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.

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.

QM: A couple of defensible statements. Also, a bit on their implications for the QC.

A Special Note (added on 17th June 2018): This post is now a sticky post; it will remain, for some time, at the top of this blog.

I am likely to keep this particular post at the top of this blog, as a sticky post, for some time in the future (may be for a few months or so). So, even if posts at this blog normally appear in the reverse chronological order, any newer entries that I may post after this one would be found below this one.

[In particular, right now, I am going through a biography: “Schrodinger: Life and Thought” by Walter Moore [^]. I had bought this book way back in 2011, but had to keep it aside back then, and then, somehow, I came to forget all about it. The book surfaced during a recent move we made, and thus, I began reading it just this week. I may write a post or two about it in the near future (say within a couple of weeks or so) if something strikes me while I am at it.]

A Yawningly Long Preamble:

[Feel free to skip to the sections starting with the “Statement 1” below.]

As you know, I’ve been thinking about foundations of QM for a long, long time, a time running into decades by now.

I thought a lot about it, and then published a couple of papers during my PhD, using a new approach which I had developed. This approach was used for resolving the wave-particle duality, but only in the context of photons. However, I then got stuck when it came to extending and applying this same approach to electrons. So, I kept on browsing a lot of QM-related literature in general. Then, I ran, notably, into the Nobel laureate W. E. Lamb’s “anti-photon” paper [^], and also the related literature (use Google Scholar). I thought a lot about this paper—and also about QM. I began thinking about QM once again from the scratch, so to speak.

Eventually, I came to abandon my own PhD-time approach. At the same time, with some vague but new ideas already somewhere at the back of my mind, I once again started studying QM, once again with a fresh mind, but this time around much more systematically. …

… In the process, I came to develop a completely new understanding of QM!… It’s been at least months since I began talking about it [^]. … My confidence in this new understanding has only increased, since then.

Today’s post will be based on this new understanding. (I could call it a new theory, perhaps.)

My findings suggest a few conclusions which I think I should not hold back any longer. Hence this post.

I have been trying to locate the right words for formulating my conclusions—but without much satisfaction. Finally, I’ve decided to go ahead and post an entry here anyway, regardless of whether the output comes out as being well formulated or not.

In other words, don’t try to pin me down with the specific words I use here in this post! Instead, try to understand what I am trying to get at. In still other words: the particular words I use may change, but the intended meaning will, from now on, “always” remain the same—ummm…. more or less the same!

OK, so here are the statements I am making today. I think they are well defensible:

Notation:
QM: Quantum Mechanics, quantum mechanically, etc.
CM: Classical Mechanics
QC: Quantum Computer
QS: Quantum Supremacy ([^] and [^])

Statement 1: It is possible to explain all quantum mechanical phenomena on the basis of those principles which are already known (or have already been developed) in the context of classical mechanics.

Informal Explanation 1.1: Statement 1 holds true. It’s just that when it comes to explaining the QM phenomena (i.e., when it comes to supplying a physical mechanism for QM), even if the principles do remain the same, the way they are to be combined and applied is different. These differences basically arise because of a reason mentioned in the next Informal Explanation.

Informal Explanation 1.2: Yes, the tradition of 80+ years, involving an illustrious string of Nobel laureates and others, is, in a way, “wrong.” The QM principles are not, fundamentally speaking, very different from those encountered in the CM. It’s just that some of the objects that QM assumes and talks about are different (only partly different) from those assumed in the CM.

Corollary 1 of Statement 1: A quantum computer could “in principle” be built as an “application layer” on top of the “OS platform” supplied by the classical mechanics.

Informal Explanation 1.C1.1: Hierarchically speaking, QM remains the most fundamental or the “ground” layer. The aspects of the physical reality that CM refers to, therefore, indeed are at a layer lying on top of QM. This part does continue to remain the same.

However, what the Corollary 1 now says is that you can also completely explain the workings of QM in terms of a virtual QM machine that is built on top of the well-known principles of CM.

If someone builds a QC on such a basis (which would be a virtual QC on top of CM), then it would be just a classical mechanically functioning simulator—an analog simulator, I should add—that simulates the QM phenomena.

Informal Explanation 1.C1.2: The phrase “in principle” does not always translate into “easily.” In this case, it in factt is very easily possible that building a big enough a QC of this kind (i.e. the simulating QC) may very well turn out to be an enterprise that is too difficult to be practically feasible.

Corollary 2 of Statement 1: A classical system can be designed in such a way that it shows all the features of the phenomenon of quantum entanglement (when the classical system is seen from an appropriately high-level viewpoint).

Informal Explanation 1.C2.1: There is nothing “inherently quantum-mechanical” about entanglement. The well-known principles of CM are enough to explain the phenomena of entanglement.

Informal Explanation 1.C2.2: We use our own terms. In particular, when we say “classical mechanics,” we do not mean these words in the same sense in which a casual reader of the QM literature, e.g. of Bell’s writings, may read them.

What we mean by “classical mechanics” is the same as what an engineer who has never studied QM proper means, when he says “classical mechanics” (i.e., the Newtonian mechanics + the Lagrangian and Hamiltonian reformulations including variational principles, as well as the more modern developments such as studies of nonlinear systems and the catastrophe theory).

Statement 2: It can be shown that even if the Corollary 1 above does hold true, the kind of quantum computer it refers to would be such that it will not be able to break a sufficiently high-end RSA encryption (such as what is used in practice today, at the high-end).

Aside 2.1: I wouldn’t have announced Statement 1 unless I was sure—absolutely goddamn sure, in fact—about the Statement 2. In fact, I must have waited for at least half a year just to make sure about this aspect, looking at these things from this PoV, then from that PoV, etc.

Statement 3: Inasmuch as the RSA-beating QC requires a controlled entanglement over thousands of qubits, it can be said, on the basis of the new understanding (the one which lies behind the Statement 1 above), that the goal of achieving even “just” the quantum supremacy seems highly improbable, at least in any foreseeable future, let alone achieving the goal of breaking the high-end RSA encryption currently in use. However, proving these points, esp. that the currently employed higher-end RSA cannot be broken, will require further development of the new theory, particularly a quantitative theory for the mechanism(s) involved in the quantum mechanical measurements.

Informal Explanation 3.1: A lot of funding has already gone into attempts to build a QC. Now, it seems that the US government, too, is considering throwing some funds at it.

The two obvious goal-posts for a proper QC are: (i) first gaining enough computational power to run past the capabilities of the classical digital computers, i.e., achieving the so-called “quantum supremacy,” and then, (ii) breaking the RSA encryption as is currently used in the real-world at the high-end.

The question of whether the QC-related researches will be able to achieve these two goals or not depends on the question of whether there are natural reasons/causes which might make it highly improbable (if not outright impossible) to achieve these two goals.

We have already mentioned that it can be shown that it will not be possible for a classical (analog) quantum simulator (of the kind we have in mind) to break the RSA encryption.

• Combination 1: CM-based QC Simulator that is able to break the RSA encryption.

We have said that it can be shown (i.e. proved) that the above combination would be impossible to have. (The combination is that extreme.)

However, it still leaves open 3 more combinations of a QC and a goal-post:

• Combination 2: CM-based QC Simulator that exceeds the classical digital computer
• Combination 3: Proper QC (working directly off the QM platform) that exceeds the classical digital computer
• Combination 4: Proper QC (working directly off the QM platform) that is able to break the RSA encryption.

As of today, a conclusive statement cannot be made regarding the last three combinations, not even on the basis of my newest approach to the quantum phenomena, because the mathematical aspects which will help settle questions of this kind, have not yet been developed (by me).

Chances are good that such a theory could be developed, at least in somewhat partly-qualitative-and-partly-quantitative terms, or in terms of some quantitative models that are based on some good analogies, sometime in the future (say within a decade or so). It is only when such developments do occur that we will be able to conclusively state something one way or the other in respect of the last three combinations.

However, relying on my own judgment, I think that I can safely state this much right away: The remaining three combinations would be tough, very tough, to achieve. The last combination, in particular, is best left aside, because the combination is far too complex that it can pose any real threat, at least as of today. I can say this much confidently—based on my new approach. (If you have some other basis to feel confident one way or the other, kindly supply the physical mechanism for the same, please, not just “math.”)

So, as of today, the completely defensible statements are the Statement No. 1 and 2 (with all their corollaries), but not the Statement 3. However, a probabilistic judgment for the Statement 3 has also been given.

A short (say, abstract-like) version:

A physical mechanism to explain QM phenomena has been developed, at least in the bare essential terms. It may perhaps become possible to use such a knowledge to build an analog simulator of a quantum computer. Such a simulator would be a machine based only on the well-known principles of classical mechanics, and using the kind of physical objects that the classical mechanics studies.

However, it can also be easily shown that such a simulator will not be able to break the RSA encryption using algorithm such as Shor’s. The proof rests on an idealized abstraction of classical objects (just the way the ideal fluid is an abstraction of real fluids).

On the basis of the new understanding, it becomes clear that trying to break RSA encryption using a QC proper (i.e. a computer that’s not just a simulator, but is a QC proper that directly operates at the level of the QM platform itself) would be a goal that is next to impossible to achieve. In fact, even achieving just the “quantum supremacy” (i.e., beating the best classical digital computer) itself can be anticipated, on the basis of the new understanding, as a goal that would be very tough to achieve, if at all.

Researches that attempt to build a proper QC may be able to bring about some developments in various related areas such as condensed matter physics, cryogenics, electronics, etc. But it is very highly unlikely that they would succeed in achieving the goal of quantum supremacy itself, let alone the goal of breaking the RSA encryption as it is deployed at the high-end today.

A Song I Like:

(Hindi) “dilbar jaani, chali hawaa mastaanee…”
Music: Laxmikant Pyarelal
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Anand Bakshi

PS: Note that, as is usual at this blog, an iterative improvement of the draft is always a possibility. Done.

Revision History:

1. First posted on 2018.06.15, about 12:35 hrs IST.
2. Considerably revised the contents on 2018.06.15, 18:41 hrs IST.
3. Edited to make the contents better on 2018.06.16, 15:30 hrs IST. Now, am mostly done with this post except, may be, for a minor typo or so, here or there.
4. Edited (notably, changed the order of the Combinations) on 2018.06.17, 23:50 hrs IST. Also corrected some typos and streamlined the content. Now, I am going to leave this post in the shape it is. If you find some inconsistency or so, simple! Just write a comment or shoot me an email.
5. 2018.06.27 02:07 hrs IST. Changed the song section.

“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
Lyrics: Majrooh Sultanpuri

“The spiritual heritage of India”

I wrote a few comments at Prof. Scott Aaronson’s blog, in response to his post of the title: “30 of my favorite books”, here [^].

Let me give you the links to my comments: [^], [^], [^] and [^].

Let me reproduce the last one of my four comments, with just so slight bit of editing. [You know I couldn’t have resisted the opportunity, right?]:

Since I mentioned the “upnishad”s above (i.e. here [ ^]), and as far as this topic is concerned, since the ‘net is so full of the reading material on this topic which isn’t so suitable for this audience, let me leave you with a right kind of a reco.

If it has to be just one short book, then the one which I would pick up is this:

Swami Prabhavananda (with assistance of Frederick Manchester), “The Spiritual Heritage of India,” Doubleday, New York, 1963.

A few notes:

1. The usual qualifications apply. For instance, I of course don’t agree with everything that has been said in the book. And, more. I may not even agree that a summary of something provided here is, in fact, a good summary thereof.

2. I read it very late in life, when I was already past my 50. Wish I had laid my hands on it, say, in my late 20s, early 30s, or so. I simply didn’t happen to know about it, or run into a copy, back then.

3. Just one more thing: a tip on how to read the above book:

First, read the Preface. Go through it real fast. (Reading it faster than you read the newspapers would be perfectly OK—by me).

Then, if you are an American who has at least a smattering of a knowledge about Buddhism, then jump directly on to the chapter on Jainism. (Don’t worry, they both advocate not eating meat!) And, vice-versa!!

If you are not an American, or,  if you have never come across any deeper treatment on any Indian tradition before, then: still jump on to the chapter on Jainism. (It really is a very good summary of this tradition, IMHO.)

Then, browse through some more material.

Then, take a moment and think: if you have appreciated what you’ve just read, think of continuing with the rest of the text.

Else, simple: just call it a book! (It’s very inexpensive.)

No need to add anything, but looking at the tone of the comments (referring to the string “Ayn Rand”) that got generated on this above-mentioned thread, I find myself thinking that, may be, given my visitor-ship pattern (there are more Americans hits today to my blog than either Indian or British), I should explain a bit of a word-play which I attempted in that comment (and evidently, very poorly—i.e. non-noticeably). It comes near the end of my above-quoted reply.

“Let’s call it a day” is a very neat British expression. In case you don’t know its meaning, please look it up on the ‘net. Here’s my take on it (without looking it up):

Softly folding away a day, with a shade of an anticipation that a day even better might be about to arrive tomorrow, and so, softly reminding yourself that you better leave the party or the function for now, so as to be able to get ready for yet another party, yet another function, some other day, later…

A sense of something like that, is implied by that expression.

I just attempted a word-play, and so, substituted “book” for the “day”.

Anyway, good night. Do read my last post, the document attached to it, and the links therefrom.

Bye for now.

Oh, yes! There is a song that’s been playing off-and-on at the back of my mind for some time. Let me share it with you.

A Song I Like:

(Hindi) “dil kaa diyaa jala ke gayaa…”
Lyrics: Majrooh Sultaanpuri
Singer: Lata Mangeshkar
Music: Chitragupt

[PS: The order of the listing of the credits, once again, is completely immaterial here.]

Anyway, enjoy the song, and the book mentioned in the quotes (and hopefully, also my past few posts and their attachments)… I should come back soon, with a maths-related puzzle/teaser/question. … Until then, take care and bye!

/