A series of posts on a few series of tweets (by me) on (my research on foundations of) QM—2

OK, after a long hiatus (mainly due to viral fever and cough etc.), I am back into the game. This post of course continues from the previous one in this series, i.e., the very last one.


On 18 July 2019 I then posted the next two tweets, now about my new approach (as in the Outline document [^]):

3/4. My new approach is something like: Quanta as Discrete Sets for the States of Fields & Changes in Them. (Hard to form a neat short-form.) I’ve abandoned the idea of the spatially delimited quantum particles—whether photons (Einstein), or others too (Feynman).

4/4. Instead, I have singular potential (V) fields for protons and electrons. These fields are continuous at all points other than their instantaneous positions where they are singular. I also have the ever continuous \Psi as a physically existing attribute / characteristic of the background object. This is quite like how stress / strain are attributes of a continuum.

Advertisements

A series of posts on a few series of tweets (by me) on (my research on foundations of) QM—1

0. Initial remarks:

OK. It’s been a little while since I wrote my last post here.

Actually, it so happened that for a while after my last post I didn’t find anything well suited for writing a blog-post. I was also busy studying topics from Data Science. It’s true that during this time I did make a few comments at others’ blogs, but these were pretty context-specific. I couldn’t easily think of making a (more general-purpose) post out of them.

At the same time, some of the things that I read on QM—whether in pop-sci books or at others’ blogs—did prompt me to note a few comments. These were very brief points. They were better fitting only as tweets—as side-remarks made in the passing. So, I tweeted them. My twitter page is here [^].

… I now realize that quite a few of such tweets (on QM) have got accumulated. So it’s high time that these occasional notings got moved here too, together with some explanation to go with them. That’s precisely what I am going to do now, in this series of posts.

Most of these points (from the tweets) refer to my Outline document on QM which was posted at iMechanica about 6 months ago [^]. The tweets wouldn’t make any sense to someone if he hasn’t thoroughly gone through this document first. So, I do assume this context here.

In fact, most of these tweets are rather direct implications of what I had already noted in the Outline document. These points (from the tweets) were quite clear to me even back then, when I wrote the document.

However, while writing that document, my purpose was, first and foremost, to state the most salient building blocks and points of the theory and to focus on the overall way in which they connect together. Thus, what I wanted to give, via that document, was a definitive sense of the overall framework—hopefully in a logically complete manner. I was in fact worried a bit that some parts of these complex considerations might get slipped out of my mind once again as they had done in the past (before I wrote that document!) [In retrospect, I think that on this count, I did a pretty good job in the Outline document. I haven’t been able to think of a really essential part of the framework which I had in mind and which inadvertently got left out from it.]

Another reason I didn’t go into detailed implications right in that document was this: I also thought that anyone who knows the mainstream QM well, and also “gets” the logic given in my document well, would be able to very easily reach these further inferences completely on his own—for instance, my position on the wave-particle duality. So, I didn’t separately mention such points in that document even if I knew that points like these would be of  much greater interest to the layman. The Outline, although very simple it looks, was definitely not written for the layman. (I tried to keep it as simple in exposition as possible, in part because I didn’t care to be seen as a respectable physicist anyway. All that I was concerned about was QM, and the new conceptual framework.)

So, all in all, it’s not an accident that I should be touching on many points like the wave-particle duality only later on, first via tweets! These really are only implications / consequences.

Anyway, here in this series we now go with these tweets of mine (made over the past month). While reproducing them here, I have expanded the short-forms or abbreviations, and also have added few additional bits of content too, just to get more streamlined sentences. Each tweet is then followed by some explanation, which very rapidly became very long—long enough that I couldn’t possibly compress all the QM-related material (tweets and my explanations of them) into a single post. So, I have no choice but to make a series of them!


1. Schemes for nonlinear QM proposed by others:

I tweeted on 12 July 2019 to this effect:

“Schrödinger eqn. revisited” by Schleich et al.  [(.PDF) ^] . Yes, it presents a nonlinearity. But no, it doesn’t even consider the physical fact that all the potentials in reality come about only from superpositions of the singular potentials of individual electrons and protons. See my Outline document.”

Indeed, what I said here applies to each and every nonlinearity-based argument (except for mine!) which has ever been offered by way of attempting a resolution to the riddles of QM—in particular, the measurement problem.

To quote from Ian Stewart’s book: “Does God Play Dice? (2/e)”, several people have proposed nonlinear theories, including:

“L. Diosi, N. Gisin, G. C. Ghirardi, R. Grassi, P. Pearle, A. Rimini, and I. Percival.”

I had very briefly gone through some of these proposals. Actually, I had mostly got to know about their proposals by reading descriptions and remarks on them as made by other commentators. However, at times, I also went rapidly browsing through some of their arXiv papers. I had come to the conclusion that what they were putting forth wasn’t anything like my ideas (later mentioned in the Outline document). To quote Stewart here,

“In all of these theories the interaction of a quantum system with its environment produces an irreversible change that turns the quantum state into an eigenstate. However, all of these theories are probabilistic: the initial quantum state undergoes a kind of random diffusion which ultimately leads to an eigenstate.” (ibid.)

To be honest, I am not sure whether all these proposals could be characterized as involving random diffusion or not. I don’t know these theories to the required level of detail to be able to confirm or deny Stewart’s characterization. However, there certainly is this element of an initial quantum state getting collapsed precisely to the measured eigenstate, which appears in all of them—and I don’t accept that idea in the first place (as explicitly put forth in my Outline document).

In a slightly different context, Stewart also notes:

“There is some interest among physicists in what they call `quantum chaos’, but quantum chaos is about the relation between non-chaotic quantum systems and chaotic classical approximations—not chaos as a mechanism for quantum indeterminacy.” (ibid.)

OK, this is one conclusion which I very distinctly remember I had reached on my own too. I guess this was in November 2018, when I had googled on “quantum chaos.” Subsequently, I re-checked the matter again (just to be sure) in February ’19 (i.e., just days after posting my Outline document.)

I agree that Stewart’s characterization is right on the target here. IMHO, you don’t need to take recourse to the prior studies of “quantam chaos” very seriously if either the QM foundations or the very feasibility of the quantum computer are your concerns.


2. A bit on my PhD-time research:

I made a series of 4 tweets on 18 July 2019. The first two of these dealt with my old, PhD time approach to photon propagation. Let me note here a clarification regarding what all other work I had performed during my PhD, before coming to my old (PhD-time) approach to QM (which I will address in the next section).

The first thing to note is that my work on QM had formed only a part (may be about 1/4th part or so) of whatever studies and research I had done during my PhD.

The other parts of my PhD thesis were notably related to the studies of the classical second-order partial-differential equations, and their computational modeling using stochastic processes. The equations on which I thus focused my attention were: the Helmholtz equation, the diffusion equation, and the Poisson-Laplace equation. In addition, I had also picked up a study of elasticity, and had added a conjecture about the possible applicability of some random-walks type of processes for modeling the classical tensor fields (of stresses and strains as used in engineering). Let me go over all these topics in brief.

2.1 Work on the diffusion equation:

I think I have posted many entries at this blog about my work on diffusion equation. So let me not regress into it all once again. Let me just note that I basically showed that, contrary to what post-graduate texts in maths (published by AMS) say, the diffusion equation does not necessarily imply an instantaneous action at a distance (IAD).

The IAD in diffusion, I pointed out, was an outcome of the features of the solution theory (Fourier’s theory, and also of Einstein’s analysis of the Brownian movement). But IAD was not necessarily implied either by the local physics of diffusion phenomena, or by the partial differential equation that is the diffusion equation. [Here, remember, a differential equation always, invariably, necessarily, etc., is local in nature—it refers to an infinitesimal CV (control volume) or CM (control mass).]

In particular, I pointed out that the compactness of the support of the solution was the crucial issue here—whether the support was infinite (as in Fourier theory and in 2nd half of Einstein’s c. 1905 paper), or finite (as in any subdomain-based numerical method, or in the Brownian movement, i.e., the first half of the same paper by Einstein). In my view of the things, you can always transition from a collection of finite subdomains to an infinity of infinitesimal CVs that are still distributed over only a finite interval, via a suitable limiting process. The finite support, of course, could grow in extent with time.

These observations had never been made in about 200 years of the existence of Fourier’s theory. (Go ahead, hunt for the precedents!) You have to make this distinction between a (local) PDE and its (possibly global) solutions obtained after conducting integration operations, and in this entire process, you have to be careful about not elevating a mere ansatz or an integration method to the high pedestal of “the” (provably unique) solution. That’s in effect what I had argued.

2.2 Work on the diffraction phenomenon (Huygens-Fresnel theory):

I also had a neat (though smallish) result concerning the obliquity factor in diffraction. I went through Huygens’, Fresnel’s and Kirchhoff’s analyses of the diffraction phenomenon (involving the Helmholtz equation—i.e., the spatial part of the wave PDE), and then pointed out the reasons why the obliquity factor could not be regarded an essential characteristic of the diffraction phenomenon itself.

Once again, the obliquity factor turned out to be a feature of how the analysis—specifically, the integration operations—had been set up. It was a feature of the mathematical solution procedure adopted for this problem. In diffraction, there was no fundamental physical process which operated in an anisotropic way, compelling the wavefield to have a greater amplitude in the forward direction and zero in the backward direction.

However, explanations for some 187 years (since Fresnel’s work) had characterized diffraction as an inherently anisotropic phenomenon. Yes, right up to my old copy of Resnick & Halliday. There was a surprise in it for me because while Fresnel was just a railroad engineer who had taught himself maths, Kirchhoff surely was a master of PDEs and their integration techniques. But this fact still had escaped even Kirchhoff.

I pointed out how even if you do keep isotropy to the Huygens’ wavelets, given the geometry of the interaction of Huygens’ wavelets and the surfaces where BCs are applied, you would still end up with the same amplitudes as those obtained by Fresnel’s or Kirchhoff’s analyses.

Come to think of it, you could even pick up this line of argument and apply it to any analysis that seeks to derive an expression for a field inside a finite domain by appeal to a pair of forward- and backward-going processes occurring within that domain; e.g., an analysis involving the advanced and retarded waves, or the transactional waves in certain interpretations of QM, etc. You just have to be careful about what BCs and integrals are being set up and how the integration processes are being conducted, that’s all!

2.3 Computational modeling of transient heat conduction:

I then tried to apply the random walks-based approach (RW) to model transients in the heat conduction, as they occur in a moving boundary problem, viz. the melting snowman. Since my focus was on conduction, I grossly simplified all the other aspects of this problem. (Having just come out of an illness, I would get easily tired back then.) The problem I considered was that of melting of a snowman.

Consider a snowman in the form of a vertical right-circular cylinder which is placed on a relatively large block of ice below. The snowman absorbs heat from the atmosphere by radiation and convection at its external surfaces. The absorbed thermal energy then flows through the volume of the cylinder to the relatively large block of ice underneath (which was regarded as infinitely large in the simulations). The temperature gradients of course come to exist. The heat in the atmosphere brings the external surface to the melting point of ice even as the interior portions remain below it. So, the surface melts—phase-transition ensures a constancy of temperature at the surface. The melting is more pronounced at the sharp corners. The resulting water gradually slips down, forming a thin and continuous layer on the external surface. (I ignored the fluid flow in my simulation.) All in all, the sharp cylindrical snowman slowly acquires a thumb-like shape over a period of time, and then still continues to shrink down in size.

I first tried to apply RW for heat conduction in this scenario, but soon found that there was a great deal of noise due to randomness. So, I set up a “conversion” from the particles-based approach of RWs to a local, continuum-based approach, thus ending up with a description which was essentially equivalent to a cellular automata-based one. I then performed the simulations with this CA-based approach (in 3D), compared the changing external contours of the melting snowman with an actual experiment (done at home, for less than Rs. 200/- as the total cost—for thermocouple wires, basically), and presented a paper at an international conference.

This piece of work added the necessary component of “engineering” and “experimentation” to my thesis. While my guide was always happy with my progress, he also was a bit worried that examiners might look at my thesis and conclude that it was all a useless piece of theoretical, almost scientific work—it had little “practical” component to it, and so, couldn’t qualify for a degree in engineering. So, he was quite relieved when I discussed this idea of snowman with him—he immediately gave me a go ahead!

2.4 Conjecture for using RWs for modeling tensor fields:

Then, in addition, I also had this conjecture regarding the feasibility of random walks for simulating tensor fields. Since I haven’t spoken at length about it here at this blog, let me note something here.

There were certain rigorous mathematical arguments (coming from Ivy League professors of mechanics as well as from seemingly competent but obscure Russian authors) which had purportedly shown that stochastic processes like random walks could provably not be used for simulating the stress/strain fields.

Yet, I was confident of my conjecture, out of some basic considerations which I had in mind. So I gave a conference presentation on it (in an international conference on mathematics), and also included it in my thesis.

Much later on (after my PhD defence), I grew further confident that this conjecture should definitely come to hold; that it could be proved. That is to say, the earlier (intricate) proofs by reputed mechanicians / mathematicians could be shown to have holes in them. (Not that my argument was flawless either. A professor had spotted a weak link in my argument at that conference, and had brought it to my attention in a most gentle, indirect manner.)

Then, some time still later on, I ran into some “simple” but directly useful work by a young Chinese author (perhaps a PhD student). If I remember it right, he had published this paper while working in China itself. His work was similar to an intermediate step I had in mind, but it was much more complete, even neat. No, he was not concerned with the random walks as such. All that he did was to give a working model for constructing stress/strain fields, by starting with a finite 3D unit cell having an internal structure of a truss and treating it as if it were a finite approximation for an infinitesimal CV of the continuum. I had somewhat similar ideas, and had in fact inserted a couple of screen-shots of the truss-based simulations I had conducted for a preliminary study. But he had gone much further. If I recall his paper right, he had even arrived at the right values for the truss-related parameters (like stiffnesses of the members) if this unit cell was to converge to the continuum equations of elasticity in the limit of vanishing size.

Now, by regarding the process of re-distribution of forces along the truss members as an abstract flow, and by randomizing it (discretizing it in the process), it should be easily possible to come to a proof of my conjecture. Also a neat computational simulation. Of course, the issue is not as simple as it looks on the surface. Free surfaces in a multiply-connected domain pose a tricky issue—they deform freely, and so, uniqueness becomes tricky to handle. Even then, with sufficient care (or appeal to ideas from CoV) I am sure that it can be done.

OK. I will do it some other time in future! (This has been a TBD paper on my list for almost a decade or so by now; I simply don’t run into suitable ME/MTech students for me to guide on this topic! … Anyway, this blog is in copyright, just in case you didn’t notice it…)


3. My PhD-time work on QM (photon propagation):

Alright, finally we come to my PhD-time work on photons propagation. In a series of tweets, I said (on 18 July 2019):

“1/4. My old (PhD-time) approach, then called “new approach” and also as FAQ (Fields As Quanta): I’ve abandoned it; the one in the Outline document replaces it completely. FAQ anyway dealt with only the propagation of only the photons, not their generation or absorption (i.e. it didn’t deal with the creation/annihilation operators). FAQ didn’t deal with the propagation of other particles, viz., electrons, protons, or neutrons either.”

and

“2/4. FAQ still remains valid as an abstract description, as referring to the propagation characteristics of photons in the limit that the medium is continuous (i.e., it is homogenized from discrete and dispersed atomic nuclei), i.e., if the propagation dynamics is diffusive, not ballistic.”

About this second tweet, I subsequently had second thoughts soon after, and so I noted, right on the next day (on 19 July 2019) the following comment (a reply) to it:

“Umm… I am not sure precisely what all considerations should enter into taking the limits (for arriving at the propagation characteristics of photons as conceptualized in my older, PhD-time, approach). Would have to work through how the Schrodinger formalism (and hence my new approach) goes from \Psi and photons to the classical, dynamical EM fields. To be done in future. But yes, FAQ dynamics *was* diffusive, that’s for certain.”

Thus, I first said that FAQ still remains valid, when seen as an abstract description. However, just one day later, I also pointed out the more basic and possibly tricky issues there might be—viz., finding the right kind of limiting processes which start from the Schrodinger formalism and end up at Maxwell’s equations.

I feel confident that people must have thrashed out this topic (TDSE \Rightarrow EM) long time ago. It’s just that I myself have never studied the topic so far (in fact I haven’t even done the literature search on it), and so, I don’t have a good idea about what all technical issues might get involved in it.

Thus, I will have to first study this topic (from the mainstream QM to EM). Only then would I be able to understand the mapping well enough that I could understand the Hertzian waves right in the QM settings. It’s only after this stage that I will be I be able to say something definitively about the manner in which FAQ can really hold, and if yes, how well. Worrying about the right kind of a limiting procedure would be just a part of it, but an important one. … So yes, you can take these particular tweets with a pinch of salt.


4. How did I get to my old PhD-time approach for photons (i.e. FAQ), in the first place?

OK. Now that we are at it, here is a question that might have arisen in your mind: If I didn’t know QM well back then (during my PhD-studies days), then how could I dare propose this approach (viz. FAQ) so confidently?

Ummm… Let’s leave the daring and the confidence parts aside for now. Let’s focus on the “how” of it—how I got to my ideas. This part is much more interesting. At least to me.

How precisely did I end up at the idea of FAQ?

Well, I began with a kind of a “correspondence principle” (not in the Copenhagen sense of the term; read on). Briefly, the “correspondence” which I had in mind was the fact that single photons one-at-a-time mark only isolated dots on the CCD surface, but in the large-flux situations, their density pattern converges to the continuum interference pattern as described by Young.

So, I imagined a point-source emitting photons. Mind you, photons for me were, back then, spatially discrete particles of light, a la Einstein and Feynman—both their ideas had held a tremendous sway over my thinking back then.

I then imagined an ideal absorber in the form of a spherical surface kept at some distance from the source, somewhat like your usual Gaussian surface from electrostatics, but the difference here was that while the Gaussian surface is imaginary and allows anything to move through it freely, here, it was an actual absorber, albeit imaginary. This spherical surface was centered on the same point source. I asked myself what kind of variations in density should light show, in the continuum description, on this concentric spherical surface if its radius was varied a bit. In essence, I was developing my logic by starting from Gauss’ theorem and the Poisson-Laplace equation.

I then transitioned, in my ideas, to the Helmholtz equation by imagining a time-steady waviness to the field. Now, if the radius of the sphere were constrained to be an integral multiple of the spatial period (i.e. wavelength) of light, then the total quantity of photons being absorbed at the spherical surface should remain the same for a sphere of any such a radius. The only rationale which could justify this assumption was: to have a conservation principle in place, by asserting that photons are conserved while they still are in transit through the empty space (i.e. before they get absorbed on the spherical surface). Again, remember, I was using the idea of photons as if they were spatially discrete particles, like the grains of mustard seed.

Conservation principles are neat, I had learnt mostly in reference to the ample evidence I found in engineering sciences. (Even if I were to know about Noether’s theorem, I would have disregarded it—such was, and still is, my temperament. I think that this theorem is merely a reformulation of a very narrow range of physics—one that is restricted to merely 2nd-order linear PDEs. Anyway, read on…)

If the photon number conservation was to be had in theory (during propagation) at integral multiples of \lambda for the radius of the sphere, then was there any sound reason to give up conservation when the radius was (n+1/2)\lambda? (Here I am assuming that at zero radius, the light has the maximum amplitude.) Couldn’t we explain the complete darkness at these odd radii by positing that the photon was still there—it’s just that the sphere of that particular radius didn’t absorb it? After all, we could always posit a variable called the absorption fraction which would be related to the local amplitude of the spatial wave, right? That’s how I decided to conserve the photon number, and thereby, shift the burden of the variable levels of brightness at the absorber by appeal to a photon-absorption process that varied in efficiency precisely in response to the local wave amplitude associated with the tiny grain which was photon. (I regarded this grain as a localized condition in the luminiferous aether.)

Now, the next question was: If the photons had a ballistic dynamics (i.e. a straight-line motion), then the point on the spherical surface where a given photon eventually would land, would have already been determined right at the source point—some internal processes in the emitter material would be responsible for ejecting it at random orientations, which would also determine its landing location. (Dear Bohmians, do you see something familiar? However, please note, this was entirely my own thinking. I had not come across Bohm back then. Please read on.)

I thought that while this was possible, it was also possible that the photons could also undergo random-walks. How did I introduce random walks?

Well, the direct experimental evidence showed that this propagation problem had two essential features: (i) many discrete spots which go in a limit to a continuous pattern of finite densities, and (ii) random locations on the absorber surface where the grainy photons land, i.e., no correlation between the two points where any two successive photons get absorbed.

Since the continuum viewpoint of light (Young’s waves) had to be reached in the limit, it was important to keep in mind always. It was here that I happened to recall Huygens’ principle. I was also quite at home with the idea of randomly intersecting a 3D surface with a linear probe—I had already studied stereology at the University of Alabama at Birmingham (UAB).

Huygens’ principle involved every point of space as if it were some kind of a “source” for the new (Huygens’) wavelets. The Young pattern could be obtained by superposing all the Huygens’ wavelets. The discrete spots could be had by dividing the surface of the Huygens wavelets and taking the individual surface patches to vanishing size (a la mesh refinement). This satisfactorily addressed the first essential feature noted above (viz. discrete spots). As to the second feature (randomness) it could also be satisfied by randomizing the selection of the spherical patch on the Huygens’ wavelet (a la stereology).

This much part, I in fact had already completed when I was right at UAB, completely on my own, though I had never shared this idea with anyone. I guess it was already over before 1992 came to an end.

More than a decade later, now in Pune: Starting with Gauss’ theorem, and touching on the Huygens process and stereology, and now, also throwing in the vector addition rules for ensuring that right phases appear throughout the propagation, and so, local amplitudes also come out right in the large-flux situation, I could get to my diffusive dynamics for the spatially discrete photons.

I did suspect that this procedure (of randomizing the selection of a point on any of Huygens’ wavelets) meant that the photons would have to be imagined either as (i) getting scattered everywhere during their propagation, or (ii) possibly getting annihilated after travelling even just an infinitesimal distance in empty space, and then, somehow, also getting re-created  (the time lag between the annihilation and the subsequent creation being zero), effectively satisfying the conservation principle. On either count, the photon would keep changing its directions randomly, because the point on the surface of the Huygens wavelet was randomized.

Of course, I could not figure out a good physical reason for such a process.

Scattering of one photon by other photons seemed implausible—though I couldn’t figure out any particular reason why it would be implausible. Anyway reliance on scattering led to an impossible situation when there was only one photon inside the interference chamber.

There also was no proper physicist who would even so much as be willing to just listen to me. (I tried more than 15–20.) On the other hand, so many leading ones among them were offering descriptions of QM in terms of a random “quantum foam/froth” which produces and annihilates any particles anywhere anytime—even massive ones and even in empty space at any random time. So, I thought that my idea of continuous disappearance and appearance but in a different direction, would not be found too odd.

(Discussions of foundations of QM has improved by leaps and bounds since engineers started taking interest in building QC. In fact, recently, a somewhat similar remark also came from Dr. Sabine Hossenfelder on her blog. But I am talking of those days—around 2005 times.)

Of course, since I myself didn’t have even an iota of a physical understanding regarding such virtual annihilation/creation pairs for photons, but since they were necessary in my scheme because I had randomized not the source point but the Huygens surface, rather than going full wacko (as most any physicist in my situation would), I did what any graduate student of engineering would do: I simply refrained from mentioning any such implications for a possible physics of it, and instead chose to phrase my description of the process in terms which heavily relied on the well-established, well-reputed, classical principle of Huygens’.

No one ever asked any questions on this part either. Neither in conference, nor in PhD defence, nor even after sharing my papers with physicists (some of who had on their own requested my papers). So, it kindaa went through!

Phewww…. All the hoops that a hapless PhD student has to jump through, just to get to his degree! (In my case, it was even worse: these were the closed surfaces of the Huygens wavelets, not mere closed curves as in the hoops.)

So, that’s how I had arrived at my PhD time approach. I did it by randomizing the spherical surfaces employed in the Huygens’ process, and by imagining a spatially discrete particle of the photon at all such locations at each one of the subsequent instants. The movement of the photon, when it goes on cutting the respective surfaces of all the freshly generated series of Huygens’ wavelets, when the cutting is randomized, obviously forms a simplest kind of a Weiner process—it’s the direct counterpart of the random-walks, but for wave-fields.

People right from Ulam et al. had proposed and used random walks (aka Monte Carlo) for diffusive and potential fields, for 50+ years. However, none had added just some more calculations with the wave- and displacement-vectors to account for the phases, and thereby generalized the random-walks to be able to handle the wavefields too. That was another neat thing to know. (Yes, please, do go ahead! Do hunt for the precedents!!)

Anyway, that’s how the FAQ dynamics came to be diffusive.

And all said and done, it did come to reproduce a seemingly same kind of a transition from a pattern of random dots to the Young interference pattern as experiments had shown!

One final point. But why did I disregard the ballistic dynamics—which would have all randomness concentrated only in the source and let photons fly straight? Yes, come to think of it, if you do assume a spatially discrete nature for the photon, then there is obviously no good reason to deny such a possibility.

Here, I am not sure, because I don’t remember having writing down any note on it. So it’s kindaa hard to tell now, from a distance of years. I will try to reconstruct some possible considerations starting from some indirect points, and purely from memory.

I seem to recall that I was apprehensive that what I called “size effects” might come into picture and make this approach unsound. I mean to say, a perfectly uniform randomness (distributed over the entire emitter surface) was hard to imagine as the emitter surface became ever smaller, and reached the natural limit of a single atom. For one thing, the emitted quantity might get affected, I thought. Secondly, single atoms, acting as emitters, had to have some directionality to their emissions because their orbitals [whatever it meant—I didn’t have a good idea about them back then] weren’t always spherically symmetric. I think I had considered this point.

Did I consider the delayed-choice kind of considerations? I think I did, but in some simple indirect ways, not very carefully or systematically. I mean to say, I don’t remember going through write-ups on the delayed-choice experiments at all, and then taking any decision. I rather remember thinking in terms like a camera shutter suddenly coming in the way of a photon when it’s still in mid-flight and all. If the shutter were to be a perfect sink (one that didn’t re-emit the photon), or if it were to re-emit photons from a different location on the shutter surface (after internal energy undergoing some unpredictable oscillations within the shutter material), then it would adversely affect the final pattern on the screen, I had thought. The real-time changes for the propagating photon might get better handled by distributing randomness over the entire spatial region of the chamber, I had thought.

But I think that all in all, it wasn’t any such careful consideration. I chose the randomized Huygens’ process because I thought it gave good enough an explanation.

In the final analysis, there are too many problems with this entire approach—even with just a spatially discrete photon anyway, and furthermore if it comes embedded in a description that has no IAD anywhere in itself. Some or the other part of QM will then have to keep getting violated. You just can’t avoid it. So, the best way to understand QM is not to begin with photons but with electrons—and with the Schrodinger formalism. The measurement problem is the only remaining issue then.


5. Homework for the skeptics among you:

Go through my PhD abstract posted at iMechanica even before the defence [(.PDF) ^], and check out if what I wrote above, purely on the fly and purely from memory, matches with what I had officially reported back then, or not. If you find serious discrepancies, please bring them to my notice. Thanks in advance.


Of course, now that I’ve completely abandoned the grainy description of photons as the actual physical reality, all the above doesn’t much matter. FAQ, even if valid, would have to be taken as only a higher-level, abstract description of an entirely different kind of a mechanism.

So, let’s leave this entire PhD-time approach right behind us (forever), and continue with the next tweet in this series. They directly deal with the aspects of my latest approach (as in the Outline document)… However, I will pick it up in the next post. It’s almost 5900 words already! Give me a break of at least a 10–15 days. Until then, take care and goodbye.


A song I like:

(Marathi) “ambaraatalyaa niLyaa ghanaachee”
Singer: Ramdas Kamat
Music and Lyrics: Veena Chitako

 

Do you really need a QC in order to have a really unpredictable stream of bits?

0. Preliminaries:

This post has reference to Roger Schlafly’s recent post [^] in which he refers to Prof. Scott Aaronson’s post touching on the issue of the randomness generated by a QC vis-a-vis that obtained using the usual classical hardware [^], in particular, to Aaronson’s remark:

“the whole point of my scheme is to prove to a faraway skeptic—one who doesn’t trust your hardware—that the bits you generated are really random.”

I do think (based on my new approach to QM [(PDF) ^]) that building a scalable QC is an impossible task.

I wonder if they (the QC enthusiasts) haven’t already begun realizing the hopelessness of their endeavours, and thus haven’t slowly begun preparing for a graceful exit, say via the QC-as-a-RNG route.

While Aaronson’s remarks also saliently involve the element of the “faraway” skeptic, I will mostly ignore that consideration here in this post. I mean to say, initially, I will ignore the scenario in which you have to transmit random bits over a network, and still have to assure the skeptic that what he was getting at the receiving end was something coming “straight from the oven”—something which was not tampered with, in any way, during the transit. The skeptic would have to be specially assured in this scenario, because a network is inherently susceptible to a third-party attack wherein the attacker seeks to exploit the infrastructure of the random keys distribution to his advantage, via injection of systematic bits (i.e. bits of his choice) that only appear random to the intended receiver. A system that quantum-mechanically entangles the two devices at the two ends of the distribution channel, does logically seem to have a very definite advantage over a combination of ordinary RNGs and classical hardware for the network. However, I will not address this part here—not for the most part, and not initially, anyway.

Instead, for most of this post, I will focus on just one basic question:

Can any one be justified in thinking that an RNG that operates at the QM-level might have even a slightest possible advantage, at least logically speaking, over another RNG that operates at the CM-level? Note, the QM-level RNG need not always be a general purpose and scalable QC; it can be any simple or special-purpose device that exploits, and at its core operates at, the specifically QM-level.

Even if I am a 100% skeptic of the scalable QC, I also think that the answer on this latter count is: yes, perhaps you could argue that way. But then, I think, your argument would still be pointless.

Let me explain, following my approach, why I say so.


2. RNGs as based on nonlinearities. Nonlinearities in QM vs. those in CM:

2.1. Context: QM involves IAD:

QM does involve either IAD (instantaneous action a distance), or very, very large (decidedly super-relativistic) speeds for propagation of local changes over all distant regions of space.

From the experimental evidence we have, it seems that there have to be very, very high speeds of propagation, for even smallest changes that can take place in the \Psi and V fields. The Schrodinger equation assumes infinitely large speeds for them. Such obviously cannot be the case—it is best to take the infinite speeds as just an abstraction (as a mathematical approximation) to the reality of very, very high actual speeds. However, the experimental evidence also indicates that even if there has to be some or the other upper bound to the speeds v, with v \gg c, the speeds still have to be so high as to seemingly approach infinity, if the Schrodinger formalism is to be employed. And, of course, as you know it, Schrodinger’s formalism is pretty well understood, validated, and appreciated [^]. (For more on the speed limits and IAD in general, see the addendum at the end of this post.)

I don’t know the relativity theory or the relativistic QM. But I guess that since the electric fields of massive QM particles are non-uniform (they are in fact singular), their interactions with \Psi must be such that the system has to suddenly snap out of some one configuration and in the same process snap into one of the many alternative possible configurations. Since there are huge (astronomically large) number of particles in the universe, the alternative configurations would be {astronomically large}^{very large}—after all, the particles positions and motions are continuous. Thus, we couldn’t hope to calculate the propagation speeds for the changes in the local features of a configuration in terms of all those irreversible snap-out and snap-in events taken individually. We must take them in an ensemble sense. Further, the electric charges are massive, identical, and produce singular and continuous fields. Overall, it is the ensemble-level effects of these individual quantum mechanical snap-out and snap-in events whose end-result would be: the speed-of-light limitation of the special relativity (SR). After all, SR holds on the gross scale; it is a theory from classical electrodynamics. The electric and magnetic fields of classical EM can be seen as being produced by the quantum \Psi field (including the spinor function) of large ensembles of particles in the limit that the number of their configurations approaches infinity, and the classical EM waves i.e. light are nothing but the second-order effects in the classical EM fields.

I don’t know. I was just loud-thinking. But it’s certainly possible to have IAD for the changes in \Psi and V, and thus to have instantaneous energy transfers via photons across two distant atoms in a QM-level description, and still end up with a finite limit for the speed of light (c) for large collections of atoms.

OK. Enough of setting up the context.

2.2: The domain of dependence for the nonlinearity in QM vs. that in CM:

If QM is not linear, i.e., if there is a nonlinearity in the \Psi field (as I have proposed), then to evaluate the merits of the QM-level and CM-level RNGs, we have to compare the two nonlinearities: those in the QM vs. those in the CM.

The classical RNGs are always based on the nonlinearities in CM. For example:

  • the nonlinearities in the atmospheric electricity (the “static”) [^], or
  • the fluid-dynamical nonlinearities (as shown in the lottery-draw machines [^], or the lava lamps [^]), or
  • some or the other nonlinear electronic circuits (available for less than $10 in hardware stores)
  • etc.

All of them are based on two factors: (i) a large number of components (in the core system generating the random signal, not necessarily in the part that probes its state), and (ii) nonlinear interactions among all such components.

The number of variables in the QM description is anyway always larger: a single classical atom is seen as composed from tens, even hundreds of quantum mechanical charges. Further, due to the IAD present in the QM theory, the domain of dependence (DoD) [^] in QM remains, at all times, literally the entire universe—all charges are included in it, and the entire \Psi field too.

On the other hand, the DoD in the CM description remains limited to only that finite region which is contained in the relevant past light-cone. Even when a classical system is nonlinear, and thus gets crazy very rapidly with even small increases in the number of degrees of freedom (DOFs), its DoD still remains finite and rather very small at all times. In contrast, the DoD of QM is the whole universe—all physical objects in it.

2.3 Implication for the RNGs:

Based on the above-mentioned argument, which in my limited reading and knowledge Aaronson has never presented (and neither has any one else either, basically because they all continue to believe in von Neumann’s characterization of QM as a linear theory), an RNG operating at the QM level does seem to have, “logically” speaking, an upper hand over an RNG operating at the CM level.

Then why do I still say that arguing for the superiority of a QM-level RNG is still pointless?


3. The MVLSN principle, and its epistemological basis:

If you apply a proper epistemology (and I have in my mind here the one by Ayn Rand), then the supposed “logical” difference between the two descriptions becomes completely superfluous. That’s because the quantities whose differences are being examined, themselves begin to lose any epistemological standing.

The reason for that, in turn, is what I call the MVLSN principle: the law of the Meaninglessness of the Very Large or very Small Numbers (or scales).

What the MVLSN principle says is that if your argument crucially depends on the use of very large (or very small) quantities and relationships between them, i.e., if the fulcrum of your argument rests on some great extrapolations alone, then it begins to lose all cognitive merit. “Very large” and “very small” are contextual terms here, to be used judiciously.

Roughly speaking, if this principle is applied to our current situation, what it says is that when in your thought you cross a certain limit of DOFs and hence a certain limit of complexity (which anyway is sufficiently large as to be much, much beyond the limit of any and every available and even conceivable means of predictability), then any differences in the relative complexities (here, of the QM-level RNGs vs. the CM-level RNGs) ought to be regarded as having no bearing at all on knowledge, and therefore, as having no relevance in any practical issue.

Both QM-level and CM-level RNGs would be far too complex for you to devise any algorithm or a machine that might be able to predict the sequence of the bits coming out of either. Really. The complexity levels already grow so huge, even with just the classical systems, that it’s pointless trying to predict the the bits. Or, to try and compare the complexity of the classical RNGs with the quantum RNGs.

A clarification: I am not saying that there won’t be any systematic errors or patterns in the otherwise random bits that a CM-based RNG produces. Sure enough, due statistical testing and filtering is absolutely necessary. For instance, what the radio-stations or cell-phone towers transmit are, from the viewpoint of a RNG based on radio noise, systematic disturbances that do affect its randomness. See random.org [^] for further details. I am certainly not denying this part.

All that I am saying is that the sheer number of DOF’s involved itself is so huge that the very randomness of the bits produced even by a classical RNG is beyond every reasonable doubt.

BTW, in this context, do see my previous couple of posts dealing with probability, indeterminism, randomness, and the all-important system vs. the law distinction here [^], and here [^].


4. To conclude my main argument here…:

In short, even “purely” classical RNGs can be way, way too complex for any one to be concerned in any way about their predictability. They are unpredictable. You don’t have to go chase the QM level just in order to ensure unpredictability.

Just take one of those WinTV lottery draw machines [^], start the air flow, get your prediction algorithm running on your computer (whether classical or quantum), and try to predict the next ball that would come out once the switch is pressed. Let me be generous. Assume that the switch gets pressed at exactly predictable intervals.

Go ahead, try it.


5. The Height of the Tallest Possible Man (HTPM):

If you still insist on the supposedly “logical” superiority of the QM-level RNGs, make sure to understand the MVLSN principle well.

The issue here is somewhat like asking this question:

What could possibly be the upper limit to the height of man, taken as a species? Not any other species (like the legendary “yeti”), but human beings, specifically. How tall can any man at all get? Where do you draw the line?

People could perhaps go on arguing, with at least some fig-leaf of epistemological legitimacy, over numbers like 12 feet vs. 14 feet as the true limit. (The world record mentioned in the Guinness Book is slightly under 9 feet [^]. The ceiling in a typical room is about 10 feet high.) Why, they could even perhaps go like: “Ummmm… may be 12 feet is more likely a limit than 24 feet? whaddaya say?”

Being very generous of spirit, I might still describe this as a borderline case of madness. The reason is, in the act of undertaking even just a probabilistic comparison like that, the speaker has already agreed to assign non-zero probabilities to all the numbers belonging to that range. Realize, no one would invoke the ideas of likelihood or probability theory if he thought that the probability for an event, however calculated, was always going to be zero. He would exclude certain kinds of ranges from his analysis to begin with—even for a stochastic analysis. … So, madness it is, even if, in my most generous mood, I might regard it as a borderline madness.

But if you assume that a living being has all the other characteristic of only a human being (including being naturally born to human parents), and if you still say that in between the two statements: (A) a man could perhaps grow to be 100 feet tall, and (B) a man could perhaps grow to be 200 feet tall, it is the statement (A) which is relatively and logically more reasonable, then what the principle (MVLSN) says is this: “you basically have lost all your epistemological bearing.”

That’s nothing but complex (actually, philosophic) for saying that you have gone mad, full-stop.

The law of the meaningless of the very large or very small numbers does have a certain basis in epistemology. It goes something like this:

Abstractions are abstractions from the actually perceived concretes. Hence, even while making just conceptual projections, the range over which a given abstraction (or concept) can remain relevant is determined by the actual ranges in the direct experience from which they were derived (and the nature, scope and purpose of that particular abstraction, the method of reaching it, and its use in applications including projections). Abstractions cannot be used in disregard of the ranges of the measurements over which they were formed.

I think that after having seen the sort of crazy things that even simplest nonlinear systems with fewest variables and parameters can do (for instance, which weather agency in the world can make predictions (to the accuracy demanded by newspapers) beyond 5 days? who can predict which way is the first vortex going to be shed even in a single cylinder experiment?), it’s very easy to conclude that the CM-level vs. QM-level RNG distinction is comparable to the argument about the greater reasonableness of a 100 feet tall man vs. that of a 200 feet tall man. It’s meaningless. And, madness.


6. Aaronson’s further points:

To be fair, much of the above write-up was not meant for Aaronson; he does readily grant the CM-level RNGs validity. What he says, immediately after the quote mentioned at the beginning of this post, is that if you don’t have the requirement of distributing bits over a network,

…then generating random bits is obviously trivial with existing technology.

However, since Aaronson believes that QM is a linear theory, he does not even consider making a comparison of the nonlinearities involved in QM and CM.

I thought that it was important to point out that even the standard (i.e., Schrodinger’s equation-based) QM is nonlinear, and further, that even if this fact leads to some glaring differences between the two technologies (based on the IAD considerations), such differences still do not lead to any advantages whatsoever for the QM-level RNG, as far as the task of generating random bits is concerned.

As to the task of transmitting them over a network is concerned, Aaronson then notes:

If you do have the requirement, on the other hand, then you’ll have to do something interesting—and as far as I know, as long as it’s rooted in physics, it will either involve Bell inequality violation or quantum computation.

Sure, it will have to involve QM. But then, why does it have to be only a QC? Why not have just special-purpose devices that are quantum mechanically entangled over wires / EM-waves?

And finally, let me come to yet another issue: But why would you at all have to have that requirement?—of having to transmit the keys over a network, and not using any other means?

Why does something as messy as a network have to get involved for a task that is as critical and delicate as distribution of some super-specially important keys? If 99.9999% of your keys-distribution requirements can be met using “trivial” (read: classical) technologies, and if you can also generate random keys using equipment that costs less than $100 at most, then why do you have to spend billions of dollars in just distributing them to distant locations of your own offices / installations—especially if the need for changing the keys is going to be only on an infrequent basis? … And if bribing or murdering a guy who physically carries a sealed box containing a thumb-drive having secret keys is possible, then what makes the guys manning the entangled stations suddenly go all morally upright and also immortal?

From what I have read, Aaronson does consider such questions even if he seems to do so rather infrequently. The QC enthusiasts, OTOH, never do.

As I said, this QC as an RNG thing does show some marks of trying to figure out a respectable exit-way out of the scalable QC euphoria—now that they have already managed to wrest millions and billions in their research funding.

My two cents.


Addendum on speed limits and IAD:

Speed limits are needed out of the principle that infinity is a mathematical concept and cannot metaphysically exist. However, the nature of the ontology involved in QM compels us to rethink many issues right from the beginning. In particular, we need to carefully distinguish between all the following situations:

  1. The transportation of a massive classical object (a distinguishable, i.e. finite-sized, bounded piece of physical matter) from one place to another, in literally no time.
  2. The transmission of the momentum or changes in it (like forces or changes in them) being carried by one object, to a distant object not in direct physical contact, in literally no time.
  3. Two mutually compensating changes in the local values of some physical property (like momentum or energy) suffered at two distant points by the same object, a circumstance which may be viewed from some higher-level or abstract perspective as transmission of the property in question over space but in no time. In reality, it’s just one process of change affecting only one object, but it occurs in a special way: in mutually compensating manner at two different places at the same time.

Only the first really qualifies to be called spooky. The second is curious but not necessarily spooky—not if you begin to regard two planets as just two regions of the same background object, or alternatively, as two clearly different objects which are being pulled in various ways at the same time and in mutually compensating ways via some invisible strings or fields that shorten or extend appropriately. The third one is not spooky at all—the object that effects the necessary compensations is not even a third object (like a field). Both the interacting “objects” and the “intervening medium” are nothing but different parts of one and the same object.

What happens in QM is the third possibility. I have been describing such changes as occurring with an IAD (instantaneous action at a distance), but now I am not too sure if such a usage is really correct or not. I now think that it is not. The term IAD should be reserved only for the second category—it’s an action that gets transported there. As to the first category, a new term should be coined: ITD (instantaneous transportation to distance). As to the third category, the new term could be IMCAD (instantaneous and mutually compensating actions at a distance). However, this all is an afterthought. So, in this post, I only have ended up using the term IAD even for the third category.

Some day I will think more deeply about it and straighten out the terminology, may be invent some or new terms to describe all the three situations with adequate directness, and then choose the best… Until then, please excuse me and interpret what I am saying in reference to context. Also, feel free to suggest good alternative terms. Also, let me know if there are any further distinctions to be made, i.e., if the above classification into three categories is not adequate or refined enough. Thanks in advance.


A song I like:

[A wonderful “koLi-geet,” i.e., a fisherman’s song. Written by a poet who hailed not from the coastal “konkaN” region but from the interior “desh.” But it sounds so authentically coastal… Listening to it today instantly transported me back to my high-school days.]

(Marathi) “suTalaa vaadaLi vaaraa…”
Singing, Music and Lyrics: Shaahir Amar Sheikh

 


History: Originally published on 2019.07.04 22:53 IST. Extended and streamlined considerably on 2019.07.05 11:04 IST. The songs section added: 2019.07.05 17:13 IST. Further streamlined, and also further added a new section (no. 6.) on 2019.07.5 22:37 IST. … Am giving up on this post now. It grew from about 650 words (in a draft for a comment at Schlafly’s blog) to 3080 words as of now. Time to move on.

Still made further additions and streamlining for a total of ~3500 words, on 2019.07.06 16:24 IST.

Update: Pursuing some simple (and possibly new) ideas in Data Science

Last Saturday, I attended a Data Science-related meetup in Pune (the one organized by DataGiri). I enjoyed all the four sessions covered in it (one each on logistic regression, SVM, clustering, and ensemble methods). … Out of the past 4/5 events or 1-day introductory workshops on ML/DL which I have attended so far in Pune, I think this one was by far the best.

Attending events like these (also conferences) often has an effect: due to the informality of the interaction, you begin to look at the same things from a slightly different perspective. That precisely is what seems to have happened to me this time round.

Cutting straight to the point, I think that after attending this event, I might have stumbled across a couple of small little ideas concerning the techniques that were discussed. These ideas could have an element of novelty. At least that’s what I feel. … Several Internet searches (and consulting standard books up to Bishop and ESLII) hasn’t thrown up something similar so far. So, who knows… And yes, it’s not just the novelty; there also should be some advantages to be had in practical applications too.

Of course, Data Science is relatively a new field for me, and so, my knowledge of these topics is pretty limited. Still, currently, I am engaged in taking these ideas a little further. From what I have come across thus far, it does look like there should be something to these ideas. But I need to both flesh out the ideas and take the literature-search further… much, much further.

At the same time, I am also having a look at the angle of whether a patent or two can come out of these ideas or not. So far, the prospects do seem promising. So, if you have the means to sponsor patents, and if NDAs are OK by you, then feel free to get in touch with me for some more details and the current status of development.

Bottomline: Nothing major here; just a couple of small ideas (or small variations on the known techniques). But they do seem neat and novel. In any case, they certainly are worth pursuing a bit further.

…Take care and bye for now…


A song I like:

(Hindi) “mere jaise ban jaaoge…”
Singers: Jagjit and Chitra Singh
Lyrics: Saeed Rahi (?)
Music: Jagjit Singh

 

My new approach to QM—an update, and a request (May 2019)

This post has reference to my earlier post of 30th March 2019, here [^]. Being busy mainly with learning Data Science, I didn’t subsequently find the time to systematically study the papers and the book which were suggested by the IIT Bombay professors back in March-end.


However, in the meanwhile, thinking about the whole issue independently (and on a part-time basis), I have come to work through a detailed scheme for calculating the wavefunctions for the case of a 1D helium atom.

In particular, the abstract case I have worked through is the following:

A single helium atom placed in a 1D domain of a finite length, and with either reflecting boundary conditions (i.e. infinite potential walls) at the two ends (i.e. a 1D box), or possibly also with periodic boundary conditions imposed at the two ends (i.e. an infinite 1D lattice of 1D helium atoms). The problem is to find the energy eigenstates for the system wavefunction, assuming that the electrons do interact with each other.

The electrons are spinless. However, note, I have now addressed the case of the interacting electrons too.


I have not performed the actual simulations, though they can be done “any time.”

Yet, before proceeding to write the code, I would like to show the scheme itself to some computational quantum chemist/physicist, and have a bit of a to-and-fro regarding how they usually handle it in the mainstream QM/QChem, and about the commonality and differences (even the very basic reasonableness or otherwise) of my proposed scheme.

I can even go further and say that I have now got stuck at this point.


I will also continue to remain stuck at this same point unless one of the following two things happens: (i) a quantum chemist having a good knowledge of the computer simulation methods, volunteers to review my scheme and offer suggestions, or (ii) I myself study and digest a couple of text-books (of 500+ pages) and a few relevant papers (including those suggested by the IIT Bombay professors).

The second alternative is not feasible right now, simply because I don’t have enough time at hand. I am now busy with learning data science, and must continue to do so, so that I can land a job ASAP. (It’s been more than a year that I have been out of a job.)


So, if you are knowledgeable about this topic (the abstract case I am dealing with above, viz., that of 1D helium atom with spinless but interacting electrons), and also want to help me, then I request you to please see if you can volunteer just a bit of your time.

If no one comes to help me, it could take a much longer period of time for me to work through it all purely on my own—anywhere from 6–8 months to a year, or as is easily possible, even much more time—may be a couple of years or so, too. … Remember, I will also be working in a very highly competitive area of data science too, during all this time.

On the other hand, to someone who has enough knowledge of this matter, it wouldn’t be very strenuous at all. He only has to review the scheme and offer comments, and generally remain available for help, that’s all.

(It would be quite like someone approaching me for some informal guidance on FEM simulation of some engineering case. Even if I might not have modeled some particular case myself in the past, say a case of some fluid-structure interaction, I still know that I could always act as a sounding board and offer some general help to such a guy. I also know that doing isn’t going to be very taxing on me, that it’s not going to take too much of my own time. The situation here is quite similar. The quantum chemist/physicist doesn’t have to exert himself too much. I am confident of this part.)

So, there. See if you can help me out yourself, or suggest someone suitable to me. Thanks in advance.


A song I like:
(Marathi) “vaaTa sampataa sampenaa…”
Lyrics: Devakinandan Saaraswat
Music: Dattaa Daavajekar
Singer: Jayawant Kulkarni