Wrapping up my research on QM—without having to give up on it

Guess I am more or less ready to wrap up my research on QM. Here is the exact status as of today.


1. The status today:

I have convinced myself that my approach (viz. the idea of singular potentials anchored into electronic positions, and with a 3D wave-field) is entirely correct, as far as QM of non-interacting particles is concerned. That is to say, as far as the abstract case of two particles in a 0-potential 1D box, or a less abstract but still hypothetical case of two non-interacting electrons in the helium atom, and similar cases are concerned. (A side note: I have worked exclusively with the spinless electrons. I don’t plan to include spin right away in my development—not even in my first paper on it. Other physicists are welcome to include it, if they wish to, any time they like.)

As to the actual case of two interacting particles (i.e., the interaction term in the Hamiltonian for the helium atom), I think that my approach should come to reproduce the same results as those obtained using the perturbation theory or the variational approach. However, I need to verify this part via discussions with physicists.

All in all, I do think that the task which I had intended to complete (and to cross-check) before this month-end, is already over—and I find that I don’t have to give up on QM (as suspected earlier [^]), because I don’t have to abandon my new approach in the first place.


2. A clarification on what had to be worked out and what had to be left alone:

To me, the crucial part at this stage (i.e., for the second-half of March) was verifying whether working with the two ideas of (i) a 3D wavefield, and (ii) electrons as “particles” having definite positions (or more correctly, as points of singularities in the potential field), still leads to the same mathematical description as in the mainstream (linear) quantum mechanics or not.

I now find that my new approach leads to the same maths—at least for the QM of the non-interacting particles. And further, I also have very definite grounds to believe that my new approach should also work out for two interacting particles (as in the He atom).

The crucial part at this stage (i.e., for the second half of March) didn’t have so much to do with the specific non-linearity which I have proposed earlier, or the details of the measurement process which it implies. Working out the details of these ideas would have been impossible—certainly beyond the capacities of any single physicist, and over such a short period. An entire team of PhD physicists would be needed to tackle the issues arising in pursuing this new approach, and to conduct the simulations to verify it.

BTW, in this context, I do have some definite ideas regarding how to hasten this process of unraveling the many particular aspects of the measurement process. I would share them once physicists show readiness to pursue this new approach. [Just in case I forget about it in future, let me note just a single cue-word for myself: “DFT”.]


3. Regarding revising the Outline document issued earlier:

Of course, the Outline document (which was earlier uploaded at iMechanica, on 11th February 2019) [^] needs to be revised extensively. A good deal of corrections and modifications are in order, and so are quite a few additions to be made too—especially in the sections on ontology and entanglement.

However, I will edit this document at my leisure later; I will not allocate a continuous stretch of time exclusively for this task any more.

In fact, a good idea here would be to abandon that Outline document as is, and to issue a fresh document that deals with only the linear aspects of the theory—with just a sketchy conceptual idea of how the measurement process is supposed to progress in a broad background context. Such a document then could be converted as a good contribution to a good journal like Nature, Science, or PRL.


4. The initial skepticism of the physicists:

Coming to the skepticism shown by the couple of physicists (with whom I had had some discussions by emails), I think that, regardless of their objections (hollers, really speaking!), my main thesis still does hold. It’s they who don’t understand the quantum theory—and let me hasten to add that by the words “quantum theory,” here I emphatically mean the mainstream quantum theory.

It is the mainstream QM which they themselves don’t understood as well as they should. What my new approach then does is to merely uncover some of these weaknesses, that’s all. … Their weakness pertains to a lack of understanding of the 3D \Leftrightarrow 3ND correspondence in general, for any kind of physics: classical or quantum. … Why, I even doubt whether they understand even just the classical vibrations themselves right or not—coupled vibrations under variable potentials, that is—to the extent and depth to which they should.

In short, it is now easy for me to leave their skepticism alone, because I can now clearly see where they failed to get the physics right.


5. Next action-item:

In the near future, I would like to make short trips to some Institutes nearby (viz., in no particular order, one or more of the following: IIT Bombay, IISER Pune, IUCAA Pune, and TIFR Mumbai). I would like to have some face-to-face discussions with physicists on this one single topic: the interaction term in the Hamiltonian for the helium atom. The discussions will be held strictly in the context that is common to us, i.e., in reference to the higher-dimensional Hilbert space of the mainstream QM.

In case no one from these Institutes responds to my requests, I plan to go and see the heads of these Institutes (i.e. Deans and Directors)—in person, if necessary. I might also undertake other action items. However, I also sincerely hope and think that such things would not at all be necessary. There is a reason why I think so. Professors may or may not respond to an outsider’s emails, but they do entertain you if you just show up in their cabin—and if you yourself are smart, courteous, direct, and well… also experienced enough. And if you are capable of holding discussions on the “common” grounds alone, viz. in terms of the linear, mainstream QM as formulated in the higher-dimensional spaces (I gather it’s John von Neumann’s formulation), that is to say, the “Copenhagen interpretation.” (After doing all my studies—and, crucially, after the development of what to me is a satisfactory new approach—I now find that I no longer am as against the Copenhagen interpretation as some of the physicists seem to be.) … All in all, I do hope and think that seeing Diro’s and all won’t be necessary.

I also equally sincerely hope that my approach comes out unscathed during / after these discussions. … Though the discussions externally would be held in terms of mainstream QM, I would also be simultaneously running a second movie of my approach, in my mind alone, cross-checking whether it holds or not. (No, they wouldn’t even suspect that I was doing precisely that.)

I will be able to undertake editing of the Outline document (or leaving it as is and issuing a fresh document) only after these discussions.


6. The bottom-line:

The bottom-line is that my main conceptual development regarding QM is more or less over now, though further developments, discussions, simulations, paper-writing and all can always go on forever—there is never an end to it.


7. Data Science!

So, I now declare that I am free to turn my main focus to the other thing that interests me, viz., Data Science.

I already have a few projects in mind, and would like to initiate work on them right away. One of the “projects” I would like to undertake in the near future is: writing very brief notes, written mainly for myself, regarding the mathematical techniques used in data science. Another one is regarding applying ML techniques to NDT (nondestructive testing). Stay tuned.


A song I like:

(Western, instrumental) “Lara’s theme” (Doctor Zhivago)
Composer: Maurice Jarre

 

 

 

 

 

Paperity

If you are in one of the S&T fields and don’t know what “paperity” means, then guess it’s time you checked out the Web site: [^].

Came to know of it only today. Was doing some Web search on QM, and landed here [^]. Then, out of curiosity, also checked out an outgoing link [^] from that page, and thus, got the idea behind the site. … Hmmm… Need to explore it a bit more, but no time right now, so, may be, some time later!

Bye for now.


A Song I Like:

(Hindi) “saawan barse, tarse dil…”
Music: Aadesh Shrivastava, Anand Milind
Singers: Hariharan, Sadhana Sargam
Lyrics: Majrooh Sultanpuri

[TBD. May be tomorrow. Done right tonight (21:40 IST, 11 July 2017). Also corrected the spelling of “paperity” in the title and in the text.]

Yo—5: Giving thanks to the Fourier transform

Every year, at the time of thanksgiving, the CalTech physicist (and author of popular science books) Sean Carroll picks up a technique, principle, or theory of physics (or mathematics), for giving his thanks. Following this tradition (of some 8 years, I gather), Carroll has, for this year, picked up the Fourier transform as the recipient of his thanks. [^]

That way, it’s quite a good choice, if you ask me. …

…Though, of course, as soon as I began reading Carroll’s post, a certain thing to immediately cross my mind was what someone had said concerning Fourier’s theory.

Fourier’s is the most widely used theory in the entire history of physics, he had said, as well as the most abused one . … The words may not be exact, but that was the sense of what had been said. Someone respectable had said it, though I can’t any longer recall exactly who. (Perhaps, an engineer, not a physicist.)

The Fourier theory has fascinated me for long; I have published not just a paper on it but also quite a few blog posts.

To cut a long story short, I would pick out (i) the Lagrangian program (including what is known as the Lagrangian mechanics as well as the calculus of variations, the stationarity/minimum/maximum/action etc. principles, the Hamiltonian mechanics, etc.) and (ii) the Fourier theory, as the two basic “pillars” over which every modern quantum-mechanical riddle rests.

Yes, including wave-particle duality, quantum entanglement, EPR, Bell’s inequalities,  whatnot….

As I have been pointing out, the biggest good point that both these theories have in common is that they allow us to at all perform at least some kind of a mathematical calculation of the analytical kind—even if, often times, only in a physically approximate sense—in situations where none would otherwise be possible.

The bad point goes with the good point.

The biggest bad point common to both of them is that they both take some physics that actually occurs only locally (say the classical Newtonian mechanics) and smear it onto a supposedly equivalent “world”—an imaginary non-entity serving as a substitute for the actually existing physical world. And, this non-entity, in both theories (Lagrangian and Fourier’s) is global in nature.

The substitution of the global mathematics in place of the local physics is the sin common to the abuse of both the theories.

Think of the brachistochrone problem, for instance [^]. The original Newtonian approach of working with the local forces using \vec{F} = d\vec{p}/dt (including their reactions), is in principle applicable also in this situation. The trouble is, both the gravitational potential field and the constraints are continuous in nature, not discrete. As the bead descends on the curve, it undergoes an infinity of collisions, and so, as far as performing calculations go, the vector approach can’t be put to use in a direct manner here: you can’t possibly calculate an infinity of forces, or reactions to them, or use them to incrementally calculate the changes in velocities that these come to enforce. Thus, it is the complexity of the constraints (or the “boundary conditions”)—though not the inapplicability of the basic governing physical laws—that make Newton’s original approach impracticable in situations like the brachistochrone. The Lagrangian approach allows us to approach the same problem in a mathematically far simpler manner. [Newton himself was one of the very first to solve this problem using this alternative approach which, later on, to be formalized by Lagrange. (Look up the “lion’s paws” story.)]

Something similar happens also with the Fourier analysis. Even if a phenomenon is decidedly local, like diffusion of the physically distinct material particles (or parcels) from one place to another, the Fourier theory takes these distinct (spatially definite) particles, and then replaces them by positing a global non-entity that is spread everywhere in the universe, but with some peak coinciding with where the actual particles physically are. The so-smeared non-entity is the place-holder [!] for the spatially delimited particles, in Fourier’s theory. The globally spread-out entity is not just an abstraction, but, really speaking, also an approximation—a mathematical approximation. And as far as the inaccuracies in the calculations go, it turns out, this approximation does work out very well in practice. (The reason is not mystical. It is simply that the diffusing particles (atoms/molecules) are so small and so numerous in the physically existing universe.) But if you therefore commit the error of substituting this approximate mathematical abstraction in place of the exact physical reality, you directly end up having the riddles of QM.

If you are interested in pursuing this matter further, you should see my conference paper, first. (Drop me a line if you haven’t already downloaded it when it was available off my Web site, or can’t locate it any other way.) … Though I have also written quite a few posts on the topic, they don’t make for the best material—they are far too informally written (meaning: written completely on the fly and without any previously thought out structure at all). They also too lengthy, and often dwell on technical aspects that are too detailed.

And, that way, they don’t have much mathematical depth, anyway.

But since I seem to be the only person in the entire world who has ever thought along these lines (and one who continues to care), you may want to have a look at myQ detailed musings, too: [^] [^] [^][^].

(… And, no, as far as this issue goes, by no means am I done. I would continue exploring this topic further in my research, also in the future. Though, let me wind it all up for now… This was supposed to be a short and sweet post—a “Yo” post!)

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A Song I Like:

(Marathi) “ekaTyaane ekaTe gardeet chaalaave”
Singer: Avadhoot Gupte
Lyrics: Mangesh Padgaonkar
Music: Shreedhar Phadake

[May be I should post a translation of this song some time later. … Also, of that another Marathi song which I have run just a few posts ago, viz., “man pisaaT majhe…” As to that song (“man pisaaT”) I know for a fact that a lot of Marathi-“knowing” people have never bothered to carefully go through the actual words, they have never tried to put them in some kind of a context, and thus, paying only a fragmentary attention here and there, they have come to associate something of a too abstract and weird (or “artsy”) kind of a sense to it. Their appreciation of that song rests mostly on the musical tune and the singer’s rendition, but their sense of the lyrics seems to be quite off the mark. The actual song isn’t of a meaningless “artsy” kind, and I hope to bring out what I think is the original sense of that song, too. And, as far as the present song goes, there isn’t just an  innovative sort of tune and a wonderful rendering by the singer. There also is a very beautiful piece of poetry lying underneath. … It’s a young new song (it came out only in 2010), but with an obvious touch of class to it. The original CD is just Rs. 100. … Enjoy…. More, later]

[E&OE]