The quantum mechanical features of my laptop…

My laptop has developed certain quantum mechanical features after its recent repairs [^]. In particular, if I press the “power on” button, it does not always get “measured” into the “power-on” state.

That’s right. In starting the machine, it is not possible to predict when the power-on button may work, when it may lead to an actual boot-up. Sometimes it does, sometimes it doesn’t.

For instance, the last time I shut it down was on the last night, just before dinner. Then, after dinner, when I tried to restart it, the quantum mechanical features kicked in and the associated randomness was such that it simply refused the request. Ditto, this morning. Ditto, early afternoon today. But now (at around 18:00 hrs on 09 October), it somehow got up and going!


Fortunately, I have taken backup of crucial data (though not all). So, I can afford to look at it with a sense of humour.

But still, if I don’t come back for a somewhat longer period of time than is usual (about 8–10 days), then know that, in all probability, I was just waiting helplessly in getting this thing repaired, once again. (I plan to take it to the repairsman tomorrow morning.) …

…The real bad part isn’t this forced break in browsing or blogging. The real bad part is: my inability to continue with my ANN studies. It’s not possible to maintain any tempo in studies in this now-on-now-off sort of a manner—i.e., when the latter is not chosen by you.

Yes, I do like browsing, but once I get into the mood of studying a new topic (and, BTW, just reading through pop-sci articles does not count as studies) and especially if the studies also involve programming, then having these forced breaks is really bad. …

Anyway, bye for now, and take care.


PS: I added that note on browsing and then it struck me. Check out a few resources while I am gone and following up with the laptop repairs (and no links because right while writing this postscript, the machine crashed, and so I am somehow completing it using smartphone—I hate this stuff, I mean typing using at most two fingers, modtly just one):

  1. As to Frauchiger and Renner’s controversial much-discussed result, Chris Lee’s account at ArsTechnica is the simplest to follow. Go through it before any other sources/commentaries, whether to the version published recently in Nature Comm. or the earlier ones, since 2016.
  2. Carver Mead’s interview in the American Spectator makes for an interesting read even after almost two decades.
  3. Vinod Khosla’s prediction in 2017 that AI will make radiologists obsolete in 5 years’ time. One year is down already. And that way, the first time he made remarks to that sort of an effect were some 6+ years ago, in 2012!
  4. As to AI’s actual status today, see the Quanta Magazine article: “Machine learning confronts the elephant in the room” by Kevin Hartnett. Both funny and illuminating (esp. if you have some idea about how ML works).
  5. And, finally, a pretty interesting coverage of something about which I didn’t have any idea beforehand whatsoever: “New AI strategy mimics how brains learn to smell” by Jordana Cepelwicz in Quanta Mag.

Ok. Bye, really, for now. See you after the laptop begins working.


A Song I Like:
Indian, instrumental: Theme song of “Malgudi Days”
Music: L. Vaidyanathan

 

 

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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.]

 

“Measure for Measure”—a pop-sci video on QM

This post is about a video on QM for the layman. The title of the video is: “Measure for Measure: Quantum Physics and Reality” [^]. It is also available on YouTube, here [^].

I don’t recall precisely where on the ‘net I saw the video being mentioned. Anyway, even though its running time is 01:38:43 (i.e. 1 hour, 38 minutes, making it something like a full-length feature film), I still went ahead, downloaded it and watched it in full. (Yes, I am that interested in QM!)

The video was shot live at an event called “World Science Festival.” I didn’t know about it beforehand, but here is the Wiki on the festival [^], and here is the organizer’s site [^].

The event in the video is something like a panel discussion done on stage, in front of a live audience, by four professors of physics/philosophy. … Actually five, including the moderator.

Brian Greene of Columbia [^] is the moderator. (Apparently, he co-founded the World Science Festival.) The discussion panel itself consists of: (i) David Albert of Columbia [^]. He speaks like a philosopher but seems inclined towards a specific speculative theory of QM, viz. the GRW theory. (He has that peculiar, nasal, New York accent… Reminds you of Dr. Harry Binswanger—I mean, by the accent.) (ii) Sheldon Goldstein of Rutgers [^]. He is a Bohmian, out and out. (iii) Sean Carroll of CalTech [^]. At least in the branch of the infinity of the universes in which this video unfolds, he acts 100% deterministically as an Everettian. (iv) Ruediger Schack of Royal Holloway (the spelling is correct) [^]. I perceive him as a QBist; guess you would, too.

Though the video is something like a panel discussion, it does not begin right away with dudes sitting on chairs and talking to each other. Even before the panel itself assembles on the stage, there is a racy introduction to the quantum riddles, mainly on the wave-particle duality, presented by the moderator himself. (Prof. Greene would easily make for a competent TV evangelist.) This part runs for some 20 minutes or so. Then, even once the panel discussion is in progress, it is sometimes interwoven with a few short visualizations/animations that try to convey the essential ideas of each of the above viewpoints.

I of course don’t agree with any one of these approaches—but then, that is an entirely different story.

Coming back to the video, yes, I do want to recommend it to you. The individual presentations as well as the panel discussions (and comments) are done pretty well, in an engaging and informal way. I did enjoy watching it.


The parts which I perhaps appreciated the most were (i) the comment (near the end) by David Albert, between 01:24:19–01:28:02, esp. near 1:27:20 (“small potatoes”) and, (ii) soon later, another question by Brian Greene and another answer by David Albert, between 01:33:26–01:34:30.

In this second comment, David Albert notes that “the serious discussions of [the foundational issues of QM] … only got started 20 years ago,” even though the questions themselves do go back to about 100 years ago.

That is so true.

The video was recorded recently. About 20 years ago means: from about mid-1990s onwards. Thus, it is only from mid-1990s, Albert observes, that the research atmosphere concerning the foundational issues of QM has changed—he means for the better. I think that is true. Very true.

For instance, when I was in UAB (1990–93), the resistance to attempting even just a small variation to the entrenched mainstream view (which means, the Copenhagen interpretation (CI for short)) was so enormous and all pervading, I mean even in the US/Europe, that I was dead sure that a graduate student like me would never be able to get his nascent ideas on QM published, ever. It therefore came as a big (and a very joyous) surprise to me when my papers on QM actually got accepted (in 2005). … Yes, the attitudes of physicists have changed. Anyway, my point here is, the mainstream view used to be so entrenched back then—just about 20 years ago. The Copenhagen interpretation still was the ruling dogma, those days. Therefore, that remark by Prof. Albert does carry some definite truth.


Prof. Albert’s observation also prompts me to pose a question to you.

What could be the broad social, cultural, technological, economic, or philosophic reasons behind the fact that people (researchers, graduate students) these days don’t feel the same kind of pressure in pursuing new ideas in the field of Foundations of QM? Is the relatively greater ease of publishing papers in foundations of QM, in your opinion, an indication of some negative trends in the culture? Does it show a lowering of the editorial standards? Or is there something positive about this change? Why has it become easier to discuss foundations of QM? What do you think?

I do have my own guess about it, and I would sure like to share it with you. But before I do that, I would very much like to hear from you.

Any guesses? What could be the reason(s) why the serious discussions on foundations of QM might have begun to occur much more freely only after mid-1990s—even though the questions had been raised as early as in 1920s (or earlier)?

Over to you.


Greetings in advance for the Republic Day. I [^] am still jobless.


[E&OE]

 

Why is the physical space 3-dimensional?

Why I write on this topic?

Well, it so happened that recently (about a month ago) I realized that I didn’t quite understand matrices. I mean, at least not as well as I should. … I was getting interested in the Data Science, browsing through a few books and Web sites on the topic, and soon enough realized that before going further, first, it would be better if I could systematically write down a short summary of the relevant mathematics, starting with the topic of matrices (and probability theory and regression analysis and the lot).

So, immediately, I fired TeXMaker, and started writing an “article” on matrices. But as is my habit, once I began actually typing, slowly, I also began to go meandering—pursuing just this one aside, and then just that one aside, and then just this one footnote, and then just that one end-note… The end product quickly became… unusable. Which means, it was useless. To any one. Including me.

So, after typing in a goodly amount, may be some 4–5 pages, I deleted that document, and began afresh.

This time round, I wrote only the abstract for a “future” document, and that too only in a point-by-point manner—you know, the way they specify those course syllabi? This strategy did help. In doing that, I realized that I still had quite a few issues to get straightened out well. For instance, the concept of the dual space [^][^].

After pursuing this activity very enthusiastically for something like a couple of days or so, my attention, naturally, once again got diverted to something else. And then, to something else. And then, to something else again… And soon enough, I came to even completely forget the original topic—I mean matrices. … Until in my random walk, I hit it once again, which was this week.

Once the orientation of my inspiration thus got once again aligned to “matrices” last week (I came back via eigen-values of differential operators), I now decided to first check out Prof. Zhigang Suo’s notes on Linear Algebra [^].

Yes! Zhigang’s notes are excellent! Very highly recommended! I like the way he builds topics: very carefully, and yet, very informally, with tons of common-sense examples to illustrate conceptual points. And in a very neat order. A lot of the initially stuff is accessible to even high-school students.

Now, what I wanted here was a single and concise document. So, I decided to take notes from his notes, and thereby make a shorter document that emphasized my own personal needs. Immediately thereafter, I found myself being engaged into that activity. I have already finished the first two chapters of his notes.

Then, the inevitable happened. Yes, you guessed it right: my attention (once again) got diverted.


What happened was that I ran into Prof. Scott Aaronson’s latest blog post [^], which is actually a transcript of an informal talk he gave recently. The topic of this post doesn’t really interest me, but there is an offhand (in fact a parenthetical) remark Scott makes which caught my eye and got me thinking. Let me quote here the culprit passage:

“The more general idea that I was groping toward or reinventing here is called a hidden-variable theory, of which the most famous example is Bohmian mechanics. Again, though, Bohmian mechanics has the defect that it’s only formulated for some exotic state space that the physicists care about for some reason—a space involving pointlike objects called “particles” that move around in 3 Euclidean dimensions (why 3? why not 17?).”

Hmmm, indeed… Why 3? Why not 17?

Knowing Scott, it was clear (to me) that he meant this remark not quite in the sense of a simple and straight-forward question (to be taken up for answering in detail), but more or less fully in the sense of challenging the common-sense assumption that the physical space is 3-dimensional.

One major reason why modern physicists don’t like Bohm’s theory is precisely because its physics occurs in the common-sense 3 dimensions, even though, I think, they don’t know that they hate him also because of this reason. (See my 2013 post here [^].)

But should you challenge an assumption just for the sake of challenging one? …

It’s true that modern physicists routinely do that—challenging assumptions just for the sake of challenging them.

Well, that way, this attitude is not bad by itself; it can potentially open doorways to new modes of thinking, even discoveries. But where they—the physicists and mathematicians—go wrong is: in not understanding the nature of their challenges themselves, well enough. In other words, questioning is good, but modern physicists fail to get what the question itself is, or even means (even if they themselves have posed the question out of a desire to challenge every thing and even everything). And yet—even if they don’t get even their own questions right—they do begin to blabber, all the same. Not just on arXiv but also in journal papers. The result is the epistemological jungle that is in the plain sight. The layman gets (or more accurately, is deliberately kept) confused.

Last year, I had written a post about what physicists mean by “higher-dimensional reality.” In fact, in 2013, I had also written a series of posts on the topic of space—which was more from a philosophical view, but unfortunately not yet completed. Check out my writings on space by hitting the tag “space” on my blog [^].

My last year’s post on the multi-dimensional reality [^] did address the issue of the n > 3 dimensions, but the writing in a way was geared more towards understanding what the term “dimension” itself means (to physicists).

In contrast, the aspect which now caught my attention was slightly different; it was this question:

Just how would you know if the physical space that you see around you is indeed was 3-, 4-, or 17-dimensional? What method would you use to positively assert the exact dimensionality of space? using what kind of an experiment? (Here, the experiment is to be taken in the sense of a thought experiment.)

I found an answer this question, too. Let me give you here some indication of it.


First, why, in our day-to-day life (and in most of engineering), do we take the physical space to be 3-dimensional?

The question is understood better if it is put more accurately:

What precisely do we mean when we say that the physical space is 3-dimensional? How do we validate that statement?

The answer is “simple” enough.

Mark a fixed point on the ground. Then, starting from that fixed point, walk down some distance x in the East direction, then move some distance y in the North direction, and then climb some distance z vertically straight up. Now, from that point, travel further by respectively the same distances along the three axes, but in the exactly opposite directions. (You can change the order in which you travel along the three axes, but the distance along a given axis for both the to- and the fro-travels must remain the same—it’s just that the directions have to be opposite.)

What happens if you actually do something like this in the physical reality?

You don’t have to leave your favorite arm-chair; just trace your finger along the edges of your laptop—making sure that the laptop’s screen remains at exactly 90 degrees to the plane of the keyboard.

If you actually undertake this strenuous an activity in the physical reality, you will find that, in physical reality, a “magic” happens: You come back exactly to the same point from where you had begun your journey.

That’s an important point. A very obvious point, but also, in a way, an important one. There are other crucially important points too. For instance, this observation. (Note, it is a physical observation, and not an arbitrary mathematical assumption):

No matter where you stop during the process of going in, say the East direction, you will find that you have not traveled even an inch in the North direction. Ditto, for the vertical axis. (It is to ensure this part that we keep the laptop screen at exactly 90 degrees to the keyboard.)

Thus, your x, y and z readings are completely independent of each other. No matter how hard you slog along, say the x-direction, it yields no fruit at all along the y– or z– directions.

It’s something like this: Suppose there is a girl that you really, really like. After a lot of hard-work, suppose you somehow manage to impress her. But then, at the end of it, you come to realize that all that hard work has done you no good as far as impressing her father is concerned. And then, even if you somehow manage to win her father on your side, there still remains her mother!

To say that the physical space is 3-dimensional is a positive statement, a statement of an experimentally measured fact (and not an arbitrary “geometrical” assertion which you accept only because Euclid said so). It consists of two parts:

The first part is this:

Using the travels along only 3 mutually independent directions (the position and the orientation of the coordinate frame being arbitrary), you can in principle reach any other point in the space.

If some region of space were to remain unreachable this way, if there were to be any “gaps” left in the space which you could not reach using this procedure, then it would imply either (i) that the procedure itself isn’t appropriate to establish the dimensionality of the space, or (ii) that it is, but the space itself may have more than 3 dimensions.

Assuming that the procedure itself is good enough, for a space to have more than 3 dimensions, the “unreachable region” doesn’t have to be a volume. The “gaps” in question may be limited to just isolated points here and there. In fact, logically speaking, there needs to be just one single (isolated) point which remains in principle unreachable by the procedure. Find just one such a point—and the dimensionality of the space would come in question. (Think: The Aunt! (The assumption here is that aunts aren’t gentlemen [^].))

Now what we do find in practice is that any point in the actual physical space indeed is in principle reachable via the above-mentioned procedure (of altering x, y and z values). It is in part for this reason that we say that the actual physical space is 3-D.

The second part is this:

We have to also prove, via observations, that fewer than 3 dimensions do fall short. (I told you: there was the mother!) Staircases and lifts (Americans call them elevators) are necessary in real life.

Putting it all together:

If n =3 does cover all the points in space, and if n > 3 isn’t necessary to reach every point in space, and if n < 3 falls short, then the inevitable conclusion is: n = 3 indeed is the exact dimensionality of the physical space.

QED?

Well, both yes and no.

Yes, because that’s what we have always observed.

No, because all physics knowledge has a certain definite scope and a definite context—it is “bounded” by the inductive context of the physical observations.

For fundamental physics theories, we often don’t exactly know the bounds. That’s OK. The most typical way in which the bounds get discovered is by “lying” to ourselves that no such bounds exist, and then experimentally discovering a new phenomena or a new range in which the current theory fails, and a new theory—which merely extends and subsumes the current theory—is validated.

Applied to our current problem, we can say that we know that the physical space is exactly three-dimensional—within the context of our present knowledge. However, it also is true that we don’t know what exactly the conceptual or “logical” boundaries of this physical conclusion are. One way to find them is to lie to ourselves that there are no such bounds, and continue investigating nature, and hope to find a phenomenon or something that helps find these bounds.

If tomorrow we discover a principle which implies that a certain region of space (or even just one single isolated point in it) remains in principle unreachable using just three dimensions, then we would have to abandon the idea that n = 3, that the physical space is 3-dimensional.

Thus far, not a single soul has been able to do that—Einstein, Minkowski or Poincare included.

No one has spelt out a single physically established principle using which a spatial gap (a region unreachable by the linear combination procedure) may become possible, even if only in principle.

So, it is 3, not 17.

QED.


All the same, it is not ridiculous to think whether there can be 4 or more number of dimensions—I mean for the physical space alone, not counting time. I could explain how. However, I have got too tired typing this post, and so, I am going to just jot down some indicative essentials.

Essentially, the argument rests on the idea that a physical “travel” (rigorously: a physical displacement of a physical object) isn’t the only physical process that may be used in establishing the dimensionality of the physical space.

Any other physical process, if it is sufficiently fundamental and sufficiently “capable,” could in principle be used. The requirements, I think, would be: (i) that the process must be able to generate certain physical effects which involve some changes in their spatial measurements, (ii) that it must be capable of producing any amount of a spatial change, and (iii) that it must allow fixing of an origin.

There would be the other usual requirements such as reproducibility etc., though the homogeneity wouldn’t be a requirement. Also observe Ayn Rand’s “some-but-any” principle [^] at work here.

So long as such requirements are met (I thought of it on the fly, but I think I got it fairly well), the physically occurring process (and not some mathematically dreamt up procedure) is a valid candidate to establish the physically existing dimensionality of the space “out there.”

Here is a hypothetical example.

Suppose that there are three knobs, each with a pointer and a scale. Keeping the three knobs at three positions results in a certain point (and only that point) getting mysteriously lit up. Changing the knob positions then means changing which exact point is lit-up—this one or that one. In a way, it means: “moving” the lit-up point from here to there. Then, if to each point in space there exists a unique “permutation” of the three knob readings (and here, by “permutation,” we mean that the order of the readings at the three knobs is important), then the process of turning the knobs qualifies for establishing the dimensionality of the space.

Notice, this hypothetical process does produce a physical effect that involves changes in the spatial measurements, but it does not involve a physical displacement of a physical object. (It’s something like sending two laser beams in the night sky, and being able to focus the point of intersection of the two “rays” at any point in the physical space.)

No one has been able to find any such process which even if only in principle (or in just thought experiments) could go towards establishing a 4-, 2-, or any other number for the dimensionality of the physical space.


I don’t know if my above answer was already known to physicists or not. I think the situation is going to be like this:

If I say that this answer is new, then I am sure that at some “opportune” moment in future, some American is simply going to pop up from nowhere at a forum or so, and write something which implies (or more likely, merely hints) that “everybody knew” it.

But if I say that the answer is old and well-known, and then if some layman comes to me and asks me how come the physicists keep talking as if it can’t be proved whether the space we inhabit is 3-dimensional or not, I would be at a loss to explain it to him—I don’t know a good explanation or a reference that spells out the “well known” solution that “everybody knew already.”

In my (very) limited reading, I haven’t found the point made above; so it could be a new insight. Assuming it is new, what could be the reason that despite its simplicity, physicists didn’t get it so far?

Answer to that question, in essential terms (I’ve really got too tired today) is this:

They define the very idea of space itself via spanning; they don’t first define the concept of space independently of any operation such as spanning, and only then see whether the space is closed under a given spanning operation or not.

In other words, effectively, what they do is to assign the concept of dimensionality to the spanning operation, and not to the space itself.

It is for this reason that discussions on the dimensionality of space remain confused and confusing.


Food for thought:

What does a 2.5-dimensional space mean? Hint: Lookup any book on fractals.

Why didn’t we consider such a procedure here? (We in fact don’t admit it as a proper procedure) Hint: We required that it must be possible to conduct the process in the physical reality—which means: the process must come to a completion—which means: it can’t be an infinite (indefinitely long or interminable) process—which means, it can’t be merely mathematical.

[Now you know why I hate mathematicians. They are the “gap” in our ability to convince someone else. You can convince laymen, engineers and programmers. (You can even convince the girl, the father and the mother.) But mathematicians? Oh God!…]


A Song I Like:

(English) “When she was just seventeen, you know what I mean…”
Band: Beatles


 

[May be an editing pass tomorrow? Too tired today.]

[E&OE]

A bit about my trade…

Even while enjoying my writer’s block, I still won’t disappoint you. … My browsing has yielded some material, and I am going to share it with you.

It all began with googling for some notes on CFD. One thing led to another, and soon enough, I was at this page [^] maintained by Prof. Praveen Chandrashekhar of TIFR Bangalore.

Do go through the aforementioned link; highly recommended. It tells you about the nature of my trade [CFD]…

As that page notes, this article had first appeared in the AIAA Student Journal. Looking at the particulars of the anachronisms, I wanted to know the precise date of the writing. Googling on the title of the article led me to a PDF document which was hidden under a “webpage-old” sub-directory, for the web pages for the ME608 course offered by Prof. Jayathi Murthy at Purdue [^]. At the bottom of this PDF document is a note that the AIAA article had appeared in the Summer of 1985. … Hmm…. Sounds right.

If you enjoy your writer’s block [the way I do], one sure way to continue having it intact is to continue googling. You are guaranteed never to come out it. I mean to say, at least as far as I know, there is no equivalent of Godwin’s law [^] on the browsing side.

Anyway, so, what I next googled on was: “wind tunnels.” I was expecting to see the Wright brothers as the inventors of the idea. Well, I was proved wrong. The history section on the Wiki page [^] mentions Benjamin Robins and his “whirling arm” apparatus to determine drag. The reference for this fact goes to a book bearing the title “Mathematical Tracts of the late Benjamin Robins, Esq,” published, I gathered, in 1761. The description of the reference adds the sub-title (or the chapter title): “An account of the experiments, relating to the resistance of the air, exhibited at different times before the Royal Society, in the year 1746.” [The emphasis in the italics is mine, of course! [Couldn’t you have just guessed it?]]

Since I didn’t know anything about the “whirling arm,” and since the Wiki article didn’t explain it either, a continuation of googling was entirely in order. [The other reason was what I’ve told you already: I was enjoying my writer’s block, and didn’t want it to go away—not so soon, anyway.] The fallout of the search was one k-12 level page maintained by NASA [^]. Typical of the government-run NASA, there was no diagram to illustrate the text. … So I quickly closed the tab, came back to the next entries in the search results, and landed on this blog post [^] by “Gina.” The name of the blog was “Fluids in motion.”

… Interesting…. You know, I knew about, you know, “Fuck Yeah Fluid Dynamics” [^] (which is a major time- and bandwidth-sink) but not about “Fluids in motion.” So I had to browse the new blog, too. [As to the FYFD, I only today discovered the origin of the peculiar name; it is given in the Science mag story here [^].]

Anyway, coming back to Gina’s blog, I then clicked on the “fluids” category, and landed here [^]… Turns out that Gina’s is a less demanding on the bandwidth, as compared to FYFD. [… I happen to have nearly exhausted my monthly data limit of 10 GB, and the monthly renewal is on the 5th June. …. Sigh!…]

Anyway, so here I was, at Gina’s blog, and the first post in the “fluids” category was on “murmuration of starlings,” [^]. There was a link to a video… Video… Video? … Intermediate Conclusion: Writer’s blocks are costly. … Soon after, a quiet temptation thought: I must get to know what the phrase “murmuration of starlings” means. … A weighing in of the options, and the final conclusion: what the hell! [what else], I will buy an extra 1 or 2 GB add-on pack, but I gotta see that video. [Writer’s block, I told you, is enjoyable.] … Anyway, go, watch that video. It’s awesome. Also, Gina’s book “Modeling Ships and Space Craft.” It too seems to be awesome: [^] and [^].

The only way to avoid further spending on the bandwidth was to get out of my writer’s block. Somehow.

So, I browsed a bit on the term [^], and took the links on the first page of this search. To my dismay, I found that not even a single piece was helpful to me, because none was relevant to my situation: every piece of advice there was obviously written only after assuming that you are not enjoying your writer’s block. But what if you do? …

Anyway, I had to avoid any further expenditure on the bandwidth—my expenditure—and so, I had to get out of my writer’s block.

So, I wrote something—this post!


[Blogging will continue to remain sparse. … Humor apart, I am in the middle of writing some C++ code, and it is enjoyable but demanding on my time. I will remain busy with this code until at least the middle of June. So, expect the next post only around that time.]

[May be one more editing pass tomorrow… Done.]

[E&OE]

 

The indistinguishability of the indistinguishable particles is the problem

For many of you (and all of you in the Western world), these would be the times of the Christmas vacations.

For us, the Diwali vacations are over, and, in fact, the new term has already begun. To be honest, classes are not yet going on in full swing. (Many students are still visiting home after their examinations for the last term—which occurred after Diwali.) Yet, the buzz is in the air, and in fact, for an upcoming accreditation visit the next month, we are once again back to working also on week-ends.

Therefore, I don’t (and for a month or so, won’t be able to) find the time to do any significant blogging.

Yes, I do have a few things lined up for blogging—in my mind. On the physical plane, there simply is no time. Still, rather than going on cribbing about lack of time, let me give you something more substantial to chew on, in the meanwhile. It’s one of the things lined up, anyway.


 

Check out this piece [^] in Nautilus by Amanda Gefter [^]; H/T to Roger Schlafly [^].

Let me reproduce the paragraph that Roger did, because it really touches on the central argument by Frank Wilczek [^][^]. In the Nautilus piece, Amanda Gefter puts him in a hypothetical court scene:

“Dr. Wilczek,” the defense attorney begins. “You have stated what you believe to be the single most profound result of quantum field theory. Can you repeat for the court what that is?”

The physicist leans in toward the microphone. “That two electrons are indistinguishable,” he says.

Dude, get it right. It’s not the uncertainty principle. It’s not the wave-particle duality. It’s not even the spooky action-at-a-distance and entanglement. It is indistinguishability. Amanda Gefter helps us understand the physics Nobel laureate’s viewpoint

The smoking gun for indistinguishability, and a direct result of the 1-in-3 statistics, is interference. Interference betrays the secret life of the electron, explains Wilczek. On observation, we will invariably find the electron to be a corpuscular particle, but when we are not looking at it, the electron bears the properties of a wave. When two waves overlap, they interfere—adding and amplifying in the places where their phases align—peaks with peaks, troughs with troughs—and canceling and obliterating where they find themselves out of sync. These interfering waves are not physical waves undulating through a material medium, but mathematical waves called wavefunctions. Where physical waves carry energy in their amplitudes, wavefunctions carry probability. So although we never observe these waves directly, the result of their interference is easily seen in how it affects probability and the statistical outcomes of experiment. All we need to do is count.

The crucial point is that only truly identical, indistinguishable things interfere. The moment we find a way to distinguish between them—be they particles, paths, or processes—the interference vanishes, and the hidden wave suddenly appears in its particle guise. If two particles show interference, we can know with absolute certainty that they are identical. Sure enough, experiment after experiment has proven it beyond a doubt: electrons interfere. Identical they are—not for stupidity or poor eyesight but because they are deeply, profoundly, inherently indistinguishable, every last one.

This is no minor technicality. It is the core difference between the bizarre world of the quantum and the ordinary world of our experience. The indistinguishability of the electron is “what makes chemistry possible,” says Wilczek. “It’s what allows for the reproducible behavior of matter.” If electrons were distinguishable, varying continuously by minute differences, all would be chaos. It is their discrete, definite, digital nature that renders them error-tolerant in an erroneous world.

You have to read the entire article in order to understand what Amanda means when she says the “1-in-3 statistics.” Here are the relevant excerpts:

An electron—any electron—is an elementary particle, which is to say it has no known substructure.

[snip]

What does this mean? That every electron is the precise spitting image of every other electron, lacking, as it does, even the slightest leeway for even the most minuscule deviation. Unlike a composite, macroscopic object [snip] electrons are not merely similar, if uncannily so, but deeply, profoundly identical—interchangeable, fungible, mere placeholders, empty labels that read “electron” and nothing more.

This has some rather curious—and measurable—consequences. Consider the following example: We have two elementary particles, A and B, and two boxes, and we know each particle must be in one of the two boxes at any given time. Assuming that A and B are similar but distinct, the setup allows four possibilities: A is in Box 1 and B is in Box 2, A and B are both in Box 1, A and B are both in Box 2, or A is in Box 2 and B is in Box 1. The rules of probability tell us that there is a 1-in-4 chance of finding the two particles in each of these configurations.

If, on the other hand, particles A and B are truly identical, we must make a rather strange adjustment in our thinking, for in that case there is literally no difference between saying that A is in Box 1 and B in Box 2, or B is in Box 1 and A is in Box 2. Those scenarios, originally considered two distinct possibilities, are in fact precisely the same. In total, now, there are only three possible configurations, and probability assigns a 1-in-3 chance that we will discover the particles in any one of them.

Some time ago, I had mentioned how, during my text-book studies of QM, I had got stuck at the topic of spin and identical particles [^]. … Well, I didn’t have this in mind, but, yes, identical particles is the topic where I had got stuck anyway. (I still am, to some extent. However, since then, this article [^] by Joshua Samani did help in getting things clarified.)

Anyway, coming back to Wilczek and QM, Gefter reports:

Wilczek puts it this way: “Another aspect of quantum mechanics closely related to indistinguishability, and a competitor for its deepest aspect, is that if you want to describe the state of two electrons, it’s not that you have a wavefunction for one and a separate wavefunction for the other, each living in three-dimensional space. You really have a six-dimensional wavefunction that has two positions in it where you can fill in two electrons.” The six-dimensional wavefunction means that the probabilities for finding each electron at a particular location are not independent—that is, they are entangled.

It is no mystery that all electrons look alike, he [i.e. Wilczek] says, because they are all manifestations, temporary excitations of one and the same underlying electron field, which permeates all space, all time. Others, like physicist John Archibald Wheeler, say one particle. He suggested that perhaps electrons are indistinguishable because there’s only one, but it traces such convoluted paths through space and time that at any given moment it appears to be many.

Ummm. Not quite—this only one electron part. Wheeler never got “it” right, IMO. He also influenced Feynman and “won” him, but in the reverse order: he first got Feynman as a graduate student, and then, of course, influenced him. … BTW, how come Wheeler’s idea hasn’t been used to put forth monotheistic arguments? Any idea? As to me, I guess, two reasons: (i) the monotheistic people wouldn’t like their God doing this frenzied a running around in the material world, and (ii) the mainstream QM insists on the vagueness in the position of the quantum particle, so that its running from “here” to “there” itself is untenable. … Anyway, let’s continue with Amanda Gefter:

So if the elementary particles of which we are made don’t really exist as objects, how do we exist?

Good job, Amanda!

… Her search for the answer involves other renowned physicists, too; in particular, Peter Pesic [^]:

“When you have more and more electrons, the state that they together form starts to be more and more capable of being distinct,” Pesic said.

Only when you have “more and more” electrons?

“So the reason that you and I have some kind of identity is that we’re composed of so enormously many of these indistinguishable components. It’s our state that’s distinguishable, not our materiality.”

IMO, Pesic nearly got it—and then, just as easily, also lost it!

It has to be something to do with the state! After all, in QM, state defines everything. But you don’t really need the many here—there is no need for a “collective” approach like that, IMO. And, as to the state vs materiality distinction: The quantum mechanical state is supposed to describe each and every material aspect of every thing.

So, that’s a physicist thinking about QM(,) for you.

…Anyway, Amanda has a job to do, and she continues doing as best of it as she can:

Our identity is a state, but if it’s not a state of matter—not a state of individual physical objects, like quarks and electrons—then a state of what?

Enter: Ladyman, a philosopher:

A state, perhaps, of information. Ladyman suggests that we can replace the notion of a “thing” with a “real pattern”—a concept first articulated by the philosopher Daniel Dennett and further developed by Ladyman and philosopher Don Ross. “Another way of articulating what you mean by an object is to talk about compression of information,” Ladyman says. “So you can claim that something’s real if there’s a reduction in the information-theoretic complexity of tracking the world if you include it in your description.”

There is more along this line:

Should such examples give the impression that the real patterns are patterns of particles, beware: Particles, like our electron, are real patterns themselves. “We’re using a particle-like description to keep track of the real patterns,” Ladyman says. “It’s real patterns all the way down.”

Honest, what I experienced when I first read this passage was: a very joyful moment!

We are nothing but fleeting patterns, signals in the noise. Drill down and the appearance of materiality gives way; underneath it, nothing.

Ladyman tutoring Amanda, that was.

Here is a conjecture about the path they trace together; the part in the square brackets [] is optional:

We (i.e. a physical object in this context)-> Fleeting Patterns -> Fleeting Patterns -> Signals in the Noise –> [We –>] Signals in the Noise –> Appearance of Materiality –> Appearance of Materiality –> Appearance –> Nothing.

Fascinating, these philosophers (really) are. Ladyman proves the point, once again:

“I think in the end,” says Ladyman, “it may well be that the world isn’t made of anything.”

You could tell how rapidly he would go from “may well be” to “is,” couldn’t you?


So, that is what I have picked up for thinking. I mean, the two issues raised by Wilczek.

(1) The first issue was about how the indistinguishability of the indistinguishable particles is a problem. I will come back at it some later time, but in the meanwhile, here is the answer in brief (and in the vague):

Electrons are identical because: (i) the only extent to which we can at all determine that they are identical is based on quantum-mechanical observations, and (ii) observables are operators in QM.

That much of an answer is enough, but just in case it doesn’t strike the right chord:

The fact that observables are operators means that they are mathematical processes. These processes operate on wavefunctions. They “bring out” a mathematical aspect of the wavefunction.

Even if electrons were not to be exactly identical in all respects, as long as the QM postulates remain valid—as long as observables must be represented via Hermitian operators so that only real eigenvalues can be had—you would have no way to tell in what micro-way they might actually be different.

If you must have a (rather bad) analogy, take two particles of sand of roughly the same size, and gently drop both of them in a jar of honey (or some suitable fluid) at the same time. Both will fall at the same rate (within the experimental margin), and if, somehow, classical mechanics were such that it was only the rate of falling that could at all be measured in experiment, or at least, if the rate of descent alone could tell you anything about the size (and shape) of the sand particle, then you would have to treat both the particles as exactly the same in all respects.

The analogy is bad because QM measurements involve eigenvalues, and, practically speaking, their measurements are more robust (involving less variability from one experiment to another) as compared to the rate of descent. Why? Simple. Because, no matter how limiting you might get, fluid dynamics equations are basically nonlinear; eigenvalue situations are basically linear. That’s why.

I don’t think this much of explanation is enough. It’s just that I haven’t the time either to think through my newer QM conjectures, or work out their maths, let alone write blog posts about them. The situation will continue definitely for at least a month or so (till the course and the labs and all settle down), perhaps also for the entire teaching term (about 4 months).

(2) The second issue was about how multi-dimensionality of the wavefunction implies entanglement of particles. As to entanglement, I will be able to come to it even later—i.e., after issue no. (1) here.

Regarding purely the multi-dimensionality part, however, I can already direct you to a recent post (by me), here [^]. (I think it can be improved—the distinction of embedded vs embedding space needs to be made more clear, and the aspect of “projection” needs to be looked into—but, once again: I’ve no time; so some time later!)

Bye for now.

 


A Song I Like:

(Marathi) “ashee nishaa punhaa kadhee disel kaa?”
Singers: Hridaynath Mangeshkar, Lata Mangeshkar
Music: Yashawant Deo
Lyrics: Yashawant Deo

 

[May be another pass tomorrow or so. I also am not sure whether I ran this song before or not. In case I did, I would come back and replace it with some other song.]

[E&OE]

 

What do physicists mean by “multidimensional” physical reality?

Update on 2015.09.07, 07 AM: I have effected a few corrections. In particular, I have made it explicit that the third quantity isn’t the strength of an independently existing third property, but merely a quantity that is registered when the two independent quantities are both being varied. Sorry about that. If the need be, I will simplify this discussion further and write another blog post clarifying such points, some time later.


The last time, I said that I am falling short on time these days. This shortfall, generally speaking, continues. However, it just so happens that I’ve essentially finished a unit each for both the UG courses by today. Therefore, I do have a bit of a breather for this week-end (only); I don’t have to dig into texts for lecture preparations this evening. (Also, it turns out that despite the accreditation-related overtime work, we aren’t working on Sundays, though that’s what I had mentioned the last time round). All in all, I can slip in a small note, and the title question seems right.


We often hear that the physical reality, according to physicists, is not the 3-dimensional reality that we perceive. Instead, it is supposed to be some n-dimensional entity. For instance, we are told that space and time are not independent; that they form a 4-dimensional continuum. (One idea which then gets suggested is that space and time are physically inter-convertible—like iron and gold, for instance. (You mean to say you had never thought of it, before?)) But that’s only for the starters. There are string theorists who say that physical universe is 10-, n-, or \infty-dimensional.

What do physicists mean when they say that reality is n-dimensional where n >3? Let’s try to understand their viewpoint with a simple example. … This being a brief post, we will not pursue all the relevant threads, even if important. … All that I want to touch upon here is just one simple—but often missed—point, via just one, simple, illustration.


Take a straight line, say of infinite length. Take a point on this line. Suppose that you can associate a physical object with this point. The object itself may have a finite extent. For example, the object may be extended over a small segment of this line. In such a case, we will associate, say the mid-point of the segment with this object.

Suppose this straight line, together with the 1-dimensionally spread-out object, defines a universe. That is a supposition; just accept that.

The 1-dimensional object, being physical, carries some physical properties (or attributes), denoted as p_1, p_2, p_3, \cdots. For example, for the usual 3-dimensional universe, each object may have some extent (which we have already seen above), as well as some mass (and therefore density), color, transmissivity, velocity, spinning rate, etc. Also, position from a chosen origin.

Since we live in a 3-dimensional universe, we have to apply some appropriate limiting processes to make sense of this 1-dimensional universe. This task is actually demanding, but for the sake of the mathematical simplicity of the resulting model, we will continue with a 1-dimensional universe.

So, coming back to the object and its properties, each property it possesses exists in a certain finite amount.

Suppose that the strength of each property depends on the position of the object in the universe. Thus, when the object is at the origin (any arbitrary point on the line chosen as the reference point), the property p_1 exists with the strength s_1(0), the property p_2 exists with the strength s_2(0), etc. In short the ith property p_i exists with a strength s_i(x) where x is the position of the object in the universe (as measured from the arbitrarily selected origin.) Suppose the physicist knows (or chooses to consider) n number of such properties.

For each of these n number of properties, you could plot a graph of its strength at various positions in the universe.

To the physicist, what is important and interesting is not the fact that the object itself is only 1-dimensionally spread; it is: how the quantitative measures s_i(x)s of these properties p_is vary with the position x. In other words, whether or not there is any co-variation that a given ith property has with another kth property, or not, and if yes, what is the nature of this co-variation.

If the variation in the ith property has no relation (or functional dependence) to the kth property, then the physicist declares these two properties to be independent of each other. (If they are dependent on each other, the physicist simply retains only one of these two properties in his basic or fundamental model of the universe; he declares the other as the derived quantity.)

Assuming that a set of some n chosen properties such that they are independent of each other, his next quest is to find the nature of their functional dependence on position x.

To this end, he considers two arbitrarily selected points, x_1 and x_2. Suppose that his initial model has only three properties: p_1, p_2 and p_3. Suppose he experimentally measures their strengths at various positions x_1, x_2, x_3, x_4, \cdots.

While doing this experimentation, suppose he has the freedom to vary only one property at a time, keeping all others constant. Or, vary two properties simultaneously, while keeping all others constant. Etc. In short, he can vary combinations of properties.

By way of an analogy, you can think of a small box carrying a few on-off buttons and some readout boxes on it. Suppose that this box is mounted on a horizontal beam. You can freely move it in between two fixed points x = x_1 and x = x_2. The `on-off’ buttons can be switched on or off independent of each other.

Suppose you put the first button b_1 in the `on’ position and keep the the rest of the buttons in the `off’ position. Then, suppose you move the box from the point x_1 to the point x_2. The box is designed such that, if you do this particular trial, you will get a readout of how the property p_1 varied between the two points; its strength at various positions s_1(x) will be shown in a readout box b_1. (During this particular trial, the other buttons are kept switched off, and so, the other readout boxes register zero).

Similarly, you can put another button b_2 into the `on’ position and the rest in the `off’ position, and you get another readout in the readout box b_2.

Suppose you systematize your observations with the following notation: (i) when only the button b_1 is switched on (and all the other buttons are switched off), the property p_1 is seen to exist with s_1(x_1) units at the position x = x_1 and s_1(x_2) units at x = x_2; this readout is available in the box b_1. (ii) When only the button b_2 is switched on (and all the other buttons are switched off), the property p_2 exists with s_2(x_1) units at x = x_1 and s_2(x_2) units at x = x_2; this readout is available in the box b_2. So on and so forth.

Next, consider what happens when more than one switch is put in the `on’ position.

Suppose that the box carries only two switches, and both are put in the `on’ position. The reading for this combination is given in a third box: b_{(1+2)}; it refers to the variation that the box registers while moving on the horizontal beam. Let’s call the strengths registered in the third box, at x_1 and x_2 positions, as s_{(1+2)}(x_1) and s_{(1+2)}(x_2), respectively; these refer to the (1+2) combination (i.e. both the switches 1 and 2 put in the `on’ position simultaneously).

Next, suppose that after his experimentation, the physicist discovers that the following relation holds:

[s_{(1+2)}(x_2) - s_{(1+2)}(x_1)]^2 = [s_1(x_2) - s_1(x_1)]^2 + [s_2(x_2) - s_2(x_1)]^2

(Remember the Pythogorean theorem? It’s useful here!) Suppose he finds the above equation holds no matter what the specific values of x_1 and x_2 may be (i.e. whatever be the distances of the two arbitrarily selected points from the same origin).

In this case, the physicist declares that this universe is a 2-dimensional vector space, with respect to these p_1 and p_2 properties taken as the bases.

Why? Why does he call it a 2-dimensional universe? Why doesn’t he continue calling it a 1-dimensional universe?

Because, he can take a 2-dimensional graph paper by way of an abstract representation of how the quantities of the properties (or attributes) vary, plot these quantities s_1 and s_2 along the two Cartesian axes, and then use them to determine the third quantity s_{(1+2)} from them. (In fact, he can use any two of these strengths to find out the third one.)

In particular, he happily and blithely ignores the fact that the object of which p_i are mere properties (or attributes), actually is spread (or extended) over only a single dimension, viz., the x-axis.

He still insists on calling this universe a 2-dimensional universe.

That’s all there is to this n-dimensional nonsense. Really.


But what about the n-dimensional space, you ask?

Well, the physicist just regards the extension and the position themselves to form the set of the physical properties p_i under discussion! The physicist regards distance as a property, even if he is going to measure the strengths or magnitudes of the properties (i.e. distances, really speaking) only in reference to x (i.e. positions)!!

But doesn’t that involve at least one kind of a circularity, you ask?

The answer is embedded right in the question.

Understand this part, and the entire mystification of physics based on the “multi-dimensional” whatever vaporizes away.

But don’t rely on the popular science paperbacks to tell you this simple truth, though!


Hopefully, the description above is not too dumbed down, and further, hopefully, it doesn’t have too significant an error. (It would be easy for me (or for that matter any one else) to commit an error—even a conceptual error—on this topic. So, if you spot something, please do point it out to me, and I will correct the description accordingly. On my part, I will come back sometime next week, and read this post afresh, and then decide whether what I wrote makes sense or not.)


A Song I Like:

For this time round, I am going to list a song even if I don’t actually evaluate it to be a very great song.

In fact, in violation of the time-honored traditions of this blog, what I am going to do is to list the video of a song. It’s the video of a 25+ years old song that I found I liked, when I checked it out recently. As to the song, well, it has only a nostalgia value to me. In fact, even the video, for the most part, has only a nostalgia value to me. The song is this:

(Hindi) “may se naa minaa se na saaki se…”
Music: Rajesh Roshan
Singers: Sadhana Sargam and Mohammad Aziz
Lyrics: Farooq Qaisar

Well, those were the technical details (regarding this song). To really quickly locate the song (and the video), forget the lyrics mentioned above. Instead, just google “aap ke aa jaane se,” and hit the first video link that the search throws up. (Yes, it’s the same song.)

As I said, I like this video mainly for its nostalgic value (to me). It instantaneously takes me back to the 1987–88 times. The other reasons are: the utter natural ease with which both the actors perform the dance here (esp. Neelam!). They both in fact look like they are authentically enjoying their dancing. Watch Neelam’s steps, in particular. She was reputed to be a good dancer, and you might think that this song must have been a cake-walk for her. Well, check out her thin (canvas-like) shoes, and the kind of rough ground in the mountains and in the fields over which she seems so effortlessly to take those steps. Govinda, in comparison, must have had it a bit easier (with his thicker, leather shoes), but in any case, in actuality, it must have been some pretty good hard work for both of them—it’s just that the hard work doesn’t show in the song. … Further, I also like the relative simplicity of the picturization. And, the catchy rhythm. Also, the absence, here, of those gaudy gestures which by now are so routine in Hindi film songs (and in fact were there even in the times of this song, and in fact also for about a decade or more earlier). I mean: those pelvic thrusts, that passing off of a thousand of people doing their PT exercises on a new, sprawling suburban street in Mumbai/Gurgaon/Lutyens’ Delhi as an instance of dance, etc.

… I don’t know if you end up liking this song or not. To me, however, it unmistakably takes me to the times when I was a freshly minted MTech from IIT Madras, was doing some good (also satisfying) work in NDT, had just recently bought a bike (the Yamaha RX 100), and was looking forward to life in general with far more enthusiasm (and in retrospect, even naivete) than I can manage to even fake these days. So, there.

[As I said, drop a line if there are mistakes in the main post. Main mistake (or omission) corrected. As I said, drop a line if there are further mistakes in the main post. And, excuse me for some time, esp. the next week-end, esp. the next Saturday late night (IST). I may not find any time the next Sunday, because I would once again be in the middle of teaching a couple of new units over the next 2–3 weeks.]

[E&OE]

The electron really always waves at you

First, a couple of notes, touching on the topic I discussed the last time.

1. Yesterday, I did unpack one of the cartons in which I had packed some of the books while making the move from Mumbai to Pune (after my job less in January this year). Turns out that Feynman’s QED book was right in this first carton that I opened!

So, I immediately consulted the index at the end of the book, and then went over the pages related to “diffraction.” The diffraction-related footnote is on p. 59, though Feynman begins the discussion of diffraction mainly from p. 53. (The index mentions p. 46–49, but that passage is mostly about diffraction grating, not about electrons or photons going through a single slit.)

However, even in this footnote, Feynman does not directly state that those outer fringes do make an appearance in the single-slit diffraction. The last time, I thought he does clarify the matter. So, there must have been a confusion in my recall.

The uncertainty principle is dealt with in the footnote beginning on p. 55. Chances are, I confused between his indirect denial of the uncertainty principle (which is present), and a noting about the outer fringes (which is not). Possible. My memory, I keep telling you, is not much reliable.

2. I then tried to recall where I had read the analogy between (i) the classical particles with the example of bullets and (ii) the quantum mechanical electron.

I now realize that, in an at least indirect way, it is none other than Feynman himself!

In his Lectures book, III volume, first chapter (the same one I referred to the last time!), Feynman first takes the example of bullets and draws a probability curve; see figure 1 (b) here [^]. He then draws an exactly analogous (i.e. misleading) probability curve—the one just one central band—for water waves, in figure 2(b), and then, also for the electrons, figure 3 (b).

Though Feynman does not directly make any statement to the effect that the single-slit diffraction has only a single band, it is obvious from the flow of the contents of his lecture—in particular, the more or less direct analogy to the bullets—that he makes it far too easier for people to draw the sort of wrong conclusions which we discussed the last time.

Feynman, thus, makes QM sound more mysterious than it actually is.

[And, of course, since it’s Fyenman, Americans, esp. Californians, will never agree with me on the last statement.]

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On another note, in the course of attempting to build a computer simulation, I have now come to notice a certain set of factors which indicate that there is a scope to formulate a rigorous theorem to the effect that it will always be logically impossible to remove all the mysteries of quantum mechanics.

… Yes, you read it right. … More on it, later!

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A Song I Like:
(Hindi) “uljhan sulajhe naa…”
Singer: Asha Bhosale
Music: Ravi
Lyrics: Sahir Ludhiyanvi

 

[E&OE]

 

The electron always waves at you

This post has reference to Aatish Bhatia’s post on the subject matter bearing the title: “Hey There Little Electron, Why Won’t You Tell Me Where You Came From?” dated 27th September 2014 and published at the “Empirical Zeal” blog [^].

The post being referred to may immediately be perused.

“… Here’s the setup. On the table in front of me there’s a box with two thin slit-like openings at one end. We’re shooting particles into this box through these slits. I did the experiment with photons, i.e. chunks of light, but others have done it with electrons and […] For convenience, I’m going to call the objects in this experiment electrons but think of that word as a stand-in for any kind of stuff that comes in chunks, really. [bold emphases added] …”

Concerning the differences between electrons and photons, it would appear that it is not essential to look into all details of the proceedings that occurred when the present author defended his PhD thesis in mechanical engineering; however inasmuch as an inclusion of a reference increases the total number of references being cited for this post, the same [^] may perhaps be found in order.

“… And indeed, if you do this experiment with only one slit open, they behave just like baseballs, hitting the wall in a single band behind the open slit. …”

Further research is needed to develop a deeper understanding of the term: “single band.”

“… You can watch the electrons coming in one at a time in this video produced by scientists at Hitachi in 1989. …”

It is with great pleasure that the present author wishes to recall the inclusion of this video clip at the time of his conference presentation; the simulation he presented however was for photons.

“…Did the electron go through the left slit?

No! Because when you cover up the right slit, the stripey pattern disappears and you get a boring single band instead. …”

As has been mentioned above, more research is needed to develop a deeper understanding of the term: “single band.”

“…Did the electron go through the right slit?

No! For the same reason as above. When you cover up the left slit, instead of the stripey pattern you get a single band. …”

However, in the light of the further and deeper study of the reference post, it would appear that when the term “single band” is being used, the meaning being indicated is that of only one band as would be produced by a classical i.e. non-quantum mechanical particle.

“…As MIT professor Allan Adams puts it, that pretty much exhausts all the logical possibilities!…”

The quantitative logical closure contained in the salient reference which has been alluded to in the main reference post would be of great theoretical interest in general.

Therefore, it is one of the intermediate and urgent proposals of the present post to peruse this reference in an expeditious manner.

As Heisenberg and others taught us, although language fails us, it’s possible to come up with rules that correctly predict how tiny things behave. Those rules are quantum mechanics. You can learn these rules for yourself by reading Richard Feynman’s classic book QED…

It is further proposed to also include this reference in the literature review on a priority basis.

Kindly refer to Appendix A for details of the funds and employment opportunities needed. Kindly refer to Appendix B for details of justifications thereof.

* * * * *   * * * * *   * * * * *

OK. I have had enough of this“research” talk (i.e. write). So let me switch back to writing in my usual blogsome way.

I think that Aatish makes a conceptual mistake here.

The electron always, say, “waves at you.” It does so even when it goes through only a single slit.

What you observe with two (or more) slits is an interference pattern. There of course is no interference pattern when only one slit is kept open. But even in this case, what you observe is not a single classical band (as for a heap of grains), but a diffraction pattern containing many fringes.

Many people, esp. science popularizers, make this error. They present QM as if a single— and by implication, classical—band is observed when one the two slits is closed.

… What could be the source of this error? Where might have it begun?

It was Feynman who highlighted the conceptual importance of the double-slit interference arrangement. He also wrote his text book in a very informal and attractive style. He has enormously influenced some two generations by now, including the pop-sci book writers. May be there was something to the way he presented this material, which misled people?

Check out the informal diagrams Feynman includes in his Lectures, esp. fig. 1.3, part (b) [^].

He draws each of the two single-slit probability curves with only single humps. Look at the curve for P2 more carefully. It gradually decreases in magnitude and becomes zero as you go up (i.e., along the positive x-axis; here the x-axis is taken vertically). However, no hint is given that this P2 curve would then once again increase in magnitude (or go to the right in this diagram) as you continue going further up, and it will thus have another, relatively much smaller peak—and then, an entire infinite series of similar (and progressively more and more faint) peaks.

In diffraction, these other peaks often are almost undetectably faint. For instance, see the two diagrams that appear just above the “Problem” section, here [^]. In fact, in terms of brightness/faintness, the first diagram just above the “Problem” section is only schematic; it depicts the other fringes with much more brightness than actually is the case. The diagram above it (i.e. the graph) is a better representation of the relative magnitudes involved. (Another point: These outer fringes in the single-slit diffraction also happen to be relatively very faint when compared to the intensity of the interference bands which appear when both the slits are kept open.)

However, in the context of the single-slit, Feynman doesn’t explicitly say anything at all about the diffraction phenomenon—either in the text or in the diagram.

People then must have over-interpreted his diagram, and wrongly thought that (i) when an electron goes through a single slit, it behaves exactly similar to how grains falling through a chute behave, and (ii) when both slits are open, the electron somehow begins to behave something like a wave, something like a superposing quantum particle.

Thus, the idea being advanced is: single-slit means classical grain nature (Bhatia uses the example of baseballs); double-slit means in part a wave nature, as in QM. This characterization is wrong.

The faulty interpretation also makes QM sound more mysterious than it actually is.

Since Feynman’s double-slit diagrams anyway were only schematic (observe that the curves for P1 and P2 are manually drawn and therefore they are not precisely symmetrical), he could have shown a bit of the fringing effect in the single-slit too, with the usual note: diagram not drawn to scale. That single feature would have saved a significant error in so many popular expositions.

Feynman himself does explicitly note the fact of appearances of fringes even in the single-slit diffraction, but only in his later QED book—and only by way of a footnote. (Sorry, can’t locate it for you. I don’t have the book ready with me right now—it is still packed in a carton when I moved from Mumbai to Pune after my job-loss in January. But I do remember that it is in the early parts of the book, very probably in chapter i.e. lecture 1.)

Since I have exhausted my ‘net bandwidth for this month, I couldn’t go through the MIT professor Allan Adam’s video that Aatish Bhatia refers to. (It’s more than 1 hour long.) Instead, I checked out his PDF course notes, to see if he too makes this common mistake. … Well, that way, I didn’t actually expect Adam to repeat this mistake, but since Bhatia makes an enthusiastic reference to it, I wanted to check out. The relevant course notes are here, L2 [(.PDF) ^]. As expected, the notes don’t actually commit the mistake, but still, they repeat the same omission (of diffraction). Adam says in his notes (p. 7–8)

Hence, determining through which slit an electron passes does away with the interference pattern.

He could add an explicit mention of the diffraction pattern.

Though both electrons and photons would show a similar behaviour, it should be easiest to demonstrate the diffraction effect using light rather than electrons. My unpublished simulation of the PhD times showed a gradual “morphing” from a full double-slit interference pattern to a full single-slit diffraction pattern, as the detection efficiency of the photon detector placed near only one of the two slits was increased. Very natural. Check out Adam’s maths on p. 6:

A(y) = A_0 \left( e^{i\theta_1(y)} + e^{i\theta_2(y)} \right)

Split it up keeping two different terms A_1 and A_2, even if we assume A_1 = A_2:

A(y) = A_1 e^{i\theta_1(y)} + A_2 e^{i\theta_2(y)}

Gradually take, say A_1, to zero. You gradually transition from interference to diffraction.

Why might Bhatia have made the error? Here is a speculation.

He mentions the experiment with photons, which he did have an opportunity to perform, as an undergraduate student.

It’s possible that the geometrical scaling of the experimental arrangement was such that the outer diffraction fringes got placed outside the detection limits of the CCD camera. It’s also possible that they ran the experiment mainly to bring out the particle nature well, and so, they effectively “expanded” the time axis a great deal (by using a very low flux rate). Now, for the single-slit version, the outer diffraction fringes are very faint, as compared to the big fringe in the middle. Therefore, in the actual experimentation, enough particles might not have been registered at the locations of these outer diffraction fringes, at least over the relatively shorter duration of the experiment.

Eleven years later, as he began sharing the joy and excitement of seeing the quantum nature in action from memory, he might have focused a bit more on the dramatic features of the experimental measurements and forgotten the correct theory that helps explain it. Possible.

Or, it is also possible that this bit simply skipped his attention. Quantum theory actually is a very big theory—it has a very large scope. As a typical university student, your goal is to master its mathematical tools. It’s easily possible that you skip over some of the rudiments rather quickly. It happens to almost everyone. The initially unintuitive nature of QM isn’t the only thing that people get used to; they also keep adding many small details in their understanding, because no one book can possibly cover all such details, applications, etc.

Anyway, he would know best.

… I have already dropped a comment at his blog, mentioning the concepts-wise serious nature of this mistake. It sets people—the newcomers, the layman—on a wrong path. It did that to me, for more than 5 years (in fact almost a decade, perhaps more, if you count the time from the very first exposure to the wave-particle duality, which was sometime in XI or XII standard in my case).

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A Song I Like:

[A very careful study of this song is advisable. There will be examination, once the song is over.]

(Marathi) “hee gulaabee hawaa, veD laavi jeevaa…”
Singer: Vaishali Samant
Music: Avadhoot Gupte
Lyrics: Guru Thakur

[Open Book Examination: Peruse online resources such as the material made available here [^] and here[^], and use it in order to determine whether the above-mentioned song may be deemed to be based on the North Indian Classical “raaga” “marwaa,” or otherwise. Provide detailed explanatory comments in similar English.

Extra Credit: Imagine how, in an Indian classical music concert held, for example in Goa, how Shobhaa ShiroDkar (i.e. Shobhaa GurTu) could have rendered this song. Then, using her Marathi song “maajhiyaa priyaalaa” as the propaedeutic for “ucchaaraNa bhed” and voice culture, render the above song the way GurTu would have, attempting to your fullest capacity an imitation of her voice and scale. Submit the evidence of your attempt via a CD-quality recording.

Extra Extra Credit: Repeat the aforementioned exercise (including GurTu’s voice and scale), but using another “raag” of the “maarwaa thaaT,” viz. “puriyaa kalyaaN!”]

 

[E&OE]

One More Recommendation for Your Holiday Reading: Manjit Kumar’s “Quantum”

This year seems to be a bit unusual. I have not one, but two very strong recommendations for your holiday reading list.

The first book, of course, was David Harriman’s “The Logical Leap: Induction in Physics,” which formed the topic of my last blog post [^]. Now I am very pleased to bring another great book to your notice: Manjit Kumar’s “Quantum: Einstein, Bohr and the Great Debate on the Nature of Reality” [^].

I am in a hurry. So, please do not regard this post even as an attempt to provide a proper review. I am just going to jot down a few points that occur to me on the fly, after having finished reading the book a week ago or so.

Here is my overall opinion of Kumar’s book: This book is the most outstanding account of quantum mechanics meant for the layman that I have ever read in print, period.

Now, that is saying a lot, and yes, I do mean it. … I have read a lot of pop-science type of material on this topic. Throw in also those philosophically oriented popular accounts. I am not exaggerating when I say that Kumar’s book is the best. Yes, Kumar’s book easily beats, just for example, both of Gribbin’s books: “In Search of Schrodinger’s Cat” [^] and its sequel “Schrodinger’s Kitten and the Search for Reality” [^], even Feynman’s books (Lectures and QED), not to mention Alastair I. M. Rae’s “Quantum Physics: Illusion or Reality?”[^].

Compared to Gribbin’s books, Kumar’s is a far more balanced, accurate, and a detailed account, with a lot of material concerning the personalities of the early quantum founders (even though Kumar does not cover the later period in much detail). Compared to Feynman’s accounts, Kumar’s book has one outstanding virtue: it is historically well-ordered, which by itself takes care of streamlining so much understanding in such a subtle manner. And, compared to Rae’s book, Kumar’s book does not care to dwell on the subtleties of the philosophical nonsense. It is a book that manages to keep physics at its focus through and through.

Kumar begins right from Planck’s hesitant acceptance of the quantum nature of emission and absorption of the cavity radiation, and then carefully goes through the evolution of ideas at the hands of Einstein (quantization of radiation itself), Rutherford and Bohr (atomic structure), and then all the European men, young and not so young, who discovered one facet after another in a breathtakingly rapid manner: Heisenberg, Pauli, Born, Jordon, Kronig, Uhlenbeck, Goudsmit, Schrodigner, et al. For each physicist, before describing his work, Kumar first provides an essentialized bio of the man: his family, inclinations in the school, academic work, supervisor and his personality, the ideas already “in the air” at that time, the initial faltering steps and false starts, and even the frustrations before the solution was discovered and the personality clashes after it was. And, Kumar also manages to place all these things in a broader cultural and historical contexts—the demands of the industry and governments to solve particular problems, the two world wars, the antisemitism, the reactions of the academic community to the evils surrounding them, etc.

Even before starting reading this book, I knew that these early quantum physicists worked in a very closely networked manner. But I had hardly realized the deep personal respect they gave each other and the deep feelings of friendship they enjoyed. It is easy to over-dramatize the tension between Bohr and Einstein; so many popular accounts have so routinely done so to such an extent that one might imagine as if Bohr and Einstein were at least playing a turf-war of sorts if not reaching for each others’ throats. You have to read this book to realize how far away such recent depictions have gone from the facts of the matter. Kumar possesses just the right sensitivity to the culture of those times to present just those essential facts with which, after finishing this book, one does come out enlightened about the way this extraordinarily brilliant chapter in the entire history of physics had actually unfolded. And, how cultured and intelligent its main actors were—regardless of whatever errors, even blunders—concerning physics or philosophy—that they might have committed.

This book has helped me correct many of the misleading or wrong impressions that I unwittingly had happened to gather, regarding many founders of QM—and even concerning the contents of their ideas.

Kumar covers the material roughly in the same sequence in which the development actually occurred. In following this policy, it is obvious that it is the author who has work harder, thereby lessening the burden of integration on the reader’s part. In this task, Kumar has succeeded brilliantly. To appreciate the sheer volume of reference material the author must have dug through, just take a look at Mehra’s volumes alone! And, yet, for many controversial ideas, Kumar manages both to present all the relevant material to the reader and and yet also to allow the reader the room to let him think about that issue and come to his own conclusions.

One also comes to develop an appreciation for the subtle nuances in the differences of the ideas held by the founders of QM, and the roles they played. Here, a few things stand out: (i) The way Heisenberg evolved matrix mechanics and the roles played by Born, Jordan, and Pauli, in developing it. (ii) How the idea of spin was so simple—and so much required in the order of development—that it could get introduced way before the 1927 Solvay conference. (iii) How close to the eventual formalism were certain nascent ideas held by the less celebrated physicists. (iv) The roles played by extraordinary mentors like Rutherford, Bohr, Sommerfeld, and others. (v) And yes, the special circumstantial reasons why the Copenhagen dogma could get established so easily in the academia.

There can be scope for improvement. However, in a book like this, it is a secondary or an outright minor matter. In any case, I don’t have any specific suggestion right away—I will have to do a more careful second/third reading before coming up with any. Yet, I must add, there is something that I found something missing right on my first reading.

I would have so much appreciated it if the author could have traced the evolution of Dirac’s re-formulation of QM. This development happened early enough, and it is important enough. The author has rendered a great service by carefully isolating and demarcating how the progression of thoughts occurred in Heisenberg’s formulation—starting with all the relevant events and ideas before his visit to that island resort and going on to the subsequent developments. It would have been a great (and easy) learning for the reader if the author could have done the same for Dirac’s development. This topic is conspicuous by its absence. The absence is all the more remarkable given the fact that (i) Dirac was a British gentleman, just the way the author is, and (ii) the author does manage to touch on such later developments like the EPR controversy and Bell’s inequalities. It is my sincere hope that the author would consider adding a chapter in a future edition. Or, make it available at his blog.

Overall, this book indeed makes for both a great read and a valuable reference. It could even be made recommended supplemental reading for university courses.

All in all, very strongly recommended.

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I don’t expect to write another blog post this year, and so, let me say “Happy New Year!” to you right away!

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A Song I Like:

(Hindi) “yeh raat bheegee bheegee…”
Music: Shankar-Jaikishen
Singers: Manna Dey and Lata Mangeshkar
Lyrics: Hasrat Jaipuri

[E&OE]