as a perfect example of the most beautiful. So, the standards themselves certainly preexisted all these Gods and Goddesses. They got scrapped sometime only later, perhaps much later; I don’t know precisely when. [It doesn’t have to be as late as the Brits; the Persian standard, too, carries a thing about the fair skin; it too regards a fair skin as being essential to beauty. And, the influence of the Persian standards predates the Mughals at least in some north-western and northern parts of India.]

… No, not all “saanwale” people are beautiful; most in fact are not. In particular, those with a very round face and thereby missing the cheek-bones cannot ever be beautiful—not at least to me: my mind automatically goes into a virtually interminable loop searching for features on such a face. E.g., the actress Sridevi. Below average. Or, Rekha, in her early, plumpy, days. Much below average. Or, Rekha, in her later, slimmer, and far better turned out version. Just about average (or, OK, slightly above that). To my mind, Moushumi Chatterjee would always beat them all very, very easily. (By them, I mean: Madhuri Dixit, Rekha, Aishwarya Rai, and Sridevi.) So, not all “saanwale” people are beautiful. But beautiful people invariably are “saanwaale”.

And, the sheer physical beauty is completely apart from factors such as that “spark” of brilliance or of life on a face, the air (or even the aura, if you wish), the habitual expressions, the manner of conducting oneself or the body language, etc. Here, I was talking only about the sheer physical aspects of beauty, its standards. [Gayatri Devi? Very impressive in looks, and with a very definite purity on the face. Also, good looking. But beautiful? Really beautiful? No, not quite. Beauty is something different than being merely impressive, imposing, or alluring. … Yes, I too could easily describe Gayatri Devi as a beautiful lady. But that’s only in the approximate sense of the term, not exact. That’s the point here.]

Anyway, to wrap up this discussion, so that’s another point about this video that I like—the distinctively Indian look of the dancers, including their beautiful (Hindi) “saanwalaa” skin tone. … And, that distinct touch of the early monsoons in the fields, which forms a very apt background for this video. … All in all, excellent!

OK. Let me not stretch your already far too stretched patience any further; the video is here [^]. Enjoy!

[I don’t know, but, may be, an update might be due. Or, a continuation of the QM topic into a third (and last) part in this series. Especially, if you raise some objections about it. I will check back tomorrow or the day after.]

[E&OE]

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