# A further general update: The motion of a single electron in a box

I am still struggling with the conceptual issues which I mentioned in my 23rd August, 2020 post [^]. In this post, let me update you on the status in a more specific way. The conceptual trouble arises even with just the $x$-motion of the electron in $1D$ simulations. So let me note the solution of the model first.

1. The $1$-dimensional Particle in a Box model:

Consider the simplest problem, a single particle in a $1D$ box with infinite potential walls at the ends, i.e., the famous particle-in-a-box problem (PIB for short). The analytical solution to this problem can be given via the following series of equations:

$k_n = n \dfrac{\pi}{L}$, where $k_n$ is the magnitude of the wavevector $\vec{k}_n$, and $L$ is the length of the box that occupies the interval $x = [0.0, L]$.

$p_n = \hbar k_n$, where $p_n$ is the magnitude of the global (aspatial, atemporal) momentum content of the system, and $\hbar$ is the reduced Planck constant (with unit of action i.e. joule second i.e. (kilogram meter per second) times meter).

$E_n = \dfrac{p_n^2}{2 m_e}$, where $E_n$ is the global (aspatial, atemporal) total internal energy content of the system, in joule, and $m_e$ is the mass of the particle, here, electron, in kilogram.

$\omega_n = \dfrac{E_n}{\hbar}$, where $\omega_n = 2 \pi \nu$ is the angular frquencey (in radian per second), and $\nu$ is the frequency (revolution per second).

$\psi(x) = A \sin(k_n x)$, is the space-dependent part of the wavefunction, and $A = \sqrt{\dfrac{2}{L}}$ is the normalization constant, in $\dfrac{1}{\sqrt{\text{m}}}$.

$\Theta(t) = e^{-i(\omega_n t)}$ is the time-dependent part of the wavefunction.

Now we can give the actual wavefunction as:

$\Psi(x,t) = \psi(x) \Theta(t) = A \sin(k_n x) \left[ \cos(\omega_n t) - i\,\sin(\omega_n t) \right]$.

The unit of $\Psi(x,t)$ and $\psi(x)$ is $\dfrac{1}{\sqrt{\text{m}^D}}$ where $D$ is the dimensionality of the physical space (here, $D=1$).

2. What view I take of the PIB solution:

2.1. $\Psi_n(x,t)$ field represents something that actually exists:

I have indicated (but not fully consistently stated) my new approach via the Outline document [^] and the Ontologies series of blog-posts [^], esp. # 8 [^], # 9 [^] and # 10 [^]. However, notice, there are certain changes to be made to the last part. According to my new approach $\Psi_n(x,t)$ is a complex-valued field that physically exists in the $1D$ physical space.

2.2 There are electrostatic interactions going on even in the PIB model, but these are implicit:

Although the equations of the PIB model does not capture the electrostatic interactions of the electron, physically, these interactions are very much present. It’s just that the PIB model has been designed in such a way that the potential energy for the electrostatic interactions can be ignored.

In the PIB model, the said “ignorance” comes about in two ways:

Firstly, the boundary walls are (i) fixed and (ii) do not exert any electrostatic forces within the domain. That’s because the model assumes that the potential energy acquired by the electron due to the electrostatic field created by the walls drops down to zero in infinitesimally small length near the boundary points. So, in effect, electron does not acquires any potential energy from the (infinitely large) negative electric charge in the side walls.

Secondly, the introduction of the electron into the system does “create” an electrostatic potential field which is always singularly anchored into its instantaneous position. (See the Note 1 in the subsection 2.4. below.) However, since the walls always remain fixed, the potential energy of the walls due to electrons is zero—there is zero displacement and so, the work done by the forces exerted by the electron on the walls is zero. This is the reason why the PE of the walls does not at all enter into analysis. (Schrodinger’s solution for the H atom does something similar: It keeps the proton fixed. The solution then takes care of the energetics (the work done on the proton by the electron) by using the reduced mass method of classical mechanics.)

Now, why did I get into all these details?

Just to point out that

The singularity of the electrostatic potential field associated with an electron is physically still present in the domain. It’s just that the PIB model need not explicitly address the potential energy acquired by the walls due to this field, because the walls remain fixed and only at the boundary point, not in the domain.

Although the energy analysis for the PIB model does not account for it, in the new approach, the electron’s position is very much identified with it. That’s my proposition. [Accept it or reject it (or ignore it); I think about it in this way.]

2.3. How should the classical electrostatic singularity for the electron move?

The question now is, how should the singularity—i.e. the classical point-position of the electron—move? What mechanism(s) should guide its $x$-motion in the $1D$ PIB model?

As I said, following my new approach, the wavefunction $\Psi(x,t)$ is a field in the aether. It is always complex-valued. Notice, in the PIB model, the purely space-dependent part is all real (as in the PIB equations given above), but the purely time-dependent part still remains full complex-valued. So, the $\Psi(x,t)$ turns out to be fully complex. It’s not real-valued. Not even in the stationary states. Not even if you fill the box with a state that is a pure eigenstate of the energy operator (as in the above mentioned equations).

So, the essential issue is this:

The $\Psi(x,t)$ is complex-valued. But there is only one $x$-axis for the singularity (i.e. the classical point-particle of the electron) to move. So, precisely how would it move? Following which law? which physical mechanism? And, if not a physical mechanism in real physical space, then at least an abstract mechanism that still has a sufficient closeness to the physical reality?

These questions are important, because unless we have a definitive law for the $x$-axis motion of the singularity within the domain, the nonlinearity in $\Psi(x,t)$ which has been proposed by me wouldn’t work. (See the Outline document [^] for how the nonlinearity comes about.) And if the law we propose isn’t correct, then the nonlinearity wouldn’t work right. So, it’s important to have a correct law for the $x$-motions of the singularities of charges.

It is in this context that I did some simulation in June/July this year, and then, in August this year, I realized that while initially it looked good, a closer examination showed that it had glorious flaws: Flaw 1: Even the $x$-motions were coming out, in the general case, as complex-valued. I could not reduce them to real-valued ones using any plausible logic. Flaw 2: Difficult to figure out, but there was a hidden logical fallacy of circularity built into it (into my June/July simulation). I figured out this flaw only during the second thoughts, which was in August this year.

So, that’s the story in short, what I have been trying to do.

2.4. Note 1:

My further development now sheds a further light on the singularity in the electrostatic potential and potential energy fields.

The singularity in the potential energy $V(x,t)$ turns out to be not a physical existent but only a mathematically abstract description which is obtained using the classical EM ontology.

The singularity in the potential energy field $V(x,t)$ gets compensated by another singularity in the kinetic energy field in such a way that the field for the total internal energy is finite.

The very last bit should not be surprising, because $E$ is finite, and $\Psi(x,t)$ is required to be square-normalizable. In fact, neither of the above two statements should be, really speaking, come as surprising—if you treat $\Psi(x,t)$ as an actually existing physical field in the $D$-dimensional physical space (and not in $ND$-dimensional configuration space). It’s just that the MSQM refuses to treat the wavefunction as a field in the physical space. (And the Bohmian mechanics has not been able to address the issue, I gather.)

However, it was a pleasant nugget to learn for me, when I noticed that the singularity is getting removed from my physics. For philosophic reasons, I’ve always believed that infinity is only a mathematical concept; that infinity of anything cannot physically exist.

Further, I also want to point out the following:

The idea of two singular fields cancelling each other and producing a finite field occurs very naturally, and therefore, seems to be on quite solid grounds. Contrast renormalization (which, really speaking, I don’t understand).

Please wait a little while before I adequately cover this aspect later on. For the time being, we will continue using the “fake” language as if the singularity physically exists.

To wind up:

In the description I am developing for QM, the $\Psi(x,t)$ field (or some other complex-valued field which can be characterized using the square-normalized $\Psi(x,t)$) has the primacy, and so, there is no singularity in the primary description. But I continue to use the established terminology of EM ontology, just out of convenience of writing and communication. (There will always be this back and forth for some time, before I come to fully straightening out the conceptual hierarchy. Until then, using the established language of the “classical” EM seems to be a good choice.)

3. The present status—i.e., the actual update:

Now, given the above context, here is the actual update I wanted to write for this post.

I have found a way or a formula which (1) seems to carry no logical circularity, (2) is simple enough, and, crucially, (3) produces a formula for the $x$-motion that is real-valued (not complex-valued), even while respecting the principles of conservation of energy and momentum for the domain.

This dynamics is simple. In fact, at least outwardly, it is so [god-damn] simple that it is plain and clear that if I were not to try the more complicated ways of thinking about this problem (for the $x$-motion of the particle i.e. singularity), I would have got to this particular dynamics within an hour … at the most, one week. Frankly, it’s not even high-school logic, it is a middle-school-level logic. … In short, the formula is very, very, simple.

It also works—quantitatively, including units/physical dimensions.

Further, it seems to make some sense even when seen from different viewpoints—not just from the viewpoint of conservation of energy and momentum, but also from that of the correspondence of quantum mechanics to classical quantities.

Due to its simplicity, this formula also seems to hint that something physical (that is actually at work) should be very close by.

It’s just that…

with all my ability to find physical correspondents for mathematical ideas (see the Less transient page of this blog [^]), I still haven’t been able to get to a point where I can confidently say that I’ve got a good conceptual handle on this matter too.

At this juncture, I could have gone ahead and done some $2$– and $3$-particle simulations. After all, the “math” does work for the $1$-particle case, doesn’t it?

But I being I [or is it me being me? or me being I? or I being me?] I couldn’t go further purely out of that one reason alone—viz., that the “math” works. I just cannot do that. I am constitutionally incapable of leaping ahead in that manner—for my own good or bad.

That’s why, I must spend some more time (say a week or two) before (i) I can tell myself that I don’t understand the detailed mechanism of how this simplest maths comes to be, (ii) keep this aside as a TBD (to be done) thing, and (iii) start using the goddamn simple formula as is, and see where it leads for the $2$– or $3$-particle systems.

So, that’s where I am, right now. I am stuck. And it’s on the conceptual side, not maths!

Within my own skill-set, I am comparatively weaker in maths, and so, if I were to get stuck somewhere in the maths, it would have been in the line of the things; something that was only to be expected. But being stuck on the conceptual side was totally unexpected—at this stage of the development anyway! [No, it’s not humiliating. Nothing is, so long as you are thinking about it. But unexpected, sure it is.]

And that was the update I had for you, for now.

… Guess, enough of writing for this post. I’ll come back, may be in a week’s time or so, either with a few links, or with a list of some of the books I’ve found useful over a period of time. At that time, I will also make sure to note whether this conceptual issue got resolved in the meanwhile, or whether I had kept it pending and proceeded ahead with the further simulations, not knowing whether they would be physically sound or not… Tough choice… Let me work through it…

A song I like:

(Marathi) चंद्र अर्धा राहिला (“chandra ardhaa raahilaa”)
Music: Yashwant Deo
Singer: Krishna Kalle

Credits happily listed in a random order. A relatively good quality audio is here [^] (and also as a part of a collection, here [^]).

Mentioning this song inevitably invites comparison to the following Hindi song—or at least, it used to, when I was young and both the songs used to be known to people. The Hindi song in question is:

Singers: Mahendra Kapoor, Asha Bhosle
Music: C. Ramchandra
Lyrics: Bharat Vyas

A relatively good quality audio is here [^].

I don’t know if this Hindi film song from “Navrang” was inspired from the Marathi non-film song, or vice-versa, or whether there was no connection at all. (Some kind of a Marathi connection is easily possible. The producer-director of the film, V. Shantaram, was… err… a Marathi Manus.)

… As to me, I like both these songs.

The Hindi song has a good, flowing kind of a tune, and beautiful rendition by both the singers—they complement each other very well. Asha’s voice here is young, thin, and sharp but silky as usual. Mahendra Kapoor supplies the right contrast to her singing in a low key manner, but may be because he was rather young and not very establishedat that time (1959), his singing style here seems to be following C. Ramchandra’s instructions to the hilt. It would be easy to mistake him for C. Ramchandra.

Yes, I like them both. But in between the two, my choice is clear. The Marathi song is not just much closer to my heart, I also think that musically it’s superior. Yashwant Deo’s tune itself is more fresh and innovative, the singing by Krishan Kalle is very nuanced, and the Marathi lyrics too are outstanding… Even if you don’t know Marathi, do give it a listen too…

All in all, I would say, listen to both these songs and see whether you like any of the two or both of them; and if both, which one you like better.

… Take care and bye for now…

I. A general update regarding my on-going research work (on my new approach to QM):

1.1 How the development is actually proceeding:

I am working through my new approach to QM. These days, I write down something and/or implement some small and simple Python code snippets (< 100 LOC Python code) every day. So, it’s almost on a daily basis that I am grasping something new.

The items of understanding are sometimes related to my own new approach to QM, and at other times, just about the mainstream QM itself. Yes, in the process of establishing a correspondence of my ideas with those of the mainstream QM, I am getting to learn the ideas and procedures from the mainstream QM too, to a better depth. … At other times, I learn something about the correspondence of both the mainstream QM and my approach, with the classical mechanics.

Yes, at times, I also spot some inconsistencies within my own framework! It too happens! I’ve spotted several “misconceptions” that I myself have had—regarding my own approach!

You see, when you are ab initio developing a new theory, it’s impossible to pursue the development of the theory very systematically. It’s impossible to be right about every thing, right from the beginning. That’s because the very theory itself is not fully known to you while you are still developing it! The neatly worked out structure, its best possible presentations, the proper hierarchical relations… all of these emerge only some time later.

Yes, you do have some overall, “vaguish” idea(s) about the major themes that are expected to hold the new theory together. You do know many elements that must be definitely there.

In my case, such essential themes or theoretical elements go, for example, like: the energy conservation principle, the reality of some complex-valued field, the specific (natural) form of the non-linearity which I have proposed, my description of the measurement process and of Born’s postulate, the role that the Eulerian (fixed control volume-based) formulations play in my theorization, etc.

But all these are just elements. Even when tied together, they still amount to only an initial framework. Many of these elements may eventually turn out to play an over-arching role in the finished theory. But during the initial stages (including the stage I am in), you can’t even tell which element is going to play a greater role. All the elements are just loosely (or flexibly) held together in your mind. Such a loosely held set does not qualify to be called a theory. There are lots and lots (and lots) of details that you still don’t even know exist. You come to grasp these only on the fly, only as you are pursuing the “fleshing out” of the “details”.

Once the initial stage gets over, and you are going through the fleshing out stage, the development has a way of progressing on multiple threads of thought, simultaneously.

There are insights or minor developments, or simply new validations of some earlier threads, which occur almost on a daily basis. Each is a separate piece of a small little development; it makes sense to you; and all such small little pieces keep adding up—in your mind and in your notebooks.

Still, there is not much to share with others, simply because in the absence of a knowledge of all that’s going through your mind, any pieces you share are simply going to look as if they were very haphazard, even “random”.

1.3. At this stage, others can easily misunderstand what you mean:

Another thing. There is also a danger that someone may misread you.

For example, because he himself is not clear on many other points which you have not noted explicitly.

Or, may be, you have noted your points somewhere, but he hasn’t yet gone through them. In my case, it is the entirety of my Ontologies series [^]. … Going by the patterns of hits at this blog, I doubt whether any single soul has ever read through them all—apart from me, that is. But this entire series is very much alive in my mind when I note something here or there, including on the Twitter too.

Or, sometimes, there is a worse possibility too: The other person may read what you write quite alright, but what you wrote down itself was somewhat misleading, perhaps even wrong!

Indeed, recently, something of this sort happened when I had a tiny correspondence with someone. I had given a link to my Outline document [^]. He went through it, and then quoted from it in his reply to me. I had said, in the Outline document, that the electrons and protons are classical point-particles. His own position was that they can’t possibly be. … How possibly could I reply him? I actually could not. So, I did not!

I distinctly remember that right when I was writing this point in the Outline document, I had very much hesitated precisely at it. I knew that the word “classical” was going to create a lot of confusions. People use it almost indiscriminately: (i) for the ontology of Newtonian particles, (ii) for the ontology of Newtonian gravity, (iii) for ontology of the Fourier theory (though very few people think of this theory in the context of ontologies), (iv) for ontology of EM as implied by Maxwell, (v) for ontology of EM as Lorentz was striving to get at and succeeded brilliantly in so many essential respects (but not all, IMO), etc.

However, if I were to spend time on getting this portion fully clarified (first to myself, and then for the Outline document), then I also ran the risk of missing out on noting many other important points which also were fairly nascent to me (in the sense, I had not noted them down in a LaTeX document). These points had to be noted on priority, right in the Outline document.

Some of these points were really crucial—the $V(x,t)$ field as being completely specified in reference to the elementary charges alone (i.e. no arbitrary PE fields), the non-linearity in $\Psi(x,t)$, the idea that it is the Instrument’s (or Detector’s) wavefunction which undergoes a catastrophic change—and not the wavefunction of the particle being measured, etc. A lot of such points. These had to be noted, without wasting my time on what precisely I meant when I used the word “classical” for the point-particle of the electron etc.

Yes, I did identify that I the elementary particles were to be taken as conditions in the aether. I did choose the word “background object” merely in order to avoid any confusion with Maxwell’s idea of a mechanical aether. But I myself wasn’t fully clear on all aspects of all the ideas. For instance, I still was not familiar with the differences of Lorentz’ aether from Maxwell’s.

All in all, a document like the Outline document had to be an incomplete document; it had to come out in the nature of a hurried job. In fact, it was so. And I identified it as such.

I myself gained a fuller clarity on many of these issues only while writing the Ontologies series, which happened some 7 months later, after putting out the Outline document online. And, it was even as recently as in the last month (i.e., about 1.5 years after the Outline document) that I was still further revising my ideas regarding the correspondence between QM and CM. … Indeed, this still remains a work in progress… I am maintaining handwritten notes and LaTeX files too (sort of like “journal”s or “diaries”).

All in all, sharing a random snapshot of a work-in-progress always carries such a danger. If you share your ideas too early, while they still are being worked out, you might even end up spreading some wrong notions! And when it comes to theoretical work, there is no product-recall mechanism here—at all! Detrimental to your goals, after all!

1.3 How my blogging is going to go, in the next few weeks:

So, though I am passing through a very exciting phase of development these days, and though I do feel like sharing something or the other on an almost daily basis, when I sit down and think of writing a blog post, unfortunately, I find that there is very little that I can actually share.

For this very reason, my blogging is going to be sparse over the coming weeks.

However, in the meanwhile, I might post some brief entries, especially regarding papers/notes/etc. by others. As in this post.

OTOH, if you want something bigger to think about, see the Q&A answers from my last post here. That material is enough to keep you occupied for a couple of decades or more… I am not joking. That’s what’s happened to others; it has happened to me; and I can guarantee you that it would happen to you too, so long as you keep forgetting whatever you’ve read about my new approach. You could then very easily spend decades and decades (and decades)…

Anyway, coming back to some recent interesting pieces by others…

2.1. Luboš Motl on TerraPower, Inc.:

Dr. Luboš Motl wrote a blog-post of the title “Green scientific illiteracy enters small nuclear reactors, too” [^]. This piece is a comment on TerraPower’s proposal. In case you didn’t know, TerraPower is a pet project of Bill Gates’.

My little note (on the local HDD), upon reading this post, had said something like, “The critics of this idea are right, from an engineering/technological viewpoint.”

In particular, I have too many apprehensions about using liquid sodium. Further, given the risk involved in distributing the sensitive nuclear material over all those geographically dispersed plants, this idea does become, err…, stupid.

In the above post, Motl makes reference to another post of his, one from 2019, regarding the renewable energies like the solar and the wind. The title of this earlier post read: “Bill Gates: advocates of dominant wind & solar energy are imbeciles” [^]. Make sure to go through this one too. The calculation given in it is of a back-of-the-envelop kind, but it also is very impeccable. You can’t find flaw with the calculation itself.

Of course, this does not mean that research on renewable energies should not be pursued. IMO, it should be!

It’s just that I want to point out a few things: (i) Motl chooses the city of Tokyo for his calculation, which IMO would be an extreme case. Tokyo is a very highly dense city—both population-wise and on the count of geographical density of industries (and hence, of industrial power consumption). There can easily be other places where the density of power consumption, and the availability of the natural renewable resources, are better placed together. (ii) Even then, calculations such as that performed by Motl must be included in all analyses—and, the cost of renewable energy must be calculated without factoring in the benefit of government subsidies. … Yes, research on renewable energy would still remain justified. (iii) Personally, I find the idea of converting the wind/solar electricity into hydrogen more attractive. See my 2018 post [^] which had mentioned the idea of using the hydrogen gas as a “flywheel” of sorts, in a distributed system of generation (i.e. without transporting the wind-generated hydrogen itself, over long distances).

2.2. Demonstrations on coupled oscillations and resonance at Harvard:

As to the relevance of this topic to my new approach to QM: The usual description of resonance proceeds by first stating a homogeneous differential equation, and then replacing the zero on the right hand-side with a term that stands for an oscillating driving force [^]. Thus, we specify a force-term for the driver, but the System under study is still being described with the separation vector (i.e. a displacement) as the primary unknown.

Now, just take the driver part of the equation, and think of it as a multi-scaled effect of a very big assemblage of particles whose motions themselves are fundamentally described using exactly the same kind of terms as those for the particles in the System, i.e., using displacements as the primary unknown. It is the multi-scaling procedure which transforms a fundamentally displacement-based description to a basically force-primary description. Got it? Hint below.

[Hint: In the resonance equation, it is assumed that form of the driving force remains exactly the same at all times: with exactly the same $F_0$, $m$, and $\omega$. If you replace the driving part with particles and springs, none of the three parameters characterizing the driving force will remain constant, especially $\omega$. They all will become functions of time. But we want all the three parameters to stay constant in time. …Now, the real hint: Think of the exact sinusoidal driving force as an abstraction, and multi-scaling as a means of reaching that abstraction.]

2.3 Visualization of physics at the University of St. Andrews:

Again, very neat [^]. The simulations here have very simple GUI, but the design of the applets has been done thoughtfully. The scenarios are at a level more advanced than the QM simulations at PhET, University of Colorado [^].

2.4. The three-body problem:

The nonlinearity in $\Psi(x,t)$ which I have proposed is, in many essential ways, similar to the classical $N$-body problem.

The simplest classical $N$-body problem is the $3$-body problem. Rhett Allain says that the only way to solve the $3$-body problem is numerically [^]. But make sure to at least cursorily note the special solutions mentioned in the Wiki [^]. This Resonance article (.PDF) [^] seems quite comprehensive, though I haven’t gone through it completely. Related, with pictures: A recent report with simulations, for search on “choreographies” (which is a technical term; it refers to trajectories that repeat) [^].

Sure there could be trajectories that repeat for some miniscule number of initial conditions. But the general rule is that the $3$-body problem already shows sensitive dependence on initial conditions. Search the ‘net for $4$-body, $5$-body problems. … In QM, we have $10^{23}$ particles. Cool, no?

2.5.1: Max Born in IISc Bangalore:

Check out a blog post/article by Karthik Ramaswamy, of the title “When Raman brought Born to Bangalore” [^]. (H/t Luboš Motl [^].)

2.5.2: Academic culture in India in recent times—a personal experience involving the University of Pune, IIT Bombay, IIT Madras, and IISc Bangalore:

After going through the above story, may I suggest that you also go through my posts on the Mechanical vs. Metallurgy “Branch Jumping” issue. This issue decidedly came up in 2002 and 2003, when I went to IIT Bombay for trying admission to PhD program in Mechanical department. I tried multiple times. They remained adamant throughout the 2002–2003 times. An associate professor from the Mechanical department was willing to become my guide. (We didn’t know each other beforehand.) He fought for me in the department meeting, but unsucessfully. (Drop me a line to know who.) One professor from their CS department, too, sympathetically listened to me. He didn’t understand the Mechanical department’s logic. (Drop me a line to know who.)

Eventually, in 2003, three departments at IISc Bangalore showed definite willingness to admit me.

One was a verbal offer that the Chairman of the SERC made to me, but in the formal interview (after I had on-the-spot cleared their written tests—I didn’t know they were going to hold these). He even offered me a higher-than-normal stipend (in view of my past experience), but he said that the topic of research would have to be one from some 4–5 ongoing research projects. I declined on the spot. (He did show a willingness to wait for a little while, but I respectfully declined it too, because I knew I wanted to develop my own ideas.)

At IISc, there also was a definite willingness to admit me by both their Mechanical and Metallurgy departments. That is, during my official interviews with them (which once again happened after I competitively cleared their separate written tests, being short-listed to within 15 or 20 out of some 180 fresh young MTech’s in Mechanical branch from IISc and IITs—being in software, I had forgotten much of my core engineering). Again, it emerged during my personal interviews with the departmental committees, that I could be in (yes, even in their Mechanical department), provided that I was willing to work on a topic of their choice. I protested a bit, and indicated the loss of my interest right then and there, during both these interviews.

Finally, at around the same time (2003), at IIT Madras, the Metallurgical Engg. department also made an offer to me (after yet another written test—which I knew was going to be held—and an interview with a big committee). They gave me the nod. That is, they would let me pursue my own ideas for my PhD. … I was known to many of them because I had done my MTech right from the same department, some 15–17 years earlier. They recalled, on their own, the hard work which I had put in during my MTech project work. They were quite confident that I could deliver on my topic even if they at that time they (and I!) had only a minimal idea about it.

However, soon enough, Prof. Kajale at COEP agreed to become my official guide at University of Pune. Since it would be convenient for me to remain in Pune (my mother was not keeping well, among other things), I decided to do my PhD from Pune, rather than broach the topic once again at SERC, or straight-away join the IIT Madras program.

Just thought of jotting down the more recent culture at these institutes (at IIT Bombay, IIT Madras, and IISc Bangalore), in COEP, and of course, in the University of Pune. I am sure it’s just a small slice in the culture, just one sample, but it still should be relevant…

Also relevant is this part: Right until I completely left academia for good a couple of years ago, COEP professors and the University of Pune (not to mention UGC and AICTE) continued barring me from becoming an approved professor of mechanical engineering. (It’s the same small set of professors who keep chairing interview processes in all the colleges, even universities. So, yes, the responsibility ultimately lies with a very small group of people from IIT Bombay’s Mechanical department—the Undisputed and Undisputable Leader, and with COEP and University of Pune—the  Faithful Followers of the former).

2.5.3. Dirac in India:

BTW, in India, there used to a monthly magazine called “Science Today.” I vaguely recall that my father used to have a subscription for it right since early 1970s or so. We would eagerly wait for each new monthly issue, especially once I knew enough English (and physics) to be able to more comfortably go through the contents. (My schooling was in Marathi medium, in rural areas.) Of course, my general browsing of this magazine had begun much earlier. [“Science Today” would be published by the Times of India group. Permanently gone are those days!]

I now vaguely remember that one of the issues of “Science Today” had Paul Dirac prominently featured in it. … I can’t any longer remember much anything about it. But by any chance, was it the case that Prof. Dirac was visiting India, may be TIFR Bombay, around that time—say in mid or late 1970s, or early 1980’s? … I tried searching for it on the ‘net, but could not find anything, not within the first couple of pages after a Google search. So, may be, likely, I have confused things. But would sure appreciate pointers to it…

PS: Yes, I found this much:

“During 1973 and 1975 Dirac lectured on the problems of cosmology in the Physical Engineering Institute in Leningrad. Dirac also visited India.’‘ [^].

… Hmm… Somehow, for some odd reason, I get this feeling that the writer of this piece, someone at Vigyan Prasar, New Delhi, must have for long been associated with IIT Bombay (or equivalent thereof). Whaddaya think?

2.6. Jim Baggott’s new book: “Quantum Reality”:

I don’t have the money to buy any books, but if I were to, I would certainly buy three books by Jim Baggott: The present book of the title “Quantum Reality,” as well as a couple of his earlier books: the “40 moments” book and the “Quantum Cookbook.” I have read a lot of pages available at the Google books for all of these three books (may be almost all of the available pages), and from what I read, I am fully confident that buying these books would be money very well spent indeed.

Dr. Sabine Hossenfelder has reviewed this latest book by Baggott, “Quantum Reality,” at the Nautil.us; see “Your guide to the many meanings of quantum mechanics,” here [^]. … I am impressed by it—I mean this review. To paraphrase Hossenfelder herself: “There is nothing funny going on here, in this review. It just, well, feels funny.”

Dr. Peter Woit, too, has reviewed “Quantum Reality” at his blog [^] though in a comparatively brief manner. Make sure to go through the comments after his post, especially the very first comment, the one which concerns classical mechanics, by Matt Grayson [^]. PS: Looks like Baggott himself is answering some of the comments too.

Sometime ago, I read a few blog posts by Baggott. It seemed to me that he is not very well trained in philosophy. It seems that he has read philosophy deeply, but not comprehensively. [I don’t know whether he has read the Objectivist metaphysics and epistemology or not; whether he has gone through the writings/lectures by Ayn Rand, Dr. Leonard Peikoff, Dr. Harry Binswanger and David Harriman or not. I think not. If so, I think that he would surely benefit by this material. As always, you don’t have to agree with the ideas. But yes, the material that I am pointing out is by all means neat enough that I can surely recommend it.]

Coming back to Baggott: I mean to say, he delivers handsomely when (i) he writes books, and (ii) sticks to the physics side of the topics. Or, when he is merely reporting on others’ philosophic positions. (He can condense down their positions in a very neat way.) But in his more leisurely blog posts/articles, and sometimes even in his comments, he does show a tendency to take some philosophic point in a something of a wrong direction, and to belabour on it unnecessarily. That is to say, he does show a certain tendency towards pedantry, as it were.  But let me hasten to add: He seems to show this tendency only in some of his blog-pieces. Somehow, when it comes to writing books, he does not at all show this tendency—well, at least not in the three books I’ve mentioned above.

So, the bottomline is this:

If you have an interest in QM, and if you want a comprehensive coverage of all its interpretations, then this book (“Quantum Reality”) is for you. It is meant for the layman, and also for philosophers.

However, if what you want is a very essentialized account of most all of the crucial moments in the development of QM (with a stress on physics, but with some philosophy also touched on, and with almost no maths), then go buy his “40 Moments” book.

Finally, if you have taken a university course in QM (or are currently taking it), then do make sure to buy his “Cookbook” (published in January this year). From what I have read, I can easily tell: You would be doing yourself a big favour by buying this book. I wish the Cookbook was available to me at least in 2015 if not earlier. But the point is, even after developing my new approach, I am still going to buy it. It achieves a seemingly impossible combination: Something that makes for an easy reading (if you already know the QM) but it will also serve as a permanent reference, something which you can look up any time later on. So, I am going to buy it, once I have the money. Also, “Quantum Reality”, the present book for the layman. Indeed all the three books I mentioned.

(But I am not interested in relativity theory, or QFT, standard model, etc. etc. etc., and so, I will not even look into any books on these topics, written by any one.)

OK then, let me turn back to my work… May be I will come back with some further links in the next post too, may be after 10–15 days. Until then, take care, and bye for now…

A song I like:

(Marathi) घन घन माला नभी दाटल्या (“ghan ghan maalaa nabhee daaTalyaa”)
Singer: Manna Dey
Music: Vasant Pawar

[A classic Marathi song. Based on the (Sanskrit, Marathi) राग मल्हार (“raaga” called “Malhaara”). The best quality audio is here [^]. Sung by Manna Dey, a Bengali guy who was famous for his Hindi film songs. … BTW, it’s been a marvellous day today. Clear skies in the morning when I thought of doing a blog post today and was wondering if I should add this song or not. And, by the time I finish it, here are strong showers in all their glory! While my song selection still remains more or less fully random (on the spur of the moment), since I have run so many songs already, there has started coming in a bit of deliberation too—many songs that strike me have already been run!

Since I am going to be away from blogging for a while, and since many of the readers of this blog don’t have the background to appreciate Marathi songs, I may come back and add an additional song, a non-Marathi song, right in this post. If so, the addition would be done within the next two days or so. …Else, just wait until the next post, please! Done, see the song below]

(Hindi) बोल रे पपीहरा (“bol re papiharaa”)
Singer: Vani Jairam
Music: Vasant Desai
Lyrics: Gulzar

[I looked up on the ‘net to see if I can get some Hindi song that is based on the same “raaga”, i.e., “Malhaar” (in general). I found this one, among others. Comparing these two songs should give you some idea about what it means when two songs are said to share the same “raaga”. … As to this song, I should also add that the reason for selecting it had more to do with nostalgia, really speaking. … You can find a good quality audio here [^].

Another thing (that just struck me, on the fly): Somehow, I also thought of all those ladies and gentlemen from the AICTE New Delhi, UGC New Delhi, IIT Bombay’s Mechanical Engg. department, all the professors (like those on R&R committees) from the University of Pune (now called SPPU), and of course, the Mechanical engg. professors from COEP… Also, the Mechanical engineering professors from many other “universities” from the Pune/Mumbai region. … पपीहरा… (“papiharaa”) Aha!… How apt are words!… Excellence! Quality! Research! Innovation! …बोल रे, पपीहरा ऽऽऽ (“bol re papiharaa…”). … No jokes, I had gone jobless for 8+ years the last time I counted…

Anyway, see if you like the song… I do like this song, though, probably, it doesn’t make it to my topmost list. … It has more of a nostalgia value for me…

Anyway, let’s wrap up. Take care and bye for now… ]

History:
— First published: 2020.09.05 18:28 IST.
— Several significant additions revisions till 2020.09.06 01:27 IST.
— Much editing. Added the second song. 2020.09.06 21:40 IST. (Now will leave this post in whatever shape it is in.)

# Talking of my attitudes…

No one asked [^] me. But I want to tell you, anyway!

1. What is your opinion about the randomness of individual quantum events (such as the decay of a radioactive nuclei)?

• The randomness is only apparent
• There is a hidden determinism
• The randomness cannot be removed from any physical theory
• Randomness is a fundamental concept of nature

Nearest option(s): The randomness is only apparent.

Comments: We have to make the laws-vs-systems distinction [^]. The fundamental laws of physics are always deterministic; e.g., Newton’s law of gravity forces on objects. The behaviour of a system, composed of many objects, may or may not be deterministic.

For example, the problem of determining trajectories in a $2$-body system exchanging Newtonian gravity forces, is deterministic. A similar problem but with $3$ or more bodies shows sensitive dependence on initial conditions. The fact that the law is expressed as a differential equation requires us to specify the initial condition exactly. The sensitive dependence on IC makes the integration procedure useless—even a small change in IC gives a wildly different prediction. Thus, the behaviour of the system becomes indistinguishable from an indeterministic system, even if the law is deterministic.

Individual quantum events still involve a large number of objects.

There can be hidden mechanisms, but that will not guarantee determinism for all systems.

2. Do you believe that physical objects have their properties well defined prior to and independent of measurement?

• Yes in all cases
• Yes in some cases
• No
• I am undecided

Nearest option(s): Yes in all cases.

Comments: The nature is not in a metaphysical flux.

3. How would you respond to the question “Where exactly in the orbital of a hydrogen atom is the electron prior to a measurement?”

• It is everywhere in its orbital
• It is not possible to know with our current understanding
• It is impossible to know
• The question is meaningless

Nearest option(s): It is not possible to know with our current understanding.

Comments: The fact that it can be anywhere does not mean that it is everywhere (cf. Wheeler, Feynman).

My new approach should give a better level clarity on this question.

4. Superpositions of macroscopically distinct states, e.g. a current loop in a superposition of two magnetic fluxes,…

• are in principle possible
• will eventually be realized experimentally
• are in principle impossible
• are impossible due to collapse theory

Nearest option(s): are in principle possible.

Clarifications/Comments: The question is fuzzy/not well-defined. If a buckyball undergoes diffraction, does it qualify to be called a macroscopically distinct state? Could Wigner’s friends be such that they exhibit QM behaviour but also are distinct enough to be called macroscopically different entities? I think yes. In such a case, their superpositions are of course possible.

5. In your opinion the observer

• is a complex quantum system
• should play no fundamental role whatsoever
• plays a fundamental role in the application of the formalism, but plays no distinguished physical role
• plays a distinguished physical role

Nearest option(s): should play no fundamental role whatsoever.

Comments: The question itself is vague or ill-posed. The term “observer” is not clear.

In the ordinary sense of the term: All observers have both consciousness and body. The body, like any other physical object, is a complex quantum system. The consciousness must not play any fundamental role in any theory of physics—QM or otherwise. (It can play a role in a theory of mind-body integration, which will be a different field. It will have to be compatible with both physics and what we know about consciousness. But you couldn’t call it a sub-field of physics or psychology. It would be an inter-disciplinary field.)

If we allow an inanimate object (like a detector) to be called an “observer”: Then the nearest option would be different. It would be: The observer “is a complex system”

6. How do you understand the measurement problem?

• It is a pseudo-problem
• It is solved by decoherence
• It is solved/will be solved in some other way
• It is a severe difficulty threatening quantum mechanics
• I don’t know the problem well enough to have formed an opinion

Nearest option(s): It is solved/will be solved in some other way.

Comments: I think my new approach solves it correctly. For the time being, see the Outline document here  (PDF) [^]. It is a real problem; decoherence doesn’t solve it; but I don’t think that the absence of a solution to it has been a source of severe difficulty threatening QM itself. The absence of a good solution does make the theory incomplete. The irrational/bad philosophies brought into the field, under the disguise of solving this problem, do threaten QM (and many other areas of physics). But leaving aside the role of irrational/bad philosophies, an unsolved problem never really speaking threaten an area of physics. The same applies here.

7. What is the message of the observed violations of Bell’s inequality?

• Hidden variables are impossible
• Some notion of non-locality
• Action-at-a-distance in the physical world
• I don’t know the inequality well enough to have formed an opinion

Nearest options(s): Some notion of non-locality. Also: Unperformed measurements have no results.

Comments: The violations don’t by themselves justify (instantaneous) action at a distance, IAD for short, in the physical world; but they are compatible with IAD.

I simulate my new approach using Fourier’s theory, which means, using IAD. However, conceptually, it could easily incorporate very high but finite speeds.

8. If two physical theories give the same predictions, what properties would make you support one over the other? (you can check more than one box)

• Simplicity—simple over complex
• Determinism—deterministic over indeterministic
• Ontic—describes nature not just our knowledge of it
• Chronology—The theory that was established first

Nearest option(s): Ontic—describes nature not just our knowledge of it. Also, as implications, and in this order (of decreasing relevance): Consistency. Simplicity. Determinism. Chronology.

9. Do physicists need an interpretation of quantum mechanics?

• Yes, it helps us understand how nature behaves
• Yes, it is important for pedagogical reasons
• No, it is irrelevant as long as quantum mechanics provides us with correct predictions/results
• No, it is entirely based on personal beliefs

Nearest option(s): Yes, it helps us understand how nature behaves.

Comments: My opinion is that those who say “no” shouldn’t even call themselves physicists. But far more important point is this: The very terms of the question assume (and exhibit) something deeply wrong.

You don’t invent a theory of physics out of the blue, say just using “math”, any more than you claim that you it was revealed to you mystically. You don’t thus formulate a theory (especially a “complete” theory like QM), and then go looking for its “interpretation” in the physical world.

You start with observations, organize your knowledge of phenomena into a consistent conceptual context, and derive or apply some good ontology—i.e., spell out what kind of objects you are assuming to exist in the reality out there, their nature (the causes), the nature of their actions (the effects), etc. On this basis, you form some hypotheses, and perform experiments—i.e. controlled observations. You then integrate the experimental findings with the pre-existing knowledge, all using the conceptually consistent phenomenological-ontological context we had talked about.

On this basis, you go about proposing what forms of equations there should be, why, and then derive the exact equations (together with units that avowed Platonists hate!). If necessary, you invent maths—whether to form equations or for finding methods to solve them. You then also show how to apply the quantitative theory.

If you follow this order, there never is an occasion to separately go hunting for “interpretations” at any stage.

In QM, physicists were not idiots—they actually were geniuses. But they also brought in bad philosophy in such a manner that one part of what they produced was indistinguishable from what an idiot would propose. To be fair, if they were to have the context of certain later developments like computational modelling, non-linear dynamics and catastrophe theory, chances are somewhat bright that they might have not said so many irrational things.

I say “somewhat” bright, and not “absolutely very bright”. The reason? von Neumann did have access to computers, did work out early computational modelling theory, but nevertheless, ended up positing the collapse postulate and axiomatizing a linear theory for QM at the same time. There won’t be many people as brilliant as him. He still did this stupid thing. Similarly, Heisenberg should have been aware of the role of non-linearities. His PhD thesis was on turbulence in fluids. He even said to the effect that QM mysteries would be solved easier than the mysteries of turbulence.

But none of them took a path to the kind of natural nonlinearity which I have proposed.

Yes, bad philosophy, and the practice of deification of towering figures/groupism/ridiculing the outsiders, etc., definitely have significant effects—even on the kind of physics you propose and/or defend.

10. What characterizes the Copenhagen interpretation of quantum mechanics? (you can check multiple boxes)

• Collapse of the wavefunction upon measurement
• Indeterminism—Results are not completely specified by initial conditions
• Nonlocality, i.e. action-at-a-distance
• Quantum mechanics works well, but does not describe nature as it really is
• The correspondence principle—quantum mechanics reproduces classic physics in the limit of high quantum numbers
• The principle of complementarity—objects have complementary properties which cannot be observed or measured at the same time

Nearest option(s): In the order of importance or how core it is to the Copenhagen interpretation: 1. Correspondence principle. 2. Indeterminism. 3. Complementarity principle.

Comments: The collapse postulate was formulated by von Neumann, and not by Bohr, Heisenberg, and the other, original, advocates of the Copenhagen interpretation (CI). However, the collapse postulate only makes explicit what was already implicit in the CI. So, if the collapse postulate to be included in the CI, then its relative importance position, IMO, would be at no. 3. (Thus, the order would be: Correspondence, Indeterminism, Collapse, Complementarity.)

Indeterminism was more important to Heisenberg than to Bohr. Yes, Bohr accepted it, and advocated it too. But he belonged to an earlier, better, generation. He had arrived at the Correspondence  principle years before 1925, and insisted on it all his life.

11. What characterizes the many worlds interpretation of quantum mechanics? (you can check multiple boxes)

• The existence of multiple parallel worlds
• The existence of multiple minds belonging to one person
• Locality, i.e no action-at-a-distance
• The observer is treated as a physical system
• No wave function collapse
• Determinism—Evolution of universal wavefunction is completely governed by the wave equation
• I don’t know the interpretation well enough to have formed an opinion

Nearest option(s): In the order of importance: 1. The existence of multiple parallel worlds. Also: 2. No wave function collapse. 3. The observer is treated as a physical system.

12. What characterizes De Broglie – Bohm pilot wave interpretation of quantum mechanics? (you can check multiple boxes)

• Hidden variables in form of the particles exact positions and momenta
• Nonlocality
• Determinism—Events are completely specified by initial conditions
• Possibility of deriving Born’s Rule
• Wave function collapse
• Quantum potential—each particle has an associated potential that guides the particle
• I don’t know the interpretation well enough to have formed an opinion

Nearest option(s): In the order of importance, both of these at no. 1: (1a) Hidden variables in form of the particles exact positions and momenta. (1b) Quantum potential—each particle has an associated potential that guides the particle. Also, 2. Nonlocality.

13. What is your favourite interpretation of quantum mechanics?

• Consistent Histories
• Copenhagen
• de Broglie-Bohm
• Everett (many worlds and/or many minds)
• Information-based / information-theoretical
• Modal interpretation
• Objective collapse (e.g., GRW, Penrose)
• Quantum Bayesianism
• Statistical (ensemble) interpretation
• Transactional interpretation
• Other
• I have no preferred interpretation of quantum mechanics

Nearest option(s): Other.

Comments: By “Other” I mean: my new approach, even though, I think, what I am doing is much more than just a new “interpretation”. Yes, I do think that, eventually, my approach should also qualify to be called a new theory of (non-relativistic) quantum phenomena. (After all, I have proposed a new form of nonlinearity—i.e. new “math” too!)

If I were not to have my new approach, I would have probably said: 1. Copenhagen and 2. de Broglie-Bohm, in that order—but I would have hastened to add the necessary qualification that these interpretations, though I used them more preferentially or more often, couldn’t possibly be called my “favourites”.

14. What are your reasons for NOT favoring the Copenhagen interpretation? (you can check multiple boxes)

• The role the observer plays in determining the physical state is too important
• The paradoxes that arise on the macroscopic scale, e.g. Scrödinger’s cat and Wigner’s friend
• Nonlocality
• Quantum mechanics describes nature as it really is
• Other

Nearest option(s): Other.

Comments: Again, by “Other”, I mean: my new approach. If I were not to have my new approach, I would’ve picked 2 options: “the paradoxes”, as well as “Other” (citing the basis of the Copenhagen interpretation in poor/irrational/inconsistent/unworkable philosophy).

15. What are your reasons for NOT favoring the many worlds interpretation? (you can check multiple boxes)

• The notion of multiple worlds seems too far-fetched
• The notion of multiple minds seems too far-fetched
• The interpretation is too complex compared to others—i.e. Ockham’s razor
• The interpretation is unable to explain the Born rule
• It can never be corroborated experimentally
• Other

Nearest option(s): Other.

Comments: By “Other”, again, I mean: my new approach.

Now that I have my approach, I could stop by just saying “Other”.

If I were not to have this new approach, however, I would’ve said: Nothing about it (MWI) is worth commenting upon, except for emphatically noting that all that this “development” actually demonstrates is an absolute lack of even the most basic philosophical sense concerning the term: “universe.”

On the question of whether there can be many universes, my position is this: To say that there is only one universe is, in a vague sense, true. But a more basic truth here is this: You cannot in principle assign any numbers/quantitative measures to the concept of universe—not if, by that concept, you mean “everything that exists/has ever existed/will ever exist”. Taken in this later sense, the universe becomes an axiomatic concept of physics. And, as in any field of knowledge, you can’t quantify axiomatic concepts. Quantification is possible only when you have two or more existents to compare in a size-wise manner. But there is nothing else with which the universe can at all be compared, because the concept, by its very definition, includes everything there is.

Accordingly, the only reasonable thing I have ever found about this whole “MWI interpretation” business here is that anecdotal story about its genesis. I mean, the story that they had “copious” amounts of sherry that night. I don’t know if this story is true. If yes, I would really wonder if they had stopped only at the sherry, for their “copious” amounts. But yes, the story does make sense. Everything else about the “theory” is senseless.

16. What are your reasons for NOT favoring De Broglie-Bohm theory? (you can check multiple boxes)

• It is too complex compared to other interpretations—i.e. Ockhams razor
• It has hidden variables, which makes the theory untenable according to Bell’s inequality
• Nonlocality
• The notion of all particles possessing a quantum potential that guides them seems too far-fetched
• Other

Closest option(s): Other.

Comments: Again, I mean: my new approach. But even if I were not to have my new approach, I still would’ve picked up many other reasons for not finding this theory as acceptable or satisfactory. If you want, I will write a bit more, in a separate post. (As stated later, I may continue this post a bit further.)

17. How often have you switched to a different interpretation?

• Never
• Once
• Several times
• I have no preferred interpretation of quantum mechanics

Closest option(s): Once.

Comments: Actually, I didn’t have any preferred interpretation of QM. For instance, Einstein found the Copenhagen interpretation (CI) unsatisfactory. But since CI (plus what others like Neumann added to it) is what they mostly follow in writing text-books (or even in pop-sci books, when they show you the lay of the land), you might say that I was following CI, but without preferring it over others. Then, during my PhD times, I tried to develop a theory for the propagation of photons based on Einstein’s idea of the spatially discrete photon. So, for photons, I could be said to have been following his “interpretation” (which I no longer believe in). Etc. In answering this question I picked up “once” mainly to indicate that I have abandoned not just the CI and Einstein’s ideas, but all others too. Instead, I am now developing a completely new approach. I find it consistent and satisfactory—at least so far.

OK. That’s where the questions in the linked paper end. In the coming weeks or so, I may provide some further, more detailed comments concerning why I chose one option vs. others, provided I find enough time to do that. (See the next section.) … Further, I have also found 2–3 other, similar, surveys, with some new questions not covered in the linked paper. I may provide my answers to these additional question via a post later on.

An update regarding development of my new approach:

Some further conceptual issues have come up.

In particular, last week, I found that a significant part of the development I did in this July (perhaps going back up to this June or so) was, conceptually wrong. Plain wrong!

Some of it might work in some scenarios, but not in general. Some other suppositions/assumptions I had made (and even implemented in code) were plain wrong. So, a lot of code written earlier has to be simply junked!

However, in the process, I also found ways to tackle these issues. I’ve found that I don’t have to give up my basic ontological ideas. My basic ontology still holds—and in fact, it also shows the way to the correct generalizations (including correct quantitative predictions). OTOH, if the basic ontology (as indicated in the Outline document and in the Ontologies series of posts here) were to be outright erroneous at its core, then it would have spelt the end of my new approach. But that’s not at all the case here.

But yes, all in all, this “discovery” of where I was going wrong, has only added to the work that still needs to be done. First of all, I have to re-work through many things. Only then can I go over to the topics that were scheduled for the current week.

However, finishing up this whole enterprise (I mean, spelling out the basic essentials of the new approach, together with at least a few minimal simulations) still does seem achievable in a time-frame that’s not extended in too far a future. One or two weeks might get added to the schedule, but the overall task, I find, is still pretty much doable in the near future.

I have changed my work-flow. I am now writing down everything (whether in LaTeX or by hand, on paper) before starting writing any code, so that some simplifications introduced just for the sake of implementing some concrete simulation, don’t end up clouding my thinking about the underlying physics too. That’s what had actually happened. (In retrospect, I think I tried to rush through the things. That’s why I didn’t notice the places where I was going wrong even conceptually.)

This change in the work-flow has already proved effective. (Writing everything down isn’t always necessary. There is a value to trying some things by immediately writing some rough-and-ready simulations too. All that I am saying here is that, for my particular problem and the particular stage that I am already at, this change in the work-flow is turning out to be effective—for the time being.)

Another point. As you know, I had plans of simulating the H atom (or two interacting electrons) in a box with PBCs. I was going to take some short-cuts for evolving the dynamics. (I think I had tweeted to that effect a while ago.) Now, I’ve found that with the new mechanisms to be implemented, there no longer is any particular advantage left with those short-cuts. So, I may or may not use those short-cuts. In case you are wondering a lot: The short-cuts involved making use of the fact that what probability represents is the ideal time-fraction that a particle spends in an infinitesimally small CV (Eulerian/fixed control volume) of the domain. I had noticed this fact on my own; had never seen it being mentioned in the QM literature. (Notice, the idea makes use of the fact that a particle does have a definite position at each time instant. Thus, we are not referring to the position as measured by the position measurement apparatus.) … Anyway, these short-cuts themselves, I think, are a pretty good set of ideas; they may come in handy some time later on.

Anyway, to sum up and conclude: I found some mistakes in my conceptual development related to my new approach to QM, and therefore also in a significant part of the code that I had implemented over the last month or so. However, I’ve also have found what I believe is the correct solution for these problems. I mean to say, I now have even better (more detailed) description of the underlying physical mechanisms.  All in all, I hope to wrap up everything by, say, by September-end. May be before that.

A song I like:

(Hindi) हे, नीले गगन के तले, धरती का प्यार पले (“hey, neele gagan ke tale, dharati kaa pyaar pale”)
Singer: Mahendra Kapoor
Music: Ravi
Lyrics: Sahir Ludhianvi

[The original song (1967) is here [^].

Also check out the live version here [^]. Notice how effortlessly Mahendra Kapoor sings here, even in his mature age….

PS: Comments on the page for the second link above say that a Thai song has priority; it came out in 1965. Out of curiousity, I checked out the link [^]. Yes, the tune is absolutely the same! Obviously, Ravi picked it up either from this song, or from some other song that preceded them both!

The sound quality for this Thai video isn’t so great, though one can make out that, what we in Hindi call तान “taan” was rendered superlatively in it! A matter of pleasure!

… Another comment linked to a more recent Thai performance of the same (Thai) song, here [^]. This looks like a “cover” version. Yes, likable, but a few pauses overemphasize the rhythm, in the process losing the fluidity of the original.

…I was definitely reminded of any number of “covers” of the old Hindi songs that I’ve tried recently. I had to discard almost all of them (even those from the Sony Jam Room), simply because all these young singers seem to follow a very weird kind of a voice-culture and a way of rendering that, as a rule, ends up killing the very soul of the original. There may be exceptions here and there, but I was talking of the rule … Mind you, I don’t have a problem with singing an old Hindi song in some “Western” style as such—certainly not when it’s done on experimental or innovative basis. I am all for “fusion” too. But the style of singing these young Indian idiots follow is not at all in any of the better Western traditions either. It is some Indian-perceived version of the Western. It’s pathetic. Their careless yoddlings and predictable but pathetic stretchings of the original tune is such that one wonders if they weren’t trying to match the experiences of a drug addict or so.

… Anyway, coming back to this new Thai song by some young singer (I mean this one [^]): The “taan” which I spoke about, now appears in a slightly modern (Westernized) form of rendering here; check out at around 2:15. Yes, the song style definitely seems to have been broken at a couple of places, but I did like the “taan” portion of it. … Anyway, enough of comments! ]

History:
— 2020.08.23 17:03 IST: First published
— 2020.08.23 20:19 IST: Revision. Added several comments; expanded a bit some existing comments. Almost 3,000 words by now! Must now leave this post in whatever condition it is in.