I’ve spotted yet another error in my new approach!
The error was conceptual in nature, not just mathematical, and it occurred at a fundamental level. … Or so, I think! As of today!
I mean, I am not even rock-sure whether, eventually, it indeed would turn out to be an error or not! … But yes, as of now, I do think that it is an error!
How did the error get into my system—I mean in my new approach?
Well, it first got subtly introduced (and thereafter got reinforced) into my very thinking mode, quite some time ago. May be around May–June times last year. How come?
Because, by a certain motivation that was vague, subtle, and definitely unidentified, I was trying to leave the mainstream QM’s postulates as unaltered as possible. Rather, the MSQM had been subtly shaping up my own “rebellious” thinking too, you know! (For the MS QM postulates, see the document attached to my last post here.)
So, yes, it certainly is time for me to be a bit sheepish. … I’ve begun wondering whether I should have hurried into blogging about my January 2021 computational result or not. I mean the result concerning the helium atom’s bonding energy. … I now think that the numerical result could be—actually, should be—erroneous too.
However, in this particular case of QM application (concerning the helium atom), and for this particular calculation (viz. the bonding energy), the impact should not be numerically so significant. But that’s only because the finite differences method itself is so crude that the error, even if present, can only be expected to get almost fully lost within the numerical approximations. (That too was another reason why I didn’t spot the error right then and there!)
So, may be, I should not have blogged about that trial with such an immediacy.
To be fair, though, I work completely alone, and have never had university courses on QM. The latter leads to two things: (1) I sure have been less susceptible to the errors of the MSQM mode of thinking (even if it can’t solve the measurement problem). (2) However, at the same time, the lack of university education in QM also means that I have also haven’t had the opportunity to discuss issues with class-mates and all. Informal discussions could have worked wonders, who knows. … But the fact is, I work completely alone (even if there are, and have been, blog-some interactions with others).
Further, realize the nature of my goals. I am not just understanding the existing QM machinery (which is complicated). I am also developing an entirely new approach to the quantum phenomena underlying it. Everything (i.e., literally, every thing) needs to be thought through. … Loftiness of the goal ought to make, I think, some sheepishness acceptable. Particularly when it’s QM.
Another thing. There is an offsetting consideration. I don’t just think up my ideas, and then hurry up to write them down in papers, and even send them for publication, expecting that someone else would verify my ideas—conceptually, numerically, or experimentally. I myself implement my ideas through computer simulation, and carefully look at the actual experimental setups that were used in validating QM. This last part is work too!
In comparison, it’s well and good that my error got caught well in time. At least, it remained confined only to my blog posts / comments. I didn’t even send it to arXiv let alone to some well received journals. … With as many as fourteen “influential” interpretations of QM listed at the Wiki [^], and with none of them being fully satisfactory, and yet, with papers still being produced on them for years on (actually, in some cases, for decades), chances are pretty good that my error too could have gone un-noticed and well published! (The nature of the error is like that!)
So, even as I pinch myself for my “recklessness” in blogging so fast, there definitely are some offsetting considerations that are worth noting. … QM, if you are going to think completely afresh about it, certainly is hard. … Take it from me!
This “development” implies having to draw up a new schedule. Indeed, I will have to work through everything completely afresh, find some suitable solutions to the issue that came to the notice, and satisfy myself that the solutions I now think of indeed are satisfactory. Then (or simultaneously), I will also have to write code and undertake calculations via completely fresh sets of trials. Only then will I be able to get back to writing the planned document on my new approach.
And, oh yes, I still have to take good notes on the QM spin and integrate my new approach to include it. (I’ve completed taking notes on the orbital angular momentum, and it’s while understanding this topic that the possibility of an error struck me. I’m using Eisberg and Resnick for these topics. This book is excellent for these topics (IMO!))
And all this happened even as I was planning, just some 3–4 days ago, to write a small little post saying that I’ve got tired by now. I actually am. But the discovery of the error has given a bit of a new enthusiasm to me. As physicists like to say, if everything is working out fine, then that’s OK, perhaps even boring. But when something doesn’t work out, then it’s exciting. Now you can think about it… (I forgot who said something like that first.)
2. Still not a mystic:
There was some minor painting work scheduled at home (actually, filling of the cracks in the plaster of the wall).
Consequence: I had to shift around, within home, all the mover’s and packer’s boxes which were lying unopened since our last move about a year ago. These boxes contained my books.
There are in all some — of these boxes, out of which about boxes should be carrying my books alone, all packed to the full capacity and a bit more. (That is, after discarding almost half the books during the last move alone (not counting the books I had to discard/sell earlier too), and after losing almost — boxes worth of books during the 29 September 2019 flash-floods in Pune.) The size of each box is about feet cubic feet.
Consequence: Now that the boxes were not stacked on top of each other in my room, but instead were lined up in a single layer on the floor in all other rooms and balcony, I could open them and check their contents. Also, a few other boxes got teared a bit during this shifting (they all are made of the cardboard). So, I had a peek into their contents too.
Consequence: I got an old book out. Somehow, I didn’t keep it back into the box.
The above-mentioned book is: My first ever bought copy of Fritjof Capra’s “The Tao of Physics.”
Here is the proof.
I had bought it for Rs. 30/- back then. Here is the proof. (Check the stamped price at the top-right corner.)
I remember later on buying a copy each in Alabama and California, but I discarded them both, while returning to India.
I had bought it on 9th January, 1984. Here is the proof. Check the top-right corner in the pic. (The squiggly looking thing above the date is my signature in Marathi.) BTW, notice, in India, we write dates in one of the two correct ways, viz., DD/MM/YY[YY]. The other correct sequence is: YYYY/MM/DD. The sequence MM/DD/YYYY is always wrong.
Notice my hand-written comment in the above pic (written in the black ink). Even today I remember the moment when I wrote it down, which was within a few days of starting reading the book. I had consciously avoided writing the comment using the cursive handwriting, because I wanted to see how the book might look if it officially carried the contents of my comment. My comment says:
“A fruitless attempt to
`Discover’ the so-called, non existing,
Modern Physics & Eastern Mysticism.”
The handwriting is uneven, because the paper didn’t respond to the pen right—or so I think. Or may be, I was lazily lying down on bed when I wrote it, I don’t remember that part. (I also don’t recollect why I capitalized the word ‘Discover’ though!)
I had also made a few more margin notes/comments in the book, especially in the earlier parts of it. (I think that I never fully finished this book. Anyway, here is one of the comments I had made (back in 1984). Capra’s book had quoted this passage from Lao Tzu’s book “Tao Te Ching”:
``He who pursues learning will increase every day;
He who pursues Tao will decrease every day.”
To which I had made an inline comment:
“Literally true, philosophically.”
Here is the proof:
It was neat to notice that, in certain ways, I’ve not changed even the slightest bit over all these years. 37 years! That’s a long time. … Actually, I began thinking about QM not so much in XI–XII times but in my UG final year at COEP, in first half of 1983 (i.e. 2nd semester of the final year), when we had a course on Structural Metallurgy. Reed-Hill’s book (Physical Metallurgy) had mentioned the Uncertainty Principle, and while talking to a friend (on the stairs at the main entrance to the Department of Metallurgy at COEP), I had confidently said that one day, I am going to prove Heisenberg wrong.
Well, cutting to the present, I am experiencing a bit of sheepishness, but not on that count. And, I’ve never turned a mystic.
3. A bit nostalgic:
I continued buying books, esp. pop-sci, philosophy and other books, even after graduation (1983). I kept discussing these with friends. That’s how I bought Capra’s book (1984). I in fact remember showing the above comments to my friends and discussing a bit on the related philosophical issues with them.
At least one such an occasion was probably on a weekend evening, and it definitely was over a beer or two (but not more—those days, we would drink far less). It was at a restaurant in Pune. I’ve forgotten the exact restaurant (and even who exactly the friends were though I do have a list of the usual suspects). Likely, the place was either Hotel Poonam at Deccan Gymkhana, or Hotel Pearl near Balagandharva. In any case, I am sure it was a place from the JM Road/Deccan area, not from the Camp, when I discussed this book.
In those days, Poonam used to be an avant-garde place with nice open spaces, and upper middle-class clientele. We had in fact spotted many Marathi cine-/theater personalities there, right at the next table or so. (Jabbar Patel once, Amol Palekar at some other time, I remember. Friends remember Jairam Hardikar, but I was not there at that time.) Poonam used to serve an out-of-the world prawns curry. Absolutely fresh prawns, and a curry in the Konkani style (with coconuts, but not in the Malwani style). As to the Hotel Pearl, it used to have a small cubby-hole of a bar (with hardly 4–5 tables)…. Both these places had been mostly out of our reach as students, though I remember going there for some big occasion like semester-end or so. However, later on, as we graduated and started earning, we could afford such hotels too, once a month or so.
As I read my comments in the book, all such memories suddenly sprang up and became lively. Automatically. …Just stumbling across this old copy of Capra’s book had that effect on me. It also threw up the song I am running for this time…
4. Alright, so, to wind up:
Yes, I might get sheepish once in a while, and I do turn a bit nostalgic at times too, but I haven’t turned mystic, ever. Certainly not for 37 years. (Which is not a big deal, really speaking!)
As to the immediate future… Well, I can’t both be sheepish and shipping-ish at the same time, can I? (See, see, how tough it is to get out of the Copenhagen interpretation?)
So… There is going to be some further delay in writing the upcoming document and code. I am certain the task won’t be done until mid-March. It may perhaps even be March-end or some time in April before I am near completion. (But also realize: Whenever it comes, it will have some definite indication regarding the QM spin too, and I will sure try to include a brief indication of this error too.)
Obviously, blogging in the meanwhile is going to be very sparse. Expect to see this same post here for quite some time, may be for another 3 weeks or more. (Frankly, I don’t even know when I am going to return to blogging/tweeting.)
Bye for now, and take care in the meanwhile (and remember, Covid-19 has begun a definite up swing!)…
A song I like:
(Western, Pop): “Homeward bound”
Band: Simon and Garfunkel
[…I had completely forgotten this song, had not played it for a long time, certainly not for at least two decades by now. … It automatically came to me as I was flipping through Capra’s book. It used to be my favourite in the IIT Madras hostels, and even later on for some time. I still seem to like the same things about this song: the general theme / backdrop (rather than the lyrics as such), the soft and informal/folksy sort of music, and yes, also the singing.
The cassette I had bought was for the album “Simon and Garfunkel’s Greatest Hits”; it carried this version [^]. I had realized that it must have been for a live event, but didn’t know which one; I discovered the event only today (at the Carnegie Hall, New York, in 1970). Another version, the original record label, is here [^]; I “discovered” this one only today. I guess I like the Carnegie Hall version better!