The monsoon is here! Also, a fun aspect of QM.

1. Status update:

The monsoon is officially here, in the Pune city, and somehow, my spring-break [^] too gets over—finally!

(…There were no rains on the day that the Met. department officially announced the arrival of monsoon in the Pune city. The skies were, in fact, fairly clear on that day! … However, this year, everything is different. It was raining on almost every day in the month of May!)

Anyway, to come back to the reason for the permanent break in the spring-break which I had taken…

Looks like I have found a minimum working clarity regarding the phenomenon of the quantum mechanical spin. … I guess the level of clarity which I have now got is, perhaps, as good as what might be possible within the confines of a strictly non-relativistic analysis.

So… I can now with some placid satisfaction proceed to watching the remaining lectures of the MIT courses.

I will begin writing the document on my new approach a little later. I now expect to be able to put it out by 15th July 2021, perhaps earlier. [Err… Any suggestions for the (Hindi) “muhurat”s for either / both?]

…But yes, the quantum spin turned out to be a tricky topic to get right. Very tricky.

…But then, that way, all of QM is tricky. … Here, let me highlight just one aspect that’s especially fun to think through…

2. One fun aspect of QM:

The Schrodinger equation for a one-particle system is given as:

$i\hbar \dfrac{\partial}{\partial t} \Psi(x,t) = \hat{H} \Psi(x,t)$,

where the notation is standard; in particular, $i$ is the imaginary unit, and $\hat{H}$ is the system Hamiltonian operator.

The observation I have in mind is the following:

Express the complex-valued function $\Psi(x,t)$ explicitly as the sum of its real and imaginary parts:

$\Psi(x,t) = \Psi_R(x,t) + i \Psi_I(x,t)$,

where $\Psi_R \in \mathcal{R}$, and do note, also $\Psi_I \in \mathcal{R}$, that is, both are real-valued functions. (In contrast, the original $\Psi(x,t) \in \mathcal{C}$; it’s a complex-valued function.)

Substitute the preceding expression into the Schrodinger equation, collect the real- and imaginary- terms, and obtain a system of two coupled equations:

$\hbar \dfrac{\partial}{\partial t} \Psi_R(x,t) = \hat{H} \Psi_I(x,t)$
and
$- \hbar \dfrac{\partial}{\partial t} \Psi_I(x,t) = \hat{H} \Psi_R(x,t)$.

The preceding system of two equations, when taken together, is fully equivalent to the single complex-valued Schrodinger’s equation noted in the beginning. The emphasis is on the phrase: “fully equivalent”. Yes. The equivalence is mathematically valid—fully!

Now, notice that this latter system of equations has no imaginary unit $i$ appearing in it. In other words, we are dealing with pure real numbers here.

Magic?

… Ummm, not really. Did you notice the negative sign stuck on the left hand-side of the second equation? That negative sign, together with the fact that the in the first equation, you have the real-part $\Psi_R$ on the left hand-side but the imaginary part $\Psi_I$ on the right hand-side, and vice versa for the second equation, pulls the necessary trick.

This way of looking at the Schrodinger equation is sometimes helpful in the computational modeling work, in particular, while simulating the time evolution, i.e., the transients. (However, it’s not so directly useful when it comes to modeling the stationary states.) For a good explanation of this viewpoint, see, e.g., James Nagel’s SciPy Cookbook write-up and Python code here [^]. The link to his accompanying PDF document (containing the explanation) is given right in the write-up. He also has an easy-to-follow peer-reviewed paper on the topic; see here [^]. I had run into this work many years ago. BTW, there is another paper dealing with the same idea, here [^]. I have known it for a long time too. …Some time recently, I recalled them both.

Now, what is so tricky about it, you ask? Well, here is a homework for you:

Homework: Compare and contrast the aforementioned, purely real-valued, formulation of quantum mechanics with the viewpoint expressed in a recent Quanta Mag article, here [^]. Also include this StackExchange thread [^] in your analysis.

Happy thinking!

OK, take care, and bye for now…

A song I like:

[TBD]

1. Spring break!

I have completed going through the first 12 lectures of the QM-I course at MIT OCW (the 08.04 course, Spring 2013 version). A “spring break” occurs in the video series at this time, and I took one.

I hadn’t exactly planned on taking the break, but it happened that way. I had completed the first 12 lectures by 11th May 2021 evening. Then I got diverted to some other sources on QM and all. So, it’s exactly a week since I’ve gone away from the course-work.

A break this long wouldn’t have happened, but frankly, I find scattering boring (the topic currently going on), and the next two lectures are on this topic. (Scattering is an essential topic in learning QM, but isn’t terribly important if your interest is rather limited to the foundational issues.)

Yes, the pace of going through the course has been somewhat slow, because I can’t stop taking fairly good notes for myself (handwritten). Still, I think I can comfortably manage two lectures per day. (The most I did was four lectures on one day. But it’s not efficient; the next day I found myself to be too tired, rather, lacking of patience to go through all the subtleties of the next lecture.)

I am not even cursorily looking into the problem sets. Yet, I’m not skipping the multiple-choice questions directly discussed in the lecture, either. … Yes, sometimes I make mistakes, but surprisingly (or perhaps not so surprisingly), I found that I was actually doing better on many of the questions where the class didn’t seem to do so well. I made mistakes on some other questions where they were doing great!… It’s all a consequence of uneven backgrounds and personal perspectives / objectives. … And yes, making mistakes is good, because you learn in the process. That’s what I believe in.

Anyway, I intend to resume the remaining lectures of this course (QM-I) soon, may be starting later today or tomorrow afternoon. Once these get over, then I intend to go over to QM-II (08.05, Fall 2013 version).

Implications for the planned document on my new approach:

I will come to writing the document (the one on my new approach) a little after I finish QM-II.

But when will it be? … I don’t know. Perhaps you can tell!… But in any case, just because I took a break in this specific MIT course, it doesn’t mean I also took a break from QM. No, I didn’t…

But yes, tentatively speaking, I could finish QM-II and start writing my document some time in June, I think. … It all depends on many things… Let’s see how it all goes.

2. The STOC Test of Time Awards:

I came to know of these awards via Prof. Scott Aaronson’s blog. I liked the idea and left a comment, here [^]. Let me copy-paste it here, for convenience (with minor editing):

Re.: The STOC Test of Time Award

Someone should study the correlations between the usual measures of (an author’s) “impact factor” on the one hand and the papers chosen for this award on the other—how well go the correlations.

I guess this is the first time I am seeing an award of this nature, and I like the idea. Reason: Mainly because it involves natural intelligence, and not some mechanically computed indices / AI… Awards like these should provide better insight into the real impact, IMO.

On another, related, point: I don’t know of any other field in engineering / physics which does something similar… May be they do, perhaps in some slightly different form(s), but I don’t know it. In case not, guess they could implement the same / similar ideas.

Best,
–Ajit

If someone is going to study correlations and all, there can be some indirect sources too, with certain parameters / weights attached to them. I mean, things like the following…

• Papers chosen for other awards (like the best thesis award, best conference presentation award, etc.)
• Papers highlighted in reputed review papers (e.g. “Annual Review” series, e.g., Annual review of Fluid Mechanics)
• Papers highlighted in reputed key-note addresses
• Salient papers from senior researchers who are specially honored / recognized (say upon super-annuation, via special conference sessions or special journal issues)
• Etc.

All in all, it should be interesting to apply statistical / ML / AI techniques in a better manner, not relying purely on the mechanically computed indices (like the h-index).

Dr. Roger Schlafly has been posting many interesting entries on QM at his blog, and I’ve been posting my replies fairly regularly. … Recently, he highlighted some of the comments I made for more detailed discussions, by mentioning them in the main text of his blog posts proper.

My comments are pretty context specific and long. So, it’s not practical to copy-paste them here. Instead, it’s best if you go visit his blog, read the main posts first, and then see my comments. The recent posts on which I posted comments are (in the chronological order):

• “Philosophers try to discredit Realism” [^]
• “Does Quantum AI have Free Will?” [^]
• “Quantum wavefunction is not everything” [^] (where I’ve made as many as five comments!)
• “Rethinking entanglement of a single particle” [^]

Just thought of letting you know…

…I guess I’ll return here after I’ve completed the MIT 08.04 (QM-I) course, or some time after that (even if I am still going through their QM-II).

…In the meanwhile, take care and bye for now…

A song I like:

(Hindi, Instrumentals version) इशारों इशारों में दिल लेने वाले (“ishaaron ishaaron mein dil lene waale…”)
Musician: Brian Silas

I good quality audio is here [^]. … Though based on a Hindi film song, this instrumentals version feels like a separate song in its own right! Silas’ treatment of this song is refined and sensitive… (In certain other songs, occasionally, he might sound just a shade mechanical, but not here…)

The credits for the original song go as:
Music: O. P. Nayyar
Lyrics: S. H. Bihari

A good quality audio for what looks like the original song can be found here [^]. An apparently “Revival” series version is here [^].

BTW, Google search throws up yet another series version over others. This version can be found here [^]. Personally, I find the sound processing in this version to be: bad!. There are unnecessary echo-like effects, and the depth is gone from the singers’ voices …

The original song has been a top favorite for many people, even for decades.

However, personally, I like the above mentioned instrumentals version (by Brian Silas) much, much more! Indeed, it’s this version that automatically surfaces up in my mind (whenever it does, that is); in comparison, the original song  is much less likely to similarly “come up”.

Anyway, see if you enjoy any of these versions and if yes, which one. … Anyway, bye for now…

Some great videos on QM…

Since my last post here, I did quite a few searches on the QM spin, and in the process, I found quite a few neat resources on QM. Let me give you the links to the neat ones among them…

The best video on the philosophical interpretations of QM:

Eugene Khutoryansky has an awesome talent for simplifying presentations and offering videos full neat of computer animations / visualization. (And they come with some neat background music too!) He has uploaded a great many videos on a lot of topics at his channel, here [^]. … Over time, I’ve watched some 8–10 of his videos.

It was only this week that I found that he has made an outstanding video on the philosophical interpretations of QM; see here [^]. The video covers all of the interpretations that are worth noting—-and then, also one or two that are not! He covers them all in a brief but illuminating manner.

The visualizations here are fairly good, though they aren’t as good as Khutoryansky’s visualizations usually are. The visualizations in this video weren’t always consistently illuminating. … Indeed, I think that for some of the interpretations, the visualizations here can be somewhat misleading! For instance, in the portion on the MWI, Khutoryansky shows all the four cats turning their heads in the same direction, all in synchronization with each other. But according to MWI, each cat (in each of the four example worlds) would be doing something little different, and so, that synch should not be there.

Yet, this video still is quite outstanding. The reason is: the script.

As I indicated above, the author is being comprehensive here. But I found really impressive was even while being brief, he so perfectly captures the peculiarity of each interpretation. He shows a marvelous talent to encapsulate the essence of these diverse set of ideas.

Another thing: The visualization here turns the meme of Schrodinger’s cat on its head—which was a neat idea, IMO.

Bottomline: Strongly recommended to all: the layman, the philosopher, and the QM specialist too!

ViaScience’s playlist on QM:

I was doing a search on the QM angular momentum when this video [^] came up. I browsed the video rapidly, liked it a lot, and so, had a rapid look at the channel [^] too.

You may perhaps want to check out the “featured video” for this channel, which is here [^]. In this video, the author says:

“Physics is not mathematics but mathematics is the language of physics. Elsewhere there are many math-free graphics-rich videos covering these topics, and there also are formal university courses and textbooks. This channel aims to following the sparsely populated region in between. We try to emphasize physical concepts but also include enough math so that the presentations are more than mere hand-waving.”

Neat! ….To be honest though, I didn’t in fact bother to see this featured video until today.

What I had done, immediately after the aforementioned video on the angular momentum, was to quickly go over to the playlist on QM [^]. Here, I noticed, as the first thing, that the ordering of the topics was more or less completely to my liking. So, I quickly browsed through a few of these videos, by way of sampling.

Highly satisfied with the treatment in those sample, I then started going through the entire playlist on QM in a systematic manner: one by one, in the order presented. … Since then, I’ve watched through all the videos up to the part “9c”. I expect to finish the remaining videos too, soon enough.

Each video of this playlist is short (something that I appreciate a lot!), fully accurate (which is a big deal with me!), and carries enough visualization to keep your attention riveted at all times. None of the videos has any clutter in any of the frames. Each video proceeds at just the right pace—a pace that is rapid enough that I never felt bored even for a second, and yet, none of the videos, I found, ever misses out on any of the truly important points. Indeed, some of the videos actually mentioned some points / perspectives that were kindaa new to me!

… All in all, these videos are a master-piece in condensation and essentialization.

Indeed, this playlist on QM was actually responsible for accelerating my research on my new approach too. (I will note a status update at the end of this post…)

…Coming back to the playlist itself, let me mention that, in the feedback of some video from this series, some viewer has left a comment which says something like: “best things are hidden in plain sight”. Spot on! These videos were posted years ago (starting the year 2013!), and despite my routine and extensive searches, I’ve managed to find them only last week or so. (On 13th April, to be exact; I began systematically watching them from 15th April.)

Now, a bit on what I found somewhat odd:

The author at times places too much emphasis on the uncertainty principle (UP for short), IMO. … I mean to say, he tries to explain the essential “quantum mechanical-ness” of some QM phenomenon / situation in reference to the UP—and not in reference to the specific details of the underlying physics for that specific situation. This was a shade disappointing to me—and unexpected, given how well these videos otherwise are!

Of course, this tendency to deploy the UP to explain the QM-ness is not peculiar to this author alone. It’s been part and parcel of the entire pedagogy of QM for decades and decades by now. Professors have been routinely presenting QM as if the UP were at the base of the theory—even if it demonstrably is not!

For one thing, historically, Heisenberg formulated the UP only in 1927, i.e., after all of non-relativistic QM had already been formulated. Even his own approach to the QM—let alone Schrodinger’s—had already been developed by that time. So, the UP was an after-thought; it was not, originally, a principle essential or vital to the very development of the mechanics.

Also, careful studies concerning the hierarchy of the concepts and principles involved in the QM have shown that the proper hierarchical place of the UP is only as a higher-level implication of certain other fundamental principles, and not as a fundamental truth/postulate itself. For evidence, refer to the postulates document [ (PDF) ^] which I’ve compiled recently (in particular, to the last section therein).

But coming back to the ViaScience’s playlist itself, speaking overall, this emphasis on the UP is only a minor short-coming it has. Indeed, this aspect becomes worth noting down precisely because the video series otherwise is so excellent!

Bottomline: To my mind, this is the best series of videos on QM that I’ve ever come across.

It’s ideally suited to the UG students. However, perhaps even the layman might want to check it out. The videos are short enough for the layman to try, and I guess he too should get a good flavour of what the actual mechanics of the actual QM is like.

[I am going to check out the other playlists on this channel too, including the one on relativity and QFT, but some time later (after I’ve put out a document on my new approach)…]

QuantumVisions Physikdidaktik WWU Münster’s video on the Stern-Gerlach experiment:

The visualization here more or less proceeds precisely like how I used to think it should be presented, but had not found thus far. The video in question is here [^]. … Of course, the visualization which I had worked out in the mind was much more detailed; in fact, it would take a computational simulation to bring out every detail I had in mind… But still, it was so wonderful to find some aspects of the broad idea so well executed.

[Viewers don’t always appreciate it, but creating a scientifically accurate visualization is a pain! It takes a lot of planning and hard-work to put out even 30 seconds of a good video. Making it involves all the troubles of the routine animation, and then, a whole bunch more complexity if you want the representation to be also accurate enough!]

2veritasium’s video: “What is quantum mechanical spin?”:

A good coverage is offered by Prof. Dr. Andrea Morello [^]. One of the notable moments occurs at around the 01:03 mark: “The neutron also has the spin, but it has no charge”. Point driven home!

The Science Asylum’s video on the QM spin:

The video [^] begins with the narrator saying:

“Hey crazies, let’s talk a little more about the quantum spins…”.

He also actually delivers on the promise… I mean, who else talks about the spin $3\,1/2$ particles—and also tries to show something about them?

Eugene Khutoryansky’s video on Pauli’s exclusion principle:

The video in question is here [^]. It is a technical video. It’s highly relevant to the UG student taking the very first course on QM/QChem. However, the technical subtleties covered are such that it’s not suitable for a lay audience.

The title of this video is: “What causes the Pauli Exclusion Principle?”. … As a title, it is somewhat misleading. The video deals only with the non-relativistic QM, and it aims to generate only an intuitive feel for the inevitability of the principle; but it does not show (and could not have actually shown) why the principle is necessary.

But it’s a very good video.

I did find the pace to be a bit too slow for my liking. The script also seems a bit too repetitive. I mean to say: Unless you are paying careful attention to the small but significant changes in the conditions of simulation that the author goes on presenting, the similar-looking phrases (and even visuals!) could easily induce erroneous impressions! You have to be careful…

However, one great point overriding all short-comings is that Khutoryansky covers not just the “spatial” part (i.e. the Schrodinger wavefunction) taken in isolation, and then just the spin part taken in isolation, but both these parts taken together too! Among the videos I’ve seen thus far, this is the only video / visualization which does that.

NoahExplainsPhysics’s playlist on the QM spin:

Here is another helpful playlist on the topic of QM spin [^].

The strong point of this series is that that author works out each and every step about the mathematical equations (or “derivation”s, as these usually get called). …Judging from the viewer-comments, a lot of people seem to have appreciated this part.

However, I found that the overall ordering of the topics wasn’t much to my liking. The author follows too deductive an approach (IMO). After going through the first two videos, I’ve kept this series on the back-burner for a while.

… Oh yes, it’s a very handy resource to have, very useful. It’s just that I am going to look into it later, as the need arises… (That’s what I do with any deduction-heavy treatment, be it the second volume of Feynman’s lectures (on EM), or the text-book on QM by another Nobel laureate: Cohen-Tannoudji. … Excellent, if you’ve already learnt all the topics being deductively tied together. Pathetic, if even a single of those topics has not been learnt—from other, better, sources!)

Apart from it all, I also watched a couple of lectures from the MIT course 08.05 (2013 version), available at OCW. … Wish I had the time to systematically pursue this entire three-course sequence!

…It’s not an empty wish. I actually haven’t learnt many of the topics that this series covers, and when physicists begin responding to my new approach (once I publish it), they all are going come from a background that includes an expertize of all of that stuff—and much more, in fact!! … Which brings me to the status update on my research.

Status update: “Yeah, kindaa…”

Guess it will be convenient to refer to the videos while giving the current status on my research.

As indicated above, it was while going through ViaScience’s series on QM that I realized that my new approach should work OK—also for the spin.

However, going through the other videos has also further highlighted the need for me to delimit my claims. …It’s going to take months before I am able to deal with every minute detail involved in the maths (like that in NoahExplainsPhysics, and more!), using my new approach.

However, I need to wrap up this full-time occupation with QM as soon as possible, so that I can turn to Data Science and start hunting for suitable jobs.

So, my tentative plan as of today is this:

I am going to resume writing my document on the new approach, now also including some basic indication regarding the spin. By “basic indication”, I mean, the case of the outer-most single electron in the Ag or H atom, in the context of the SG experiment.

A rigorous theory for photons cannot anyway be developed within the non-relativistic QM, and so, a treatment of the photons was always out of the scope of my upcoming document. Now, the spin for all the other particles (neutron, photon, higher-spin particles) also will be kept out of the scope. …Also out of the scope will be more detailed look at the case of the spin in multi-electron atoms like He, Li, etc. (I will cover the He atom, and will conceptually indicate the Schrodinger wavefunctions for an arbitrary number of particles. But I will not cover the spin for such systems.)

Now, two possibilities open up.

If I am able to finish such a document by this month-end, then I will upload it soon later, say by the first week of May.

OTOH, if I find, over the next few days, that I will not be able to finish the document (to the detail indicated above), then I will still write down my theory for the spinless particles (i.e. up to the Schrodinger wavefunctions, including the GS energy of the He atom). Then, I will also throw in a purely conceptual level description for the QM spin, and be done with this project, in the same time-frame. … As to working out the exact details of QM spin and writing them down, I will take up that part of the project only after I am already in a good Data Science job, and am already settled enough in it to be able to find time to work on QM on the weekends and all.

So, either way, I am wrapping up this project by this month-end. At the most, by the first week of May 2021. … I’ve had enough of this research project by now, and the series by ViaScience has told me that I need not bother a lot about every query on every aspect of QM that every random physicist may throw up at me (especially those concerning the QM spin). They are important, but not so important!

So, there.

Take care and bye for now…

A song I like:

(Western, instrumental) “Wonderful land”