# Still loitering around…

As noted in the last post, I’ve been browsing a lot. However, I find that the signal-to-noise ratio is, in a way, too low. There are too few things worth writing home about. Of course, OTOH, some of these things are so deep that they can keep one occupied for a long time.

Anyway, let me give many (almost all?) of the interesting links I found since my last post. These are being noted in no particular order. In most cases, the sub-title says it all, and so, I need not add comments. However, for a couple of videos related to QM, I do add significant amount of comments. … BTW, too many hats to do the tipping to. So let me skip that part and directly give you the URLs…

“A digital alchemist’ unravels the mysteries of complexity”:

“Computational physicist Sharon Glotzer is uncovering the rules by which complex collective phenomena emerge from simple building blocks.” [^]

“Up and down the ladder of abstraction. A systematic approach to interactive visualization.” [^]

The tweet that pointed to this URL had this preface: “One particular talent stands out among the world-class programmers I’ve known—namely, an ability to move effortlessly between different levels of abstraction.”—Donald Knuth.

My own thinking processes are such that I use visualization a lot. Nay, I must. That’s the reason I appreciated this link. Incidentally, it also is the reason why I did not play a lot with the interactions here! (I put it in the TBD / Some other day / Etc. category.)

“The 2021 AI index: major growth despite the pandemic.”

“This year’s report shows a maturing industry, significant private investment, and rising competition between China and the U.S.” [^]

“Science relies on constructive criticism. Here’s how to keep it useful and respectful.” [^]

The working researcher, esp. the one who blogs / interacts a lot, probably already knows most all this stuff. But for students, it might be useful to have such tips collected in one place.

“How to criticize with kindness: Philosopher Daniel Dennett on the four steps to arguing intelligently.” [^].

Ummm… Why four, Dan? Why not, say, twelve? … Also, what if one honestly thinks that retards aren’t ever going to get any part of it?… Oh well, let me turn to the next link though…

“Susan Sontag on censorship and the three steps to refuting any argument” [^]

I just asked about four steps, and now comes Sontag. She comes down to just three steps, and also generalizes the applicability of the advice to any argument… But yes, she mentions a good point about censorship. Nice.

“The needless complexity of modern calculus: How 18th century mathematicians complicated calculus to avoid the criticisms of a bishop.” [^]

Well, the article does have a point, but if you ask me, there’s no alternative to plain hard work. No alternative to taking a good text-book or two (like Thomas and Finney, as also Resnick and Halliday (yes, for maths)), paper and pen / pencil, and working your way through. No alternative to that… But if you do that once for some idea, then every idea which depends on it, does become so simple—for your entire life. A hint or a quick reference is all you need, then. [Hints for the specific topic of this piece: the Taylor series, and truncation thereof.] But yes, the article is worth a fast read (if you haven’t read / used calculus in a while). … Also, Twitterati who mentioned this article also recommended the wonderful book from the next link (which I had forgotten)…

The above link is to the Wiki article, which in turn gives the link to the PDF of the book. Check out the preface of the book, first thing.

“The first paper published in the first overlay journal (JTCAM) in Solid Mechanics” [^]

It’s too late for me (I have left mechanics as a full-time field quite a while ago) but I do welcome this development. … A few years ago, Prof. Timothy Gowers had begun an overlay journal in maths, and then, there also was an overlay journal for QM, and I had welcomed both these developments back then; see my blog post here [^].

“The only two equations that you should know: Part 1” [^].

Dr. Joglekar makes many good points, but I am not sure if my choice for the two equations is going to be the same.

[In fact, I don’t even like the restriction that there should be just two equations. …And, what’s happenning? Four steps. Then, three steps. Now, two equations… How long before we summarily turn negative, any idea?]

But yes, a counter-balance like the one in this article is absolutely necessary. The author touches on $E = mc^2$ and Newton’s laws, but I will go ahead and add topics like the following too: Big Bang, Standard Model, (and, Quantum Computers, String Theory, Multiverses, …).

“Turing award goes to creators of computer programming building blocks” [^] “Jeffrey Ullman and Alfred Aho developed many of the fundamental concepts that researchers use when they build new software.”

Somehow, there wasn’t as much of excitement this year as the Turing award usually generates.

Personally, though, I could see why the committee might have decided to recognize Aho and Ullman’s work. I had once built a “yacc”-like tool that would generate the tables for a table-driver parser, given the abstract grammar specification in the extended Backus-Noor form (EBNF). I did it as a matter of hobby, working in the evenings. The only resource I used was the “dragon book”, which was written by Profs. Aho, Sethi, and Ullman. It was a challenging but neat book. (I am not sure why they left Sethi out. However, my knowledge of the history of development of this area is minimal. So, take it as an idle wondering…)

Congratulations to Profs. Aho and Ullman.

“Stop calling everything AI, machine-learning pioneer says” [^] “Michael I. Jordan explains why today’s artificial-intelligence systems aren’t actually intelligent”

Well, “every one” knows that, but the fact is, it still needs to be said (and even explained!)

“How a gene for fair skin spread across India” [^] “A study of skin color in the Indian subcontinent shows the complex movements of populations there.”

No, the interesting thing about this article, IMO, was not that it highlighted Indians’ fascination / obsession for fairness—the article actually doesn’t even passingly mention this part. The real interesting thing, to me, was: the direct visual depiction, as it were, of Indian Indologists’ obsession with just one geographical region of India, viz., the Saraswati / Ghaggar / Mohan Ja Daro / Dwaarkaa / Pakistan / Etc. And, also the European obsession with the same region! … I mean check out how big India actually is, you know…

H/W for those interested: Consult good Sanskrit dictionaries and figure out the difference between निल (“nila”) and नील (“neela”). Hint: One of the translations for one of these two words is “black” in the sense “dark”, but not “blue”, and vice-versa for the other. You only have to determine which one stands for what meaning.

Want some more H/W? OK… Find out the most ancient painting of कृष्ण (“kRSNa”) or even राम (“raama”) that is still extant. What is the colour of the skin as shown in the painting? Why? Has the painting been dated to the times before the Europeans (Portugese, Dutch, French, Brits, …) arrived in India (say in the second millennium AD)?

“Six lessons from the biotech startup world” [^]

Dr. Joglekar again… Here, I think every one (whether connected with a start-up or not) should go through the first point: “It’s about the problem, not about the technology”.

Too many engineers commit this mistake, and I guess this point can be amplified further—the tools vs. the problem. …It’s but one variant of the “looking under the lamp” fallacy, but it’s an important one. (Let me confess: I tend to repeat the same error too, though with experience, one does also learn to catch the drift in time.)

“The principle of least action—why it works.” [^].

Neat article.

I haven’t read the related book [“The lazy universe: an introduction to the principle of least action”] , but looking at the portions available at Google [^], even though I might have objections to raise (or at least comments to make) on the positions taken by the author in the book, I am definitely going to add it to the list of books I recommend [^].

Let me mention the position from which I will be raising my objections (if any), in the briefest (and completely on-the-fly) words:

The principle of the least action (PLA) is a principle that brings out what is common to calculations in a mind-bogglingly large variety of theoretical contexts in physics. These are the contexts which involve either the concept of energy, or some suitable mathematical “generalizations” of the same concept.

As such, PLA can be regarded as a principle for a possible organization of our knowledge from a certain theoretical viewpoint.

However, PLA itself has no definite ontological content; whatever ontological content you might associate with PLA would go on changing as per the theoretical context in which it is used. Consequently, PLA cannot be seen as capturing an actual physical characteristic existing in the world out there; it is not a “thing” or “property” that is shared in common by the objects, facts or phenomena in the physical world.

Let me give you an example. The differential equation for heat conduction has exactly the same form as that for diffusion of chemical species. Both are solved using exactly the same technique, viz., the Fourier theory. Both involve a physical flux which is related to the gradient vector of some physically existing scalar quantity. However, this does not mean that both phenomena are produced by the same physical characteristic or property of the physical objects. The fact that both are parabolic PDEs can be used to organize our knowledge of the physical world, but such organization proceeds by making appeal to what is common to methods of calculations, and not in reference to some ontological or physical facts that are in common to both.

Further, it must also be noted, PLA does not apply to all of physics, but only to the more fundamental theories in it. In particular, try applying it to situations where the governing differential equation is not of the second-order, but is of the first- or the third-order [^]. Also, think about the applicability of PLA for dissipative / path-dependent processes.

… I don’t know whether the author (Dr. Jennifer Coopersmith) covers points like these in the book or not… But even if she doesn’t (and despite any differences I anticipate as of now, and indeed might come to keep also after reading the book), I am sure, the book is going to be extraordinarily enlightening in respect of an array of topics. … Strongly recommended.

Muon $g-2$.

I will give some the links I found useful. (Not listed in any particular order)

• Dennis Overbye covers it for the NYT [^],
• Natalie Wolchoever for the Quanta Mag [^],
• Dr. Luboš Motl for his blog [^],
• Dr. Peter Woit for his blog [^],
• Dr. Adam Falkowski (“Jester”) for his blog [^],
• Dr. Ethan Siegel for the Forbes [^], and,
• Dr. Sabine Hossenfelder for Sci-Am [^].

If you don’t want to go through all these blog-posts, and only are looking for the right outlook to adopt, then check out the concluding parts of Hossenfelder’s and Siegel’s pieces (which conveniently happen to be the last two in the above list).

As to the discussions: The Best Comment Prize is hereby being awarded, after splitting it equally into two halves, to “Manuel Gnida” for this comment [^], and to “Unknown” for this comment [^].

The five-man quantum mechanics (aka “super-determinism”):

By which, I refer to this video on YouTube: “Warsaw Spacetime Colloquium #11 – Sabine Hossenfelder (2021/03/26)” [^].

In this video, Dr. Hossenfelder talks about… “super-determinism.”

Incidentally, this idea (of super-determinism) had generated a lot of comments at Prof. Dr. Scott Aaronson’s blog. See the reader comments following this post: [^]. In fact, Aaronson had to say in the end: “I’m closing this thread tonight, honestly because I’m tired of superdeterminism discussion.” [^].

Hossenfelder hasn’t yet posted this video at her own blog.

There are five people in the entire world who do research in super-determinism, Hossenfelder seems to indicate. [I know, I know, not all of them are men. But I still chose to say the five-man QM. It has a nice ring to it—if you know a certain bit from the history of QM.]

Given the topic, I expected to browse through the video really rapidly, like a stone that goes on skipping on the surface of water [^], and thus, being done with it right within 5–10 minutes or so.

Instead, I found myself listening to it attentively, not skipping even a single frame, and finishing the video in the sequence presented. Also, going back over some portions for the second time…. And that’s because Hossenfelder’s presentation is so well thought out. [But where is the PDF of the slides?]

It’s only after going through this video that I got to understand what the idea of “super-determinism” is supposed to be like, and how it differs from the ordinary “determinism”. Spoiler: Think “hidden variables”.

My take on the video:

No, the idea (of super-determinism) isn’t at all necessary to explain QM.

However, it still was neat to get to know what (those five) people mean by it, and also, more important: why these people take it seriously.

In fact, given Hossenfelder’s sober (and intelligent!) presentation of it, I am willing to give them a bit of a rope too. …No, not so long that they can hang themselves with it, but long enough that they can perform some more detailed simulations. … I anticipate that when they conduct their simulations, they themselves are going to understand the query regarding the backward causation (raised by a philosopher during the interactive part of the video) in a much better manner. That’s what I anticipate.

Another point. Actually, “super-determinism” is supposed to be “just” a theory of physics, and hence, it should not have any thing to say about topics like consciousness, free-will, etc. But I gather that at least some of them (out of the five) do seem to think that the free-will would have to be denied, may be as a consequence of super-determinism. Taken in this sense, my mind has classified “super-determinism” as being the perfect foil to (or the other side of) panpsychism. … As to panpsychism, if interested, check out my take on it, here [^].

All along, I had always thought that super-determinism is going to turn out to be a wrong idea. Now, after watching this video, I know that it is a wrong idea.

However, precisely for the same reason (i.e., coming to know what they actually have in mind, and also, how they are going about it), I am not going to attack them, their research program. … Not necessary… I am sure that they would want to give up their program on their own, once (actually, some time after) I publish my ideas. I think so. … So, there…

“Video: Quantum mechanics isn’t weird, we’re just too big” YouTube video at: [^]

The speaker is Dr. Phillip Ball; the host is Dr. Zlatko Minev. Let me give some highlights of their bio’s: Ball has a bachelor’s in chemistry from Oxford and a PhD in physics from Bristol. He was an editor at Nature for two decades. Minev has a BS in physics from Berkeley and a PhD in applied physics from Yale. He works in the field of QC at IBM (which used to be the greatest company in the computers industry (including software)).

The abstract given at the YouTube page is somewhat misleading. Ignore it, and head towards the video itself.

The video can be divided into two parts: (i) the first part, ~47 minutes long, is a presentation by Ball; (ii) the second part is a chat between the host (Minev) and the guest (Ball). IMO, if you are in a hurry, you may ignore the second part (the chat).

The first two-third portion of the first part (the presentation) is absolutely excellent. I mean the first 37 minutes. This good portion (actually excellent) gets over once Ball goes to the slide which says “Reconstructing quantum mechanics from informational rules”, which occurs at around 37 minutes. From this point onward, Ball’s rigour dilutes a bit, though he does recover by the 40:00 minutes mark or so. But from ~45:00 to the end (~47:00), it’s all down-hill (IMO). May be Ball was making a small little concession to his compatriots.

However, the first 37 minutes are excellent (or super-excellent).

But even if you are absolutely super-pressed for time, then I would still say: Check out at least the first 10 odd minutes. … Yes, I agree 101 percent with Ball, when it comes to the portion from ~5:00 through 06:44 through 07:40.

Now, a word about the mistakes / mis-takes:

Ball says, in a sentence that begins at 08:10 that Schrodinger devised the equation 1924. This is a mistake / slip of the tongue. Schrodinger developed his equation in late 1925, and published it in 1926, certainly not in 1924. I wonder how come it slipped past Ball.

Also, the title of the video is somewhat misleading. “Bigness” isn’t really the distinguishing criterion in all situations. Large-distance QM entanglements have been demonstrated; in particular, photons are (relativistic) QM phenomena. So, size isn’t necessarily always the issue (even if the ideas of multi-scaling must be used for bridging between “classical” mechanics and QM).

And, oh yes, one last point… People five-and-a-half feet tall also are big enough, Phil! Even the new-borns, for that matter…

A personal aside: Listening to Ball, somehow, I got reminded of some old English English movies I had seen long back, may be while in college. Somehow, my registration of the British accent seems to have improved a lot. (Or may be the Brits these days speak with a more easily understandable accent.)

Status of my research on QM:

If I have something to note about my research, especially that related to the QM spin and all, then I will come back a while later and note something—may be after a week or two. …

As of today, I still haven’t finished taking notes and thinking about it. In fact, the status actually is that I am kindaa “lost”, in the sense: (i) I cannot stop browsing so as to return to the study / research, and (ii) even when I do return to the study, I find that I am unable to “zoom in” and “zoom out” of the topic (by which, I mean, switching the contexts at will, in between all: the classical ideas, the mainstream QM ideas, and the ideas from my own approach). Indeed (ii) is the reason for (i). …

If the same thing continues for a while, I will have to rethink whether I want to address the QM spin right at this stage or not…

You know, there is a very good reason for omitting the QM spin. The fact of the matter is, in the non-relativistic QM, the spin can only be introduced on an ad-hoc basis. … It’s only in the relativistic QM that the spin comes out as a necessary consequence of certain more basic considerations (just the way in the non-relativistic QM, the ground-state energy comes out as a consequence of the eigenvalue nature of the problem; you don’t have to postulate a stable orbit for it as in the Bohr theory). …

So, it’s entirely possible that my current efforts to figure out a way to relate the ideas from my own approach to the mainstream QM treatment of the spin are, after all, a basically pointless exercise. Even if I do think hard and figure out some good and original ideas / path-ways, they aren’t going to be enough, because they aren’t going to be general enough anyway.

At the same time, I know that I am not going to get into the relativistic QM, because it has to be a completely distinct development—and it’s going require a further huge effort, perhaps a humongous effort. And, it’s not necessary for solving the measurement problem anyway—which was my goal!

That’s why, I have to really give it a good thought—whether I should be spending so much time on the QM spin or not. May giving some sketchy ideas (rather, making some conceptual-level statements) is really enough… No one throws so much material in just one paper, anyway! Even the founders of QM didn’t! … So, that’s another line of thought that often pops up in my mind. …

My current plan, however, is to finish taking the notes on the mainstream QM treatment of the spin anyway—at least to the level of Eisberg and Resnick, though I can’t finish it, because this desire to connect my approach to the mainstream idea also keeps on interfering…

All in all, it’s a weird state to be in! … And, that’s what the status looks like, as of now…

… Anyway, take care and bye for now…

A song I, ahem, like:

It was while browsing that I gathered, a little while ago, that there is some “research” which “explains why” some people “like” certain songs (like the one listed below) “so much”.

The research in question was this paper [^]; it was mentioned on Twitter (where else?). Someone else, soon thereafter, also pointed out a c. 2014 pop-sci level coverage [^] of a book published even earlier [c. 2007].

From the way this entire matter was now being discussed, it was plain and obvious that the song had been soul-informing for some, not just soul-satisfying. The song in question is the following:

(Hindi) सुन रुबिया तुम से प्यार हो गया (“sun rubiyaa tum se pyaar ho gayaa”)
Music: Anu Malik
Lyrics: Prayag Raj
Singers: S. Jaanaki, Shabbir Kumar

Given the nature of this song, it would be OK to list the credits in any order, I guess. … But if you ask me why I too, ahem, like this song, then recourse must be made not just to the audio of this song [^] but also to its video. Not any random video but the one that covers the initial sequence of the song to an adequate extent; e.g., as in here [^].

History:
2021.04.09 19:22 IST: Originally published.
2021.04.10 20:47 IST: Revised considerably, especially in the section related to the principle of the least action (PLA), and the section on the current status of my research on QM. Also minor corrections and streamlining. Guess now I am done with this post.

A Special note for the Potential Employers from the Data Science field:

Recently, in April 2020, I achieved a World Rank # 5 on the MNIST problem. The initial announcement can be found here [^], and a further status update, here [^].

All my data science-related posts can always be found here [^].

1. A series of tweets on the Bhagawad-Geetaa, chapter 2, verse 47, posted by me today:

Today, I posted a series of tweets. These are quoted (plain copy-pasted) below:

With a good knowledge of the original Sanskrit here, and with my philosophic convictions, I am happy to state that I *don’t* believe in this verse of the Geeta: कर्मण्येवाधिकारस्ते मा फलेषु कदाचन | मा कर्मफलहेतुर्भूर्मा ते सङ्गोऽस्त्वकर्मणि || “karmaNye vaadhikaaraste…” 1/n

This verse quotes one principle that *in principle* can *never* be realized, in practice, by any one. Reason: It goes against the nature of man. So, the only use it can be put to, is: as a means of exhortation. That’s the only viable use-case it at all has. 2/n

BTW, it also goes against Aristotle, *and* *against* the better (more consistent) parts of Vedant (वेदांत) i.e. Upanishad (उपनिषद). It’s quite likely that this verse represents a later-day interpolation by the priestly / Intellectual class as the original जय “Jay” became 3/n

laden with many^2 extraneous things and eventually became महाभारत “Mahaabhaarat”. … Go through the literal translation of this verse, and then ask yourself: Who could have done it? For what purpose? To answer those two questions, ask yourself, in turn, the following: 4/n

Who was at all allowed / authorized to recite and transmit *any* *Sanskrit* verses for a few couple of millennia at least? Who would benefit from its insertion? Who would prescribe it to the *common man*—i.e., reaching beyond the संन्यासी i.e. the renunciates? 5/n

Answers: Power-lusters among the Intellectual/Priestly *castes* (a word which means much more than just “class”). Totalitarian rulers (of any caste, Brahmins/Dalits included.) Other powerful people from society who collude with, or help, both the former. 6/n

The only virtues of this verse are: a superlatively smooth way of *expression*, and the purity of the formulation. Its formulation is so pure, so direct, so open, so *undiluted* by anything extraneous, that these very qualities are likely to make you disregard its actual, 7/n

directly given, meaning. So, you are likely to add your own *loving/lovable* layers of meaning on to it. Which is what people do! Not just foreigners/Christians/Muslims/others, but primarily Indians / Hindus themselves. Which isn’t just a mistake—it’s a grave error. 8/n

What the verse *actually* says to the common man is nothing but a purest form of naked evil. (Telling it to the “sanyaasi” is superfluous / redundant.) Some day, I’ll give you the exact translation sans any interpolations / extraneous additions, 9/n

so that you can see the whole thing by yourself. Yes, many sources (e.g. ISKON’s “as it is”) do give split-ups of words & meanings. But their stated meanings are *not* exact—there’s a lot of distortion in them! 10/n

Till date, I haven’t come across a fully accurate translation—one which hasn’t added something extraneous or given a slant towards a more palatable meaning, etc. (Certainly not S. Radhakrishnan’s version either!_ So, guess, I will have to write the translation myself. 11/n

Fortunately, I do happen to know all the words & the roots (बीज) operative here. (Else, I wouldn’t write this series of tweets either!) Remind me after a few days… 12/12

I have been working on my new approach to QM. Frankly, I have been struggling through it—in trying to showing how my new approach does make sense. (If I find some error in my approach in this process, well and good! I will abandon it. However, things aren’t even as easy as that. So, working through the details takes time.)

I reached a certain definitely identifiable stage in my own thoughts over the past couple of days. So, a break away from QM would have been welcome too. At the same time, I saw someone (once again!) praising the verse in the title of this post. So, I tweeted the above series. Then, to continue with my break (for today or so), I also decided to write a blog post offering a translation of the present verse.

It so turned out that one blog post wouldn’t be enough. A more circumspect approach is called for. Accordingly, I am making a series of posts on this single verse. This post is the very first in this series, it covers just the कर्मण्येवाधिकारस्ते (“karmaNyevaadhikaaraste”) part. This joint-word is split up as: कर्मण्य (“karmaNya”) + एव (“eva”) + अधिकार (“adhikaar”) + : (the sound “h!” called by the name of हलन्त (“halant”)) + ते. Let’s see each part, one by one, splitting each part down to its most basic Sanskrit root, and then building back the meaning in a bottom-to-top manner…

1. कर्म (“karma”):

कर्म (“karma”) = क् (the elemental sound “k”, not the completely uttered sound of क “ka”, and certainly not the “ka” with a long “aaa” as in “kaa”) + “:” (“h!”) + म (“ma”, not “maa”).

क् (the elemental “k”, not क “ka” let alone का “kaa”):  It means (here): A negligibly small or insignificant part. Something for which “what is that? where did it get lost?” can be raised. Here, something which is so negligibly small as it might have to be searched for. Note: the same seed also means a lot of other things too.

Related: कण (“kaNa”) means embodiment of क (“ka”), the imperceptibly small part of the material world, a material particle.

BTW, क “ka” also lies at the base of the more direct seed of the sound कृ (“kru”), which itself is a seed sound for words like “cutting” and “action”. However, क “ka” by itself does not mean “action”. “Action” (whether as a noun or as a verb) lies at way too higher level. क “ka” is very basic. (The usual translators simply rush through, and declare the whole word कर्म (“karma”) to be merely only an action. It is not. Read on…

“:” (the हलन्त), whichi is pronounced as the sharp “h!” sound, and which is modified according to the vowel preceding it (e.g. “hi!”, “hoo!”, etc.). Think of this as a postfix operator which denotes the following sense: “the aforementioned word-part has been completed, though the full jointed word may still continue”.

म (“ma”, not “maa”): It connotes: the self, the direct self-awareness, a consideration or assertion of a distinctive (differentiated) self-identity, the direct awareness of emotions, emotions. It is also the root or seed-sound (बीज) for: eating/drinking, mother, moon, water, liquids, attractions, attention, etc.

Related: मम् (“mam_”) means: “my own”, or “pertaining to my own [self or attributes or possessions]”.

कर्म (“karma”, not “karmaa”) = क्  + : + m, therefore,  literally denotes:

1. That state of being in which the following characteristics or attributes are so small as to be insignificant or vanishingly small: an awareness of your own self, yours being engaged in exploring or weighing alternatives for your own person, or your deliberations over something (anything) of interest to your conscious individuality. Everything of the kind given in the preceding list is, by etymological roots, made insignificant in the concept of कर्म (“karma”).

Realize, कर्म (“karma”) is not mean just “action”. It means “action” in which nothing coming from the self participates—no emotions, no love, no thought, no thinking, no creativity, no judgement, no maths, no poetry, no words, no expression, no communication, nothing whatsoever of this sort—one that involves the self or the mind. That’s what the “self-less-ness” required in the concept of कर्म (“karma”) actually and directly says. Like it or not, but that’s what the word actually means.

2. By implication, qua noun, कर्म (“karma”) also means something which exists whether you exercise self-awareness, self-interest, free-will, or not.

3. By further development, qua noun, it means: an apersonal but life- or consciousness-altering effect caused in the universe by your even just deliberations. An effect which will continue influencing you in future regardless of your present or future self-awareness, your free-will, possibly to avoid it.

4. By implication of 3.: Something outside of you which you set in action and which revisits you, and which is such that your self-consciousness, thinking, actions to evade or counter it cannot evade or counter it.

5. By implication of 4. All consequences (foreseen and unforeseen) of the actions you undertake.

This last sense is how people use the word when they say “law of karma”. However, this is a highly derivative sense. The most primary sense is that given in 1.

Examples in which कर्म (“karma”, not “karmaa”) qua a quality of action in the sense of 1. above is the most saliently visible:

Yours being totally engrossed in some manual work which does not involve even a trace of a deliberation while the action is going on. Your being engrossed in a manual or menial kind of a labour requiring minimal application of the mind. Your being engaged in activities which do not involve any weighing of evidence or any explicit mental processes like judgement, thinking, maths, even just feeling.

Examples also include: Being so engrossed in such a kind of an activity that you lose the sense of self-awarenes, while performing it. The actions which best fit this description are those involved in the manual labour such as: weaving, forging, chipping away wood or rock, manually sowing etc.

As an example on the bad (or undesirable) side: the well known phenomenon of the driver-fatigue induced by the monotony of driving a vehicle. If you drive your car in after mentally reaching in a certain “zone” wherein all thought, all feelings have ceased, when you don’t even care whether you are driving safely or crashing into a wall but you just simply keep driving on…. Such an action does positively qualify to be called कर्म (“karma”), in the primary sense of the term. Remember, not just deductive thinking but every function of the mind is to be minimized to a vanishing size. That includes exercising judgment about road conditions and your driving, too!

Contrast: Being so intently absorbed in stepping through a piece of code for debugging that you don’t notice someone calling out for a cup of coffee. This instance does not count. A crucial element of कर्म (“karma”) is the negligibly small extent of any deliberate or distinctly identifiable conscious thought processes. In short, in the literal sense, कर्म (“karma”) means: Your turning into manual, menial labourer who has lost himself in the activity.

After exaggeration, i.e. not as a part of the meaning of the word, but just to extra-polate the meaning purely for clarification: Your turning into a robot specializing in repetitive tasks.

कर्मण्य (“karmaNya”) comes from कर्म (“karma”). It means: assiduosly or diligently performed “karma”. The sense here is something like: (As seen from a higher viewpoint) pertaining to or about or over “karma”.

2. एव (“eva”):

एव (“eva”) = ए (“e”) + व (“va”)

ए (“e”) connotes pointing out to an end of a de-finite something or a definite point in some progression of concretes.

व (“va”) connotes the action of efflux, going out, pointing out setting forth, throwing out, etc.

एव (“eva”) literally denotes: By direct pointinng out, i.e. by enumeration of some positively or definitively pointed out concrete instances: “Up to this point within this collection”. That is: “Only this much”.

The actual usage is like: “From A, B, C, एव”, but it is understood that the actual sense is: saying explicitly only “A, B, C”, and then, also implying, “but not D, E, F,…, Y, Z”. Thus, एव (“eva”) stands for: “this, this, this, this, and that’s it! Done! Nothing more!!”

Confusing: In Hindi, एवम (“evam”) means: “and”, as while enumering some concretes. Thus, it denotes a concrete continuation, an inclusion of one more instance. In Sanskrit, it denotes the exclusion of every other instance; it means: “[having seen every concrete in the list], thusly”.

Contrasts:

इति (“iti”): It denotes: The end of an abstract composition: a completed sentence, proposition, idea, poem, thesis, book, etc. It also denotes coming to the end. (Think: “The End” in movies, though not the climax scence when the police arrive.) इति (“iti”) doesn’t apply to a *boundary* or an *end-point* of a mere collection of *concretes*. It denotes the *completion* of a piece of *thought* (which is necessarily occurs at an abstract or conceptual level).

आदि (“aadi”): It denotes: An indefinitely specified continuation of the aforementioned list, lit. “and others”.

When someone says रविचंद्रादि देवता (“ravi chandraadi devataa” lit: “Sun, Moon, and other gods”), you can take a reasonable guess that the author should be talking about the 7 gods after whom the 7 days of the week have been named. However, you can’t be very sure whether he also means to include राहु केतु (“raahu, ketu” i.e. the northern and southern lunar nodes) in the same list or not. That’s because the continuation of the sequence implied by आदि (“aadi”) is rather vague; its meaning in a usage has to be determined by reference to the context.

In contrast, इत्यादि (“ityaadi”), from इति (“iti”) + आदि (“aadi”), does give you a complete definition of the sequence and also indicates continuation. Enough concrete instances are given, or the abtract definition is given in sufficient detail, that the nature of the continuation is unambiguous, it is not very indefinite.

To come back to एव (“eva”), it literally means something like this. Imagine someone saying the following to you:

“Don’t mistake me! What I am saying is not a mere hint or an idea; it is an exact enumeration. You are not supposed to imagine a continuation of the list of objects in here. Every thing to be stated has been stated in its full and complete entirety. Nothing else is to be included.”

That’s the एव (“eva”, not pronounced as “evaa”), for you.

For example, it does not mean “certainly” (the word chosen in “Bhagavad-gita As It Is”). The closest English word is: “only”, though the emphasis on concrete instances, implied by एव (“eva”), is not conveyed by “only”.

Related: अत: ए्व (“ata-h! eva”) = अत: + एव (“eva”). अत: = अ (“a”) + त (“ta”) + “:”. In brief, the parts mean: अ (“a”), meaning “Logical complementation or negation (like in non-A)” + त (“ta”) meaning “that which is directly pointed at”, + “:” denoting a sense of a completion of a part, as explained earlier. अत: (“ata-h!”) then literally means something like “no more direct pointing out the instances is necessary any more!” or “Enough said already!”. In the usual Sanskrit usage, it is taken to mean: “[Pause to indicate a break,] so / therefore.”

अत: ए्व (“ata-h! eva”) thus just adds one more emphasis about completion of enumeration. The sense is this: “OK! I have shown you this, this, this, and that. That’s all there is to it! Done! No more concerete instances are left to be pointed out! [Don’t include anything else in this list! Etc.]” Having established the sense, a good translation given, for the closely related अतए्व (“ataeva”) is this: “for this very reason”.

अधिकार (“adhikaar”): अधि (“adhi”) + कार (“kaar”). More technically: अध् (“adh_”) + इ (“i”) + कार (“kaar”).

3.1 अधि (“adhi”): अ (“a”) + ध् (the elemental “dh_”) + इ (the soft vowel “i”).

अ (“a”) as a prefix denotes the logical complement of that which follows. It also denotes the absence of or the end of that which follows. The meaning here is: the “non-A”, given a proposition/set “A”.

ध् (the elemental sound “dh_”) connotes: striking down, holding (one given object with another given object), holding fast, supporting, spanning, bridging, stead-fast, etc. Related: धन (“dhana”) means: Holdings, i.e., fixed assets. Related: अध: = अ + ध् + : = in the (naturally) downwards direction, not holding up, not supporting or supported (hence, by implication, in “free fall”), below, down, etc.

इ (the soft vowel “i”) connotes: the soft spiritual energy, the animating spirit, the living force, etc. Related: धैर्य (“dhairya”) means the ability to hold on, integrity, courage, etc.

धि (“dhi”) = ध् (the elemental “dh_”) + इ (the soft vowel “i”) connotes: The living energy that supports (someone else) from below (by being at a lower station in a social hierarchy).

अधि (“adhi”), therefore, first and foremost (i.e. literally, paying respect to the actual language-roots) means:

1. Being supported by others’ living energies from down below. Being obeyed by the people below.

2. By (Sanskrit) usage, this word-part has come to mean:

“Primacy or higher station in a hierarchical social arrangement of people, gods, or things.”

However note, the word “social” is important, nay, crucially essential. Also crucial to the meaning is the sense of there being a hierarchy. The support being referred to here is not of a material kind; it is a support of other people—their lives, living energy, minds, spirits included.

3. By (Sanskrit) usage, this word-part has come to also mean:

“Primacy or precedence in any hierarchical arrangement of anything.”

Note, the last usage is what your ordinary Sanskrit teacher would tell you. But realize, the meaning he conveys to you quite loose, secondary, derivative, usage-driven sense. The primary sense has to do with the specifically social hierarchy, and specifically with mental energies of the people below you. It has a military kind of a command-and-control structure built right into it—no escape from it.

Related: अधोमुख (“adhomukh”) = अध: + मुख = Facing downwards: lit.: with own mouth turned downwards (so as to directly point the head towards the ground below).

3.2 कार (“kaar”)

कार (“kaar”) means “form”/”essence”/—“ness”; also, “the person who gives form to something”.

Here, “form” is to be taken in exactly the same sense in which Aristotle received and used this term. It means that which is in common to every part, even in a vanishingly small part (after a process of reification or a limiting process), and hence, “of essence”. Perhaps one way to grasp कार (“kaar”) is to translate it as “ness”, as in “man-ness”. However, do note, कार (“kaar”) is often used in a more narrower, material sense too. Thus, its meaning is closer to “state” (as in a state of a physical system or software) or “position” in some unspecified “abstract space”.

Does कार (“kaar”) split up further? Sure it does. Let me not get too much into it. But the very nature of Sanskrit is like that. It derives all its words in reference to some attributes or adjectives possessed by the entity in question, using a simple small set of seed roots.

कार (“kaar”) splits up as: क् (the elemental “k_”) + आ (“aa”) + र (“ra”).

You know a bit about the seed क् (the elemental “k_”) already from the discussion in the section on कर्म (“karma”). आ (“aa”) means that form or essence which is obtained after taking into account (after “taking together”, “collecting”, or “integrating”) the forms or essences of *all* the constiutuent parts. र (“ra”) here means “nature”. (Actually, it basically stands for things like “removal” or “taking away”, but the exact sense depends on the context. Here, it is to be taken in the sense of “reification”.)

Related: आकार (“aakaar”) = आ (“aa”) + कार (“kaar”), Thus, आकार (“aakaar”) means: “The form of something in its totality”. Usage-wise, it means (even in Sanskrit, not just in Indian languages): The geometrical shape (of an object), the geometrical form, the extent of an object, the distinctiveness of an object’s externally visible contours, etc.

Another Meaning: Be careful! कार (“kaar”) is also taken to mean as the person who is responsible for giving the form to an object. For example: 1. ग्रन्थकार (“granthakaar”) means: the author of book; lit. (and if I am fully correct): one who grasps or catches unyielding hold of [pieces of knowledge] and compiles them into an enduring form. 2. शिल्पकार (“shilpakaar”) means: sculptor; lit. (if I am any correct): one who imparts an appearance of motion / life by chipping away at an inanimate object (like a piece of rock). 3. चित्रकार (“chitrakaar”) means: painter / fine-artist; lit. (if I am fully correct, but here, I think, I am): one who makes an attention-capturing or attention-rivetting object (actually, an object that makes you lose all your attention into it). By implication, a beautiful work of fine arts. Etc.

Related: धिक्कार (“dhikkar”) = धिक् + कार. All the elements used in this compound word have already been spelt out by now. This word denotes: Being put into the state of being a living energy that supports the higher ups from below. That is, to be relegated to a lower station in the social hierarchy. By implication, धिक्कार (“dhikkar”) also has come to mean moral denunciation, censure, etc. However, note there are better fitting words like निषेध (“nishedha”) too. In terms of the actual original meaning, धिक्कार (“dhikkar”) cannot be used if there is no context of an implicit *social* hierarchy. (Merely a worse off condition does not qualify. It’s the living energy which must go down below, to support and hold something—obviously, someone—else up.)

Anyway, to wrap up the current discussion: कार (“kaar”) here is to be taken in the sense of: “essence”, “form”, “nature”, “that which makes a thing itself”, etc.

Given the meaning of अधि (“adhi”) and कार (“kaar”), you know can figure out what अधिकार (“adhikaar”) means, in a *literal* sense:

अधिकार (“adhikaar”) literally means, first and foremost:

1. A position of primacy that is supported by other living people in a social hierarchy from below the given person, primarily via their life-energy, spiritual energy, mental energy.

It also means:

2. A state of being in a primary or commanding or principal position among people where other people serve you with their “body and soul”.

Secondary/implied/derivative/by usage meanings: By implication, and after diluting the meaning in mundane usage, अधिकार (“adhikaar”) has also been used (both in Sanskrit and in other Indian languages) variously to mean:

3. Power, Powerful position, 4. Controlling position, 5. Authority (whether of declaration by fiat or by virtue of scholarship), 6. License (as issued by the state so that you can buy a can of beer in India), etc. However, notice, there are other, more fitting words to denote each of these latter usages.

Speaking of the derivative usages, notice, inasmuch as you choose to forget the essential element of the layer of people holding you from below, you are that much going away from the very essence of this formulation, viz., अधिकार (“adhikaar”).

अधिकार: (“adhikaar-h!”) indicates that the preceding word part (अधिकार “adhikaar”) has been completed, with a sharp stress.

ते (“te”) means: “of you”. (Qua a masculine plural, it also means: “they”. However, this verse doesn’t make as much sense with this meaning, as it does with “of you”.)

4. Wrapping up the discussion for today:

The one and only explicitly stated position of command or primacy in the social hierarchy which you have is that pertaining to (or about) being so totally absorbed in, or being so thoroughly engrossed in doing, such a kind a menial (or as mindless as possible) work [prescribed by your higher ups] that it simply cannot have any connection left with you performing any deliberation, undertaking any thought, exercising any part of your mind, or have any concern left with your own self as such.

That, dear reader, is the exact, literal, sense of the opening compound word of what, arguably, is the most oft-quoted verse from the Geetaa.

Speaking off hand, perhaps the only verse which gets as frequently quoted as कर्मण्येवाधिकारस्ते “karmaNyevaadhikaaraste” is: यदायदाहि धर्मस्य “yadaa yadaahi dharmasya”. However, comparatively speaking, the latter is quite straightforward to translate. The reason is, it is not very philosophical or abstract in nature! It is just an assuarance from The Divine.

In contrast, I find that the present verse (कर्मण्येवाधिकारस्ते “karmaNyevaadhikaaraste” ) is quite attractive—it’s very difficult to translate it right!

Finally, just one more thought / comment before parting ways for now, in the next section.

5. अधिकार (“adhikaar”) has absolutely nothing to do with the modern concept of “rights”, let alone that of “individual rights”:

Let me first of all note this very curious fact:

In the context of the verse currently under discussion, every source I ever consulted has translated अधिकार (“adhikaar”) to “right”.

Uh oh! Not at all right! Bad! Very bad and misleading sort of a translation it is! (Why, they don’t even mention just “primacy”. They go all the way to “rights”!)

Let me explain the issues here in the briefest possible way:

The concept of rights, as a moral-political abstraction is, comparatively, a very, very recent development.

Now, note carefully that Sanskrit has no word whatsoever to denote the exact sense of the word “rights” as we use it today.

The idea behind the meaning of the word “rights” (in the sense we today use it and the sense which we recognize it in any literature from the past), began only after Aristotle’s philosophy gained ascendency in the West, about a millenium ago (or slightly later, I think). The British Common Law is a landmark in this development. The meaning of the word “rights” already had begun acquiring noticeably modern undertones by then. This is a certain sense which is not at all discernible in any ancient literature or language, whether Sanskrit, Greek, or others (say from Egypt, or other cultures).

The idea of rights got further developed by great thinkers like John Locke. In its well-refined form, the idea came to be known as “individual rights”. The inclusion of the word “individual” most clearly announces the radical nature of the change in the meaning of the term. See the entry in the Ayn Rand Lexicon, here [^].

अधिकार (“adhikaar”), as we saw, by very roots must have other people to define its basic sense. In fact, as a crucial essence, it must have other people—their mental/spiritual/psychological energies—available at a lower hierarchical station. Only then does the word begins to make any sense. Even if you take the word in the loose sense of just a “primacy”, the actual sense in the Sanskrit word is in a collectivised sense: “primacy of one man in a hierarchy of men”, and not “the metaphysical primacy of man qua individual to take any action he chooses to take (so long as it does not interfere with similar rights of other people)”.

Thus, the idea of “rights”, properly defined as “individual rights”, stands completely on its own—it doesn’t need any primacy or elitism or elevated prestige/station with respect to other people.

Also realize: The Founding Fathers of USA well understood that “rights” are a part of the metaphysical nature of man, that their source is not to be found in any other order, whether social or divine (in the sense, of preachers’).

That sense of “rights” is not just absent in अधिकार (“adhikaar”), but worse, as we saw above, the concept behind this word also positively includes for its crucial essentials, the ideas of social hierarchies and of the people below you. The exact sense of the discourse in the verse would be impossible to convey without including these two elements.

Therefore, if the word अधिकार (“adhikaar”) is at all to be included in a discourse on this verse, then elements such as these two must invariably enter the discourse too. That’s what the Sanskrit language itself says—whether other people tell you this fact or not, and regardless of how they put up sweet layers on top of this ugly truth, how many such layers they lay on, and what precisely is the extent of evasion they do engage themselves in. The truth of matter remains just as it is, regardless of their evasions.

The actual verse does actually tell you the actual story.

6. Wrapping up:

In the next part, we will continue examining the rest of the phrases from this verse—my favorite verse, in a sense! However, please note, blog posts on other topics of interest may also come in between. … The thing is, we have already past the most badly translated—and the most critical—part of the verse. So, we can afford to be a bit leisurely about it. Also, something else to do with my interests (like QM, data science, foundations of physics, etc.) may come in between…

Homework: In the meanwhile…

1. Work out the meaning of: अन्ध (“andha”) usually used (even in Sanskrit), and invariably translated, as “blind person” or “darkness”, though the exact shade of the meaning here is slightly different. With the material explained above, you should be able to easily work your way through this word too.

2. Also try a few good English-to-Sanskrit dictionaries, and see the various meanings of the word “right” and also “rights”. You should find that there is none, but do give it a try… (Remember, स्वाम्य “swaamya” means “ownership” but not the “right” of the “rights”. Of course, you should also think about the other terms…)

Caveat Emptor: As always, I am not an expert of Sanskrit; I am just a happy dilettante who loves to explore it. But sometimes, yes, I do reach the right meaning, and I do share it, that’s all. You are, however, encouraged to consult the actual Sanskrit experts. (Fee free to share with them what I said here in this post too.) All the best!

Take care, and bye for now…

A song I like:

(Marathi) घाई नको बाई अशी, आले रे बकुळफुला (“ghaaee nako baaee ashee, aale re bakuLaphulaa”)
Music: Pt. Jitendra AbhiSheki

[Though I have tried to order the credits right, I also think that all of them are so excellent here, that the order, really speaking, doesn’t matter!]

# Ontologies in physics—7: To understand QM, you have to first solve yet another problem with the EM

In the last post, I mentioned the difficulty introduced by (i) the higher-dimensional nature of $\Psi$, and (ii) the definition of the electrostatic $V$ on the separation vectors rather than position vectors.

Turns out that while writing the next post to address the issue, I spotted yet another issue. Its maths is straight-forward (the X–XII standard one). But its ontology is not at all so easy to figure out. So, let me mention it. (This upsets the entire planning I had in mind for QM, and needs small but extensive revisions all over the earlier published EM ontology as well. Anyway, read on.)

In QM, we do use a classical EM quantity, namely, the electrostatic potential energy field. It turns out that the understanding of EM which we have so painfully developed over some 4 very long posts, still may not be adequate enough.

To repeat, the overall maths remains the same. But it’s the physics—rather, the detailed ontological description—which has to be changed. And with it, some small mathematical details would change as well.

I will mention the problem here in this post, but not the solution I have in mind; else this post will become huuuuuge. (Explaining the problem itself is going to take a bit.)

1. Potential energy function for hydrogen atom:

Consider a hydrogen atom in an otherwise “empty” infinite space, as our quantum system.

The proton and the electron interact with each other. To spare me too much typing, let’s approximate the proton as being fixed in space, say at the origin, and let’s also assume a $1D$ atom.

The Coulomb force by the proton (particle 1) on the electron (particle 2) is given by $\vec{f}_{12} = \dfrac{(e)(-e)}{r^2} \hat{r}_{12}$. (I have rescaled the equations to make the constants “disappear” from the equation, though physically they are there, through the multiplication by $1$ in appropriate units.) The potential energy of the electron due to the proton is given by: $V_{12} = \dfrac{(e)(-e)}{r}$. (There is no prefactor of $1/2$ because the proton is fixed.)

The potential energy profile here is in the form of a well, vaguely looking like the letter V’;  it goes infinitely deep at the origin (at the proton’s position), and its wings asymptotically approach zero at $\pm \infty$.

If you draw a graph, the electron will occupy a point-position at one and only one point on the $r$-axis at any instant; it won’t go all over the space. Remember, the graph is for $V$, which is expressed using the classical law of Coulomb’s.

2. QM requires the entire $V$ function at every instant:

In QM, the measured position of the electron could be anywhere; it is given using Born’s rule on the wavefunction $\Psi(r,t)$.

So, we have two notions of positions for the supposedly same existent: the electron.

One notion refers to the classical point-position. We use this notion even in QM calculations, else we could not get to the $V$ function. In the classical view, the electronic position can be variable; it can go over the entire infinite domain; but it must refer to one and only one point at any given instant.

The measured position of the electron refers to the $\Psi$, which is a function of all infinite space. The Schrodinger evolution occurs at all points of space at any instant. So, the electron’s measured position could be found at any location—anywhere in the infinite space. Once measured, the position “comes down” to a single point. But before measurement, $\Psi$ sure is (nonuniformly) spread all over the infinite domain.

Schrodinger’s solution for the hydrogen atom uses $\Psi$ as the unknown variable, and $V$ as a known variable. Given the form of this equation, you have no choice but to consider the entire graph of the potential energy ($V$) function into account at every instant in the Schrodinger evolution. Any eigenvalue problem of any operator requires the entire function of $V$; a single value at a time won’t do.

Just a point-value of $V$ at the instantaneous position of the classical electron simply won’t do—you couldn’t solve Schrodinger’s equation then.

If we have to bring the $\Psi$ from its Platonic “heaven” to our $1D$ space, we have to treat the entire graph of $V$ as a physically existing (infinitely spread) field. Only then could we possibly say that $\Psi$ too is a $1D$ field. (Even if you don’t have this motivation, read on, anyway. You are bound to find something interesting.)

Now an issue arises.

3. In Coulomb’s law, there is only one value for $V$ at any instant:

The proton is fixed. So, the electron must be movable—else, despite being a point-particle, it is hard to think of a mechanism which can generate the whole $V$ graph for its local potential energies.

But if the electron is movable, there is a certain trouble regarding what kind of a kinematics we might ascribe to the electron so that it generates the whole $V$ field required by the Schrodinger equation. Remember, $V$ is the potential energy of the electron, not of proton.

By classical EM, $V$ at any instant must be a point-property, not a field. But Schrodinger’s equation requires a field for $V$.

So, the only imaginable solutions are weird: an infinitely fast electron running all over the domain but lawfully (i.e. following the laws at every definite point). Or something similarly weird.

So, the problem (how to explain how the $V$ function, used in Schrodinger’s equation) still remains.

4. Textbook treatment of EM has fields, but no physics for multiplication by signs:

In the textbook treatment of EM (and I said EM, not QM), the proton does create its own force-field, which remains fixed in space (for a spatially fixed proton). The proton’s $\vec{E}$ field is spread all over the infinite space, at any instant. So, why not exploit this fact? Why not try to get the electron’s $V$ from the proton’s $\vec{E}$?

The potential field (in volt) of a proton is denoted as $V$ in EM texts. So, to avoid confusion with the potential energy function (in joule) of the electron, let’s denote the proton’s potential (in volt) using the symbol $P$.

The potential field $P$ does remain fixed and spread all over the space at any instant, as desired. But the trouble is this:

It is also positive everywhere. Its graph is not a well, it is a peak—infinitely tall peak at the proton’s position, asymptotically approaching zero at $\pm \infty$, and positive (above the zero-line) everywhere.

Therefore, you have to multiply this $P$ field by the negative charge of electron $e$, so that $P$ turns into the required $V$ field of the electron.

But nature does no multiplications—not unless there is a definite physical mechanism to “convert” the quantities appropriately.

For multiplications with signed quantities, a mechanism like the mechanical lever could be handy. One small side goes down; the other big side goes  up but to a different extent; etc. Unfortunately, there is no place for a lever in the EM ontology—it’s all point charges and the “empty” space, which we now call the aether.

Now, if multiplication of constant magnitudes alone were to be a problem, we could have always taken care of it by suitably redefining $P$.

But the trouble caused by the differing sign still remains!

And that’s where the real trouble is. Let me show you how.

If a proton has to have its own $P$ field, then its role has to stay the same regardless of the interactions that the proton enters into. Whether a given proton interacts with an electron (negatively charged), or with another proton (positively charged), the given proton’s own field still has to stay the same at all times, in any system—else it will not be its own field but one of interactions. It also has to remain positive by sign—even if $P$ is rescaled to avoid multiplications.

But if $V$ has to be negative when an electron interacts with it, and if $V$ also has to be positive when another proton interacts with it, then a multiplication by the signs (by $\pm 1$ must occur. You just can’t avoid multiplications.

But there is no mechanism for the multiplications mandated by the sign conversions.

How do we resolve this issue?

5. The weakness of a proposed solution:

Here is one way out that we might think of.

We say that a proton’s $P$ field stays just the same (positive, fixed) at all times. However, when the second particle is positively charged, then it moves away from the proton; when the second particle is negatively charged, then it moves towards the proton. Since $V$ does require a dot product of a force with a displacement vector, and since the displacement vector does change signs in this procedure, the problem seems to have been solved.

So, the proposed solution becomes: the direction of the motion of the forced particle is not determined only by the field (which is always positive here), but also by the polarity of that particle itself. And, it’s a simple change, you might argue. There is some unknown physics to the very abstraction of the point charge itself, you could say, which propels it this way instead of that way, depending on its own sign.

Thus, charges of opposing polarities go in opposite directions while interacting with the same proton. That’s just how charges interact with fields. By definition. You could say that.

What could possibly be wrong with that view?

Well, the wrong thing is this:

If you imagine a classical point-particle of an electron as going towards the proton at a point, then a funny situation ensues while using it in QM.

The arrows depicting the force-field of the proton always point away from it—except for the one distinguished position, viz., that of the electron, where a single arrow would be found pointing towards the proton (following the above suggestion).

So, the action of the point-particle of the electron introduces an infinitely sharp discontinuity in the force-field of the proton, which then must also seep into its $V$ field.

But a discontinuity like that is not basically compatible with Schrodinger’s equation. It will therefore lead to one of the following two consequences:

It might make the solution impossible or ill-defined. I don’t know enough about maths to tell if this could be true.  But what I can tell is this: Even if a solution is possible (including solutions that possibly may be asymptotic, or are approximate but good enough) then the presence of the discontinuity will sure have an impact on the nature of the solution. The calculated $\Psi$ wouldn’t be the same as that for a $V$ without the discontinuity. That’s inevitable.

But why can’t we ignore the classical point-position of the electron? Well, the answer is that in a more general theory which keeps both particles movable, then we have to calculate the proton’s potential energy too. To do that, we have to take the electric potential (in volts) $P$ of the electron, and multiply it by the charge of the proton. The trouble is: The electric potential field of the electron has singularity at its classical position. So, classical positions cannot be dropped out of the calculations. The classical position of a given particle is necessary for calculating the $V$ field of the other particle, and, vice-versa.

In short, to ensure consistency in the two ways of the interaction, we must regard the singularities as still being present where they are.

And with that consideration, essentially, we have once again come back to a repercussion of the idea that the classical electron has a point position, but its potential energy field in the electrostatic interaction with the proton is spread everywhere.

To fulfill our desire of having a $3D$ field for $\Psi$, we have to have a certain kind of a field for $V$. But $V$ should not change its value in just one isolated place, just in order to allow multiplication by $-1$, because doing so introduces a very bad discontinuity. It should remain the same smooth $V$ that we have always seen in the textbooks on QM.

6. The problem statement, in a nutshell:

So, here is the problem statement:

To find a physically realizable way such that: even if we use the classical EM properties of the electron while calculating $V$, and even if the electron is classically a point-particle, its $V$ function (in joules) should still turn out to be negative everywhere—even if the proton has its own potential field ($P$, in volts) that is positive everywhere in the classical EM.

In short, we have to change the way we look at the physics of the EM fields, and then also make the required changes to any maths, as necessary. Without disturbing the routine calculations either in EM or in QM.

Can it be done? Well, I think the answer is “yes.”

7. A personal note:

While I’ve been having some vague sense of there being some issue “to be looked into later on” for quite some time (months, at least), it was only over the last week, especially over the last couple of days (since the publication of the last post), that this problem became really acute. I always used to skip over this ontology/physics issue and go directly over to using the EM maths involved in the QM. I used to think that the ontology of such EM as it is used in the QM, would be pretty easy to explain—at least as compared to the ontology of QM. Looks like despite spending thousands of words (some 4–5 posts with a total of may be 15–20 K words) there still wasn’t enough of a clarity—about EM.

Not if we adopt the principle, which I discovered on the fly, right while in the middle of writing this series, that nature does no multiplications without there being a physical mechanism for it.

Fortunately, the problem did become clear. Clear enough that, I think, I also found a satisfactory enough solution to it too. Right today (on 2019.10.15 evening IST).

Would you like to give it a try? (I anyway need a break. So, take about a week’s time or so, if you wish.)

Bye for now, take care, and see you the next time.

A song I like:

(Hindi) “jaani o jaani”
Singer: Kishore Kumar
Music: Laxmikant-Pyarelal
Lyrics: Anand Bakshi

History:

— Originally published: 2019.10.16 01:21 IST
— One or two typos corrected, section names added, and a few explanatory sentences added inline: 2019.10.17 22:09 IST. Let’s leave this post right in this form.