# See, how hard I am trying to become an Approved (Full) Professor of Mechanical Engineering in SPPU?—2

Remember the age-old decade-old question, viz.:

“Stress or strain: which one is more fundamental?”

I myself had posed it at iMechanica about a decade ago [^]. Specifically, on 8th March 2007 (US time, may be EST or something).

The question had generated quite a bit of discussion at that time. Even as of today, this thread remains within the top 5 most-hit posts at iMechanica.

In fact, as of today, with about 1.62 lakh reads (i.e. 162 k hits), I think, it is the second most hit post at iMechanica. The only post with more hits, I think, is Nanshu Lu’s, providing a tutorial for the Abaqus software [^]; it beats mine like hell, with about 5 lakh (500 k) hits! The third most hit post, I think, again is about sharing scripts for the Abaqus software [^]; as of today, it lags mine very closely, but could overtake mine anytime, with about 1.48 lakh (148 k) hits already. There used to be a general thread on Open Source FEM software that used to be very close to my post. As of today, it has fallen behind a bit, with about 1.42 lakh (142 k) hits [^]. (I don’t know, but there could be other widely read posts, too.)

Of course, the attribute “most hit” is in no fundamental way related to “most valuable,” “most relevant,” or even “most interesting.”

Yet, the fact of the matter also is that mine is the only one among the top 5 posts which probes on a fundamental theoretical aspect. All others seem to be on software. Not very surprising, in a way.

Typically, hits get registered for topics providing some kind of a practical service. For instance, tips and tutorials on software—how to install a software, how to deal with a bug, how to write a sub-routine, how to produce visualizations, etc. Topics like these tend to get more hits. These are all practical matters, important right in the day-to-day job or studies, and people search the ‘net more for such practically useful services. Precisely for this reason—and especially given the fact that iMechanica is a forum for engineers and applied scientists—it is unexpected (at least it was unexpected to me) that a “basically useless” and “theoretical” discussion could still end up being so popular. There certainly was a surprise about it, to me. … But that’s just one part.

The second, more interesting part (i.e., more interesting to me) has been that, despite all these reads, and despite the simplicity of the concepts involved (stress and strain), the issue went unresolved for such a long time—almost a decade!

Students begin to get taught these two concepts right when they are in their XI/XII standard. In my XI/XII standard, I remember, we even had a practical about it: there was a steel wire suspended from a cantilever near the ceiling, and there was hook with a supporting plate at the bottom of this wire. The experiment consisted of adding weights, and measuring extensions. … Thus, the learning of these concepts begins right around the same time that students are learning calculus and Newton’s  3 laws… Students then complete the acquisition of these two concepts in their “full” generality, right by the time they are just in the second- or third-year of undergraduate engineering. The topic is taught in a great many branches of engineering: mechanical, civil, aerospace, metallurgical, chemical, naval architecture, and often-times (and certainly in our days and in COEP) also electrical. (This level of generality would be enough to discuss the question as posed at iMechanica.)

In short, even if the concepts are so “simple” that UG students are routinely taught them, a simple conceptual question involving them could go unresolved for such a long time.

It is this fact which was (honestly) completely unexpected to me, at least at the time when I had posed the question.

I had actually thought that there would surely be some reference text/paper somewhere that must have considered this aspect already, and answered it. But I was afraid that the answer (or the reference in which it appears) could perhaps be outside of my reach, my understanding of continuum mechanics. (In particular, I knew only a little bit of tensor calculus—only that as given in Malvern, and in Schaum’s series, basically. (I still don’t know much more about tensor calculus; my highest reach for tensor calculus remains limited to the book by Prof. Allan Bower of Brown [^].)) Thus, the reason I wrote the question in such a great detail (and in my replies, insisted on discussing the issues in conceptual details) was only to emphasize the fact that I had no hi-fi tensor calculus in mind; only the simplest physics-based and conceptual explanation was what I was looking for.

And that’s why, the fact that the question went unresolved for so long has also been (actually) fascinating to me. I (actually) had never expected it.

And yes, “dear” Officially Approved Mechanical Engineering Professors at the Savitribai Phule Pune University (SPPU), and authorities at SPPU, as (even) you might have noticed, it is a problem concerning the very core of the Mechanical Engineering proper.

I had thought once, may be last year or so, that I had finally succeeded in nailing down the issue right. (I might have written about it on this blog or somewhere else.) But, still, I was not so sure. So, I decided to wait.

I now have come to realize that my answer should be correct.

I, however, will not share my answer right away. There are two reasons for it.

First, I would like it if someone else gives it a try, too. It would be nice to see someone else crack it, too. A little bit of a wait is nothing to trade in for that. (As far as I am concerned, I’ve got enough “popularity” etc. just out of posing it.)

Second, I also wish to see if the Officially Approved Mechanical Engineering Professors at the Savitribai Phule Pune University (SPPU)) would be willing and able to give it a try.

(Let me continue to be honest. I do not expect them to crack it. But I do wish to know whether they are able to give it a try.)

In fact, come to think of it, let me do one thing. Let me share my answer only after one of the following happens:

• either I get the Official Approval (and also a proper, paying job) as a Full Professor of Mechanical Engineering at SPPU,
• or, an already Officially Approved Full Professor of Mechanical Engineering at SPPU (especially one of those at COEP, especially D. W. Pande, and/or one of those sitting on the Official COEP/UGC Interview Panels for faculty interviews at SPPU) gives it at least a try that is good enough. [Please note, the number of hits on the international forum of iMechanica, and the nature of the topic, once again.]

I will share my answer as soon as either of the above two happens—i.e., in the Indian government lingo: “whichever is earlier” happens.

But, yes, I am happy that I have come up with a very good argument to finally settle the issue. (I am fairly confident that my eventual answer should also be more or less satisfactory to those who had participated on this iMechanica thread. When I share my answer, I will of course make sure to note it also at iMechanica.)

This time round, there is not just one song but quite a few of them competing for inclusion on the “A Song I Like” section. Perhaps, some of these, I have run already. Though I wouldn’t mind repeating a song, I anyway want to think a bit about it before finalizing one. So, let me add the section when I return to do some minor editing later today or so. (I certainly want to get done with this post ASAP, because there are other theoretical things that beckon my attention. And yes, with this announcement about the stress-and-strain issue, I am now going to resume my blogging on topics related to QM, too.)

Update at 13:40 hrs (right on 19 Dec. 2016): Added the section on a song I like; see below.

A Song I Like:

(Marathi) “soor maagoo tulaa mee kasaa? jeevanaa too tasaa, mee asaa!”
Lyrics: Suresh Bhat
Music: Hridaynath Mangeshkar
Singer: Arun Date

It’s a very beautiful and a very brief poem.

As a song, it has got fairly OK music and singing. (The music composer could have done better, and if he were to do that, so would the singer. The song is not in a bad shape in its current form; it is just that given the enormously exceptional talents of this composer, Hridaynath Mangeshkar, one does get a feel here that he could have done better, somehow—don’t ask me how!) …

I will try to post an English translation of the lyrics if I find time. The poem is in a very, very simple Marathi, and for that reason, it would also be very, very easy to give a rough sense of it—i.e., if the translation is to be rather loose.

The trouble is, if you want to keep the exact shade of the words, it then suddenly becomes very difficult to translate. That’s why, I make no promises about translating it. Further, as far as I am concerned, there is no point unless you can convey the exact shades of the original words. …

Unless you are a gifted translator, a translation of a poem almost always ends up losing the sense of rhythm. But even if you keep a more modest aim, viz., only of offering an exact translation without bothering about the rhythm part, the task still remains difficult. And it is more difficult if the original words happen to be of the simple, day-to-day usage kind. A poem using complex words (say composite, Sanskrit-based words) would be easier to translate precisely because of its formality, precisely because of the distance it keeps from the mundane life… An ordinary poet’s poem also would be easy to translate regardless of what kind of words he uses. But when the poet in question is great, and uses simple words, it becomes a challenge, because it is difficult, if not impossible, to convey the particular sense of life he pours into that seemingly effortless composition. That’s why translation becomes difficult. And that’s why I make no promises, though a try, I would love to give it—provided I find time, that is.

Second Update on 19th Dec. 2016, 15:00 hrs (IST):

A Translation of the Lyrics:

I offer below a rough translation of the lyrics of the song noted above. However, before we get to the translation, a few notes giving the context of the words are absolutely necessary.

Notes on the Context:

Note 1:

Unlike in the Western classical music, Indian classical music is not written down. Its performance, therefore, does not have to conform to a pre-written (or a pre-established) scale of tones. Particularly in the Indian vocal performance, the singer is completely free to choose any note as the starting note of his middle octave.

Typically, before the actual singing begins, the lead singer (or the main instrument player) thinks of some tone that he thinks might best fit how he is feeling that day, how his throat has been doing lately, the particular settings at that particular time, the emotional interpretation he wishes to emphasize on that particular day, etc. He, therefore, tentatively picks up a note that might serve as the starting tone for the middle octave, for that particular performance. He makes this selection not in advance of the show and in private, but right on the stage, right in front of the audience, right after the curtain has already gone up. (He might select different octaves for two successive songs, too!)

Then, to make sure that his rendition is going to come out right if he were to actually use that key, that octave, what he does is to ask a musician companion (himself on the stage besides the singer) to play and hold that note on some previously well-tuned instrument, for a while. The singer then uses this key as the reference, and tries out a small movement or so. If everything is OK, he will select that key.

All this initial preparation is called (Hindi) “soor lagaanaa.” The part where the singer turns to the trusted companion and asks for the reference note to be played is called (Hindi) “soor maanganaa.” The literal translation of the latter is: “asking for the tone” or “seeking the pitch.”

After thus asking for the tone and trying it out, if the singer thinks that singing in that specific key is going to lead to a good concert performance, he selects it.

At this point, both—the singer and that companion musician—exchange glances at each other, and with that indicate that the tone/pitch selection is OK, that this part is done. No words are exchanged; only the glances. Indian performances depend a great deal on impromptu variations, on improvizations, and therefore, the mutual understanding between the companion and the singer is of crucial importance. In fact, so great is their understanding that they hardly ever exchange any words—just glances are enough. Asking for the reference key is just a simple ritual that assures both that the mutual understanding does exist.

And after that brief glance, begins the actual singing.

Note 2:

Whereas the Sanskrit and Marathi word “aayuShya” means life-span (the number of years, or the finite period that is life), the Sanskrit and Marathi word “jeevan” means Life—with a capital L. The meaning of “jeevan” thus is something like a slightly abstract outlook on the concrete facts of life. It is like the schema of life. The word is not so abstract as to mean the very Idea of Life or something like that. It is life in the usual, day-to-day sense, but with a certain added emphasis on the thematic part of it.

Note 3:

Here, the poet is addressing this poem to “jeevan” i.e., to the Life with a capital L (or the life taken in its more abstract, thematic sense). The poet is addressing Life as if the latter is a companion in an Indian singing concert. The Life is going to help him in selecting the note—the note which would define the whole scale in which to sing during the imminent live performance. The Life is also his companion during the improvisations. The poem is addressed using this metaphor.

Now, my (rough) translation:

The Refrain:
[Just] How do I ask you for the tone,
Life, you are that way [or you follow some other way], and I [follow] this way [or, I follow mine]

Stanza 1:
You glanced at me, I glanced at you,
[We] looked full well at each other,
Pain is my mirror [or the reference instrument], and [so it is] yours [too]

Stanza 2:
Even once, to [my] mind’s satisfaction,
You [oh, Life] did not ever become my [true]  mate
[And so,] I played [on this actual show of life, just whatever] the way the play happened [or unfolded]

And, finally, Note 4 (Yes, one is due):

There is one place where I failed in my translation, and most any one not knowing both the Marathi language and the poetry of Suresh Bhat would.

In Marathi, “tu tasaa, [tar] mee asaa,” is an expression of a firm, almost final, acknowledgement of (irritating kind of) differences. “If you must insist on being so unreasonable, then so be it—I am not going to stop following my mind either.” That is the kind of sense this brief Marathi expression carries.

And, the poet, Suresh Bhat, is peculiar: despite being a poet, despite showing exquisite sensitivity, he just never stops being manly, at the same time. Pain and sorrow and suffering might enter his poetry; he might acknowledge their presence through some very sensitively selected words. And yet, the underlying sense of life which he somehow manages to convey also is as if he is going to dismiss pain, sorrow, suffering, etc., as simply an affront—a summarily minor affront—to his royal dignity. (This kind of a “royal” sense of life often is very well conveyed by ghazals. This poem is a Marathi ghazal.) Thus, in this poem, when Suresh Bhat agrees to using pain as a reference point, the words still appear in such a sequence that it is clear that the agreement is being conceded merely in order to close a minor and irritating part of an argument, that pain etc. is not meant to be important even in this poem let alone in life. Since the refrain follows immediately after this line, it is clear that the stress gets shifted to the courteous question which is raised following the affronts made by one fickle, unfaithful, even idiotic Life—the question of “Just how do I treat you as a friend? Just how do I ask you for the tone?” (The form of “jeevan” or Life used by Bhat in this poem is masculine in nature, not neutral the way it is in normal Marathi.)

I do not know how to arrange the words in the translation so that this same sense of life still comes through. I simply don’t have that kind of a command over languages—any of the languages, whether Marathi or English. Hence this (4th) note. [OK. Now I am (really) done with this post.]

Anyway, take care, and bye for now…

Update on 21st Dec. 2016, 02:41 AM (IST):

Realized a mistake in Stanza 1, and corrected it—the exchange between yours and mine (or vice versa).

[E&OE]

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# Conservation of angular momentum isn’t [very] fundamental!

What are the conservation principles (in physics)?

In the first course on engineering mechanics (i.e. the mechanics of rigid bodies) we are taught that there are these three conservation principles: Conservation of: (i) energy, (ii) momentum, and (iii) angular momentum. [I am talking about engineering programs. That means, we live entirely in a Euclidean, non-relativistic, world.]

Then we learn mechanics of fluids, and the conservation of (iv) mass too gets added. That makes it four.

Then we come to computational fluid dynamics (CFD), and we begin to deal with only three equations: conservation of (i) mass, (ii) momentum, and (iii) energy. What happens to the conservation of the angular momentum? Why does the course on CFD drop it? For simplicity of analysis?

Ask that question to postgraduate engineers, even those who have done a specialization in CFD, and chances are, a significant number of them won’t be able to answer that question in a very clear manner.

Some of them may attempt this line of reasoning: That’s because in deriving the fluids equations (whether for a Newtonian fluid or a non-Newtonian one), the stress tensor is already assumed to be symmetrical: the shear stresses acting on the adjacent faces are taken to be equal and opposite (e.g. $\sigma_{xy} = \sigma_{yx}$). The assumed equality can come about only after assuming conservation of the angular momentum, and thus, the principle is already embedded in the momentum equations, as they are stated in CFD.

If so, ask them: How about a finite rotating body—say a gyroscope? (Assume rigidity for convenience, if you wish.) Chances are, a great majority of them will immediately agree that in this case, however, we have to apply the angular momentum principle separately.

Why is there this difference between the fluids and the finite rotating bodies? After all, both are continua, as in contrast to point-particles.

Most of them would fall silent at this point. [If not, know that you are talking with someone who knows his mechanics well!]

Actually, it so turns out that in continua, the angular momentum is an emergent/derivative property—not the most fundamental one. In continua, it’s OK to assume conservation of just the linear momentum alone. If it is satisfied, the conservation of angular momentum will get satisfied automatically. Yes, even in case of a spinning wheel.

Don’t believe me?

Let me direct you to Chad Orzel; check out here [^]. Orzel writes:

[The spinning wheel] “is a classical system, so all of its dynamics need to be contained within Newton’s Laws. Which means it ought to be possible to look at how angular momentum comes out of the ordinary linear momentum and forces of the components making up the wheel. Of course, it’s kind of hard to see how this works, but that’s what we have computers for.” [Emphasis in italics is mine.]

He proceeds to put together a simple demo in Python. Then, he also expands on it further, here [^].

Cool. If you think you have understood Orzel’s argument well, answer this [admittedly deceptive] question: How about point particles? Do we need a separate conservation principle for the angular momentum, in addition to that for the linear momentum at least in their case? How about the earth and the moon system, granted that both can be idealized as point particles (the way Newton did)?

A Song I Like:

(Hindi) “baandhee re kaahe preet, piyaa ke sang”
Singer: Sulakshana Pandit
Music: Kalyanji-Anandji
Lyrics: M. G. Hashmat

[E&OE]

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# My answers to the Edge questions

I was supposed to come back and write a better version of the QM-related comment which I had made at Scott Aaronson’s blog (see my last post). However, I am not going to do that right away because of two reasons: (i) I think that leaving aside a typo or two, the comment isn’t in all that bad a condition, and (ii) I have begun thinking about some of the issues involved, and so would like to come back only after getting them straightened out (with a better order of presentation).

In the meanwhile, I decided to check out my blog-ideas folder (yes, I do “maintain” one), and found that I already had some material for a post.

It had so happened that while going through Scott’s post on the Edge question, especially the beginning of that post, an idea had struck me:

why not write my own one-line answers to all the Edge questions thus far?

So, I had gone to the Edge home page, and jotted down my answers in a .txt file. That was on 4th January 2016, between 4:17 PM–5:43 PM, IST (which means, one day before I wrote my comment on Scott’s blog). The answers were jotted down very, very rapidly—average time between reading a question and starting typing answer could be barely 10–15 seconds. That’s because we were very busy with the accreditation related work, remember? Though I don’t remember that particular day, I must have finished the day’s work and only then done this thing. Here I am going to mostly copy-paste its contents.

A couple of notes before we go over to my answers:

1. I just copy-pasted the Edge questions in the order I saw them on their home page. The order of answers was, thus, determined more or less by their Web page layout. So, the answers are not in the chronological sequence of the years over which they were raised.
2. I am reproducing the contents of a very whimsically written file (which was written, as I said, near the end of a long work-day), and without effecting any editing at all. Today, right within a week of writing the answers, I find that I want to change the answers to some of the questions. In any case, I would certainly want to make the answers more streamlined. But, today’s editing is minimal; whatever whimsicality that had crept in, I have decided to keep its original flavor as is.

So, here we go, with a copy-paste from that file:

The front velocity in the linear diffusion is a finite quantity (and in the first-order analysis, it is a constant).

2003 : WHAT ARE THE PRESSING SCIENTIFIC ISSUES FOR THE NATION AND THE WORLD, AND WHAT IS YOUR ADVICE ON HOW I CAN BEGIN TO DEAL WITH THEM? – GWB

The nation (i.e. USA): I don’t care a hoot about. The position was reciprocally derived.
The world: More or less the same. More or less the same.
My advise (to any President of the USA): Embrace 100% pure capitalism.

2002 : WHAT IS YOUR QUESTION? … WHY?

In his evolution, exactly for how long has the modern man been in the junglee-like state? (Rough estimates go like: lakhs of years of the jungle state vs. 5700 years of civilization, if you want to believe in the Western/modern science.)

Why it’s important? From many viewpoints: What led to the dominance of reason implicit in civilization? To what extent are the biological structural features really important in the mind-body connection? In what subtle ways must we still be junglee-like?

2001 : WHAT NOW?

Revising my viewpoint concerning non-relativistic quantum mechanics.
Reaching a conclusion concerning the issue of “stress or strain—which one is more fundamental?”
Writing some toy CFD code

2001 : WHAT QUESTIONS HAVE DISAPPEARED?

Whether the following phenomena are real or not: (i) rebirth, (ii) tele-many things such as telepathy, mind-reading, etc. (iii) psychic attacks, (iv) the actual American depravity in practice. Also the question of where Osama was hiding. Answer: In a cantonment town in a mostly army-ruled country that is a friend of USA.

2000 : WHAT IS TODAY’S MOST IMPORTANT UNREPORTED STORY?

How telecommunications actually changed the attitudes of rural people in India

1999 : WHAT IS THE MOST IMPORTANT INVENTION IN THE PAST TWO THOUSAND YEARS?

I don’t answer such silly questions. Idea? I would have attempted; generalization is possible with ideas. But not with inventions.

1998 : WHAT QUESTIONS ARE YOU ASKING YOURSELF?

Are the reported incidents in which some people could predict the future events true? If yes, what could be the mechanism in the pycho-somatic i.e. yogic terms? What implication does it hold for free will (properly defined, most fundamentally, only as the choice to focus or to evade), and the nature of soul and of consciousness.

2015: WHAT DO YOU THINK ABOUT MACHINES THAT THINK?

It’s a stupid idea. Thinking requires a conceptual (i.e. volitional) consciousness, which in turn requires life.

2014: WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?

None. Proper ideas belonging to proper science never retire, they get subsumed away.

There are any number of ideas that should be retired because they were neither proper ideas nor scientific. For instance, the idea of an infinite physical universe. Or, the idea that ascribing anything quantitative to the universe (as a whole) is epistemologically valid. Etc. Also, string theory.

2013 : WHAT *SHOULD* WE BE WORRIED ABOUT?

The String Theory.

More seriously, government control of science and education.

2012: WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

The mathematical aspects of the non-relativistic quantum mechanics. (A proper theory for its physical aspects is not yet available—despite my own attempts to build one.)

2011: WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY’S COGNITIVE TOOLKIT?

The idea that all physical theories should be local.

I wrote that down, and then realized that the question asks for a toolkit.

I think computational modeling as easily realizable using Python and its ecosystem. It should be a part of every scientist’s grooming up. (Python is already being used to introduce programming to the CBSE XI-XII students in India.)

2010: HOW IS THE INTERNET CHANGING THE WAY YOU THINK?

It hasn’t changed *my* way of thinking, much. I always was more conceptual, and always had relatively lower working memory (and therefore also lessser maths skills) as compared to the class-mates who I ended up competing or at least [being] compared with. Internet has made more people forgetful and overall more like me, simply because they can just google up a lot of the concrete information.

2009: WHAT WILL CHANGE EVERYTHING?

I have no idea. Also, I don’t think it really is important or even desirable to change everything.

My view of quantum mechanics. I used to think that physicists were conceptually dumb. I now know that the original discoverers were not dumb—not even conceptually—but that their major flaw was either too much of careless[ness] about basic philosophical ideas, or too much of a diffidence towards bad philosophers.

Also, my view of Objectivists, Americans, and in fact, Western people in general. I no longer think that any of them could be fully relied on, practically speaking. They are not bad. [Here I meant morally bad.] In fact, they are pretty OK. They are just OK in the sense, they can be nice if you already are a practical success yourself. But if you are not a success, [they won’t bother to find that] hidden talent or spark in you. They are too crude and/or dumb and/or isolated, to be able to do that. Especially to an Indian-born. (They are rather like Brahmins in the Indian cities [and in the SF Bay Area]. The Brahmin-borns are not bad [by birth]. It’s just that a Maratha-born growing up rural areas cannot rely on them. He may receive acknowledgement of his talents from them, but not so reliably frequently to be a social norm. [Note today: It’s the elite vs non-elite phenomenon, really speaking, but the point is: I had never imagined as a young man that it would be as bad as it is, esp. in America.]

2007: WHAT ARE YOU OPTIMISTIC ABOUT?

That my new theory of QM will work out.

Actually, on most things, and speaking in terms of how I am habitually like, I am neither optimistic nor pessimistic. Habitually, if there is any one option towards which I do almost habitually get inclined, it is that: I like to know.

2006: WHAT IS YOUR DANGEROUS IDEA?

Dangerous in general? I have none. But if you mean those tiny cultural points of conversation that society people and people of culture (esp. writers of novels like Ayn Rand) use, you know, BS like: “he is too dangerous because he is too independent,” etc., then guess *my* most dangerous idea has been my sharing of the dimmed view of many people (Americans, Objectivists, Brahmins, army people, Indian University people, Westerners). Dangerous to me, that is.

2005: WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?

But I don’t always look for proofs, that’s the point. Validation is one thing, proofs is another. I do make sure to know the meaning and the roots of the concepts that I use. (And, sometimes, I have spent decades understanding their meaning and/or roots.)

But knowing the roots isn’t the same as proving, esp. to someone else, esp. to his satisfaction. You know how increasingly pointless and dangerous this enterprise gets.

Anyway, as the “cultural” kind of a fraud kind of an answer: My new theory of QM.

2016: WHAT DO YOU CONSIDER THE MOST INTERESTING RECENT [SCIENTIFIC] NEWS? WHAT MAKES IT IMPORTANT?

I can’t think of any. It has to be at least interesting, right? And, it has to be recent. Sorry. Can’t think of something that has both. At least not off the hand.

It would also be fun writing my own answers afresh some time later on.

A Song I Like:

(Hindi) “dil lagaa kar hum yeh samajhe”

Singers (separate versions each): Mahendra Kapoor and Asha Bhosale
Music: C. Ramchandra

[Another whimsicality of mine: Unlike most people whose opinions I usually find sensible, here I find that it is tough to decide which singer’s version is better. I mean to say, I don’t automatically find Asha’s version better. In fact, I like Mahendra Kapoor’s version [just] a shade better.]

[E&OE]

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# In QM, local action does make sense

We have been too busy with our accreditation-related work, but I still had to squeeze in a comment at Scott Aaronson’s blog.

In case you don’t know, Scott Aarsonson is a tenured Associate Professor in CS at MIT (I mean the one in Cambridge, MA, USA). Scott’s opinions count—at least, they are very widely read (and often, also very extensively commented on and discussed).

This year, Scott was invited to respond to the Edge’s annual question [^]. In the latest post on his blog covering his and others’ responses to the question [^], Scott singled out three answers by others (at the Edge forum) which he thought were heading in the wrong direction. In Scott’s own words:

Then there were three answers for which the “progress” being celebrated, seemed to me to be progress racing faster into WrongVille

In particular, the following residents of the so-called “WrongVille” were of immediate interest to me; let me continue quoting Scott’s words:

Ross Anderson on an exciting conference whose participants aim to replace quantum mechanics with local realistic theories.  (Anderson, in particular, is totally wrong that you can get Bell inequality violation from “a combination of local action and global correlation,” unless the global correlation goes as far as a ‘t-Hooft-like superdeterministic conspiracy.) [Emphasis in bold is mine.]

The minimum implications here are these two: (i) quantum mechanics—not this interpretation or that interpretation of its existing mathematics, but the entire mechanics of the quanta itself—cannot ever be local, and (ii) therefore, any attempts to build a local theory to explain the quantum phenomena must be seen as a replacement for QM [a lock, stock and barrel replacement, I suppose].

One further implicit idea here seems to be that any local theory, if it yields the necessary global correlation, must also imply superdeterminism. In case you don’t know, “superdeterminism” here is primarily a technical term, not philosophical; it is about a certain idea put forth by the Nobel laureate ‘t Hooft.

As you know, my theorization has been, and will always remain, local in nature. Naturally, I had to intervene! As fast as I could!!

So I wrote a comment at Scott’s blog, right on the fly. (Literally. By the time I finished typing it and hit the Submit Comment button, I was already in the middle of some informal discussions in my cabin with my colleagues, regarding arrangements to be made for the accreditation-related work.)

Naturally, my comment isn’t as clear as it should be.

It so happens that our accreditation-related activities would be over on the upcoming Sunday, and so, I should be able to find the time to come back and post an expanded and edited version early next week. Until then, please make do with my original reply at Scott’s blog [^]; I am copy-pasting the relevant portion “as is” below:

Anderson’s (or others’) particular theory (or theories) might not be right, but the very idea that there can be this combination of a local action + a global correlation, isn’t. It is in fact easy to show how:

The system evolution in QM is governed by the TDSE, and it involves a first derivative in time and a second in space. TDSE thus has a remarkable formal similarity to the (linear) diffusion equation (DE for short).

It is easy to show that a local solution to the DE can be constructed. Indeed, any random walks-based solution involves only a local action. More broadly, starting with any sub-domain method and using a limiting argument, a deterministic solution that is local, can always be constructed.

Of course, there *are* differences between DE and TDSE. TDSE has the imaginary $i$ multiplying the time derivative term (I here assume TDSE in exactly that form as given on the first page of Griffith’s text), an imaginary “diffusion coefficient,” and a complex-valued \Psi. The last two differences are relatively insignificant; they only make the equation consistent with the requirement that the measurements-related eigenvalues be real. The “real” difference arises due to the first factor, i.e. the existence of the i multiplying the $\partial \Psi/\partial t$ term. Its presence makes the solution oscillatory in time (in TDSE) rather than exponentially decaying (as in DE).

However, notice, in the classical DE too, a similar situation exists. “Waves” do exist in the space part of the solution to DE; they arise due to the separation hypothesis and the nature of the Fourier method. OTOH, a sub domain-based or random walks-based solution (see Einstein’s 1905 derivation of the diffusion equation) remains local even if eigenwaves exist in the Fourier modeling of the problem.

Therefore, as far as the local vs. global debate is concerned, the oscillatory nature of the time-dependence in TDSE is of no fundamental relevance.

The Fourier-theoretical solution isn’t unique in DE; hence local solutions to TDSE are possible. Local and propagating processes can “derive” diffusion, and therefore, must be capable of producing the TDSE.

Note, my point is very broad. Here, I am not endorsing any particular local-action + global-correlation theory. In fact, I don’t have to.

All that I am saying is (and it is enough to say only this much) that (i) the mathematics involved is such that it allows building of a local theory (primarily because Fourier theoretical solutions can be shown not to be unique), and (ii) the best experiments done so far are still so “gross” that existence of such fine differences in the time-evolution cannot be ruled out.

One final point. I don’t know how the attendees of that conference think like, but at least as far as I am concerned, I am (also) informally convinced that it will be impossible to give a thoroughly classical mechanics-based mechanism for the quantum phenomena. The QM is supposed to give rise to CM (Classical Mechanics) in the “grossing out” limit, not the other way around. Here, by CM, I mean: Newton’s postulates (and subsequent reformulations of his mechanics by Lagrange and Hamilton). If there are folks who think that they could preserve all the laws of Newton’s, and still work out a QM as an end product, I think, they are likely to fail. (I use “likely” simply because I cannot prove it. However, I *have* thought about building a local theory for QM, and also do have some definite ideas for a local theory of QM. One aspect of this theory is that it can’t preserve a certain aspect of Newton’s postulates, even if my theorization remains local and propagational in nature (with a compact support throughout).)

OK. So think about it in the meanwhile, and bye for now.

[BTW, though I believe that QM theory must be local, I don’t agree that something such as superdeterminism is really necessary.]

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(Hindi) “aaj un se pehli mulaaqaat hogi…”
Singer: Kishore Kumar
Music: R. D. Burman
Lyrics: Anand Bakshi

[E&OE]

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