The bouncing droplets imply having to drop the Bohmian approach?

If you are interested in the area of QM foundations, then may be you should drop everything at once, and go, check out the latest pop-sci news report: “Famous experiment dooms alternative to quantum weirdness” by Natalie Wolchover in the Quanta Magazine [^].

Remember the bouncing droplets experiments performed by Yves Couder and pals? In 2006, they had reported that they could get the famous interference pattern even if the bouncing droplets passed through the double slit arrangement only one at a time. … As the Quanta article now reports, it turns out that when other groups in the USA and France tried to reproduce this result (the single-particle double-slit interference), they could not.

“Repeat runs of the experiment, called the “double-slit experiment,” have contradicted Couder’s initial results and revealed the double-slit experiment to be the breaking point of both the bouncing-droplet analogy and de Broglie’s pilot-wave vision of quantum mechanics.”

Well, just an experimental failure or two in reproducing the interference, by itself, wouldn’t make for a “breaking point,”i.e., if the basic idea itself were to be sound. So the question now becomes whether the basic idea itself is sound enough or not.

Turns out that a new argument has been put forth, in the form of a thought experiment, which reportedly shows why and how the very basic idea itself must be regarded as faulty. This thought experiment has been proposed by a Danish professor of fluid dynamics, Prof. Tomas Bohr. (Yes, there is a relation: Prof. Tomas Bohr is a son of the Nobel laureate Aage Bohr, i.e., a grandson of the Nobel laureate Niels Bohr [^].)

Though related to QM foundations, this thought experiment is not very “philosophical” in nature; on the contrary, it is very, very “physics-like.” And the idea behind it also is “simple.” … It’s one of those ideas which make you exclaim “why didn’t I think of it before?”—at least the first time you run into it. Here is an excerpt (which actually is the caption for an immediately understandable diagram):

“Tomas Bohr’s variation on the famous double-slit experiment considers what would happen if a particle must go to one side or the other of a central dividing wall before passing through one of the slits. Quantum mechanics predicts that the wall will have no effect on the resulting double-slit interference pattern. Pilot-wave theory, however, predicts that the wall will prevent interference from happening.”

… Ummm… Not quite.

From whatever little I know about the pilot-wave theory, I think that the wall wouldn’t prevent the interference from occurring, even if you use this theory. … It all seems to depend on how you interpret (and/or extend) the pilot-wave theory. But if applied right (which means: in its own spirit), then I guess that the theory is just going to reproduce whatever it is that the mainstream QM predicts. Given this conclusion I have drawn about this approach, I did think that the above-quoted portion was a bit misleading.

The main text of the article then proceeds to more accurately point out the actual problem (i.e., the way Prof. Tomas Bohr apparently sees it):

“… the dividing-wall thought experiment highlights, in starkly simple form, the inherent problem with de Broglie’s idea. In a quantum reality driven by local interactions between a particle and a pilot wave, you lose the necessary symmetry to produce double-slit interference and other nonlocal quantum phenomena. An ethereal, nonlocal wave function is needed that can travel unimpeded on both sides of any wall. [snip] But with pilot waves, “since one of these sides in the experiment carries a particle and one doesn’t, you’ll never get that right. You’re breaking this very important symmetry in quantum mechanics.””

But isn’t the pilot wave precisely ethereal and nonlocal in nature, undergoing instantaneous changes to itself at all points of space? Doesn’t the pilot theory posit that this wave doesn’t consist of anything material that does the waving but is just a wave, all by itself?


…So, if you think it through, people seem to be mixing up two separate issues here:

  1. One issue is whether it will at all be possible for any real physical experiment done up with the bouncing droplets to be able to reproduce the predictions of QM or not.
  2. An entirely different issue is whether, in Bohr’s dividing-wall thought-experiment, the de Broglie-Bohm approach actually predicts something that is at a variance from what QM predicts or not.

These two indeed are separate issues, and I think that the critics are right on the first count, but not necessarily on the second.

Just to clarify: The interference pattern as predicted by the mainstream QM itself would undergo a change, a minor but a very definite change, once you introduce the middle dividing wall; it would be different from the pattern obtained for the “plain-vanilla” version of the interference chamber. And if what I understand about the Bohmian mechanics is correct, then it too would proceed to  produce exactly the same patterns in both these cases.


With that said, I would still like to remind you that my own understanding of the pilot-wave theory is only minimal, mostly at the level of browsing of the Wiki and a few home pages, and going through a few pop-sci level explanations by a few Bohmians. I have never actually sat down to actually go through even one paper on it fully (let alone systematically study an entire book or a whole series of articles on this topic).

For this reason, I would rather leave it to the “real” Bohmians to respond to this fresh argument by Prof. Tomas Bohr.

But yes, a new argument—or at least, an old argument but in a remarkably new settings—it sure seems to be.


How would the Bohmians respond?

If you ask me, from whatever I have gathered about the Bohmians and their approach, I think that they are simply going to be nonchalant about this new objection, too. I don’t think that you could possibly hope to pin them down with this argument either. They are simply going to bounce back, just like those drops. And the reason for that, in turn, is what I mentioned already here in this post: their pilot-wave is both ethereal and nonlocal in the first place.


So, yes, even if Wolchover’s report does seem to be misguided a bit, I still liked it, mainly because it was informative on both the sides: experimental as well as theoretical (viz., as related to the new thought-experiment).

In conclusion, even if the famous experiment does not doom this (Bohmian) alternative to the quantum weirdness, the basic reason for its unsinkability is this:

The Bohmian mechanics is just as weird as the mainstream QM is—even if the Bohmians habitually and routinely tell you otherwise.

When a Bohmian tells you that his theory is “sensible”/“realistic”/etc/, what he is talking about is: the nature of his original ambition—but not the actual nature of his actual theory.


To write anything further about QM is to begin dropping hints to my new approach. So let me stop right here.

[But yes, I am fully ready willing from my side to disclose all details about it at any time to a suitable audience. … Let physics professors in India respond to my requests to let me conduct an informal (but officially acknowledged) seminar on my new approach, and see if I get ready to deliver it right within a week’s time, or not!

[Keep waiting!]]


Regarding other things, as you know, the machine I am using right now is (very) slow. Even then, I have managed to run a couple of 10-line Python scripts, using VSCode.

I have immediately taken to liking this IDE “code-editor.” (Never had tried it before.) I like it a lot. … Just how much?

I think I can safely say that VSCode is the best thing to have happened to the programming world since VC++ 6 about two decades ago.

Yes, I have already stopped using PyCharm (which, IMHO, is now the second-best alternative, not the best).


No songs section this time, because I have already run a neat and beautiful song just yesterday. (Check out my previous post.) … OK, if some song strikes me in a day or two, I will return here to add it. Else, wait until the next time around. … Until then, take care and bye for now…


[Originally published on 16 October 2018 22:09 hrs IST. Minor editing (including to the title line) done by 17 October 2018 08:09 hrs IST.]

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Absolutely Random Notings on QM—Part 3: Links to some (really) interesting material, with my comments

Links, and my comments:


The “pride of place” for this post goes to a link to this book:

Norsen, Travis (2017) “Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory,” Springer

This book is (i) the best supplementary book for a self-study of QM, and simultaneously, also (ii) the best text-book on a supplementary course on QM, both at the better-prepared UG / beginning PG level.

A bit expensive though, but extensive preview is available on Google books, here [^]. (I plan to buy it once I land a job.)

I was interested in the material from the first three chapters only, more or less. It was a delight even just browsing through these chapters. I intend to read it more carefully soon enough. But even on the first, rapid browsing, I noticed that several pieces of understanding that I had so painstakingly come to develop (over a period of years) are given quite straight-forwardly here, as if they were a matter of well known facts—even if other QM text-books only cursorily mention them, if at all.

For instance, see the explanation of entanglement here. Norsen begins by identifying that there is a single wavefunction, always—even for a multi-particle system. Then after some explanation, he states: “But, as usual in quantum mechanics, these states do not exhaust the possibilities—instead, they merely form a basis for the space of all possible wave functions. …”… Note the emphasis on the word “basis” which Norsen helpfully puts.

Putting this point (which Norsen discusses with a concrete example), but in my words: There is always a single wavefunction, and for a multi-particle system, its basis is bigger; it consists of the components of the tensor product (formed from the components of the basis of the constituent systems). Sometimes, the single wavefunction for the multi-particle system can be expressed as a result of a single tensor-product (in which case it’s a separable state), and at all other times, only as an algebraic sum of the results of many such tensor-products (in which case they all are entangled states).

Notice how there is no false start of going from two separate systems, and then attempting to forge a single system out of them. Notice how, therefore, there is no hand-waving at one electron being in one galaxy, and another electron in another galaxy, and so on, as if to apologize for the very idea of the separable states. Norsen achieves the correct effect by beginning on the right note: the emphasis on the single wavefunction for the system as a whole to begin with, and then clarifying, at the right place, that what the tensor product gives you is only the basis set for the composite wavefunction.

There are many neat passages like this in the text.


I was about to say that Norsen’s book is the Resnick and Halliday of QM, but then came to hesitate saying so, because I noticed something odd even if my browsing of the book was rapid and brief.

Then I ran into

Ian Durham’s review of Norsen’s book, at the FQXi blog,

which is our link # 2 for this post [^].

Durham helpfully brings out the following two points (which I then verified during a second visit to Norsen’s book): (i) Norsen’s book is not exactly at the UG level, and (ii) the book is a bit partial to Bell’s characterization of the quantum riddles as well as to the Bohmian approach for their resolution.

The second point—viz., Norsen’s fascination for / inclination towards Bell and Bohm (B&B for short)—becomes important only because the book is, otherwise, so good: it carries so many points that are not even passingly mentioned in other QM books, is well written (in a conversational style, as if a speech-to-text translator were skillfully employed), easy to understand, thorough, and overall (though I haven’t read even 25% of it, from whatever I have browsed), it otherwise seems fairly well balanced.

It is precisely because of these virtues that you might come out giving more weightage to the B&B company than is actually due to them.

Keep that warning somewhere at the back of your mind, but do go through the book anyway. It’s excellent.

At Amazon, it has got 5 reader reviews, all with 5 stars. If I were to bother doing a review there, I too perhaps would give it 5 stars—despite its shortcomings/weaknesses. OK. At least 4 stars. But mostly 5 though. … I am in an indeterminate state of their superposition.

… But mark my words. This book will have come to shape (or at least to influence) every good exposition of (i.e. introduction to) the area of the Foundations of QM, in the years to come. [I say that, because I honestly don’t expect a better book on this topic to arrive on the scene all that soon.]


Which brings us to someone who wouldn’t assign the |4\rangle + |5\rangle stars to this book. Namely, Lubos Motl.

If Norsen has moved in the Objectivist circles, and is partial to the B&B company, Motl has worked in the string theory, and is not just partial to it but even today defends it very vigorously—and oddly enough, also looks at that “supersymmetric world from a conservative viewpoint.” More relevant to us: Motl is not partial to the Copenhagen interpretation; he is all the way into it. … Anyway, being merely partial is something you wouldn’t expect from Motl, would you?

But, of course, Motl also has a very strong grasp of QM, and he displays it well (even powerfully) when he writes a post of the title:

“Postulates of quantum mechanics almost directly follow from experiments.” [^]

Err… Why “almost,” Lubos? 🙂

… Anyway, go through Motl’s post, even if you don’t like the author’s style or some of his expressions. It has a lot of educational material packed in it. Chances are, going through Motl’s posts (like the present one) will come to improve your understanding—even if you don’t share his position.

As to me: No, speaking from the new understanding which I have come to develop regarding the foundations of QM [^] and [^], I don’t think that all of Motl’s objections would carry. Even then, just for the sake of witnessing the tight weaving-in of the arguments, do go through Motl’s post.


Finally, a post at the SciAm blog:

“Coming to grips with the implications of quantum mechanics,” by Bernardo Kastrup, Henry P. Stapp, and Menas C. Kafatos, [^].

The authors say:

“… Taken together, these experiments [which validate the maths of QM] indicate that the everyday world we perceive does not exist until observed, which in turn suggests—as we shall argue in this essay—a primary role for mind in nature.”

No, it didn’t give me shivers or something. Hey, this is QM and its foundations, right? I am quite used to reading such declarations.

Except that, as I noted a few years ago on Scott Aaronson’s blog [I need to dig up and insert the link here], and then, recently, also at

Roger Schlafly’s blog [^],

you don’t need QM in order to commit the error of inserting consciousness into a physical theory. You can accomplish exactly the same thing also by using just the Newtonian particle mechanics in your philosophical arguments. Really.


Yes, I need to take that reply (at Schlafly’s blog), edit it a bit and post it as a separate entry at this blog. … Some other time.

For now, I have to run. I have to continue working on my approach so that I am able to answer the questions raised and discussed by people such as those mentioned in the links. But before that, let me jot down a general update.


A general update:

Oh, BTW, I have taken my previous QM-related post off the top spot.

That doesn’t mean anything. In particular, it doesn’t mean that after reading into materials such as that mentioned here, I have found some error in my approach or something like that. No. Not at all.

All it means is that I made it once again an ordinary post, not a sticky post. I am thinking of altering the layout of this blog, by creating a page that highlights that post, as well as some other posts.

But coming back to my approach: As a matter of fact, I have also written emails to a couple of physicists, one from IIT Bombay, and another from IISER Pune. However, things have not worked out yet—things like arranging for an informal seminar to be delivered by me to their students, or collaborating on some QM-related simulations together. (I could do the simulations on my own, but for the seminar, I would need an audience! One of them did reply, but we still have to shake our hands in the second round.)

In the meanwhile, I go jobless, but I keep myself busy. I am preparing a shortish set of write-ups / notes which could be used as a background material when (at some vague time in future) I go and talk to some students, say at IIT Bombay/IISER Pune. It won’t be comprehensive. It will be a little more than just a white-paper, but you couldn’t possibly call it even just the preliminary notes for my new approach. Such preliminary notes would come out only after I deliver a seminar or two, to physics professors + students.

At the time of delivering my proposed seminar, links like those I have given above, esp. Travis Norsen’s book, also should prove a lot useful.

But no, I haven’t seen something like my approach being covered anywhere, so far, not even Norsen’s book. There was a vague mention of just a preliminary part of it somewhere on Roger Schlafly’s blog several years ago, only once or so, but I can definitely say that I had already had grasped even that point on my own before Schlafly’s post came. And, as far as I know, Schlafly hasn’t come to pursue that thread at all, any time later…

But speaking overall, at least as of today, I think I am the only one who has pursued this (my) line of thought to the extent I have [^].

So, there. Bye for now.


I Song I Like:
(Hindi) “suno gajar kya gaaye…”
Singer: Geeta Dutt
Music: S. D. Burman
Lyrics: Sahir Ludhianvi
[There are two Geeta’s here, and both are very fascinating: Geeta Dutt in the audio, and Geeta Bali in the video. Go watch it; even the video is recommended.]


As usual, some editing after even posting, would be inevitable.

Some updates made and some streamlining done on 30 July 2018, 09:10 hrs IST.

 

And to think…

Many of you must have watched the news headlines on TV this week; many might have gathered it from the ‘net.

Mumbai—and much of Maharashtra—has gone down under. Under water.

And to think that all this water is now going to go purely to waste, completely unused.

… And that, starting some time right from say February next year, we are once again going to yell desperately about water shortage, about how water-tankers have already begun plying on the “roads” near the drought-hit villages. … May be we will get generous and send not just 4-wheeler tankers but also an entire train to a drought-hit city or two…

Depressing!


OK. Here’s something less depressing. [H/t Jennifer Ouellette (@JenLucPiquant) ]:

“More than 2,000 years ago, people were able to create ice in the desert even with temperatures above freezing!” [^]

The write-up mentions a TED video by Prof. Aaswath Raman. Watched it out of idle interest, checked out his Web site, and found another TED video by him, here [^]. Raman cites statistics that blew me!

They spend “only” $24 billion on supermarket refrigeration (and other food-related cooling), but they already spend $42 billion on data-center cooling!!


But, any way, I did some further “research” and landed at a few links, like the Wiki on Yakhchal [^], on wind-catcher [^], etc.  Prof. Raman’s explanation in terms of the radiative cooling was straight-forwards, but I am not sure I understand the mechanism behind the use of a qanat [^] in Yakhchal/windcatcher cooling. It would be cool to do some CFD simulations though.


Finally, since I am once again out of a job (and out of all my saved money and in fact also into credit-card loans due to some health issue cropping up once again), I was just idly wondering about all this renewable energy business, when something struck me.


The one big downside of windmills is that the electricity they generate fluctuates too much. You can’t rely on it; the availability is neither 24X7 nor uniform. Studies in fact also show that in accommodating the more or less “random” output of windmills into the conventional grid, the price of electricity actually goes up—even if the cost of generation alone at the windmill tower may be lower. Further, battery technology has not improved to such a point that you could store the randomly generated electricity economically.

So, I thought, why not use that randomly fluctuating windmill electricity in just producing the hydrogen gas?

No, I didn’t let out a Eureka. Instead, I let out a Google search. After all, the hydrogen gas could be used in fuel-cells, right? Would the cost of packaging and transportation of hydrogen gas be too much? … A little searching later, I landed at this link: [^]. Ummm… No, no, no…. Why shoot it into the natural gas grid? Why not compress it into cylinders and transport by trains? How does the cost economics work out in that case? Any idea?


Addendum on the same day, but after about a couple of hours:

Yes, I did run into this link: “Hydrogen: Hope or Hype?” [^] (with all the links therein, and then, also this: [^]).

But before running into those links, even as my googling on “hydrogen fuel energy density” still was in progress, I thought of this idea…

Why at all transport the hydrogen fuel from the windmill farm site to elsewhere? Why not simply install a fuel cell electricity generator right at the windmill farm? That is to say, why not use the hydrogen fuel generated via electrolysis as a flywheel of sorts? Get the idea? You introduce a couple of steps in between the windmill’s electricity and the conventional grid. But you also take out the fluctuations, the bad score on the 24X7 availability. And, you don’t have to worry about the transportation costs either.

What do you think?


Addendum on 12th July 2018, 13:27 hrs IST

Further, I also browsed a few links that explore another,  solution: using compressed air: a press report [^], and a technical paper [^]. (PDF of the paper is available, but the paper would be accessible only to mechanical engineers though. Later Update: As to the press report, well, the company it talks about has already merged with another company, and has abandoned the above-ground storage of compressed air [^])

I think that such a design reduces the number of steps of energy conversions. However, that does not necessarily mean that the solution involving hydrogen fuel generation and utilization (both right at the wind-farm) isn’t going to be economical.

Economics determines (or at least must determine) the choice. Enough on this topic for now. Wish I had a student working with me; I could have then written a paper after studying the solution I have proposed above. (The idea is worth a patent too. Too bad I don’t have the money to file one. Depressing, once again!!)


OK. Enough for the time being. I may later on add the songs section if I feel like it. And, iterative modifications will always be done, but will be mostly limited to small editorial changes. Bye for now.

 

QM: A couple of defensible statements. Also, a bit on their implications for the QC.

A Special Note (added on 17th June 2018): This post is now a sticky post; it will remain, for some time, at the top of this blog.

I am likely to keep this particular post at the top of this blog, as a sticky post, for some time in the future (may be for a few months or so). So, even if posts at this blog normally appear in the reverse chronological order, any newer entries that I may post after this one would be found below this one.

[In particular, right now, I am going through a biography: “Schrodinger: Life and Thought” by Walter Moore [^]. I had bought this book way back in 2011, but had to keep it aside back then, and then, somehow, I came to forget all about it. The book surfaced during a recent move we made, and thus, I began reading it just this week. I may write a post or two about it in the near future (say within a couple of weeks or so) if something strikes me while I am at it.]


A Yawningly Long Preamble:

[Feel free to skip to the sections starting with the “Statement 1” below.]

As you know, I’ve been thinking about foundations of QM for a long, long time, a time running into decades by now.

I thought a lot about it, and then published a couple of papers during my PhD, using a new approach which I had developed. This approach was used for resolving the wave-particle duality, but only in the context of photons. However, I then got stuck when it came to extending and applying this same approach to electrons. So, I kept on browsing a lot of QM-related literature in general. Then, I ran, notably, into the Nobel laureate W. E. Lamb’s “anti-photon” paper [^], and also the related literature (use Google Scholar). I thought a lot about this paper—and also about QM. I began thinking about QM once again from the scratch, so to speak.

Eventually, I came to abandon my own PhD-time approach. At the same time, with some vague but new ideas already somewhere at the back of my mind, I once again started studying QM, once again with a fresh mind, but this time around much more systematically. …

… In the process, I came to develop a completely new understanding of QM!… It’s been at least months since I began talking about it [^]. … My confidence in this new understanding has only increased, since then.

Today’s post will be based on this new understanding. (I could call it a new theory, perhaps.)


My findings suggest a few conclusions which I think I should not hold back any longer. Hence this post.

I have been trying to locate the right words for formulating my conclusions—but without much satisfaction. Finally, I’ve decided to go ahead and post an entry here anyway, regardless of whether the output comes out as being well formulated or not.

In other words, don’t try to pin me down with the specific words I use here in this post! Instead, try to understand what I am trying to get at. In still other words: the particular words I use may change, but the intended meaning will, from now on, “always” remain the same—ummm…. more or less the same!

OK, so here are the statements I am making today. I think they are well defensible:


Notation:
QM: Quantum Mechanics, quantum mechanically, etc.
CM: Classical Mechanics
QC: Quantum Computer
QS: Quantum Supremacy ([^] and [^])


Statement 1: It is possible to explain all quantum mechanical phenomena on the basis of those principles which are already known (or have already been developed) in the context of classical mechanics.

Informal Explanation 1.1: Statement 1 holds true. It’s just that when it comes to explaining the QM phenomena (i.e., when it comes to supplying a physical mechanism for QM), even if the principles do remain the same, the way they are to be combined and applied is different. These differences basically arise because of a reason mentioned in the next Informal Explanation.

Informal Explanation 1.2: Yes, the tradition of 80+ years, involving an illustrious string of Nobel laureates and others, is, in a way, “wrong.” The QM principles are not, fundamentally speaking, very different from those encountered in the CM. It’s just that some of the objects that QM assumes and talks about are different (only partly different) from those assumed in the CM.


Corollary 1 of Statement 1: A quantum computer could “in principle” be built as an “application layer” on top of the “OS platform” supplied by the classical mechanics.

Informal Explanation 1.C1.1: Hierarchically speaking, QM remains the most fundamental or the “ground” layer. The aspects of the physical reality that CM refers to, therefore, indeed are at a layer lying on top of QM. This part does continue to remain the same.

However, what the Corollary 1 now says is that you can also completely explain the workings of QM in terms of a virtual QM machine that is built on top of the well-known principles of CM.

If someone builds a QC on such a basis (which would be a virtual QC on top of CM), then it would be just a classical mechanically functioning simulator—an analog simulator, I should add—that simulates the QM phenomena.

Informal Explanation 1.C1.2: The phrase “in principle” does not always translate into “easily.” In this case, it in factt is very easily possible that building a big enough a QC of this kind (i.e. the simulating QC) may very well turn out to be an enterprise that is too difficult to be practically feasible.


Corollary 2 of Statement 1: A classical system can be designed in such a way that it shows all the features of the phenomenon of quantum entanglement (when the classical system is seen from an appropriately high-level viewpoint).

Informal Explanation 1.C2.1: There is nothing “inherently quantum-mechanical” about entanglement. The well-known principles of CM are enough to explain the phenomena of entanglement.

Informal Explanation 1.C2.2: We use our own terms. In particular, when we say “classical mechanics,” we do not mean these words in the same sense in which a casual reader of the QM literature, e.g. of Bell’s writings, may read them.

What we mean by “classical mechanics” is the same as what an engineer who has never studied QM proper means, when he says “classical mechanics” (i.e., the Newtonian mechanics + the Lagrangian and Hamiltonian reformulations including variational principles, as well as the more modern developments such as studies of nonlinear systems and the catastrophe theory).


Statement 2: It can be shown that even if the Corollary 1 above does hold true, the kind of quantum computer it refers to would be such that it will not be able to break a sufficiently high-end RSA encryption (such as what is used in practice today, at the high-end).

Aside 2.1: I wouldn’t have announced Statement 1 unless I was sure—absolutely goddamn sure, in fact—about the Statement 2. In fact, I must have waited for at least half a year just to make sure about this aspect, looking at these things from this PoV, then from that PoV, etc.


Statement 3: Inasmuch as the RSA-beating QC requires a controlled entanglement over thousands of qubits, it can be said, on the basis of the new understanding (the one which lies behind the Statement 1 above), that the goal of achieving even “just” the quantum supremacy seems highly improbable, at least in any foreseeable future, let alone achieving the goal of breaking the high-end RSA encryption currently in use. However, proving these points, esp. that the currently employed higher-end RSA cannot be broken, will require further development of the new theory, particularly a quantitative theory for the mechanism(s) involved in the quantum mechanical measurements.

Informal Explanation 3.1: A lot of funding has already gone into attempts to build a QC. Now, it seems that the US government, too, is considering throwing some funds at it.

The two obvious goal-posts for a proper QC are: (i) first gaining enough computational power to run past the capabilities of the classical digital computers, i.e., achieving the so-called “quantum supremacy,” and then, (ii) breaking the RSA encryption as is currently used in the real-world at the high-end.

The question of whether the QC-related researches will be able to achieve these two goals or not depends on the question of whether there are natural reasons/causes which might make it highly improbable (if not outright impossible) to achieve these two goals.

We have already mentioned that it can be shown that it will not be possible for a classical (analog) quantum simulator (of the kind we have in mind) to break the RSA encryption.

Thus, we have already made a conclusive statement about this combination of a QC and a goal-post:

  • Combination 1: CM-based QC Simulator that is able to break the RSA encryption.

We have said that it can be shown (i.e. proved) that the above combination would be impossible to have. (The combination is that extreme.)

However, it still leaves open 3 more combinations of a QC and a goal-post:

  • Combination 2: CM-based QC Simulator that exceeds the classical digital computer
  • Combination 3: Proper QC (working directly off the QM platform) that exceeds the classical digital computer
  • Combination 4: Proper QC (working directly off the QM platform) that is able to break the RSA encryption.

As of today, a conclusive statement cannot be made regarding the last three combinations, not even on the basis of my newest approach to the quantum phenomena, because the mathematical aspects which will help settle questions of this kind, have not yet been developed (by me).

Chances are good that such a theory could be developed, at least in somewhat partly-qualitative-and-partly-quantitative terms, or in terms of some quantitative models that are based on some good analogies, sometime in the future (say within a decade or so). It is only when such developments do occur that we will be able to conclusively state something one way or the other in respect of the last three combinations.

However, relying on my own judgment, I think that I can safely state this much right away: The remaining three combinations would be tough, very tough, to achieve. The last combination, in particular, is best left aside, because the combination is far too complex that it can pose any real threat, at least as of today. I can say this much confidently—based on my new approach. (If you have some other basis to feel confident one way or the other, kindly supply the physical mechanism for the same, please, not just “math.”)


So, as of today, the completely defensible statements are the Statement No. 1 and 2 (with all their corollaries), but not the Statement 3. However, a probabilistic judgment for the Statement 3 has also been given.


A short (say, abstract-like) version:

A physical mechanism to explain QM phenomena has been developed, at least in the bare essential terms. It may perhaps become possible to use such a knowledge to build an analog simulator of a quantum computer. Such a simulator would be a machine based only on the well-known principles of classical mechanics, and using the kind of physical objects that the classical mechanics studies.

However, it can also be easily shown that such a simulator will not be able to break the RSA encryption using algorithm such as Shor’s. The proof rests on an idealized abstraction of classical objects (just the way the ideal fluid is an abstraction of real fluids).

On the basis of the new understanding, it becomes clear that trying to break RSA encryption using a QC proper (i.e. a computer that’s not just a simulator, but is a QC proper that directly operates at the level of the QM platform itself) would be a goal that is next to impossible to achieve. In fact, even achieving just the “quantum supremacy” (i.e., beating the best classical digital computer) itself can be anticipated, on the basis of the new understanding, as a goal that would be very tough to achieve, if at all.

Researches that attempt to build a proper QC may be able to bring about some developments in various related areas such as condensed matter physics, cryogenics, electronics, etc. But it is very highly unlikely that they would succeed in achieving the goal of quantum supremacy itself, let alone the goal of breaking the RSA encryption as it is deployed at the high-end today.


A Song I Like:

(Hindi) “dilbar jaani, chali hawaa mastaanee…”
Music: Laxmikant Pyarelal
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Anand Bakshi

 


PS: Note that, as is usual at this blog, an iterative improvement of the draft is always a possibility. Done.

Revision History:

  1. First posted on 2018.06.15, about 12:35 hrs IST.
  2. Considerably revised the contents on 2018.06.15, 18:41 hrs IST.
  3. Edited to make the contents better on 2018.06.16, 15:30 hrs IST. Now, am mostly done with this post except, may be, for a minor typo or so, here or there.
  4. Edited (notably, changed the order of the Combinations) on 2018.06.17, 23:50 hrs IST. Also corrected some typos and streamlined the content. Now, I am going to leave this post in the shape it is. If you find some inconsistency or so, simple! Just write a comment or shoot me an email.
  5. 2018.06.27 02:07 hrs IST. Changed the song section.

 

Some suggested time-pass (including ideas for Python scripts involving vectors and tensors)

Actually, I am busy writing down some notes on scalars, vectors and tensors, which I will share once they are complete. No, nothing great or very systematic; these are just a few notings here and there taken down mainly for myself. More like a formulae cheat-sheet, but the topic is complicated enough that it was necessary that I have them in one place. Once ready, I will share them. (They may get distributed as extra material on my upcoming FDP (faculty development program) on CFD, too.)

While I remain busy in this activity, and thus stay away from blogging, you can do a few things:


1.

Think about it: You can always build a unique tensor field from any given vector field, say by taking its gradient. (Or, you can build yet another unique tensor field, by taking the Kronecker product of the vector field variable with itself. Or, yet another one by taking the Kronecker product with some other vector field, even just the position field!). And, of course, as you know, you can always build a unique vector field from any scalar field, say by taking its gradient.

So, you can write a Python script to load a B&W image file (or load a color .PNG/.BMP/even .JPEG, and convert it into a gray-scale image). You can then interpret the gray-scale intensities of the individual pixels as the local scalar field values existing at the centers of cells of a structured (squares) mesh, and numerically compute the corresponding gradient vector and tensor fields.

Alternatively, you can also interpret the RGB (or HSL/HSV) values of a color image as the x-, y-, and z-components of a vector field, and then proceed to calculate the corresponding gradient tensor field.

Write the output in XML format.


2.

Think about it: You can always build a unique vector field from a given tensor field, say by taking its divergence. Similarly, you can always build a unique scalar field from a vector field, say by taking its divergence.

So, you can write a Python script to load a color image, and interpret the RGB (or HSL/HSV) values now as the xx-, xy-, and yy-components of a symmetrical 2D tensor, and go on to write the code to produce the corresponding vector and scalar fields.


Yes, as my resume shows, I was going to write a paper on a simple, interactive, pedagogical, software tool called “ToyDNS” (from Toy + Displacements, Strains, Stresses). I had written an extended abstract, and it had even got accepted in a renowned international conference. However, at that time, I was in an industrial job, and didn’t get the time to write the software or the paper. Even later on, the matter kept slipping.

I now plan to surely take this up on priority, as soon as I am done with (i) the notes currently in progress, and immediately thereafter, (ii) my upcoming stress-definition paper (see my last couple of posts here and the related discussion at iMechanica).

Anyway, the ideas in the points 1. and 2. above were, originally, a part of my planned “ToyDNS” paper.


3.

You can induce a “zen-like” state in you, or if not that, then at least a “TV-watching” state (actually, something better than that), simply by pursuing this URL [^], and pouring in all your valuable hours into it. … Or who knows, you might also turn into a closet meteorologist, just like me. [And don’t tell anyone, but what they show here is actually a vector field.]


4.

You can listen to this song in the next section…. It’s one of those flowy things which have come to us from that great old Grand-Master, viz., SD Burman himself! … Other songs falling in this same sub-sub-genre include, “yeh kisine geet chheDaa,” and “ThanDi hawaaein,” both of which I have run before. So, now, you go enjoy yet another one of the same kind—and quality. …


A Song I Like:

[It’s impossible to figure out whose contribution is greater here: SD’s, Sahir’s, or Lata’s. So, this is one of those happy circumstances in which the order of the listing of the credits is purely incidental … Also recommended is the video of this song. Mona Singh (aka Kalpana Kartik (i.e. Dev Anand’s wife, for the new generation)) is sooooo magical here, simply because she is so… natural here…]

(Hindi) “phailee huyi hai sapanon ki baahen”
Music: S. D. Burman
Lyrics: Sahir
Singer: Lata Mangeshkar


But don’t forget to write those Python scripts….

Take care, and bye for now…

 

“Blog” less; write journal papers!

“‘Blog’ less; write journal papers.”

That’s my NYR for 2018.

Allow me to explain.


My research is not experimental, neither is it connected with, say, design of a new machine or development of a new manufacturing process. The most concrete aspect my work involves only computational modeling. But that too is not of the kind which engineering researchers typically undertake. I don’t do FEM of this multi-physics problem or that. What I work on are some very fundamental issues of physics and engineering.

My research thus is decidedly theoretical, often bordering on being “speculative.” It tends to concentrate on fundamental aspects. For decades by now, I have been trying to tackle some of the trickiest, deepest or very abstract problems (e.g. foundations of QM). At other times, I have been busy just isolating something new as a problem in its right (e.g., instantaneous action-at-a-distance in diffusion, or non-uniqueness of solution to the diffusion equation, or the fundamentality of stress vis-a-vis strain, or mode transitions in ideal vibrations and their relation to vibrations in the real mechanical system, or the physical meaning of the delta of calculus of variations….).

OK, there are some simple experiments here and there I might do. But they are not a very significant aspect of my work. The experiments are more in the nature of illustrations (e.g. melting snowman). They are not even fully in the nature of quantitative validations, let alone the prime vehicles to discovery. So, they are just “potatoes” of my research. The meat is: deep theoretical issues themselves. That’s what it’s like when you say “fundamental.”

The only way in which you can formulate or tackle such problems—fundamental or foundational—is by being a bit “relaxed” about both the specifics of your topic and the way you go about tackling it.

If you believed too much in the existing theory, you wouldn’t be able to spot unidentified problems with it or find new solutions to the known ones. If you try to do theoretical research and if you still try to stick to a schedule like what they do in experimental research (say in designing and fabricating a gadget, complete with bill of materials, or in developing a process, complete with prototype 1, prototype 2, etc.), you wouldn’t able to even get off to a decent start. After all, a schedule can be made from only those ingredients that are already known to you, not of never seen possibilities or unknown ideas. And, while in experimental research, reality has a wonderful way to throw up new possibilities, you have no such luxury in theoretical research. Every “never seen” possibility has to be forged by your own mind. If you don’t think in a relaxed manner, you are never going to believe that the issue is easy enough for you to tackle it.

But one unintended consequence of it all is that, in theoretical research like mine, it’s easy (far too easy in fact) to get a bit too relaxed. It is easy to pursue too many diverse theoretical threads, and in examining them, to run around in circles and so keep on getting back to the same points again and again.

But now I have come to realize that perhaps time has come to stop pursuing new threads in my research and to consolidate what has already been learnt.

The best way I can think of for doing the latter is: writing papers.

In particular, I have to kick aside this one habit: writing things down only when and as “inspiration” strikes.

Writing thoughts down (maintaining pocket diaries) has done a world of good to me. But this long-pursued activity seems to have by now come, in my case, to the point of diminishing marginal utility.

In place of this habit (of keeping on idly brain-storming and noting down possibilities it throws up) I would now like to put in place another habit: writing things (papers, actually) down in a structured, routine, regular, day-to-day, and time-bound manner. Allow me to explain this part too.

Given the way I have pursued my research (and in fact, given even the very nature of problems I ended up tackling), it would have been impossible for me to say something like this:

“OK! January, diffusion paper! February, stress-strain paper! March and April, QM position paper!”

“… What, in February, I don’t write something on QM? neither on diffusion? How ridiculous?”

That is how I would have reacted. But not any more.

Instead, I am now going to be a bit “bureaucratic” about my research. (UGC and AICTE folks ought to be happy in discovering a new soul-mate in me!)

What I am going to do is what I indicated just minutes ago. I am going to make some kind of a “time-table”: this period, work (i.e. actually write papers about) only this particular problem. Leave aside all other issues. Just finish that particular paper. Only then move to those other, more interesting (even alluring) issues in a next delimited period specifically allocated for that. I will have to pursue this policy. And I had better.

After all, while “passively” letting myself jump from issues to issues has yielded a lot of new insights, there are any number of issues where I have “hit the plateau” by now—and I mean those words in a positive sense. By “hitting the plateau,” I mean not a loss of creativity or originality, but a sense, even a firm realization (based on logic) that a certain stage of completeness is already achieved.

And that’s why, I am going to concentrate on “professionally” writing papers, in the next year. Following some kind of a time-bound schedule. As if I were writing a report, or delivering a software product on its schedule. So, it’s high time I became a bit less “creative” and more “professional,” to put it vaguely.

Since I will not be pursuing this bit of this idea or that bit of that idea a lot, I will be blogging less. And since a lot of my research seems to have actually “hit the plateau” in the above-mentioned, positive sense, I would instead be writing papers.

Hence the “slogan”: “`Blog’ less, write journal papers!”

That’s my NYR for 2018…. though I wouldn’t wait for 2018 to arrive before getting going on it. After all, a new year is just an excuse to make resolutions. The digits in the date aren’t important. A definite, demarcated change (“quantum jump” if you will! [LOL!]) is. But a change of the last digit in the YYYY, since it comes only after as long a period as one complete year, is a good time to making the required definite change.

So, there. I will keep you posted, with very brief notes here and there, as to how this paper-writing “business” is actually progressing in my case. My immediate plan is to get going writing the diffusion papers, and to finish writing them, right in January 2018.

Let’s see how things actually progress.


A Song I Like:

This is that Marathi song which I said I had liked a lot during my childhood vacation (see my last 2–3 posts). I still like it. It is the one which has a decidedly Western touch, but without spoiling or compromising on the Indian sense of melody. …

(Marathi) “raajaa saarangaa, maajyaa saarangaa”
Music: Hridaynath Mangeshkar
Singer: Lata Mangeshkar
Lyrics: Shanta Shelke


Bye for now, make a time-table you can stick to, and also take care to execute on it. … Best wishes for a happy and prosperous new year!

Yes I know it!—Part 2

This post directly continues from my last post. The content here was meant to be an update to my last post, but it grew, and so, I am noting it down as a separate post in its own right.


Thought about it [I mean my last post] a lot last night and this morning. I think here is a plan of action I can propose:

I can deliver a smallish, informally conducted, and yet, “official” sort of a seminar/talk/guest lecture, preferably at an IIT/IISER/IISc/similar institute. No honorarium is expected; just arrange for my stay. (That too is not necessary if it will be IIT Bombay; I can then stay with my friend; he is a professor in an engineering department there.)

Once arranged by mutual convenience, I will prepare some lecture notes (mostly hand-written), and deliver the content. (I guess at this stage, I will not prepare Beamer slides, though I might include some audio-visual content such as simulations etc.)

Questions will be OK, even encouraged, but the format will be that of a typical engineering class-room lecture. Discussions would be perfectly OK, but only after I finish talking about the “syllabus” first.

The talk should preferably be attended also by a couple of PhD students or so (of physics/engineering physics/any really relevant discipline, whether it’s acknowledged as such by UGC/AICTE or not). They should separately take down their notes and show me these later. This will help me understand where and how I should modify my notes. I will then myself finalize my notes, perhaps a few days after the talk, and send these by email. At that stage, I wouldn’t mind posting the notes getting posted on the ‘net.

Guess I will think a bit more about it, and note about my willingness to deliver the talk also at iMechanica. The bottom-line is that I am serious about this whole thing.

A few anticipated questions and their answers (or clarifications):

  1. What I have right now is, I guess, sufficient to stake a claim. But I have not taken the research to sufficiently advanced stage that I can say that I have all the clarifications worked out. It’s far more than just a sketchy conceptual idea, and does have a lot of maths too, but it’s less than, say, a completely worked out (or series of) mathematical theory. (My own anticipation is that if I can do just a series of smaller but connected mathematical models/simulations, it should be enough as my personal contribution to this new approach.)
  2. No, as far as QM is concerned, the approach I took in my PhD time publications is not at all relevant. I have completely abandoned that track (I mean to say as far as QM is concerned).
  3. However, my PhD time research on the diffusion equation has been continuing, and I am happy to announce that it has by now reached such a certain stage of maturation/completion that I should be writing another paper(s) on it any time now. I am happy that something new has come out of some 10+ years of thought on that issue, after my PhD-time work. Guess I could now send the PhD time conference paper to a journal, and then cover the new developments in this line in continuation with that one.
  4. Coming back to QM: Any one else could have easily got to the answers I have. But no, to the best of my knowledge, none else actually has. However, it does seem to me now that time is becoming ripe, and not to stake a claim at least now could be tantamount to carelessness on my part.
  5. Yes, my studies of philosophy, especially Ayn Rand’s ITOE (and Peikoff’s explanations of that material in PO and UO) did help me a lot, but all that is in a more general sense. Let me put it this way: I don’t think that I would have had to know (or even plain be conversant with) ITOE to be able to formulate these new answers to the QM riddles. And certainly, ITOE wouldn’t at all be necessary to understand my answers; the general level of working epistemology still is sufficiently good in physics (and more so, in engineering) even today.  At the same time, let me tell you one thing: QM is very vast, general, fundamental, and abstract. I guess you would have to be a “philosophizing” sort of a guy. Only then could you find this continuous and long preoccupation with so many deep and varied abstractions, interesting enough. Only then could the foundations of QM interest you. Not otherwise.
  6. To formulate answers, my natural proclivity to have to keep on looking for “physical” processes/mechanisms/objects for every mathematical idea I encounter, did help. But you wouldn’t have to have the same proclivity, let alone share my broad convictions, to be able to understand my answers. In other words, you could be a mathematical Platonist, and yet very easily come to understand the nature of my answers (and perhaps even come to agree with my positions)!
  7. To arrange for my proposed seminar/talk is to agree to be counted as a witness (for any future issues related to priority). But that’s strictly in the usual, routine, day-to-day academic sense of the term. (To wit, see how people interact with each other at a journal club in a university, or, say, at iMechanica.)
  8. But, to arrange for my talk is not to be willing to certify or validate its content. Not at all.
  9. With that being said, since this is India, let me also state a relevant concern. Don’t call me over just to show me down or ridicule me either. (It doesn’t happen in seminar talks, but it does happen during job interviews in Pune. It did happen to me in my COEP interview. It got repeated, in a milder way, in other engineering colleges in SPPU (the Pune University). So I have no choice but to note this part separately.)
  10. Once again, the issue is best clarified by giving the example. Check out how people treated me at iMechanica. If you are at an IIT/IISc/similar institute/university and are willing to treat me similarly, then do think of calling me over.

More, may be later. I will sure note my willingness to deliver a seminar at an IIT (or at a good University department) or so, at iMechanica also, soon enough. But right now I don’t have the time, and have to rush out. So let me stop here. Bye for now, and take care… (I would add a few more tags to the post-categories later on.)

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.

 

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, Mary 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.]