Is something like a re-discovery of the same thing by the same person possible?

Yes, we continue to remain very busy.


However, in spite of all that busy-ness, in whatever spare time I have [in the evenings, sometimes at nights, why, even on early mornings [which is quite unlike me, come to think of it!]], I cannot help but “think” in a bit “relaxed” [actually, abstract] manner [and by “thinking,” I mean: musing, surmising, etc.] about… about what else but: QM!

So, I’ve been doing that. Sort of like, relaxed distant wonderings about QM…

Idle musings like that are very helpful. But they also carry a certain danger: it is easy to begin to believe your own story, even if the story itself is not being borne by well-established equations (i.e. by physic-al evidence).

But keeping that part aside, and thus coming to the title question: Is it possible that the same person makes the same discovery twice?

It may be difficult to believe so, but I… I seemed to have managed to have pulled precisely such a trick.

Of course, the “discovery” in question is, relatively speaking, only a part of of the whole story, and not the whole story itself. Still, I do think that I had discovered a certain important part of a conclusion about QM a while ago, and then, later on, had completely forgotten about it, and then, in a slow, patient process, I seem now to have worked inch-by-inch to reach precisely the same old conclusion.

In short, I have re-discovered my own (unpublished) conclusion. The original discovery was may be in the first half of this calendar year. (I might have even made a hand-written note about it, I need to look up my hand-written notes.)


Now, about the conclusion itself. … I don’t know how to put it best, but I seem to have reached the conclusion that the postulates of quantum mechanics [^], say as stated by Dirac and von Neumann [^], have been conceptualized inconsistently.

Please note the issue and the statement I am making, carefully. As you know, more than 9 interpretations of QM [^][^][^] have been acknowledged right in the mainstream studies of QM [read: University courses] themselves. Yet, none of these interpretations, as far as I know, goes on to actually challenge the quantum mechanical formalism itself. They all do accept the postulates just as presented (say by Dirac and von Neumann, the two “mathematicians” among the physicists).

Coming to me, my positions: I, too, used to say exactly the same thing. I used to say that I agree with the quantum postulates themselves. My position was that the conceptual aspects of the theory—at least all of them— are missing, and so, these need to be supplied, and if the need be, these also need to be expanded.

But, as far as the postulates themselves go, mine used to be the same position as that in the mainstream.

Until this morning.

Then, this morning, I came to realize that I have “re-discovered,” (i.e. independently discovered for the second time), that I actually should not be buying into the quantum postulates just as stated; that I should be saying that there are theoretical/conceptual errors/misconceptions/misrepresentations woven-in right in the very process of formalization which produced these postulates.

Since I think that I should be saying so, consider that, with this blog post, I have said so.


Just one more thing: the above doesn’t mean that I don’t accept Schrodinger’s equation. I do. In fact, I now seem to embrace Schrodinger’s equation with even more enthusiasm than I have ever done before. I think it’s a very ingenious and a very beautiful equation.


A Song I Like:

(Hindi) “tum jo hue mere humsafar”
Music: O. P. Nayyar
Singers: Geeta Dutt and Mohammad Rafi
Lyrics: Majrooh Sultanpuri


Update on 2017.10.14 23:57 IST: Streamlined a bit, as usual.

 

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A prediction. Also, a couple of wishes…

The Prediction:

While the week of the Nobel prizes always has a way to generate a sense of suspense, of excitement, and even of wonderment, as far as I am concerned, the one prize that does that in the real sense to me is, of course, the Physics Nobel. … Nothing compares to it. Chemistry can come close, but not always. [And, Mr. Nobel was a good guy; he instituted no prize for maths! [LOL!]]. …

The Physics Nobel is the King of all awards in all fields, as far as I am concerned.

That’s why, this year, I have this feeling of missing something. … The reason is, this year’s Physics Nobel is already “known”; it will go to Kip Thorne and pals.

[I will not eat crow even if they don’t get it. [… Unless, of course, you know a delicious recipe or two for the same, and also demonstrate it to me, complete with you sampling it first.]]

But yes, Kip Thorne richly deserves it, and he will get it. That’s the prediction. I wanted to slip it in even if only few hours before the announcement arrives.

I will update this post later right today/tonight, after the Physics Nobel is actually announced.


Now let me come to the couple of wishes, as mentioned in the title. I will try to be brief. [Have been too busy these days… OK. Will let you know. We are going in for accreditation, and so, it’s been all heavy documentation-related work for the past few months. Despite all that hard-work, we still have managed to slip a bit on the progress, and so, currently, we are working on all week-ends and on most public holidays, too. [Yes, we came to work yesterday.] So, it’s only somehow that I manage to find some time to slip in this post—which is written absolutely on the fly, with no second thoughts or re-reading before posting. … So excuse me if there is a bit of lack of balance in the presentation, and of course, typos etc.]


Wish # 1:

The first wish is that a Physics Nobel should go, in a combined way, to what actually are two separate, but very intimately related, and two most significant advances in the physical understanding of man: (i) chaos theory (including fractals) and (ii)catastrophe theory.

If you don’t like the idea of two ideas being given a single Nobel, then, well, let me put it this way: the Nobel should be given for achieving the most significant advancements in the field of the differential nonlinearities, for a very substantial progress in the physical understanding of the behaviour of nonlinear physical systems, forging pathways for predictive capacity.

Let me emphasize, this has been one of the most significant advances in physics in the last century. No, saying so is emphatically not a hyperbole.

And, yes, it’s an advance in physics, primarily, and then, also in maths—but only secondarily.

… It’s unfortunate that an advancement which has been this remarkable never did register as such with most of the S&T “manpower”, esp., engineers and practical designers. It’s also unfortunate that the twin advancement arrived on the scene at the time of bad cultural (even epistemological) trends, and so, the advancements got embedded in a fabric of hyperbole, even nonsense.

But regardless of the cultural tones in which the popular presentations of these advancements (esp. of the chaos theory) got couched, taken as a science, the studies of nonlinearity in the physical systems has been a very, very, original, and a very, very creative, advancement. It needs to be recognized as such.

That way, I don’t much care for what it helped produce on the maths side of it. But yes, even a not very extraordinarily talented undergraduate in CS (one with a special interest in deterministic methods in cryptography) would be able to tell you how much light got shone on their discipline because of the catastrophe and chaos theories.

The catastrophe theory has been simply marvellous in one crucial aspect: it actually pushed the boundaries of what is understood by the term: mathematics. The theory has been daring enough to propose, literally for the first time in the entire history of mankind, a well-refined qualitative approach to an infinity of quantitative processes taken as a group.

The distinction between the qualitative and the quantitative had kept philosophers (and laymen) pre-occupied for millenia. But the nonlinear theory has been the first theoretical approach that tells you how to spot and isolate the objective bases for distinguishing what we consider as the qualitative changes.

Remove the understanding given by the nonlinear theory—by the catastrophe-theoretical approach—and, once in the domain of the linear theory, the differences in kind immediately begin to appear as more or less completely arbitrary. There is no place in theory for them—the qualitative distinctions are external to the theory because a linear system always behaves exactly the same with any quantitative changes made, at any scale, to any of the controlling parameters. Since in the linear theory the qualitative changes are not produced from within the theory itself, such distinctions must be imported into it out of some considerations that are in principle external to the theory.

People often confuse such imports with “applications.” No, when it comes to the linear theory, it’s not the considerations of applications which can be said to be driving any divisions of qualitative changes. The qualitative distinctions are basically arbitrary in a linear theory. It is important to realize that that usual question: “Now where do we draw the line?” is basically absolutely superfluous once you are within the domain of the linear systems. There are no objective grounds on the basis of which such distinctions can be made.

Studies of the nonlinear phenomena sure do precede the catastrophe and the chaos theories. Even in the times before these two theories came on the scene, applied physicists would think of certain ideas such as differences of regimes, esp. in the areas like fluid dynamics.

But to understand the illuminating power of the nonlinear theory, just catch hold of an industrial CFD guy (or a good professor of fluid dynamics from a good university [not, you know, from SPPU or similar universities]), and ask him whether there can be any deeper theoretical significance to the procedure of the Buckingham Pi Theorem, to the necessity, in his art (or science) of having to use so many dimensionless numbers. (Every mechanical/allied engineering undergraduate has at least once in life cursed the sheer number of them.) The competent CFD guy (or the good professor) would easily be at a loss. Then, toss a good book on the Catastrophe Theory to him, leave him alone for a couple of weeks or may be a month, return, and raise the same question again. He now may or may not have a very good, “flowy” sort of a verbal answer ready for you. But one look at his face would tell you that it has now begun to reflect a qualitatively different depth of physical understanding even as he tries to tackle that question in his own way. That difference arises only because of the Catastrophe Theory.

As to the Chaos Theory (and I club the fractal theory right in it), more number of people are likely to know about it, and so, I don’t have to wax a lot (whether eloquently or incompetently). But let me tell you one thing.

Feigenbaum’s discovery of the universal constant remains, to my mind, one of the most ingenious advancements in the entire history of physics, even of science. Especially, given the experimental equipment with which he made that discovery—a handheld HP Calculator (not a computer) in the seventies (or may be in the sixties)! … And yes, getting to that universal constant was, if you ask me, an act of discovery, and not of invention. (Invention was very intimately involved in the process; but the overall act and the end-product was one of discovery.)

So, here is a wish that these fundamental studies of the nonlinear systems get their due—the recognition they so well deserve—in the form of a Physics Nobel.

…And, as always, the sooner the better!


Wish # 2:

The second wish I want to put up here is this: I wish there was some commercial/applied artist, well-conversant with the “art” of supplying illustrations for a physics book, who also was available for a long-term project I have in mind.

To share a bit: Years ago (actually, almost two decades ago, in 1998 to be precise), I had made a suggestion that novels by Ayn Rand be put in the form of comics. As far as I was concerned, the idea was novel (i.e. new). I didn’t know at that time that a comics-book version of The Fountainhead had already been conceived of by none other than Ayn Rand herself, and it, in fact, had also been executed. In short, there was a comics-book version of The Fountainhead. … These days, I gather, they are doing something similar for Atlas Shrugged.

If you think about it, my idea was not at all a leap of imagination. Newspapers (even those in India) have been carrying comic strips for decades (right since before my own childhood), and Amar Chitrakatha was coming of age just when I was. (It was founded in 1967 by Mr. Pai.)

Similarly, conceiving of a comics-like book for physics is not at all a very creative act of imagination. In fact, it is not even original. Everyone knows those books by that Japanese linguistics group, the books on topics like the Fourier theory.

So, no claim of originality here.

It’s just that for my new theory of QM, I find that the format of a comics-book would be most suitable. (And what the hell if physicists don’t take me seriously because I put it in this form first. Who cares what they think anyway!)

Indeed, I would even like to write/produce some comics books on maths topics, too. Topics like grads, divs, curls, tensors, etc., eventually. … Guess I will save that part for keeping me preoccupied during my retirement. BTW, my retirement is not all that far away; it’s going to be here pretty soon, right within just five years from now. (Do one thing: Check out what I was writing, say in 2012 on this blog.)

But the one thing I would like write/produce right in the more immediate future is: the comics book on QM, putting forth my new approach.

So, in the closing, here is a request. If you know some artist (or an engineer/physicist with fairly good sketching/computer-drawing skills), and has time at hand, and has the capacity to stay put in a sizeable project, and won’t ask money for it (a fair share in the royalty is a given—provided we manage to find a publisher first, that is), then please do bring this post to his notice.

 


A Song I Like:

And, finally, here is the Marathi song I had promised you the last time round. It’s a fusion of what to my mind is one of the best tunes Shrinivas Khale ever produced, and the best justice to the words and the tunes by the singer. Imagine any one else in her place, and you will immediately come to know what I mean. … Pushpa Pagdhare easily takes this song to the levels of the very best by the best, including Lata Mangeshkar. [Oh yes, BTW, congrats are due to the selection committe of this year’s Lata Mangeshkar award, for selecting Pushpa Pagdhare.]

(Marathi) “yeuni swapnaat maajhyaa…”
Singer: Pushpa Pagdhare
Music: Shrinivas Khale
Lyrics: Devakinandan Saraswat

[PS: Note: I am going to come back and add an update once this year’s Physics Nobel is announced. At that time (or tonight) I will also try to streamline this post.

Then, I will be gone off the blogging for yet another couple of weeks or so—unless it’s a small little “kutty” post of the “Blog-Filler” kind or two.]

 

Off the blog. [“Matter” cannot act “where” it is not.]

I am going to go off the blogging activity in general, and this blog in most particular, for some time. [And, this time round, I will keep my promise.]


The reason is, I’ve just received the shipment of a book which I had ordered about a month ago. Though only about 300 pages in length, it’s going to take me weeks to complete. And, the book is gripping enough, and the issue important enough, that I am not going to let a mere blog or two—or the entire Internet—come in the way.


I had read it once, almost cover-to-cover, some 25 years ago, while I was a student in UAB.

Reading a book cover-to-cover—I mean: in-sequence, and by that I mean: starting from the front-cover and going through the pages in the same sequence as the one in which the book has been written, all the way to the back-cover—was quite odd a thing to have happened with me, at that time. It was quite unlike my usual habits whereby I am more or less always randomly jumping around in a book, even while reading one for the very first time.

But this book was different; it was extraordinarily engaging.

In fact, as I vividly remember, I had just idly picked up this book off a shelf from the Hill library of UAB, for a casual examination, had browsed it a bit, and then had began sampling some passage from nowhere in the middle of the book while standing in an library aisle. Then, some little time later, I was engrossed in reading it—with a folded elbow resting on the shelf, head turned down and resting against a shelf rack (due to a general weakness due to a physical hunger which I was ignoring [and I would have have to go home and cook something for myself; there was none to do that for me; and so, it was easy enough to ignore the hunger]). I don’t honestly remember how the pages turned. But I do remember that I must have already finished some 15-20 pages (all “in-the-order”!) before I even realized that I had been reading this book while still awkwardly resting against that shelf-rack. …

… I checked out the book, and once home [student dormitory], began reading it starting from the very first page. … I took time, days, perhaps weeks. But whatever the length of time that I did take, with this book, I didn’t have to jump around the pages.


The issue that the book dealt with was:

[Instantaneous] Action at a Distance.

The book in question was:

Hesse,┬áMary B. (1961) “Forces and Fields: The concept of Action at a Distance in the history of physics,” Philosophical Library, Edinburgh and New York.


It was the very first book I had found, I even today distinctly remember, in which someone—someone, anyone, other than me—had cared to think about the issues like the IAD, the concepts like fields and point particles—and had tried to trace their physical roots, to understand the physical origins behind these (and such) mathematical concepts. (And, had chosen to say “concepts” while meaning ones, rather than trying to hide behind poor substitute words like “ideas”, “experiences”, “issues”, “models”, etc.)

Twenty-five years later, I still remain hooked on to the topic. Despite having published a paper on IAD and diffusion [and yes, what the hell, I will say it: despite claiming a first in 200+ years in reference to this topic], I even today do find new things to think about, about this “kutty” [Original: IITM lingo; English translation: “small”] topic. And so, I keep returning to it and thinking about it. I still am able to gain new insights once in an odd while. … Indeed, my recent ‘net search on IAD (the one which led to Hesse and my buying the book) precisely was to see if someone had reported the conceptual [and of course, mathematical] observation which I have recently made, or not. [If too curious about it, the answer: looks like, none has.]


But now coming to Hesse’s writing style, let me quote a passage from one of her research papers. I ran into this paper only recently, last month (in July 2017), and it was while going through it that I happened [once again] to remember her book. Since I did have some money in hand, I did immediately decide to order my copy of this book.

Anyway, the paper I have in mind is this:

Hesse, Mary B. (1955) “Action at a Distance in Classical Physics,” Isis, Vol. 46, No. 4 (Dec., 1955), pp. 337–353, University of Chicago Press/The History of Science Society.

The paper (it has no abstract) begins thus:

The scholastic axiom that “matter cannot act where it is not” is one of the very general metaphysical principles found in science before the seventeenth century which retain their relevance for scientific theory even when the metaphysics itself has been discarded. Other such principles have been fruitful in the development of physics: for example, the “conservation of motion” stated by Descartes and Leibniz, which was generalized and given precision in the nineteenth century as the doctrine of the conservation of energy; …

Here is another passage, once again, from the same paper:

Now Faraday uses a terminology in speaking about the lines of force which is derived from the idea of a bundle of elastic strings stretched under tension from point to point of the field. Thus he speaks of “tension” and “the number of lines” cut by a body moving in the field. Remembering his discussion about contiguous particles of a dielectric medium, one must think of the strings as stretching from one particle of the medium to the next in a straight line, the distance between particles being so small that the line appears as a smooth curve. How seriously does he take this model? Certainly the bundle of elastic strings is nothing like those one can buy at the store. The “number of lines” does not refer to a definite number of discrete material entities, but to the amount of force exerted over a given area in the field. It would not make sense to assign points through which a line passes and points which are free from a line. The field of force is continuous.

See the flow of the writing? the authentic respect for the intellectual history, and yet, the overriding concern for having to reach a conclusion, a meaning? the appreciation for the subtle drama? the clarity of thought, of expression?

Well, these passages were from the paper, but the book itself, too, is similarly written.


Obviously, while I remain engaged in [re-]reading the book [after a gap of 25 years], don’t expect me to blog.

After all, even I cannot act “where” I am not.


A Song I Like:

[I thought a bit between this song and another song, one by R.D. Burman, Gulzar and Lata. In the end, it was this song which won out. As usual, in making my decision, the reference was exclusively made to the respective audio tracks. In fact, in the making of this decision, I happened to have also ignored even the excellent guitar pieces in this song, and the orchestration in general in both. The words and the tune were too well “fused” together in this song; that’s why. I do promise you to run the RD song once I return. In the meanwhile, I don’t at all mind keeping you guessing. Happy guessing!]

(Hindi) “bheegi bheegi…” [“bheege bheege lamhon kee bheegee bheegee yaadein…”]
Music and Lyrics: Kaushal S. Inamdar
Singer: Hamsika Iyer

[Minor additions/editing may follow tomorrow or so.]

 

Expanding on the procedure of expanding: Where is the procedure to do that?

Update on 18th June 2017:

See the update to the last post; I have added three more diagrams depicting the mathematical abstraction of the problem, and also added a sub-question by way of clarifying the problem a bit. Hopefully, the problem is clearer and also its connection to QM a bit more apparent, now.


Here I partly expand on the problem mentioned in my last post [^]. … Believe me, it will take more than one more post to properly expand on it.


The expansion of an expanding function refers to and therefore requires simultaneous expansions of the expansions in both the space and frequency domains.

The said expansions may be infinite [in procedure].


In the application of the calculus of variations to such a problem [i.e. like the one mentioned in the last post], the most important consideration is the very first part:

Among all the kinematically admissible configurations…

[You fill in the rest, please!]


A Song I Like:

[I shall expand on this bit a bit later on. Done, right today, within an hour.]

(Hindi) “goonji see hai, saari feezaa, jaise bajatee ho…”
Music: Shankar Ahasaan Loy
Singers: Sadhana Sargam, Udit Narayan
Lyrics: Javed Akhtar