Postulates of quantum mechanics, as stated by various authors

OK, here [^] is the postulates document I had mentioned in the last post. Below the fold, I copy-paste the section called “About this document” from it.


About this document:

Quantum mechanics is the most fundamental theory of physics. As such, there are no known principles or truths of physics that logically precede those lying at the foundational level of QM itself. The foundational propositions of QM must first be accepted as postulates, if the body of knowledge that is physics, taken in its entirety, is to remain logically consistent and physically meaningful.

Owing to their roots in inductive reasoning performed within a certain phenomenological context, and not in deductive reasoning as within the relatively narrower confines of mathematics, the postulates of QM cannot be regarded as mathematical axioms—whether in terms of form or function.

The postulates should instead be seen as a minimalist set of propositions that serve as the conceptual anchor-points, or core nodes in concept-map, in reference to which our knowledge of the physical world may best be organized. The sheer scope and variety of physical phenomena being encapsulated makes it impossible to impart the mathematical kind of rigour to the postulates of QM. In other words, there cannot be a Euclid for QM.

As to the current state of this topic, viz., Foundations of QM, while there indeed is a very good general agreement on what facts of nature must be encapsulated within these postulates if they are to serve their foundational purpose, the specific formulations put forth by various authors do differ significantly in terms of their detail. Almost a century after the currently accepted theory of QM was completed, at least in terms of the mathematical principles lying at its core, the process of refining the statements for its postulatory basis still goes on—at times, with good reasons too!

The variety of available formulations can easily get confusing to the beginning student. At least, such was my own experience. That’s why, during my studies and research, I decided to compile in one place a few of these differing sets of statements. The result is this document.

Almost all of this document consists of verbatim reproduction from the original sources. My own contribution is limited to one or two editorial remarks; these have been explicitly noted as such.

This is very much a work in progress. Typographical errors are easily possible. Therefore, it is advisable not to rely on this document fully, but instead to make reference to the original sources themselves. Needless to add, copyrights and any other rights belong to the respective owners of the original sources.

If you spot some errors that crept in during the compilation process, then please do not hesitate to let me know. Thanks in advance.

NB: This document may change at any time without notice. (Indeed, in future, I do plan to include the formulations by several more authors too.) Hence, for any correspondence or reference purposes, the time-stamp of the LaTeX compilation should be taken as the “edition” or “version” number.


You might notice that the dates noted in the document seem odd. The beginning date is from 2018, while the completion date is today’s. … No, I was not writing the document for 2+ years! When I wrote the first version of this document back in November of 2018, it had the sections 1–3, 5, and 6 to it; I had written it only for myself. However, I had also downloaded the papers mentioned in the reference section. Last week, I completed fully going through Dorabantu’s paper (earlier, I had only browsed through it). I also went through the postulates part of Nottale et al’s paper, and then began adding the remaining 2 sections. That’s when I also decided to upload this version of the document.

Now that I have uploaded it, I might be away from blogging for more than two weeks.

The thing is, I’ve had only a sketchy idea concerning incorporating the quantum spin into my new approach. While writing the upcoming document on my new approach, I came to a point where I felt that perhaps it would be a good idea to see if I can work out the details concerning the spin, and include these right away. Now, the QM spin is a very interesting topic, but it also is a bit complicated. I’ll have to see if the ideas I currently have, are fully consistent or not, by going through the points again and again, from as many different points of view as I can… So, it might delay the completion of the document by a couple of weeks. However, I think, it might be—should be—worth it. … That’s why, I plan to be taking a longer break.

… Of course, if something short and sweet occurs to me in the meanwhile, I don’t mind coming back here and adding a bit here, though it’s not at all likely. Also, I think it’s best to take an off from blogging (and even from the ‘net, for the most part), so I can focus on the work better.

Alright. Take care, and bye for now.


A song I like:

(Hindi) लिखा है तेरी आँखों में किसका (“likha hai teri aankhon mein”)
Singers: Lata Mangeshkar, Kishore Kumar
Music: S. D. Burman
Lyrics: Majrooh Sultanpuri

[A long time favourite… Right from the early childhood, in fact. The usual magic of SD, Dev Anand, Lata & Kishore is at work here. … A good quality video is here [^]. …Yes, for this song, as a matter of exception, the video is being recommended. A few reasons:

1. Great picturization: A field of millets is quite a common scene in Maharashtra’s country side. If you actually visit a field like that, then chances are very bright that you would get bored pretty soon. A rather prosaic scene, especially when standing there under the afternoon sun. Nothing remarkable. Just the crop and a few scattered trees around. Rather grayish, and definitely dull …

Now just see how the director takes such a location, and still manages to impart subtle drama into the song… In fact, if you ask me, he manages to transform even that dull backdrop into a visual poetry of sorts. The camera-work too is flaw-less here. (Run the video a second time just to see how the cinematographer has managed the tonal quality of the frames. It also helps that the quality of this YouTube video is good too.) As to the quality of music, well, something like this is not at all unusual for SD, but Lata brings in a special conversational quality to this song, especially to the teasing part, and then, Kishore responds as only he can. …As to the lyrics, just check the lines given to Lata: mocking, just to feign a lack of interest that’s only thinly disguised. As to the lines given to Kishore, a sense of exasperation and light sarcasm put together so wonderfully. …Acting by Nanda is uber natural too, and Dev Anand, as usual, is shown as a carefree and cheerful character. (And, the camera doesn’t mind moving away from him; this was not a Navketan film anyway.) All in all, a wonderful song to watch.

2. A bit personal: I spent a part of my early childhood (roughly, age 2 through 5.75) in a village which was not far off from the location for this song (say 50 km or so), and roughly at around the same time (mid ’60s). I remember my parents mentioning about the shooting of this film. If I recall correctly what they said, the locations for this film were multiple: near the Ankaai-Tankaai hills (near Manmad junction on the Central Railway), and near some Ranjangaon village (though I am not sure if it’s the Ranjangaon on the Pune–Nagar road or some other Ranjangaon from the northern parts of the Ahmednagar district). …I am not sure… If you ask me, the location for this song could well have been from near Igatpuri or Nasik too, who knows…  As to the place where we lived, it was Chitali, near Shrirampur. I did my first standard there…

Update on 2021.02.04 17:15 IST: My father had mentioned Ranjangaon yesterday when I casually checked with him before writing this post. Today, I asked him further details, and he confirmed that it indeed was Ranjangaon, the small village on the Shrirampur to Shirdi road, near Ganesh Nagar sugar factory. [It’s there in the Google maps, as Ranjangaon Khurd.] When I asked him whether they saw the shooting, he told me this: Once he and his colleagues were going in their jeep for some office work (my father worked as an engineer in the irrigation department), and on that narrow road, a jeep without roof came from the other side. They must have slowed down because the roads were narrow. As they passed each other by, he clearly saw Dev Anand sitting in the front. He looked handsome, and also very fair, because he already had the make-up on. The film unit people were staying in some bungalow nearby, and may be they were on their way to the shoot. But Dev Anand definitely was already wearing the make-up, and he had a jacket on. Anand generally waved his hand as the two jeeps crossed each other. When I asked him if he saw Nanda too, he said no, may be she was sitting on the back side of the jeep. It was just a glimpse, but a clear one. …And yes, Ranjangaon is only about 10–11 km from Chitali. Update over.

Now, it just so happens that I have relatively few but very vivid memories of those times from my childhood. So much so, that I actually think that the combination of the fields, the trees, the color of the sky and the clouds, when taken together, look a certain special way in that part of the world, and in no other. Really! Just a few years ago, I actually took a couple of aimless drives through that part (both on an evening and on a morning, each time spending more than a couple of hours in that small area), and I can confirm that this is not just a suspicion of mine, it’s a fact! The clouds do look different there! Not to mention the smell in the air, especially when you are in the fields. … Anyway, the picturization of this song is such that, whether it was actually shot around that specific area or not, it does also revive those happy memories for me. So, that’s another, personal, reason for me.

Anyway, see how you find it.


History:
— 2021.02.04 00:20 IST: First published
— 2021.02.04 17:50 IST: Updates made in the songs section