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.

 

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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.)

Yes I know it!

Note: A long update was posted on 12th December 2017, 11:35 IST.


This post is spurred by my browsing of certain twitter feeds of certain pop-sci. writers.

The URL being highlighted—and it would be, say, “negligible,” but for the reputation of the Web domain name on which it appears—is this: [^].


I want to remind you that I know the answers to all the essential quantum mysteries.

Not only that, I also want to remind you that I can discuss about them, in person.

It’s just that my circumstances—past, and present (though I don’t know about future)—which compel me to say, definitely, that I am not available for writing it down for you (i.e. for the layman) whether here or elsewhere, as of now. Neither am I available for discussions on Skype, or via video conferencing, or with whatever “remoting” mode you have in mind. Uh… Yes… WhatsApp? Include it, too. Or something—anything—like that. Whether such requests come from some millionaire Indian in USA (and there are tons of them out there), or otherwise. Nope. A flat no is the answer for all such requests. They are out of question, bounds… At least for now.

… Things may change in future, but at least for the time being, the discussions would have to be with those who already have studied (the non-relativistic) quantum physics as it is taught in universities, up to graduate (PhD) level.

And, you have to have discussions in person. That’s the firm condition being set (for the gain of their knowledge 🙂 ).


Just wanted to remind you, that’s all!


Update on 12th December 2017, 11:35 AM IST:

I have moved the update to a new post.

 


A Song I Like:

(Western, Instrumental) “Berlin Melody”
Credits: Billy Vaughn

[The same 45 RPM thingie [as in here [^], and here [^]] . … I was always unsure whether I liked this one better or the “Come September” one. … Guess, after the n-th thought, that it was this one. There is an odd-even thing about it. For odd ‘n” I think this one is better. For even ‘n’, I think the “Come September” is better.

… And then, there also are a few more musical goodies which came my way during that vacation, and I will make sure that they find their way to you too….

Actually, it’s not the simple odd-even thing. The maths here is more complicated than just the binary logic. It’s an n-ary logic. And, I am “equally” divided among them all. (4+ decades later, I still remain divided.)… (But perhaps the “best” of them was a Marathi one, though it clearly showed a best sort of a learning coming from also the Western music. I will share it the next time.)]


[As usual, may be, another revision [?]… Is it due? Yes, one was due. Have edited streamlined the main post, and then, also added a long update on 12th December 2017, as noted above.]

 

 

Blog-Filling—Part 3

Note: A long Update was added on 23 November 2017, at the end of the post.


Today I got just a little bit of respite from what has been a very tight schedule, which has been running into my weekends, too.

But at least for today, I do have a bit of a respite. So, I could at least think of posting something.

But for precisely the same reason, I don’t have any blogging material ready in the mind. So, I will just note something interesting that passed by me recently:

  1. Catastrophe Theory: Check out Prof. Zhigang Suo’s recent blog post at iMechanica on catastrophe theory, here [^]; it’s marked by Suo’s trademark simplicity. He also helpfully provides a copy of Zeeman’s 1976 SciAm article, too. Regular readers of this blog will know that I am a big fan of the catastrophe theory; see, for instance, my last post mentioning the topic, here [^].
  2. Computational Science and Engineering, and Python: If you are into computational science and engineering (which is The Proper And The Only Proper long-form of “CSE”), and wish to have fun with Python, then check out Prof. Hans Petter Langtangen’s excellent books, all under Open Source. Especially recommended is his “Finite Difference Computing with PDEs—A Modern Software Approach” [^]. What impressed me immediately was the way the author begins this book with the wave equation, and not with the diffusion or potential equation as is the routine practice in the FDM (or CSE) books. He also provides the detailed mathematical reason for his unusual choice of ordering the material, but apart from his reason(s), let me add in a comment here: wave \Rightarrow diffusion \Rightarrow potential (Poisson-Laplace) precisely was the historical order in which the maths of PDEs (by which I mean both the formulations of the equations and the techniques for their solutions) got developed—even though the modern trend is to reverse this order in the name of “simplicity.” The book comes with Python scripts; you don’t have to copy-paste code from the PDF (and then keep correcting the errors of characters or indentations). And, the book covers nonlinearity too.
  3. Good Notes/Teachings/Explanations of UG Quantum Physics: I ran across Dan Schroeder’s “Entanglement isn’t just for spin.” Very true. And it needed to be said [^]. BTW, if you want a more gentle introduction to the UG-level QM than is presented in Allan Adam (et al)’s MIT OCW 8.04–8.06 [^], then make sure to check out Schroeder’s course at Weber [^] too. … Personally, though, I keep on fantasizing about going through all the videos of Adam’s course and taking out notes and posting them at my Web site. [… sigh]
  4. The Supposed Spirituality of the “Quantum Information” Stored in the “Protein-Based Micro-Tubules”: OTOH, if you are more into philosophy of quantum mechanics, then do check out Roger Schlafly’s latest post, not to mention my comment on it, here [^].

The point no. 4. above was added in lieu of the usual “A Song I Like” section. The reason is, though I could squeeze in the time to write this post, I still remain far too rushed to think of a song—and to think/check if I have already run it here or not. But I will try add one later on, either to this post, or, if there is a big delay, then as the next “blog filler” post, the next time round.

[Update on 23 Nov. 2017 09:25 AM IST: Added the Song I Like section; see below]

OK, that’s it! … Will catch you at some indefinite time in future here, bye for now and take care…


A Song I Like:

(Western, Instrumental) “Theme from ‘Come September'”
Credits: Bobby Darin (?) [+ Billy Vaughn (?)]

[I grew up in what were absolutely rural areas in Maharashtra, India. All my initial years till my 9th standard were limited, at its upper end in the continuum of urbanity, to Shirpur, which still is only a taluka place. And, back then, it was a decidedly far more of a backward + adivasi region. The population of the main town itself hadn’t reached more than 15,000 or so by the time I left it in my X standard; the town didn’t have a single traffic light; most of the houses including the one we lived in) were load-bearing structures, not RCC; all the roads in the town were of single lanes; etc.

Even that being the case, I happened to listen to this song—a Western song—right when I was in Shirpur, in my 2nd/3rd standard. I first heard the song at my Mama’s place (an engineer, he was back then posted in the “big city” of the nearby Jalgaon, a district place).

As to this song, as soon as I listened to it, I was “into it.” I remained so for all the days of that vacation at Mama’s place. Yes, it was a 45 RPM record, and the permission to put the record on the player and even to play it, entirely on my own, was hard won after a determined and tedious effort to show all the elders that I was able to put the pin on to the record very carefully. And, every one in the house was an elder to me: my siblings, cousins, uncle, his wife, not to mention my parents (who were the last ones to be satisfied). But once the recognition arrived, I used it to the hilt; I must have ended up playing this record for at least 5 times for every remaining day of the vacation back then.

As far as I am concerned, I am entirely positive that appreciation for a certain style or kind of music isn’t determined by your environment or the specific culture in which you grow up.

As far as songs like these are concerned, today I am able to discern that what I had immediately though indirectly grasped, even as a 6–7 year old child, was what I today would describe as a certain kind of an “epistemological cleanliness.” There was a clear adherence to certain definitive, delimited kind of specifics, whether in terms of tones or rhythm. Now, it sure did help that this tune was happy. But frankly, I am certain, I would’ve liked a “clean” song like this one—one with very definite “separations”/”delineations” in its phrases, in its parts—even if the song itself weren’t to be so directly evocative of such frankly happy a mood. Indian music, in contrast, tends to keep “continuity” for its own sake, even when it’s not called for, and the certain downside of that style is that it leads to a badly mixed up “curry” of indefinitely stretched out weilings, even noise, very proudly passing as “music”. (In evidence: pick up any traditional “royal palace”/”kothaa” music.) … Yes, of course, there is a symmetrical downside to the specific “separated” style carried by the Western music too; the specific style of noise it can easily slip into is a disjointed kind of a noise. (In evidence, I offer 90% of Western classical music, and 99.99% of Western popular “music”. As to which 90%, well, we have to meet in person, and listen to select pieces of music on the fly.)

Anyway, coming back to the present song, today I searched for the original soundtrack of “Come September”, and got, say, this one [^]. However, I am not too sure that the version I heard back then was this one. Chances are much brighter that the version I first listened to was Billy Vaughn’s, as in here [^].

… A wonderful tune, and, as an added bonus, it never does fail to take me back to my “salad days.” …

… Oh yes, as another fond memory: that vacation also was the very first time that I came to wear a T-shirt; my Mama had gifted it to me in that vacation. The actual choice to buy a T-shirt rather than a shirt (+shorts, of course) was that of my cousin sister (who unfortunately is no more). But I distinctly remember she being surprised to learn that I was in no mood to have a T-shirt when I didn’t know what the word meant… I also distinctly remember her assuring me using sweet tones that a T-shirt would look good on me! … You see, in rural India, at least back then, T-shirts weren’t heard of; for years later on, may be until I went to Nasik in my 10th standard, it would be the only T-shirt I had ever worn. … But, anyway, as far as T-shirts go… well, as you know, I was into software engineering, and so….

Bye [really] for now and take care…]