Absolutely Random Notings on QM—Part 3: Links to some (really) interesting material, with my comments

Links, and my comments:


The “pride of place” for this post goes to a link to this book:

Norsen, Travis (2017) “Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory,” Springer

This book is (i) the best supplementary book for a self-study of QM, and simultaneously, also (ii) the best text-book on a supplementary course on QM, both at the better-prepared UG / beginning PG level.

A bit expensive though, but extensive preview is available on Google books, here [^]. (I plan to buy it once I land a job.)

I was interested in the material from the first three chapters only, more or less. It was a delight even just browsing through these chapters. I intend to read it more carefully soon enough. But even on the first, rapid browsing, I noticed that several pieces of understanding that I had so painstakingly come to develop (over a period of years) are given quite straight-forwardly here, as if they were a matter of well known facts—even if other QM text-books only cursorily mention them, if at all.

For instance, see the explanation of entanglement here. Norsen begins by identifying that there is a single wavefunction, always—even for a multi-particle system. Then after some explanation, he states: “But, as usual in quantum mechanics, these states do not exhaust the possibilities—instead, they merely form a basis for the space of all possible wave functions. …”… Note the emphasis on the word “basis” which Norsen helpfully puts.

Putting this point (which Norsen discusses with a concrete example), but in my words: There is always a single wavefunction, and for a multi-particle system, its basis is bigger; it consists of the components of the tensor product (formed from the components of the basis of the constituent systems). Sometimes, the single wavefunction for the multi-particle system can be expressed as a result of a single tensor-product (in which case it’s a separable state), and at all other times, only as an algebraic sum of the results of many such tensor-products (in which case they all are entangled states).

Notice how there is no false start of going from two separate systems, and then attempting to forge a single system out of them. Notice how, therefore, there is no hand-waving at one electron being in one galaxy, and another electron in another galaxy, and so on, as if to apologize for the very idea of the separable states. Norsen achieves the correct effect by beginning on the right note: the emphasis on the single wavefunction for the system as a whole to begin with, and then clarifying, at the right place, that what the tensor product gives you is only the basis set for the composite wavefunction.

There are many neat passages like this in the text.


I was about to say that Norsen’s book is the Resnick and Halliday of QM, but then came to hesitate saying so, because I noticed something odd even if my browsing of the book was rapid and brief.

Then I ran into

Ian Durham’s review of Norsen’s book, at the FQXi blog,

which is our link # 2 for this post [^].

Durham helpfully brings out the following two points (which I then verified during a second visit to Norsen’s book): (i) Norsen’s book is not exactly at the UG level, and (ii) the book is a bit partial to Bell’s characterization of the quantum riddles as well as to the Bohmian approach for their resolution.

The second point—viz., Norsen’s fascination for / inclination towards Bell and Bohm (B&B for short)—becomes important only because the book is, otherwise, so good: it carries so many points that are not even passingly mentioned in other QM books, is well written (in a conversational style, as if a speech-to-text translator were skillfully employed), easy to understand, thorough, and overall (though I haven’t read even 25% of it, from whatever I have browsed), it otherwise seems fairly well balanced.

It is precisely because of these virtues that you might come out giving more weightage to the B&B company than is actually due to them.

Keep that warning somewhere at the back of your mind, but do go through the book anyway. It’s excellent.

At Amazon, it has got 5 reader reviews, all with 5 stars. If I were to bother doing a review there, I too perhaps would give it 5 stars—despite its shortcomings/weaknesses. OK. At least 4 stars. But mostly 5 though. … I am in an indeterminate state of their superposition.

… But mark my words. This book will have come to shape (or at least to influence) every good exposition of (i.e. introduction to) the area of the Foundations of QM, in the years to come. [I say that, because I honestly don’t expect a better book on this topic to arrive on the scene all that soon.]


Which brings us to someone who wouldn’t assign the |4\rangle + |5\rangle stars to this book. Namely, Lubos Motl.

If Norsen has moved in the Objectivist circles, and is partial to the B&B company, Motl has worked in the string theory, and is not just partial to it but even today defends it very vigorously—and oddly enough, also looks at that “supersymmetric world from a conservative viewpoint.” More relevant to us: Motl is not partial to the Copenhagen interpretation; he is all the way into it. … Anyway, being merely partial is something you wouldn’t expect from Motl, would you?

But, of course, Motl also has a very strong grasp of QM, and he displays it well (even powerfully) when he writes a post of the title:

“Postulates of quantum mechanics almost directly follow from experiments.” [^]

Err… Why “almost,” Lubos? 🙂

… Anyway, go through Motl’s post, even if you don’t like the author’s style or some of his expressions. It has a lot of educational material packed in it. Chances are, going through Motl’s posts (like the present one) will come to improve your understanding—even if you don’t share his position.

As to me: No, speaking from the new understanding which I have come to develop regarding the foundations of QM [^] and [^], I don’t think that all of Motl’s objections would carry. Even then, just for the sake of witnessing the tight weaving-in of the arguments, do go through Motl’s post.


Finally, a post at the SciAm blog:

“Coming to grips with the implications of quantum mechanics,” by Bernardo Kastrup, Henry P. Stapp, and Menas C. Kafatos, [^].

The authors say:

“… Taken together, these experiments [which validate the maths of QM] indicate that the everyday world we perceive does not exist until observed, which in turn suggests—as we shall argue in this essay—a primary role for mind in nature.”

No, it didn’t give me shivers or something. Hey, this is QM and its foundations, right? I am quite used to reading such declarations.

Except that, as I noted a few years ago on Scott Aaronson’s blog [I need to dig up and insert the link here], and then, recently, also at

Roger Schlafly’s blog [^],

you don’t need QM in order to commit the error of inserting consciousness into a physical theory. You can accomplish exactly the same thing also by using just the Newtonian particle mechanics in your philosophical arguments. Really.


Yes, I need to take that reply (at Schlafly’s blog), edit it a bit and post it as a separate entry at this blog. … Some other time.

For now, I have to run. I have to continue working on my approach so that I am able to answer the questions raised and discussed by people such as those mentioned in the links. But before that, let me jot down a general update.


A general update:

Oh, BTW, I have taken my previous QM-related post off the top spot.

That doesn’t mean anything. In particular, it doesn’t mean that after reading into materials such as that mentioned here, I have found some error in my approach or something like that. No. Not at all.

All it means is that I made it once again an ordinary post, not a sticky post. I am thinking of altering the layout of this blog, by creating a page that highlights that post, as well as some other posts.

But coming back to my approach: As a matter of fact, I have also written emails to a couple of physicists, one from IIT Bombay, and another from IISER Pune. However, things have not worked out yet—things like arranging for an informal seminar to be delivered by me to their students, or collaborating on some QM-related simulations together. (I could do the simulations on my own, but for the seminar, I would need an audience! One of them did reply, but we still have to shake our hands in the second round.)

In the meanwhile, I go jobless, but I keep myself busy. I am preparing a shortish set of write-ups / notes which could be used as a background material when (at some vague time in future) I go and talk to some students, say at IIT Bombay/IISER Pune. It won’t be comprehensive. It will be a little more than just a white-paper, but you couldn’t possibly call it even just the preliminary notes for my new approach. Such preliminary notes would come out only after I deliver a seminar or two, to physics professors + students.

At the time of delivering my proposed seminar, links like those I have given above, esp. Travis Norsen’s book, also should prove a lot useful.

But no, I haven’t seen something like my approach being covered anywhere, so far, not even Norsen’s book. There was a vague mention of just a preliminary part of it somewhere on Roger Schlafly’s blog several years ago, only once or so, but I can definitely say that I had already had grasped even that point on my own before Schlafly’s post came. And, as far as I know, Schlafly hasn’t come to pursue that thread at all, any time later…

But speaking overall, at least as of today, I think I am the only one who has pursued this (my) line of thought to the extent I have [^].

So, there. Bye for now.


I Song I Like:
(Hindi) “suno gajar kya gaaye…”
Singer: Geeta Dutt
Music: S. D. Burman
Lyrics: Sahir Ludhianvi
[There are two Geeta’s here, and both are very fascinating: Geeta Dutt in the audio, and Geeta Bali in the video. Go watch it; even the video is recommended.]


As usual, some editing after even posting, would be inevitable.

Some updates made and some streamlining done on 30 July 2018, 09:10 hrs IST.

 

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Absolutely Random Notings on QM—Part 1: Bohr. And, a bad philosophy making its way into physics with his work, and his academic influence

TL;DR: Go—and keep—away.


I am still firming up my opinions. However, there is never a harm in launching yet another series of posts on a personal blog, is there? So here we go…


Quantum Mechanics began with Planck. But there was no theory of quanta in what Planck had offered.

What Planck had done was to postulate only the existence of the quanta of the energy, in the cavity radiation.

Einstein used this idea to predict the heat capacities of solids—a remarkable work, one that remains underappreciated in both text-books as well as popular science books on QM.

The first pretense at a quantum theory proper came from Bohr.


Bohr was thinking not about the cavity radiations, but about the spectra of the radiations emitted or absorbed by gases.

Matter, esp. gases, following Dalton, …, Einstein, and Perin, were made of distinct atoms. The properties of gases—especially the reason why they emitted or absorbed radiation only at certain distinct frequencies, but not at any other frequencies (including those continuous patches of frequencies in between the experimentally evident sharp peaks)—had to be explained in reference to what the atoms themselves were like. There was no other way out—not yet, not given the sound epistemology in physics of those days.

Thinking up a new universe still was not allowed back then in science let alone in physics. One still had to clearly think about explaining what was given in observations, what was in evidence. Effects still had be related back to causes; outward actions still had to be related back to the character/nature of the entities that thus acted.

The actor, unquestionably by now, was the atom. The effects were the discrete spectra. Not much else was known.

Those were the days were when the best hotels and restaurants in Berlin, London, and New York would have horse-driven buggies ushering in the socially important guests. Buggies still was the latest technology back then. Not many people thus ushered in are remembered today. But Bohr is.


If the atom was the actor, and the effects under study were the discrete spectra, then what was needed to be said, in theory, was something regarding the structure of the atom.

If an imagined entity sheer by its material/chemical type doesn’t do it, then it’s the structure—its shape and size—which must do it.

Back then, this still was regarded as one of the cardinal principles of science, unlike the mindless opposition to the science of Homeopathy today, esp. in the UK. But back then, it was known that one important reason that Calvin gets harassed by the school bully was that not just the sheer size of the latter’s matter but also that the structure of the latter was different. In other words: If you consumed alcohol, you simply didn’t take in so many atoms of carbon as in proportion to so many atoms of hydrogen, etc. You took in a structure, a configuration with which these atoms came in.


However, the trouble back then was, none had have the means to see the atoms.

If by structure you mean the geometrical shape and size, or some patterns of density, then clearly, there was no experimental observations pertaining to the same. The only relevant observation available to people back then was what had already been encapsulated in Rutherford’s model, viz., the incontestable idea that the atomic nucleus had to be massive and dense, occupying a very small space as compared to an atom taken as a whole; the electrons had to carry very little mass in comparison. (The contrast of Rutherford’s model of c. 1911 was to the earlier plum cake model by Thomson.)

Bohr would, therefore, have to start with Rutherford’s model of atoms, and invent some new ideas concerning it, and see if his model was consistent with the known results given by spectroscopic observations.

What Bohr offered was a model for the electrons contained in a nuclear atom.


However, even while differing from the Rutherford’s plum-cake model, Bohr’s model emphatically lacked a theory for the nature of the electrons themselves. This part has been kept underappreciated by the textbook authors and science teachers.

In particular, Bohr’s theory had absolutely no clue as to the process according to which the electrons could, and must, jump in between their stable orbits.


The meat of the matter was worse, far worse: Bohr had explicitly prohibited from pursuing any mechanism or explanation concerning the quantum jumps—an idea which he was the first to propose. [I don’t know of any one else originally but independently proposing the same idea.]

Bohr achieved this objective not through any deployment of the best possible levels of scientific reason but out of his philosophic convictions—the convictions of the more irrational kind. The quantum jumps were obviously not observable, according to him, only their effects were. So, strictly speaking, the quantum jumps couldn’t possibly be a part of his theory—plain and simple!

But then, Bohr in his philosophic enthusiasm didn’t stop just there. He went even further—much further. He fully deployed the powers of his explicit reasoning as well as the weight of his seniority in prohibiting the young physicists from even thinking of—let alone ideating or offering—any mechanism for such quantum jumps.

In other words, Bohr took special efforts to keep the young quantum enthusiasts absolutely and in principle clueless, as far as his quantum jumps were concerned.


Bohr’s theory, in a sense, was in line with the strictest demands of the philosophy of empiricism. Here is how Bohr’s application of this philosophy went:

  1. This electron—it can be measured!—at this energy level, now!
  2. [May be] The same electron, but this energy level, now!
  3. This energy difference, this frequency. Measured! [Thank you experimental spectroscopists; hats off to you, for, you leave Bohr alone!!]
  4. OK. Now, put the above three into a cohesive “theory.” And, BTW, don’t you ever even try to think about anything else!!

Continuing just a bit on the same lines, Bohr sure would have said (quoting Peikoff’s explanation of the philosophy of empiricism):

  1. [Looking at a tomato] We can only say this much in theory: “This, now, tomato!”
  2. Making a leeway for the most ambitious ones of the ilk: “This *red* tomato!!”

Going by his explicit philosophic convictions, it must have been a height of “speculation” for Bohr to mumble something—anything—about a thing like “orbit.” After all, even by just mentioning a word like “orbit,” Bohr was being absolutely philosophically inconsistent here. Dear reader, observe that the orbit itself never at all was an observable!

Bohr must have in his conscience convulsed at this fact; his own philosophy couldn’t possibly have, strictly speaking, permitted him to accommodate into his theory a non-measurable feature of a non-measurable entity—such as his orbits of his electrons. Only the allure of outwardly producing predictions that matched with the experiment might have quietened his conscience—and that too, temporarily. At least until he got a new stone-building housing an Institute for himself and/or a Physics Nobel, that is.

Possible. With Herr Herr Herr Doktor Doktor Doktor Professor Professors, anything is possible.


It is often remarked that the one curious feature of the Bohr theory was the fact that the stability of the electronic orbits was postulated in it, not explained.

That is, not explained in reference to any known physical principle. The analogy to the solar system indeed was just that: an analogy. It was not a reference to an established physical principle.

However, the basically marvelous feature of the Bohr theory was not that the orbits were stable (in violation of the known laws of electrodynamics). It was: there at all were any orbits in it, even if no experiment had ever given any evidence for the continuously or discontinuously subsequent positions electrons within an atom or of their motions.

So much for originator of the cult of sticking only to the “observables.”


What Sommerfeld did was to add footnotes to Bohr’s work.

Sommerfeld did this work admirably well.

However, what this instance in the history of physics clearly demonstrates is yet another principle from the epistemology of physics: how a man of otherwise enormous mathematical abilities and training (and an academically influential position, I might add), but having evidently no remarkable capacity for a very novel, breakthrough kind of conceptual thinking, just cannot but fall short of making any lasting contributions to physics.

“Math” by itself simply isn’t enough for physics.

What came to be known as the old quantum theory, thus, faced an impasse.

Under Bohr’s (and philosophers’) loving tutorship, the situation continued for a long time—for more than a decade!


A Song I Like:

(Marathi) “sakhi ga murali mohan mohi manaa…”
Music: Hridaynath Mangeshkar
Singer: Asha Bhosale
Lyrics: P. Savalaram


PS: Only typos and animals of the similar ilk remain to be corrected.

 

“Philosophical Orientation”

An update on 27 April 2018 06:30 HRS IST, noted at the end:


Here is a beginning of a passage, a section, from a book on QM (now-a-days available through the Dover). The section was the very first one from the very first chapter, and was aptly called “Philosophical Orientation.” It began thus:

\dots For what purpose, dear reader, do you study physics?

To use it technologically? Physics can be put to use; so can art and music. But that’s not why you study them.

It isn’t their social relevance that attracts you. The most precious things in life are the irrelevant ones. It is a meager life, indeed, that is consumed only by the relevant, by the problems of mere survival.

You study physics because you find it fascinating. You find poetry in conceptual structures. You find it romantic to understand the working of nature. You study physics to acquire an intimacy with nature’s way.

Our entire understanding of nature’s way is founded on the subject called quantum mechanics. No fact of nature has ever been discovered that contradicts quantum mechanics. \dots


A good passage to read, that one was. \dots. It was (I guess originally) published as late as in 1987. \dots


An update on 27 April 2018 06:30 HRS IST:

Initially, when I put this post online, I had thought that, sure, people would be able to copy-paste the quote, and thereby get to the book. But looks like they won’t. Hence this update.

The book in question is this:

Chester, Marvin (1987) “Primer of Quantum Mechanics,” Wiley; reproduced as a Dover ed. (2003) from the corrected Krieger ed. (1992).

If you ask for my opinion about the book: It’s a (really) good one, but despite being “philosophical,” like all texts on QM, it still tends to miss the forest for the trees. And it doesn’t even mention entanglement (not in the index, anyway). Entanglement began to appear in the text-books only after the mid-90’s, I gather. Also another thing: It’s not a primer. It’s a summary, meant for the graduate student. But it’s written in a pretty neat way. If you have already had a course on QM, then you should go through it. Several issues (say those related to measurement, and the QM machinery) are explained very neatly here.


A Song I Like:

[Yet another song I liked as a school-boy child; one of those which I still do. \dots Not too sure about the order of the credits though \dots]

(Hindi) “meraa to jo bhi kadam hai…”
Music: Laxmikant-Pyarelal
Singer: Mohammad Rafi
Lyrics: Majrooh Sultanpuri

 

Yes I know it!

Note: A long update was posted on 12th December 2017, 11:35 IST.


This post is spurred by my browsing of certain twitter feeds of certain pop-sci. writers.

The URL being highlighted—and it would be, say, “negligible,” but for the reputation of the Web domain name on which it appears—is this: [^].


I want to remind you that I know the answers to all the essential quantum mysteries.

Not only that, I also want to remind you that I can discuss about them, in person.

It’s just that my circumstances—past, and present (though I don’t know about future)—which compel me to say, definitely, that I am not available for writing it down for you (i.e. for the layman) whether here or elsewhere, as of now. Neither am I available for discussions on Skype, or via video conferencing, or with whatever “remoting” mode you have in mind. Uh… Yes… WhatsApp? Include it, too. Or something—anything—like that. Whether such requests come from some millionaire Indian in USA (and there are tons of them out there), or otherwise. Nope. A flat no is the answer for all such requests. They are out of question, bounds… At least for now.

… Things may change in future, but at least for the time being, the discussions would have to be with those who already have studied (the non-relativistic) quantum physics as it is taught in universities, up to graduate (PhD) level.

And, you have to have discussions in person. That’s the firm condition being set (for the gain of their knowledge 🙂 ).


Just wanted to remind you, that’s all!


Update on 12th December 2017, 11:35 AM IST:

I have moved the update to a new post.

 


A Song I Like:

(Western, Instrumental) “Berlin Melody”
Credits: Billy Vaughn

[The same 45 RPM thingie [as in here [^], and here [^]] . … I was always unsure whether I liked this one better or the “Come September” one. … Guess, after the n-th thought, that it was this one. There is an odd-even thing about it. For odd ‘n” I think this one is better. For even ‘n’, I think the “Come September” is better.

… And then, there also are a few more musical goodies which came my way during that vacation, and I will make sure that they find their way to you too….

Actually, it’s not the simple odd-even thing. The maths here is more complicated than just the binary logic. It’s an n-ary logic. And, I am “equally” divided among them all. (4+ decades later, I still remain divided.)… (But perhaps the “best” of them was a Marathi one, though it clearly showed a best sort of a learning coming from also the Western music. I will share it the next time.)]


[As usual, may be, another revision [?]… Is it due? Yes, one was due. Have edited streamlined the main post, and then, also added a long update on 12th December 2017, as noted above.]

 

 

Blog-Filling—Part 3

Note: A long Update was added on 23 November 2017, at the end of the post.


Today I got just a little bit of respite from what has been a very tight schedule, which has been running into my weekends, too.

But at least for today, I do have a bit of a respite. So, I could at least think of posting something.

But for precisely the same reason, I don’t have any blogging material ready in the mind. So, I will just note something interesting that passed by me recently:

  1. Catastrophe Theory: Check out Prof. Zhigang Suo’s recent blog post at iMechanica on catastrophe theory, here [^]; it’s marked by Suo’s trademark simplicity. He also helpfully provides a copy of Zeeman’s 1976 SciAm article, too. Regular readers of this blog will know that I am a big fan of the catastrophe theory; see, for instance, my last post mentioning the topic, here [^].
  2. Computational Science and Engineering, and Python: If you are into computational science and engineering (which is The Proper And The Only Proper long-form of “CSE”), and wish to have fun with Python, then check out Prof. Hans Petter Langtangen’s excellent books, all under Open Source. Especially recommended is his “Finite Difference Computing with PDEs—A Modern Software Approach” [^]. What impressed me immediately was the way the author begins this book with the wave equation, and not with the diffusion or potential equation as is the routine practice in the FDM (or CSE) books. He also provides the detailed mathematical reason for his unusual choice of ordering the material, but apart from his reason(s), let me add in a comment here: wave \Rightarrow diffusion \Rightarrow potential (Poisson-Laplace) precisely was the historical order in which the maths of PDEs (by which I mean both the formulations of the equations and the techniques for their solutions) got developed—even though the modern trend is to reverse this order in the name of “simplicity.” The book comes with Python scripts; you don’t have to copy-paste code from the PDF (and then keep correcting the errors of characters or indentations). And, the book covers nonlinearity too.
  3. Good Notes/Teachings/Explanations of UG Quantum Physics: I ran across Dan Schroeder’s “Entanglement isn’t just for spin.” Very true. And it needed to be said [^]. BTW, if you want a more gentle introduction to the UG-level QM than is presented in Allan Adam (et al)’s MIT OCW 8.04–8.06 [^], then make sure to check out Schroeder’s course at Weber [^] too. … Personally, though, I keep on fantasizing about going through all the videos of Adam’s course and taking out notes and posting them at my Web site. [… sigh]
  4. The Supposed Spirituality of the “Quantum Information” Stored in the “Protein-Based Micro-Tubules”: OTOH, if you are more into philosophy of quantum mechanics, then do check out Roger Schlafly’s latest post, not to mention my comment on it, here [^].

The point no. 4. above was added in lieu of the usual “A Song I Like” section. The reason is, though I could squeeze in the time to write this post, I still remain far too rushed to think of a song—and to think/check if I have already run it here or not. But I will try add one later on, either to this post, or, if there is a big delay, then as the next “blog filler” post, the next time round.

[Update on 23 Nov. 2017 09:25 AM IST: Added the Song I Like section; see below]

OK, that’s it! … Will catch you at some indefinite time in future here, bye for now and take care…


A Song I Like:

(Western, Instrumental) “Theme from ‘Come September'”
Credits: Bobby Darin (?) [+ Billy Vaughn (?)]

[I grew up in what were absolutely rural areas in Maharashtra, India. All my initial years till my 9th standard were limited, at its upper end in the continuum of urbanity, to Shirpur, which still is only a taluka place. And, back then, it was a decidedly far more of a backward + adivasi region. The population of the main town itself hadn’t reached more than 15,000 or so by the time I left it in my X standard; the town didn’t have a single traffic light; most of the houses including the one we lived in) were load-bearing structures, not RCC; all the roads in the town were of single lanes; etc.

Even that being the case, I happened to listen to this song—a Western song—right when I was in Shirpur, in my 2nd/3rd standard. I first heard the song at my Mama’s place (an engineer, he was back then posted in the “big city” of the nearby Jalgaon, a district place).

As to this song, as soon as I listened to it, I was “into it.” I remained so for all the days of that vacation at Mama’s place. Yes, it was a 45 RPM record, and the permission to put the record on the player and even to play it, entirely on my own, was hard won after a determined and tedious effort to show all the elders that I was able to put the pin on to the record very carefully. And, every one in the house was an elder to me: my siblings, cousins, uncle, his wife, not to mention my parents (who were the last ones to be satisfied). But once the recognition arrived, I used it to the hilt; I must have ended up playing this record for at least 5 times for every remaining day of the vacation back then.

As far as I am concerned, I am entirely positive that appreciation for a certain style or kind of music isn’t determined by your environment or the specific culture in which you grow up.

As far as songs like these are concerned, today I am able to discern that what I had immediately though indirectly grasped, even as a 6–7 year old child, was what I today would describe as a certain kind of an “epistemological cleanliness.” There was a clear adherence to certain definitive, delimited kind of specifics, whether in terms of tones or rhythm. Now, it sure did help that this tune was happy. But frankly, I am certain, I would’ve liked a “clean” song like this one—one with very definite “separations”/”delineations” in its phrases, in its parts—even if the song itself weren’t to be so directly evocative of such frankly happy a mood. Indian music, in contrast, tends to keep “continuity” for its own sake, even when it’s not called for, and the certain downside of that style is that it leads to a badly mixed up “curry” of indefinitely stretched out weilings, even noise, very proudly passing as “music”. (In evidence: pick up any traditional “royal palace”/”kothaa” music.) … Yes, of course, there is a symmetrical downside to the specific “separated” style carried by the Western music too; the specific style of noise it can easily slip into is a disjointed kind of a noise. (In evidence, I offer 90% of Western classical music, and 99.99% of Western popular “music”. As to which 90%, well, we have to meet in person, and listen to select pieces of music on the fly.)

Anyway, coming back to the present song, today I searched for the original soundtrack of “Come September”, and got, say, this one [^]. However, I am not too sure that the version I heard back then was this one. Chances are much brighter that the version I first listened to was Billy Vaughn’s, as in here [^].

… A wonderful tune, and, as an added bonus, it never does fail to take me back to my “salad days.” …

… Oh yes, as another fond memory: that vacation also was the very first time that I came to wear a T-shirt; my Mama had gifted it to me in that vacation. The actual choice to buy a T-shirt rather than a shirt (+shorts, of course) was that of my cousin sister (who unfortunately is no more). But I distinctly remember she being surprised to learn that I was in no mood to have a T-shirt when I didn’t know what the word meant… I also distinctly remember her assuring me using sweet tones that a T-shirt would look good on me! … You see, in rural India, at least back then, T-shirts weren’t heard of; for years later on, may be until I went to Nasik in my 10th standard, it would be the only T-shirt I had ever worn. … But, anyway, as far as T-shirts go… well, as you know, I was into software engineering, and so….

Bye [really] for now and take care…]

 

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

Yes, we continue to remain very busy.


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

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

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

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

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

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

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


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

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

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

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

Until this morning.

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

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


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


A Song I Like:

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


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

 

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.]

 

Causality. And a bit miscellaneous.

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Best,

–Ajit


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

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


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

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


A Song I Like:

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

 

Relating the One with the Many

0. Review and Context: This post is the last one in this mini-series on the subject of the one vs. many (as understood in the context of physics). The earlier posts in this series have been, in the chronological and logical order, these:

  1. Introducing a very foundational issue of physics (and of maths) [^]
  2. The One vs. the Many [^]
  3. Some of the implications of the “Many Objects” idea… [^]
  4. Some of the implications of the “One Object” idea… [^]

In the second post in this series, we had seen how a single object can be split up into many objects (or the many objects seen as parts of a single object). Now, in this post, we note some more observations about relating the One with the Many.

The description below begins with a discussion of how the One Object may be separated into Many Objects. However, note that the maths involved here is perfectly symmetrical, and therefore, the ensuing discussion for the separation of the one object into many objects also just as well applies for putting many objects together into one object, i.e., integration.


In the second and third posts, we handled the perceived multiplicity of objects via a spatial separation according to the varying measures of the same property. A few remarks on the process of separation (or, symmetrically, on the process of integration) are now in order.

1. The extents of spatial separation depends on what property you choose on the basis of which to effect the separation:

To begin with, note that the exact extents of any spatial separations would vary depending on what property you choose for measuring them.

To take a very “layman-like” example, suppose you take a cotton-seed, i.e. the one with a soft ball of fine cotton fibres emanating from a hard center, as shown here [^]. Suppose if you use the property of reflectivity (or, the ability to be seen in a bright light against a darker background), then for the cotton-seed, the width of the overall seed might come out to be, say, 5 cm. That is to say, the spatial extent ascribable to this object would be 5 cm. However, if you choose some other physical property, then the same object may end up registering quite a different size. For instance, if you use the property: “ability to be lifted using prongs” as the true measure for the width for the seed, then its size may very well come out as just about 1–2 cm, because the soft ball of the fibres would have got crushed to a smaller volume in the act of lifting.

In short: Different properties can easily imply different extensions for the same distinguished (or separated)“object,” i.e., for the same distinguished part of the physical universe.

2. The One Object may be separated into Many Objects on a basis other than that of the spatial separation:

Spatial attributes are fundamental, but they don’t always provide the best principle to organize a theory of physics.

The separation of the single universe-object into many of its parts need not proceed on the basis of only the “physical” space.

It would be possible to separate the universe on the basis of certain basis-functions which are defined over every spatial part of the universe. For instance, the Fourier analysis gives rise to a separation of a property-function into many complex-valued frequencies (viz. pairs of spatial undulations).

If the separation is done on the basis of such abstract functions, and not on the basis of the spatial extents, then the problem of the empty regions vaporizes away immediately. There always is some or the other “frequency”, with some or the other amplitude and phase, present at literally every point in the physical universe—including in the regions of the so-called “empty” space.

However, do note that the Fourier separation is a mathematical principle. Its correspondence to the physical universe must pass through the usual, required, epistemological hoops. … Here is one instance:

Question: If infinity cannot metaphysically exist (simply because it is a mathematical concept and no mathematical concept physically exists), then how is it that an infinite series may potentially be required for splitting up the given function (viz. the one which specifies the variations the given property of the physical universe)?

Answer: An infinite Fourier series cannot indeed be used by way of a direct physical description; however, a truncated (finite) Fourier series may be.

Here, we are basically relying on the same trick as we saw earlier in this mini-series of posts: We can claim that what the truncated Fourier series represents is the actual reality, and that that function which requires an infinite series is merely a depiction, an idealization, an abstraction.

3. When to use which description—the One Object or the Many Objects:

Despite the enormous advantages of the second approach (of the One Object idea) in the fundamental theoretical physics, in classical physics as well as in our “day-to-day” life, we often speak of the physical reality using the cruder first approach (the one involving the Many Objects idea). This we do—and it’s perfectly OK to do so—mainly because of the involved context.

The Many Objects description of physics is closer to the perceptual level. Hence, its more direct, even simpler, in a way. Now, note a very important consideration:

The precision to used in a description (or a theory) is determined by its purpose.

The purpose for a description may be lofty, such as achieving fullest possible consistency of conceptual interrelations. Or it may be mundane, referring to what needs to be understood in order to get the practical things done in the day-to-day life. The range of integrations to be performed for the day-to-day usage is limited, very limited in fact. A cruder description could do for this purpose. The Many Objects idea is conceptually more economical to use here. [As a polemical remark on the side, observe that while Ayn Rand highlighted the value of purpose, neither Occam nor the later philosophers/physicists following him ever even thought of that idea: purpose.]

However, as the scope of the physical knowledge increases, the requirements of the long-range consistency mandate that it is the second approach (the one involving the One Object idea) which we must adopt as being a better representative of the actual reality, as being more fundamental.

Where does the switch-over occur?

I think that it occurs at a level of those physics problems in which the energetics program (initiated by Leibnitz), i.e., the Lagrangian approach, makes it easier to solve them, compared to the earlier, Newtonian approach. This answer basically says that any time you use the ideas such as fields, and energy, you must make the switch-over, because in the very act of using such ideas, implicitly, you are using the One Object idea anyway. Which means, EM theory, and yes, also thermodynamics.

And of course, by the time you begin tackling QM, the second approach becomes simply indispensable.

A personal side remark: I should have known better. I should have adopted the second approach earlier in my life. It would have spared me a lot of agonizing over the riddles of quantum physics, a lot of running in loops over the same territory (like a dog chasing his own tail). … But it’s OK. I am glad that at least by now, I know better. (And, engineers anyway don’t get taught the Lagrangian mechanics to the extent physicists do.)

A few days ago, Roger Schlafly had written a nice and brief post at his blog saying that there is a place for non-locality in physics. He had touched on that issue more from a common-sense and “practical” viewpoint of covering these two physics approaches [^].

Now, given the above write-up, you know that a stronger statement, in fact, can be made:

As soon as you enter the realm of the EM fields and the further development, the non-local (or the global or the One Object) theories are the only way to go.


A Song I Like:

[When I was a school-boy, I used to very much like this song. I would hum [no, can’t call it singing] with my friends. I don’t know why. OK. At least, don’t ask me why. Not any more, anyway 😉 .]

(Hindi) “thokar main hai meri saaraa zamaanaa”
Singer: Kishore Kumar
Music: R. D. Burman
Lyrics: Rajinder Krishan


OK. I am glad I have brought to a completion a series of posts that I initiated. Happened for the first time!

I have not been able to find time to actually write anything on my promised position paper on QM. … Have been thinking about how to present certain ideas better, but not making much progress… If you must ask: these involve entangled vs. product states—and why both must be possible, etc.

So, I don’t think I am going to be able to hold the mid-2017 deadline that I myself had set for me. It will take longer.

For the same reasons, may be I will be blogging less… Or, who knows, may be I will write very short general notings here and there…

Bye for now and take care…

 

Some of the implications of the “One Object” idea…

0. Review and Context: This post continues with the subject of one vs. many physical objects. The earlier posts in this series have been, in the chronological and logical order, these:

  1. Introducing a very foundational issue of physics (and of maths) [^]
  2. The One vs. the Many [^]
  3. Some of the implications of the “Many Objects” idea… [^]

In this post, we cover the implications of the second description, i.e., of the “one object” idea.


1. The observed multiplicity of objects as corresponding to certain quantitative differences in the attributes possessed by the universe-object:

In the second description, there exists one and only one object, which is the entire universe itself. This singleton object carries a myriad of attributes—literally each and everything that you ever see/touch/etc. around you (including your physical body) exists as “just” an attribute of this singleton object. In the general case, such attributes exist with quantitatively different degrees in different parts of the singleton universe-object. Those contiguous regions of the singleton object where the quantitative degrees of the given attribute fall sufficiently closer in range are treated by our perceptual faculty as separate objects.

In the general philosophy, there is a certain observation: Everything is interconnected. However, following the second description, not only are all objects interconnected, but at a deeper level, they are literally one and the same object! It’s just that each perceptually separate object has been distinguished on the basis of some quantitative measures (or amounts) of some or the other attribute or property with which that distinguished region exists.

A few consequences are noteworthy.

2. Implications for what precisely the law of causality refers to:

In the second description, what physically exists is the single physical object (that is the physical universe) and nothing else but that physical object.

The physical actor, in the primary sense of the term, therefore always is the entire universe itself, acting as a whole. The “appearance” of multiple objects—and their separate actions—is only a consequence of the universe having varying properties in different parts of or logically within itself.

Just the way the attributes carried by the universe are inhomogeneous (i.e., they differ in quantitative measures over different parts), so are the actions. The quantitative measures of actions too are inhomogeneous. In the general case, for any of the actions taken by the universe, the same action in general occurs to different degrees in different parts.

In the deepest and the most fundamental sense, since there is only one physical actor viz. the entire physical universe, what the law of causality refers to it is nothing but this physical actor, i.e., to the entire universe taken as a whole.

However, since the very nature of the singleton object includes the fact that different parts of itself exist with different attributes of differing degrees and therefore can and do act differently, the law of causality can also be seen to apply, in a secondary or derivative sense, to these distinguishable parts taken in isolation. The differing natures of the inhomogeneous parts together constitute all the causes existing in the physical universe, and the nature of the actions that this singleton object takes, to differing measures in different parts of itself, constitute all the effects.

The fact that the universe-object exists with various physical attributes or properties, leads to different concepts with which the universe-object can be studied.

3. The idea of space as derived from the physical universe:

One most prominent, general and fundamental property which may be used for distinguishing different parts of the universe-object is the fact that the distinguishable parts, taken by themselves, are spatially extended, and the related fact that they carry the attribute of being located where they are.

Locations and extensions are given in the sensory perceptual evidence. Thus, extensions and locations are directly perceived. They in part form the perceptual basis for the concept of space.

Space is an abstract, mathematical concept. Using this higher level concept, we are able to ascribe places even to those combinations of spatial relations where there is no concrete object existing.

4. A (mathematical) space as an abstraction based on certain attributes of the (physical) universe:

The above discussion makes it clear that the universe does not exist in space. On the other hand, space may be said to exist “in” the universe. However, here, here, the word “in” is to be taken in an abstract logical sense, not in the sense of a concrete existence. Space does exist in the universe but not concretely.

Space is an abstraction based on certain fundamental, directly perceived, spatial attributes or properties possessed by the singular universe-object. The two most fundamental of such (spatial) attributes are extensions and locations; other spatial attributes such as connectivity/topology, of being enclosed or covered or placed inside/outside, etc. are merely higher-level ideas that isolate different ways in which groups of objects with various extensions and locations exist. The extensions and locations themselves pertain to certain quantitative but directly perceived differences over different parts of the universe-object. Thus, ultimately, all spatial properties are possessed by the perceptually distinguishable parts of the singleton universe-object.

Since the concept of space is mathematical and abstract, many different ideas or imaginations may be used in formulating the concept of a space. For instance, Euclidean vs. hyperbolic space, or continuous vs. discrete space, etc. Not only that, multiple instances of a given space also are easily possible. In contrast, the idea of instances, of quantities, does not apply to the universe-object; it remains the unique, singular, concept, one which, when taken as a whole, must remain beyond any quantitative characterization.

Since there is nothing but the universe object to exist physically, the only spatially relevant statement we can make about the universe itself is this: if some part of the universe does indeed exist, then this part can be put in a quantitative relation with one of the instances of some or the other space.

The italicized part is based on the assumption that every part of the universe does carry spatial attributes. This itself is just an assumption; there is no way to directly validate it.

Note that the aforementioned statement does not imply that the physical universe can be said as being present everywhere. The universe does not exist everywhere.

To say that the physical universe is present everywhere is an epistemologically misconceived formulation. It is indicative of an intellectually sloppy, inconsistent way of connecting the two ideas: (i) physical universe (which is what actually exists, in the physical sense), and (ii) space (which is a mathematical and abstract concept).

“Everywhere” refers to a set of all possible places implied by a certain concept of space. Physical universe, on the other hand, refers what actually exists. It is possible that the procedure of constructing a concept of space includes places that have no correspondence to any part of the physical universe.

5. A space can be finite or infinite, but the physical universe is neither:

Space, being a mathematical concept, can be imagined as infinitely extended. However, the physical universe cannot be. And the reason that an infinitely extended physical universe is a nonsense idea is not because the physical universe is, or even can be known to be, finite.

The fact of the matter is, no quantitative statement can at all be made in respect of the physical universe taken as a whole.

Quantitative statements can only be made if some suitable mathematical procedure is available for making the requisite measurements. Now, any and all mathematical procedures are constructed only in reference to some or the other parts of the universe, not in reference to the entirety of the universe taken as a whole. The very nature of mathematics is like that. The epistemological procedures of differentiation and integration must first be performed before any mathematical procedure can at all be constructed or applied. (For instance, before inventing or applying even the simplest mathematical procedure of counting, you must have first performed integration of a group of similar concrete objects such as identical balls, and differentiated this group from the background of the rest of the she-bang.) But as soon as you say: “differentiate,” you already concede the idea that the entirety of the universe is not being considered in the further thought. To differentiate is to agree to selectively pick up only a part and thereby to agree to leave some other part(s). So, as soon as you perform differentiation, from that point on, you no longer are referring to all the parts at the same time. That’s why, no concrete mathematical procedure can at all be constructed which possibly can allow you to measure the universe as a whole. The very idea itself does not make sense. There can be a measure for this part of the universe or for that part. But there can be no measure for the universe taken as a whole. That’s why, its meaningless to talk of applying any quantitative attributes to the entirety of the physical universe taken as a whole—including the talk of the universe being even finite in extent.

No procedure can be said to have yielded even a finite amount as a measurement outcome, if the thing asserted as measured is taken to be the universe as a whole. As a result, no statement regarding even finitude can be made for the physical universe. (I here differ from the Objectivist position, e.g., Dr. Peikoff’s writings in OPAR; they believe that the universe is finite.)

It is true that every property shown by every actually observed part of the physical universe is finite. The inference from this statement to the conclusion that every part of the not-actually-observed but in-principle possibly existing part itself must also be finite, also is valid—within its context. However, the validity of this inference cannot be extended to the idea of a mathematical procedure that applies to all the parts of the universe at the same time. The objection is: we cannot speak of “all” parts itself unless we specify a procedure to include and exhaust every existing part—but no such procedure can ever be specified because differentiation and integration are at the base of the very conceptual level (i.e. at the base of every mathematical procedure).

The idea of an infinite physical universe [^] is flawed at a deep level. Infinity is a mathematical concept. Physical universe is what exists. The two cannot be related—there can be no mathematical procedure to relate the two.

Similarly, the idea of a finite physical universe also is flawed at a deep level.

Now, the idea that every part of the physical universe is finite, can be taken to be valid, simply because the procedure of measuring parts can at all be conducted, and such a procedure does in principle yield outcomes that are finite.

To speak of an infinite space, in contrast, also is OK. The idea here is to make a mental note to the effect that any  statements being made for some parts (possibly infinite number of parts) of this space need not have any correspondence with the spatial attributes of the actually existing physical universe-object—that the logical mapping from a part of a space to a physically existing spatial attribute would necessarily break down for every infinite part of an infinite space.

As far as physics is concerned, infinity is only a useful device for simplifying—reifying out—the complications due to certain possible variations in the boundary conditions of physics problems. When the domain is finite, changes in boundary conditions make the problem so complex that is is impossible to yield a law in the form of a differential equation. The idea of an infinite domain allows us to do precisely that. I had covered this aspect in an earlier post, here [^].

6. Implications for the gaps between perceived objects, and the issue of whether empty space plays a causal role or not:

There is no such a thing as a really “empty” part in the physical universe; the idea is a contradiction in terms.

In contrast, on the basis of our above discussion, notice that there can be empty regions of space(s), in fact even infinitely large empty regions of space(s) where literally nothing may be said to exist.

However, the ideas of emptiness or filled-ness can refer only to space, not to the physical universe.

Since there is no empty part in the universe, the issue of what causal role such an empty part can or does play, does not arise. As to the empty regions of space, since there can be no mapping from such regions to the physical universe, once again, the issue of its causal role does not arise. An empty space (or an empty part of a space) does not physically exist, period. Hence, it has no causal role to play, period.

However, if by empty space you mean such things as the region between two grey “objects” (i.e. two grey parts of the physical universe), then: that region is not, really speaking, empty; a part of what actually is the physical universe does exist there; otherwise, during their motions, the grey parts could not have come to occupy this supposedly empty regions of the space. In other words, if literally nothing were to exist in the gap between two objects, then the attribute of grayness could never possibly travel over there. But no such restriction on the movement of distinguishable objects has ever been observed, reported, or rationally conceived of, directly or indirectly. Hence, in conclusion, the gap region is not really speaking empty.

7.  The issue of the local vs. the “non-local” actions:

In the second description, since only one causal agent exists, what-ever physical action happens, it is taken by this one and the only physical universe. As a particular implication of that fact, where-ever any physical action happens, it again is to be attributed to the same physical universe.

In taking a physical action, it is easily conceivable that wherever the physical universe is actually extended, it simultaneously takes action at all those locations—and therefore, in all those abstract places which correspond to these locations.

As a consequence, it is possible that the physical universe simultaneously takes the same action, but to differing degrees, in different places. Since the actor is a singleton, since it anyway is present wherever any action occurs at all, any and all mystification arising from ascribing a cause and its effect to two separate entities simply vaporizes away. So does any and all mystification arising from ascribing a cause and its effect to two spatially separated locations. The locations may be different, but the actor remains the same.

For the above reasons, in the second description, instantaneous action-at-a-distance no longer remains a spooky idea. The reason is: there indeed is no instantaneous action at a distance, really speaking. IAD is only a loose way of saying that there is simultaneous action of, by, in, etc., the same causal (and effectual) actor that is the singleton object of the physical universe.

In fact we can go ahead and even say that in the second description, every action always is necessarily a global action (albeit with zero magnitudes in some parts of the universe); that there is no such a thing as an in-principle local action.

However, the aforementioned statement does not mean that spatially separated causes and effects cannot be observed. All that it means is that such multiple-objects-like phenomena are not primary; they are only higher-level, abstract, consequences of the more fundamental processes that are necessarily global in nature.


In the second post of this series [^], we saw how the grey regions of our illustrative example can be distinguished from each other (and from the background object) by using some critical density value as the criterion of their distinction or separation.

Since the second description involves only a single object, it necessarily requires a procedure for separating this singleton universe-object into multiple objects. There are certain interesting ideas concerning such a separation, and we will have a closer look at this very idea of separation, in the next post.


Of all the posts in this series, it is this post where I remain the most unsatisfied as far as my expression is concerned. I think a lot of simplification is called for. But in the choice between a better but very late expression and a timely but poor, awkward, expression, I have chosen the latter.

May be I will come back later and try to improve the flow and the expression of this post.

Next time,  I will also try to write something on how the two objections to the aether idea (mentioned in the last post) can be overcome.


A Song I Like:

(Marathi) “maajhee na mee raahile”
Music: Bal Parte
Singer: Lata Mangeshkar
Lyrics: Shanta Shelke


[A very minor revision done on 4th May 2017, 15:19 IST. May be, I will effect some more revisions later on.]