Realization of bliss

OK, I will come to the title topic, but before that, let me get one thing out of the way.


Covid-19 jab:

It’s been more than a week that I got my second dose of the Covid-19 vaccine.

The systems at the vaccination center were, once again, excellent. In fact, they have improved and streamlined the processes even further from the last time [^]! Also, once again, there were no issues or side effects at all.

… Yes, knowing that you are fully vaccinated does bring a sense of relief. … A big thanks to all the doctors, nurses, and also the entire administrative machinery, yes including the people from government!…

Alright.


Bliss. (Actually, “blisses”.):

All this while, I have been working on QM, mostly on the topic of quantum mechanical angular momentum (which topic, in case you don’t know, includes the quantum mechanical spin). It’s been hard work, though mostly involving thinking in the head, and not writing down something in LaTeX or doing simulations.

In this process of thinking things through, pieces began to fall together in place, and simultaneously, pieces also began to fall apart!

I began to see how the QM textbooks fall short, so short in fact—even if you ignore all the misleading parts in them (which have been inserted because of the mainstream QM’s attempt to adhere to the Copenhagen interpretation—though no one knows precisely what it is, anyway!)… Descriptions in the standard treatments are so incomplete.

At the same time, I also began to see how my own ideas related to the spin were … err… wrong, meaningless, arbitrary, whimsical, nonsensical, etc. Yes, actually!

Ignorance, they say, is bliss. But what they say isn’t, as usual, sufficient. The complete statement is this: Realization of such bliss isn’t automatic. It requires hard work on your part! Knowing precisely what you are ignorant of, requires tremendous hard work. Only then can you enjoy the bliss because only then can you realize that you do carry ignorance.

Towards the end of the last week, I entered the aforementioned state. As a consequence, I can now confidently say the following.

I don’t know anything about the QM spin.

… It would be wrong to say that my new approach doesn’t handle the spin right. The correct statement here would be to say that my new approach, as of today, doesn’t even handle the quantum mechanical spin.

Why? Let me explain.

Here is the hierarchy of the topics. To understand any given node, you have to understand all its sub-nodes.

  • Quantum Mechanical Spin
    • Relativistic QM
      • Special Theory of Relativity
        • Electrodynamics in its entirety
    • Non-Relativistic QM
      • Electrostatics

Now, as you know, I don’t know electro-dynamics. Ergo….

But it was only about a week ago that I began to fully realize the implications of the above structure. All along, I was thinking that I could at least offer some conjectures, if not qualitative statements, for the QM spin. (I wans’t even aiming for quantitative treatment.) But all my conjectures began to turn out, first, insufficient to explain different scenarios I imagined, and then, soon later, plain wrong.

So, now, I’ve came to realize that I can’t any longer do even just that—I mean, plain conjecturing. My ignorance is that total, complete, and full. A state of a lovely, dark, and thick… bliss!

But my enlightenment didn’t stop just there. Soon later, as I began to think about what I was thinking (regarding the quantum mechanical spin), one thing suddenly came in sharp focus.

… It’s true that when it comes to the quantum mechanical spin, not just me but the entire community of physicists is blissful. Utterly so. … Now, what needs to be highlighted here is the method which physicists use while staying blissful.

Physicists have nothing more than some purely formal (and mostly algebraic) similarity, elevated to the exalted status of postulates, when it comes to the theorization for the spin. Their entire theoretical structure for the spin rests, purely, on similarities with some parts of the theoretical structure for the orbital angular momentum. And it was this similarity which now suddenly came in the spotlight of my mind. And with it, I began to trace everything back, to see if there is any further sources of bliss still left for me.

And sure enough, I found some more. I realized that I am quite blissful about many aspects regarding the orbital angular momentum too!

Here is how. Once again, what else, a tree. (In theoretical physics and indeed in any knowledge, we don’t do graphs in their fully generality. We do only the directed acyclic graphs. [Ask me some time why. There is a neat epistemological point about it.]) So, anyway, here is the tree:

  • Orbital Angular Momentum in QM
    • Interaction of the electron with an external magnetic field
      • Magnetic fields

OK, can you see my point? … No? … Well, let me spell it out for you.

At the most fundamental level, I gather, magnetism itself is a relativistic effect!

Therefore, the following bit is true:

Even in order to understand the non-relativistic QM well, you still first have to understand the relativity theory.

That was the second source of the bliss for me. Two blisses, back to back, right within one week! … Ah!

No one tells you that—the second source of the bliss. Professors of computer science are in fact busy attempting teaching “QM” without using Schrodinger’s equation. Yet, the aforementioned bit is true. The founders of QM were all well versed with the relativity theory, and of course, with the Maxwell-Lorentz electrodynamics (which precedes the relativity theory). But as a metallurgical-materials and then mechanical-software engineer, I haven’t ever studied this topic of electrodynamics (to the required depth and breadth). Hence…

But why is magnetic field required here at all? Well, that’s because, in experiments, you don’t measure the orbital angular momentum \vec{L} directly. You only measure the magnetic dipole moment \vec{\mu} of the electron, and then infer information about its \vec{L} from the former. And, experimentally measuring \vec{\mu} involves interaction of the electron with external magnetic fields.

That’s the reason why I have now realized such bliss about many aspects of the orbital angular momentum too, not just the spin angular momentum!


But why so late?

Why did the “blisses” come so late in my studies and research?

Well, the topics themselves are like that. You have to read the books again and again. It’s only in multiple passes that you spot the fine points, a few in each pass. That is, if such points are mentioned at all in the books.

Let me give you a concrete example. Here is an excerpt from Eisberg and Resnick, one of the best sources for an introduction to the non-relativistic QM. See for yourself how this passage (2e, p. 269) goes:

The ratio of \mu_l to L does not depend on the size of the orbit or on the orbital frequency. By making a calculation similar to the one above for an elliptical orbit, it can be shown that \mu/L is independent of the shape of the orbit. That this ratio is completely independent of the details of the orbit suggests its value might not depend on the details of the mechanical theory used to evaluate it, and this is actually the case. Upon evaluation of \mu_l quantum mechanically (which cannot be done here because the electromagnetic theory required is too sophisticated), and dividing by the quantum mechanical expression L = \sqrt{l(l+1)} \hbar, the ratio of \mu to L is found to have the same value that we obtained. Granting this, the student will accept that the correct quantum mechanical expressions for the magnetic and z component of the orbital magnetic dipole moment are

\mu_l = \dfrac{g_l \mu_b}{\hbar} L = \dfrac{g_l \mu_b}{\hbar} \sqrt{l(l+1)}\hbar = g_l \mu_b \sqrt{l(l+1)}
and

\mu_{l_z} = - \dfrac{g_l \mu_b}{\hbar} L_z = - \dfrac{g_l \mu_b}{\hbar} m_l \hbar = - g_l \mu_b m_l.

The minus sign in the last equation reflects the fact that the vector \vec{\mu_l} is antiparallel to the vector \vec{L}.

If you are studying QM in the pure self-studies mode, without any teacher to clarify matters or friends for discussions, then it does so happen that you don’t realize the full import of some fine points—like the one given in the parentheses above.

Here is another example, this time literally printed in the fine print in the book [ibid., p. 270]:

To simplify the discussion in subsequent sections, we shall frequently speak of the precession of a quantum mechanical magnetic dipole moment in a magnetic field, although to be strictly correct we should speak of the cyclic changes in the expectation values of its perpendicular components.

…But yes, at least Eisberg and Resnick do tell you many such things. Many other books don’t even bother to mention most of such things, not even via footnotes.

And then, there are tens of books to be looked into anyway, with each book giving its own share of such points! And, also committing its own share of misleading statements or even some small mistakes too. For example, even such careful authors as Eisberg and Resnick say [ibid. p. 269] that associated with the torque on a magnetic dipole is a potential energy of orientation. Strictly speaking, yes, there is an energy associated with the orientation of the dipole, but no, it’s not a potential energy proper—or so I gather. [I don’t quite understand this point, but I read something to this effect in Sears and Zemansky. Is it that you can’t take the gradient of this energy and obtain a force? Who knows. …Hmmm… Yet another [minor] bliss!]

Points like these may look minor, but at least some of them can become important when what you are aiming at is not an “A” grade in a university course but a proper answer to the measurement problem, which, in turn, requires a more or less complete reformulation of QM. It’s then that all such fine points begin to matter.

And then, you figure out something.

And then, come those moments of bliss!

I wasn’t so stupid to have theorized a sharp vector for the dipole moment in my new approach. The idea of vectors itself is rooted in classical mechanics; it doesn’t apply “as is” in QM, and I knew that. Yet, I must say that I had definitely underestimated what would be required to simulate the Larmour precession [^].

But why would I want to simulate the Larmour precession? After all, this topic doesn’t enter into QM postulates, does it?

Well, even if I don’t actually simulate it, I would have to know how a simulation can be done. And the reason for that, in turn, is because solving the measurement problem requires understanding, at least in schematic terms, how the new description would work out in various experimental arrangements for measuring various variables (or at least a few salient ones among them).


OK, what else? Did I reach a similar bliss regarding the measurement problem too?

Well, the answer, at least at this point of time, seems to be: no!

One last minute addition: Why “seems”? … Well, the point is this. I don’t understand electrodynamics, and hence, the magnetic field. However, the moving electron has a magnetic field associated with it—its own. The non-relativistic theory completely ignores this “internal” magnetic field. I can just hope, but don’t know for sure, that neglecting this field doesn’t matter much in the mechanism which I am proposing for solving the measurement problem… Hence the “seems”.

Let me leave this post on that note.


I could be away from blogs and all for quite some time… In the meanwhile, take care, and bye for now…


A song I like:

(Fusion) “Passages — Offering”
Composers: Ravi Shankar and Philip Glass

[I used to have the high-quality cassette of this album, back in the mid-1980s. It was released in India by Magnasound. A good quality audio is here [^]. See if you too like it…]

Monsoon. No Dirac. Also, PI i.e. IP.

Monsoon:

The monsoon is back in Pune, from an intermediate lull of about two weeks.

Pune is a city. I don’t get to hear the sound of frogs here in Pune.

In my mother-tongue, i.e. Marathi, the sound of frogs is transcribed not with the phonetic “k” as in “croaking” but with the phonetic “D”, as in, e.g., ड्-राॅव, ड्-राॅव (“D-rrow, D-rrow!”).

Instead of physically hearing the sound of the croak i.e. the “D-rrow”, these days, I find myself mentally “hearing” the “sound” which goes like: “Dirac!”, “Dirac!”.

However, I find that I can’t deal with it—I mean, the thing which I keep “hear”ing in my “head”.

Dealing with the Dirac equation will take a loooong time. Long enough that (this year’s) monsoon will definitely be gone before I am done understanding it right.

Hence, a plan. (What else?) A plan that progresses in several stages. (How else?) Seven stages, to be precise. (You could’ve predicted this number, couldn’t you?)


The Plan:

Stage 1: Notes on the QM spin:

Finish, in an irresponsible[*] manner, writing my notes on the QM spin (as taught in the mainstream courses on non-relativistic QM).

Stage 2: Monsoon. (This one!)

Put out a document on my new approach, right this monsoon.

It will mainly deal with the non-relativistic Schrodinger equation, and show my solution to the measurement problem.

It will also put down some irresponsible[*] conjectures concerning the quantum mechanical spin. It will be done before—perhaps way before—this monsoon ends. (I mean not the present spell, but the season.)

Stage 3: Electrodynamics:

Take notes on classical electrodynamics, with Griffiths’ book as the main reference. Publish these notes often—as soon as a chapter (and sometimes, even a section) is done.

Stage 4: Relativity:

Take notes on the Special theory of Relativity too, starting with Griffiths’ book, and consulting a few other sources. Notes need not be comprehensive. Publish irregularly.

Stage 5: SR + mainstream QM:

Take notes on the special relativistic treatment of quantum mechanics, up to, and including, the Klein-Gordon and the Dirac equations. No need to publish a lot.

Stage 6: SR + my new theory of QM:

Revise the theory from the Monsoon document and turn it into a special relativistic description. Once again, follow the Principle of Irresponsibility[*].

Stage 7: Malcolm Longair’s book on QM

Only then turn to drawing notes from Longair’s book on QM. (For context, see this post [^].)


The Principle of Irresponsibility:

Broadly speaking, I shall totally be held irresponsible for any and all points / contents that I publish, with the following provisos:

  • If any part of the content eventually turns out to be correct, then I shall be given full credit.
  • However, if any part of the content is eventually found to be incorrect to any degree, then no blame or negative judgment or debit of any kind shall accrue.

Hints regarding explanation and application:

The Principle of Irresponsibility can be extended further, to include the feature of iterative changes of any kind: for the better, for the worse, or any combination of the two.

Accordingly, the entire Monsoon edition (of the upcoming document) shall be deemed as being merely tentative, and accordingly, shall be posted in an iterative manner. Thus, I may post the first draft on the ‘net (say at iMechanica and here at my blog). Then, I may try to improve it further. Many outcomes are possible:

The document improves, or the document deteriorates, or some combination of the two.

In all such cases, credit shall only accumulate, and any debit shall always be reset to zero at each stage / act of posting—both, automatically.

Thus, if there is a good point I make in first posting, and then in the second posting I make an error in part, and then, in the third post, I further partly improve the erroneous part by adding something new, then it shall summarily be deemed that there has been only a net improvement at the end of the third posting—and, even that, despite any deterioration at the second stage, the net credit would still be only positive at that stage.

In any event, the reader shall instantaneously forget each and every and all erroneous part(s) at each stage.

As the astute reader would immediately notice, the Official short form of the Principle of Irresponsibility is PI, and of course, the same principle can also be stated as the Irresponsibility Principle, IP for short. Thus PI necessarily implies and is implied by IP.

The aforementioned Principle shall also apply to any and all considerations and issues related to priority of discovery or invention. Needless to add, the aforementioned Principle shall also apply to any and all the code I post. It also applies to all my blog posts and all my writings, comments, etc.—with immediate retrospective effect too (effective already!).

The aforementioned principle shall also apply to the order in which to pick up different topics and / or write posts or notes—and in whatever time-frame.

Needless to add, the present post, including the plan outlined above as also statement of PI i.e. IP, itself is subject to the IP i.e. PI.


Status update:

This is a status update subsequent to my comment at Dr. Roger Schlafly’s blog, here [^]. I seem to be reaching the following conclusions:

  1. My ideas related to the QMcal spin seem to be internally consistent. It seems to me, more than ever, that this set of ideas ought to be the only such set which can possibly correctly handle the QMcal spin within a non-relativistic framework. As far as I know, these ideas are new.

    Notice, in the non-relativistic framework, the QMcal spin can only be postulated, on a rather ad-hoc basis.

    Currently, I am in the process of verifying that even if only within the non-relativistic framework, these ideas make sense at the quantitative level too. I keep myself ready for any bad surprises too, but the current status is: So far, so good!

  2. My ideas are in many aspects similar to those put forth by Dr. Christof Schiller, the author of the excellent book “Motion Mountain” [^].

    However, there appear to be some definite differences in certain places, especially at the most fundamental level. I don’t mean to say that Dr. Schiller’s ideas are wrong—i.e., to the extent I can at all make out the nature of any preexisting ideas for a relativistic treatment of QM. But yes, I seem to have some definite reasons (based on my ontological understanding) to believe that our respective perspectives do differ (as seems to be the case with any preexisting theories regarding special relativistic QM).

But of course, needless to add, the PI i.e. the IP applies.


A song I like:

(Hindi) सा रे गा मा मा गा रे सा (“sa re ga ma ma ga re sa”)
Singers: Kishore Kumar, Mohammad Rafi
Music: S. D. Burman
Lyrics: Anand Bakshi

A good quality audio is here [^]. Don’t skip the initial part. Unfortunately, the best quality video I could find [^] skips this initial part.

That’s all for now, folks! Take care and bye for now…

Time dilation

Tried to get a quick overview of the Special Theory of Relativity. So, looked up Beiser’s book on Modern Physics.

Got stuck right at the section number 1.2, i.e., the one on time dilation.

Then recalled the last chapter in Griffith’s book on Electrodynamics. So, browsed real quick through it. Found the treatment satisfactory.

But also found that time would dilate even further. Hence, stopped immediately.

Decided to return to entangled QM particles. Recalled the video of the song below.

Hence, stopped again.

Will return to the notes on QM, tomorrow.

The schedule for the document (on the new approach) stands further dilated. By an indefinite amount. Enjoy the song.


A song I like:

(Hindi) रुबी ओ रुबी (“Ruby o Ruby”)
Singers: Lata Mangeshkar, Mukesh
Music: Laxmikant-Pyarelal
Lyrics: Anand Bakshi

A good quality audio is hard to find. An audio that is fairly OK, is here [^]. But make sure to check out the video too, here [^].