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

Yes, we continue to remain very busy.


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

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

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

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

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

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

In short, I have re-discovered my own (unpublished) conclusion.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


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

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

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

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

Until this morning.

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

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


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


A Song I Like:

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


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

 

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Causality. And a bit miscellaneous.

0. I’ve been too busy in my day-job to write anything at any one of my blogs, but recently, a couple of things happened.


1. I wrote what I think is a “to read” (if not a “must read”) comment, concerning the important issue of causality, at Roger Schlafly’s blog; see here [^]. Here’s the copy-paste of the same:

1. There is a very widespread view among laymen, and unfortunately among philosophers too, that causality requires a passage of time. As just one example: In the domino effect, the fall of one domino leads to the fall of another domino only after an elapse of time.

In fact, all their examples wherever causality is operative, are of the following kind:

“If something happens then something else happens (necessarily).”

Now, they interpret the word `then’ to involve a passage of time. (Then, they also go on to worry about physics equations, time symmetry, etc., but in my view all these are too advanced considerations; they are not fundamental or even very germane at the deepest philosophical level.)

2. However, it is possible to show other examples involving causality, too. These are of the following kind:

“When something happens, something else (necessarily) happens.”

Here is an example of this latter kind, one from classical mechanics. When a bat strikes a ball, two things happen at the same time: the ball deforms (undergoes a change of shape and size) and it “experiences” (i.e. undergoes) an impulse. The deformation of the ball and the impulse it experiences are causally related.

Sure, the causality here is blatantly operative in a symmetric way: you can think of the deformation as causing the impulse, or of the impulse as causing the deformation. Yet, just because the causality is symmetric here does not mean that there is no causality in such cases. And, here, the causality operates entirely without the dimension of time in any way entering into the basic analysis.

Here is another example, now from QM: When a quantum particle is measured at a point of space, its wavefunction collapses. Here, you can say that the measurement operation causes the wavefunction collapse, and you can also say that the wavefunction collapse causes (a definite) measurement. Treatments on QM are full of causal statements of both kinds.

3. There is another view, concerning causality, which is very common among laymen and philosophers, viz. that causality necessarily requires at least two separate objects. It is an erroneous view, and I have dealt with it recently in a miniseries of posts on my blog; see https://ajitjadhav.wordpress.com/2017/05/12/relating-the-one-with-the-many/.

4. Notice, the statement “when(ever) something happens, something else (always and/or necessarily) happens” is a very broad statement. It requires no special knowledge of physics. Statements of this kind fall in the province of philosophy.

If a layman is unable to think of a statement like this by way of an example of causality, it’s OK. But when professional philosophers share this ignorance too, it’s a shame.

5. Just in passing, noteworthy is Ayn Rand’s view of causality: http://aynrandlexicon.com/lexicon/causality.html. This view was basic to my development of the points in the miniseries of posts mentioned above. … May be I should convert the miniseries into a paper and send it to a foundations/philosophy journal. … What do you think? (My question is serious.)

Thanks for highlighting the issue though; it’s very deeply interesting.

Best,

–Ajit


3. The other thing is that the other day (the late evening of the day before yesterday, to be precise), while entering a shop, I tripped over its ill-conceived steps, and suffered a fall. Got a hairline crack in one of my toes, and also a somewhat injured knee. So, had to take off from “everything” not only on Sunday but also today. Spent today mostly sleeping relaxing, trying to recover from those couple of injuries.

This late evening, I naturally found myself recalling this song—and that’s where this post ends.


4. OK. I must add a bit. I’ve been lagging on the paper-writing front, but, don’t worry; I’ve already begun re-writing (in my pocket notebook, as usual, while awaiting my turn in the hospital’s waiting lounge) my forth-coming paper on stress and strain, right today.

OK, see you folks, bye for now, and take care of yourselves…


A Song I Like:

(Hindi) “zameen se hamen aasmaan par…”
Singer: Asha Bhosale and Mohammad Rafi
Music: Madan Mohan
Lyrics: Rajinder Krishan

 

I’ve been slacking, so bye for now, and see you later!

Recently, as I was putting finishing touches in my mind as to how to present the topic of the product states vs. the entangled states in QM, I came to realize that while my answer to that aspect has now come to a stage of being satisfactory [to me], there are any number of other issues on which I am not as immediately clear as I should be—or even used to be! That was frightening!! … Allow me to explain.

QM is hard. QM is challenging. And QM also is vast. Very vast.

In trying to write about my position paper on the foundations of QM, I have been focusing mostly on the axiomatic part of it. In offering illustrative examples, I found, that I have been taking only the simplest possible examples. However, precisely in this process, I have also gone away, and then further away, from the more concrete physics of it. … Let me give you one example.

Why must the imaginary root of the unity i.e. the i appear in the Schrodinger equation? … Recently, I painfully came to realize that I had no real good explanation ready in mind.

It just so happened that I was idly browsing through Eisberg and Resnick’s text “Quantum Physics (of Atoms, Molecules…).” In my random browsing, I happened to glance over section 5.3, p. 134, and was blown over by the argument to this question, presented in there. I must have browsed through this section, years ago, but by now, I had completely forgotten anything about it. … How could I be so dumb as to even forget the fact that here is a great argument about this issue? … Usually, I am able to recall at least the book and the section where an answer to a certain question is given. At least that’s what happens for any of the engineering courses I am teaching. I am easily able to rattle off, for any question posed from any angle, a couple (if not more) books that deal with that particular aspect best. For instance, in teaching FEM: the best treatment on how to generate interpolation polynomials? Heubner (and also Rajasekaran), and only then Zienkiwicz. In teaching CFD: the most concise flux-primary description? Murthy’s notes (at Purdue), and only then followed by Versteeg and Mallasekara. Etc.

… But QM is vast—a bit too vast for me to recall even that much about answers, let alone have also the answers ready in my mind.

Also, around the same time, I ran into these two online resources  on UG QM:
1. The course notes at Reed (I suppose by Griffiths himself): [^] and [^]
2. The notes and solved problems here at “Physics pages” [^]. A very neat (and laudable) an effort!

It was the second resource, in particular, which now set me thinking. … Yes, I was aware of it, and might have referred to it earlier on my blog, too. But it was only now that this site set me into thinking…

As a result of that thinking, I’ve decided to do something similar.

I am going to start writing answers at least to questions (and not problems) given in the first 12 or 14 chapters of Eisberg and Resnick’s abovementioned text. I am going to do that before coming to systematically writing my new position paper.

And I am going to undertake this exercise in place of blogging. … It’s important that I do it.

Accordingly, I am ceasing blogging for now.

I am first going to take a rapid first cut at answering at least the (conceptual) questions if not also the (quantitative) problems from Eisberg and Resnick’s book. I would be noting down my answers in an off-line LaTeX document. Tentatively speaking, I have decided to try to get through at least the first 6 chapters of this book, before resuming blogging. In the second phase, it would be chapters 7 through 11 or so, and the rest, in the third phase.

Once I finish the first phase, I may begin sharing my answers here on this blog.

Believe me, this exercise is necessary for me to do.

There certainly are some drawbacks to this procedure. Heisenberg’s formulation (which, historically, occurred before Schrodinger’s) would not receive a good representation. However, that does not mean that I should not be “finishing” this (E&R’s) book either. May be I will have to do a similar exercise (of answering the more conceptual or theoretical questions or drawing notes from) a similar book but on Heisenberg’s approach, too; e.g., “Quantum Mechanics in Simple Matrix Form” by Thomas Jordan [^]. … For the time being, though, I am putting it off to some later time. (Just a hint: As it so happens, my new position is closer—if at all it is that—to the Schrodinger’s “picture” as compared to Heisenberg’s.)

In the meanwhile, if you feel like reading something interesting on QM, do visit the above-mentioned resources. Very highly recommended.

In the meanwhile, take care, and bye for now.


And, oh, just one more thing…

…Just to remind you. Yes, regardless of it all, as mentioned earlier on this blog, even though I won’t be blogging for a while (say a month or more, till I finish the first phase) I would remain completely open to disclosing and discussing my new ideas about QM to any interested PhD physicist, or even an interested and serious PhD student. … If you are one, just drop me a line and let’s see how and when—and assuredly not if—we can meet.


Which Song Do You Like?

Check out your city’s version of Pharrell Williams’ “Happy” song. Also check out a few other cities’. Which one do you like more? Think about it (though I won’t ask you the reasons for your choices!)

OK. Take care, and bye (really) for now…

 

The Infosys Prizes, 2015

I realized that it was the end of November the other day, and it somehow struck me that I should check out if there has been any news on the Infosys prizes for this year. I vaguely recalled that they make the yearly announcements sometime in the last quarter of a year.

Turns out that, although academic bloggers whose blogs I usually check out had not highlighted this news, the prizes had already been announced right in mid-November [^].

It also turns out also that, yes, I “know”—i.e., have in-person chatted (exactly once) with—one of the recipients. I mean Professor Dr. Umesh Waghmare, who received this year’s award for Engineering Sciences [^]. I had run into him in an informal conference once, and have written about it in a recent post, here [^].

Dr. Waghmare is a very good choice, if you ask me. His work is very neat—I mean both the ideas which he picks out to work on, and the execution on them.

I still remember his presentation at that informal conference (where I chatted with him). He had talked about a (seemingly) very simple idea, related to graphene [^]—its buckling.

Here is my highly dumbed down version of that work by Waghmare and co-authors. (It’s dumbed down a lot—Waghmare et al’s work was on buckling, not bending. But it’s OK; this is just a blog, and guess I have a pretty general sort of a “general readership” here.)

Bending, in general, sets up a combination of tensile and compressive stresses, which results in the setting up of a bending moment within a beam or a plate. All engineers (except possibly for the “soft” branches like CS and IT) study bending quite early in their undergraduate program, typically in the second year. So, I need not explain its analysis in detail. In fact, in this post, I will write only a common-sense level description of the issue. For technical details, look up the Wiki articles on bending [^] and buckling [^] or Prof. Bower’s book [^].

Assuming you are not an engineer, you can always take a longish rubber eraser, hold it so that its longest edge is horizontal, and then bend it with a twist of your fingers. If the bent shape is like an inverted ‘U’, then, the inner (bottom) surface has got compressed, and the outer (top) surface has got stretched. Since compression and tension are opposite in nature, and since the eraser is a continuous body of a finite height, it is easy to see that there has to be a continuous surface within the volume of the eraser, some half-way through its height, where there can be no stresses. That’s because, the stresses change sign in going from the compressive stress at the bottom surface to the tensile stresses on the top surface. For simplicity of mathematics, this problem is modeled as a 1D (line) element, and therefore, in elasticity theory, this actual 2D surface is referred to as the neutral axis (i.e. a line).

The deformation of the eraser is elastic, which means that it remains in the bent state only so long as you are applying a bending “force” to it (actually, it’s a moment of a force).

The classical theory of bending allows you to relate the curvature of the beam, and the bending moment applied to it. Thus, knowing bending moment (or the applied forces), you can tell how much the eraser should bend. Or, knowing how much the eraser has curved, you can tell how big a pair of fforces would have to be applied to its ends. The theory works pretty well; it forms of the basis of how most buildings are designed anyway.

So far, so good. What happens if you bend, not an eraser, but a graphene sheet?

The peculiarity of graphene is that it is a single atom-thick sheet of carbon atoms. Your usual eraser contains billions and billions of layers of atoms through its thickness. In contrast, the thickness of a graphene sheet is entirely accounted for by the finite size of the single layer of atoms. And, it is found that unlike thin paper, the graphen sheet, even if it is the the most extreme case of a thin sheet, actually does offer a good resistance to bending. How do you explain that?

The naive expectation is that something related to the interatomic bonding within this single layer must, somehow, produce both the compressive and tensile stresses—and the systematic variation from the locally tensile to the locally compressive state as we go through this thickness.

Now, at the scale of single atoms, quantum mechanical effects obviously are dominant. Thus, you have to consider those electronic orbitals setting up the bond. A shift in the density of the single layer of orbitals should correspond to the stresses and strains in the classical mechanics of beams and plates.

What Waghmare related at that conference was a very interesting bit.

He calculated the stresses as predicted by (in my words) the changed local density of the orbitals, and found that the forces predicted this way are way smaller than the experimentally reported values for graphene sheets. In other words, the actual graphene is much stiffer than what the naive quantum mechanics-based model shows—even if the model considers those electronic orbitals. What is the source of this additional stiffness?

He then showed a more detailed calculation (i.e. a simulation), and found that the additional stiffness comes from a quantum-mechanical interaction between the portions of the atomic orbitals that go off transverse to the plane of the graphene sheet.

Thus, suppose a graphene sheet is initially held horizontally, and then bent to form an inverted U-like curvature. According to Waghmare and co-authros, you now have to consider not just the orbital cloud between the atoms (i.e. the cloud lying in the same plane as the graphene sheet) but also the orbital “petals” that shoot vertically off the plane of the graphene. Such petals are attached to nucleus of each C atom; they are a part of the electronic (or orbital) structure of the carbon atoms in the graphene sheet.

In other words, the simplest engineering sketch for the graphene sheet, as drawn in the front view, wouldn’t look like a thin horizontal line; it would also have these small vertical “pins” at the site of each carbon atom, overall giving it an appearance rather like a fish-bone.

What happens when you bend the graphene sheet is that on the compression side, the orbital clouds for these vertical petals run into each other. Now, you know that an orbital cloud can be loosely taken as the electronic charge density, and that the like charges (e.g. the negatively charged electrons) repel each other. This inter-electronic repulsive force tends to oppose the bending action. Thus, it is the petals’ contribution which accounts for the additional stiffness of the graphene sheet.

I don’t know whether this result was already known to the scientific community back then in 2010 or not, but in any case, it was a very early analysis of bending of graphene. Further, as far as I could tell, the quality of Waghmare’s calculations and simulations was very definitely superlative. … You work in a field (say computational modeling) for some time, and you just develop a “nose” of sorts, that allows you to “smell” a superlative calculation from an average one. Particularly so, if your own skills on the calculations side are rather on the average, as happens to be the case with me. (My strengths are in conceptual and computational sides, but not on the mathematical side.) …

So, all in all, it’s a very well deserved prize. Congratulations, Dr. Waghmare!

 


A Song I Like:

(The so-called “fusion” music) “Jaisalmer”
Artists: Rahul Sharma (Santoor) and Richard Clayderman (Piano)
Album: Confluence

[As usual, may be one more editing pass…]

[E&OE]