A neat experiment concerning quantum jumps. Also, an update on the data science side.

1. A new paper on quantum jumps:

This post has a reference to a paper published yesterday in Nature by Z. K. Minev and pals [^]; h/t Ash Joglekar’s twitter feed (he finds this paper “fascinating”). The abstract follows; the emphasis in bold is mine.

In quantum physics, measurements can fundamentally yield discrete and random results. Emblematic of this feature is Bohr’s 1913 proposal of quantum jumps between two discrete energy levels of an atom[1]. Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement[2,3,4]. The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Despite the non-deterministic character of quantum physics, is it possible to know if a quantum jump is about to occur? Here we answer this question affirmatively: we experimentally demonstrate that the jump from the ground state to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable ‘flight’, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the evolution of each completed jump is continuous, coherent and deterministic. We exploit these features, using real-time monitoring and feedback, to catch and reverse quantum jumps mid-flight—thus deterministically preventing their completion. Our findings, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory[5,6,7,8,9] and should provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as the early detection of error syndromes in quantum error correction.

Since the paper was behind the paywall, I quickly did a bit of googling and then (very) rapidly browsed through the following three: [^], [^] and [(PDF) ^].

Since I didn’t find the words “modern quantum trajectory theory” explained in simple enough terms in these references, I did some further googling on “quantum trajectory theory”, high-speed browsed through them a bit, in the process browsing jumping through [^], [^], and landed first at [^], then at the BKS paper [(PDF) ^]. Then, after further googling on “H. J. Carmichael”, I high-speed browsed through the Wiki on Prof. Carmichael [^], and from there, through the abstract of his paper [^], and finally took the link to [^] and to [^].

My initial and rapid judgment:

Ummm… Minev and pals might have concluded that their experimental work lends “support” to “the modern quantum trajectory theory” [MQTT for short.] However, unfortunately, MQTT itself is not sufficiently deep a theory.

…  As an important aside, despite the word “trajectory,” thankfully, MQTT is, as far as I gather it, not Bohmian in nature either. [Lets out a sigh of relief!]

Still, neither is MQTT deep enough. And quite naturally so… After all, MQTT is a theory that focuses only on the optical phenomena. However, IMO, a proper quantum mechanical ontology would have the photon as a derived object—i.e., a higher-level abstraction of an object. This is precisely the position I adopted in my Outline document as well [^].

Realize, there  can be no light in an isolated system if there are no atoms in it. Light is always emitted from, and absorbed in, some or the other atoms—by phenomena that are centered around nuclei, basically. However, there can always be atoms in an isolated system even if there never occurs any light in it—e.g., in an extremely rare gas of inert gas atoms, each of which is in the ground state (kept in an isolated system, to repeat).

Naturally, photons are the derived or higher-level objects. And that’s why, any optical theory would have to assume some theory of electrons lying at even deeper a level. That’s the reason why MQTT cannot be at the deepest level.

So, my overall judgment is that, yes, Minev and pals’ work is interesting. Most important, they don’t take Bohr’s quantum jumps as being in principle un-analyzable, and this part is absolutely delightful. Still, if you ask me, for the reasons given above, this work also does not deal with the quantum mechanical reality at its deepest possible level. …

So, in that sense, it’s not as fascinating as it sounds on the first reading. … Sorry, Ash, but that’s how the things are here!

…Today was the first time in a couple of weeks or so that I read anything regarding QM. And, after this brief rendezvous with it in this post, I am once again choosing to close that subject right here. … In the absence of people interacting with me on QM (computational QChem, really speaking), and having already reached a very definite point of development concerning my new approach, I don’t find QM to be all that interesting these days.

For some good pop. sci-level coverage of the paper, see Chris Lee’s post at his ArsTechnica blog [^], and Phillip Ball’s story at the Quanta Magazine [^].

2. An update on the Data Science side:

As you know, these days, I have been pursuing data science full-time.

Earlier, in the second half of 2018, I had gone through Michael Nielsen’s online book on ANNs and DL [^]. At that time, I had also posted a few entries here on this blog concerning ANNs and DL [^]. For instance, see my post explaining, with real-time visualization, why deep learning is hard [^].

Now, in the more recent times, I have been focusing more on the other (“canonical”) machine learning techniques in general—things like (to list in a more or less random an order) regression, classification, clustering, dimensionality reduction, etc. It’s been fun. In particular, I have come to love scikit-learn. It’s a neat library. More about it all, later—may be I should post some of the toy Python scripts which I tried.

… BTW, I am also searching for one or two good, “industrial scale” projects from data science. So, if you are from industry and are looking for some data-science related help, then feel free to get in touch. If the project is of the right kind, I may even work on it on a pro-bono basis.

… Yes, the fact is that I am actively looking out for a job in data science. (Have uploaded my resume at naukri.com too.) However, at the same time, if a topic is interesting enough, I don’t mind lending some help on a pro bono basis either.

The project topic could be anything from applications in manufacturing engineering (e.g. NDT techniques like radiography, ultrasonics, eddy current, etc.) to financial time-series predictions, to some recommendation problem, to… I am open for virtually anything in data science. It’s just that I have to find the project to be interesting enough, that’s all… So, feel free to get in touch.

… Anyway, it’s time to wrap up. … So, take care and bye for now.

A song I like

(Western, pop) “Money, money, money…”
Band: ABBA

An update on my research

28th February is the National Science Day in India.

The story goes that it was on this day (in 1928) that C. V. Raman discovered the effect known by his name.

I don’t believe that great discoveries like that are made in just one single day. There is a whole sequence of many crucially important days involved in them.

Yes, on this day, Raman might have achieved a certain milestone or made a key finding regarding his discovery. However, even if true in this case (which I very much doubt), it’s not true in general. Great discoveries are not made in a single day; they are usually spread over much longer span of time. A particular instant or a day has more of just a symbolic value—no matter how sudden the discovery might have looked to someone, including to the discoverer.

There of course was a distinguished moment when Kekule, in his famous dream, saw a snake swallowing its own tail. However, therefore to say that he made the discovery concerning the ring structure of the benzene molecule, just in a single moment, or in a single flash of imagination, is quite a bit of a stretch.

Try it out yourself. Think of a one-line statement that encapsulates the findings of a discovery made by a single man. Compare it with another statement which encapsulates any of the previous views regarding the same matter (i.e., before this discovery came along). This way, you can isolate the contributions of a single individual. Then analyze those contributions. You would invariably find that there are several different bits of progress that the discovery connected together, and these bits themselves (i.e., the contributions made individually by the discoverer himself) were not all discovered on the same day. Even if a day or an hour is truly distinctive in terms of the extent of progress made, it invariably has the character of taking an already ongoing process to a state of completion—but not of conducting that entire process. Mystical revelation is never a good metaphor to employ in any context—not even in the spiritual matters, let alone in the scientific ones.

Anyway, it’s nice that they didn’t choose Raman’s birth-day for this Day, but instead chose a day that was related to his most famous work in science. Good sense! And easy to remember too: 28-02-’28.

Let me celebrate this year’s Science Day in my own, small, personal way. Let me note down a bit of an update on my research.

1. I have had a bit of a correspondence, regarding my new approach, with a couple of physicists. Several objections were made by them, but to cut a long story short, neither seemed to know how to get into that mode kind of thinking which most naturally leads to my main thesis, and hence helps understand it.

The typical thought process both these physicists displayed was the one which is required in finding analytical solutions of problems of a certain kind, using an analysis of a specific kind. But it is not the kind of thought process which is typically required in the computational modeling of complex phenomena. Let me remind you that my theory is nonlinear in nature. Nonlinearity, in particular, is best approached only computationally—you would be hopelessly out of your wits if you try to find analytical solutions to a nonlinear system. What you should instead pursue is: thinking in terms of the following ingredients: certain objects, an algorithm to manipulate their states, and tracing the run-time evolution of the system. You try this algorithmic way of thinking, and the whole thing (I mean understanding the nature of a nonlinear system) becomes easy. Otherwise, it looks hopelessly complicated, incomprehensible, and therefore, deeply suspicious, if not outright wrong. Both the physicists with who I interacted seemed to be thinking in terms of the linear theory of QM, thereby restricting their thought modes to only the traditional formalism based on the abstract Hilbert-spaces and linear Hermitian operators. Uh oh! Not good. QM is fundamentally nonlinear; the linear formulations of QM are merely approximations to its true nature. No matter how analytically rigorous you can get in the traditional QM, it’s not going to help you understand the true nature of quantum phenomena, simply because a linear system is incapable of throwing much light on the nonlinear system of which it is an approximation.

I believe it was out of this reason—their continuing to think in terms of linear systems defined over hyperspaces and the operator algebra—that one of them raised the objection that if $\Psi$ in MSQM (mainstream QM) is defined on a $3ND$ configuration space, how come my $\Psi(x,t)$ could be defined over the physical $3D$ space. He didn’t realize, even after I supplied the example of the classical $N$-particle molecular dynamics (MD) simulations, that using an abstract higher-dimensional space isn’t the only viable manner in which you can capture the physics of a situation. (And I had indicated right in the Outline document too, that you first try to understand how a Newtonian evolution would work for multiple, charged, point-particles as in classical physics, and only then modify this evolution by introducing the system wavefunction.)

I came to gather that apparently, some people (who follow the Bohmian mechanics doctrine) have tried to find a $3ND \leftrightarrow 3D$ correspondence for a decade, if not more. Apparently, they didn’t succeed. I wonder why, because doing so should be so damn straight-forward (even if it would not be easy). You only have to realize that a configuration space refers to all possible configurations, whereas what an evolution over a $3D$ physical space directly deals with is only one initial configuration at a time. That is what specifying the ICs and the BCs does for you.

In case of MD simulations, you don’t define a function over the entire $3ND$ configuration space in the first place. You don’t try to produce an evolution equation which relies on only those kinds of operators which modify all parts of the entire hyperspace-function in one shot, simultaneously. Since you don’t think in such hyperspace terms in the first place, you also don’t have to think in terms of the projection operators bringing the system dynamics down to $3D$ in particular cases either. You don’t do that in the context of MD simulations, and you don’t do it in the context of my approach either.

This physicist also didn’t want me to say something using analogies and metaphors, and so I didn’t mention it to him, but I guess I can use an analogy here. It will allow even a layman to get a sense of the issue right.

This physicist was insisting on having a map of an entire territory, and was more or less completely dismissing my approach on the grounds that I only supply the surveying instruments like the theodolite and the triangulation algorithm. He expected to see the map—even when a theory is at a fledgling stage. He nevertheless was confident that I was wrong because I was insisting that each physical object in the actual territory is only at one place at any given instant, that it is not spread all over the map. This analogy is not exact, but it is helpful: it does bring out the difference of focusing on only the actually followed trajectory in the configuration space, vs. an insistence on using the entirety of the configuration space for any description of an evolution. But that guy didn’t get this point either. And he wanted equations, not analogies or metaphors.

Little wonder they have not been successful in finding out what logical connection there is between the abstract $3ND$ hyperspace on the one hand, and the $3D$ physical space on the other hand. Little wonder they don’t progress despite having worked on the problem for a decade or so (as this guy himself said).

Yeah, physicists, work harder, I say! [LOL!]

2. Apart from it all—I mean all those “discussions”—I have also realized that there are several errors or confusing explanations in the Outline document which I uploaded at iMechanica on 11th February 2019. Of course, these errors are more minor in nature. There are many, many really important ideas in that document which are not in error.

The crucially important and new ideas which are valid include, just to cite a few aspects: (i) my insistence on using only those potentials that are singularly anchored into the point-particle charges, (ii) the particular nonlinearity I have proposed for the system evolution, (iii) the idea that during a measurement it is the Instrument whose state undergoes a cascade of bifurcations or catastrophic changes, whereas the System state essentially remains the same (that there is no wavefunction collapse). And, many, many other ideas too. These ideas are not only crucial to my approach but they also are absolutely new and original. (Yes, you can be confident about this part, too—else, Americans would have pointed out the existing precedence by now. (They are just looking to find errors in what(ever) I say.)) All these ideas do remain intact. The confusing part or the one having erroneous statements indeed is more minor. It concerns more with how I tried to explain things. And I am working on removing these errors too.

I have also come to realize that I need to explicitly give a set of governing equations, as well as describe the algorithm that could be used in building the simulations. Yes, the physicist had asked me for an evolution equation. I thought that any one, given the Schrodinger equation and my further verbal additions / modifications to it, could easily “get” it. But apparently, he could not. So, yes, I will explicitly write down the evolution equation for my approach, as an equation that is separate from Schrodinger’s. In the next revision of the document (or addition to it) I will not rely on the only implicitly understood constraints or modifications to the TDSE.

3. There also are some other issues which I noticed entirely on my own, and I am working on them.

One such issue concerns the way the kinetic energy is captured in the MSQM vs. how my approach ought to handle and capture it.

In MSQM, the kinetic energy consists of a sum of 1-particle Laplacian operators that refer to particle coordinates. Given the fact that my approach has the wavefunction defined over the $3D$ space, how should this aspect be handled? … By the time I wrote my Outline document (version 11 February 2019), I had not thought a lot about the kinetic energy part. Now, I found out, I have to think really deep about it. May be, I will have to abandon the form of Schrodinger’s equation itself to a further extent. Of course, the energy analysis will progress on the same lines (total energy = kinetic + potential), and the de Broglie relations will have to be honored. But the form of the equation may turn out to be a bit different.

You see, what MSQM does is to represent the particles using only the $\Psi(x,t)$ field. The potential energy sure can be constructed in reference to a set of discrete particle positions even in MSQM, but what the $\hat{V}$ operator then yields is just a single number. (In case of time-dependent potentials, the value of this variable varies in time.) The multiplication by the hyperspace-function $\Psi(x,t)$ then serves to distribute this much amount of energy (that single number) over the entire hyperspace. Now realize that $|\Psi(x,t)|^2$ gives the probability. So, in a way, indirectly, even if you can calculate / compute the potential energy of the system starting from a certain set of particle positions, in the MSQM, you then have to immediately abandon them—the idea of the discrete particles. The MSQM formalism doesn’t need it—the particle positions. You deal only with the hyperspace-occupying $\Psi(x,t)$. The formulation of kinetic energy also refers to only the $\Psi(x,t)$ field. Thus, in MSQM, particles are ultimately represented only via the $\Psi(x,t)$ field. The $\Psi(x,t)$ is the particles.

In contrast, in my approach, the particles are represented directly as point-phenomena, and their positions remain significant throughout. The $\Psi(x,t)$ field of my approach connects, and causally interacts with, the particles. But it does not represent the particles. Ontologically, $\Psi(x,t)$ is basically different from particles, even if the background object does interacts with the particles. Naturally, why should I represent their kinetic energies via the Laplacian terms? … Got the idea? The single number that is the kinetic energy of the particles, need not be regarded as being distributed over the $3D$ space at all, in my approach. But in 11th February version of the Outline document, I did say that the governing equation is only Schrodinger’s. The modifications required to be made to the TDSE on account of the kinetic energy term, is something I had not even thought of, because in writing that version, I was trying focusing on getting as many details regarding the potential energy out as possible. After all, the nonlinear nature of QM occurs due to the potential term, doesn’t it?

So, I need to get issues like these straightened out too.

… All in all, I guess I can say that I am more or less (but not completely) done with the development concerning the spin-less 1-particle systems, esp. the time-independent states. So far, it seems that my approach does work fine with them. Of course, new issues continue to strike me all the time, and I continue finding answers to them as well—as happens in any approach that is completely new. New, right from the stage of the very basic ideation  concerning what kind of objects there should be, in the theory.

I have just about begun looking into the (spin-less) multi-particle states. That is the natural order in which the theory should progress, and my work is tracing just this same path. But as I said, I might also be revising some parts of the earlier presented theory, as and when necessary.

4. I also realized on my own, but only after the interaction with the physicists was already over, that actually, I need not wait for the entire multi-particle theory to get developed before beginning with simulations. In fact, it should be possible to handle some simple 1-particle $1D$ cases like the particle in a box or the QHO (quantum-mechanical oscillator) right away.

I plan to pursue these simulations right in the near future. However, I will not be able to complete pursuing all their aspects in the near future—not even in the simple cases involving just $1D$ simulations. I plan to do a preliminary simulation or two, and then suspend this activity until the time that I land a well-paying job in data science in Pune.

No songs section this time because I happened to post several entries almost back to back here, and in the process, I seem to have used up all the songs that were both new (not run here before) and also on the top of my mind. … May be I will return later and add a song if one strikes me easily.

Bye for now, and have a happy Science Day!

Minor editing may be done later today. Done by 20:15 hrs the same day.

The bouncing droplets imply having to drop the Bohmian approach?

If you are interested in the area of QM foundations, then may be you should drop everything at once, and go, check out the latest pop-sci news report: “Famous experiment dooms alternative to quantum weirdness” by Natalie Wolchover in the Quanta Magazine [^].

Remember the bouncing droplets experiments performed by Yves Couder and pals? In 2006, they had reported that they could get the famous interference pattern even if the bouncing droplets passed through the double slit arrangement only one at a time. … As the Quanta article now reports, it turns out that when other groups in the USA and France tried to reproduce this result (the single-particle double-slit interference), they could not.

“Repeat runs of the experiment, called the “double-slit experiment,” have contradicted Couder’s initial results and revealed the double-slit experiment to be the breaking point of both the bouncing-droplet analogy and de Broglie’s pilot-wave vision of quantum mechanics.”

Well, just an experimental failure or two in reproducing the interference, by itself, wouldn’t make for a “breaking point,”i.e., if the basic idea itself were to be sound. So the question now becomes whether the basic idea itself is sound enough or not.

Turns out that a new argument has been put forth, in the form of a thought experiment, which reportedly shows why and how the very basic idea itself must be regarded as faulty. This thought experiment has been proposed by a Danish professor of fluid dynamics, Prof. Tomas Bohr. (Yes, there is a relation: Prof. Tomas Bohr is a son of the Nobel laureate Aage Bohr, i.e., a grandson of the Nobel laureate Niels Bohr [^].)

Though related to QM foundations, this thought experiment is not very “philosophical” in nature; on the contrary, it is very, very “physics-like.” And the idea behind it also is “simple.” … It’s one of those ideas which make you exclaim “why didn’t I think of it before?”—at least the first time you run into it. Here is an excerpt (which actually is the caption for an immediately understandable diagram):

“Tomas Bohr’s variation on the famous double-slit experiment considers what would happen if a particle must go to one side or the other of a central dividing wall before passing through one of the slits. Quantum mechanics predicts that the wall will have no effect on the resulting double-slit interference pattern. Pilot-wave theory, however, predicts that the wall will prevent interference from happening.”

… Ummm… Not quite.

From whatever little I know about the pilot-wave theory, I think that the wall wouldn’t prevent the interference from occurring, even if you use this theory. … It all seems to depend on how you interpret (and/or extend) the pilot-wave theory. But if applied right (which means: in its own spirit), then I guess that the theory is just going to reproduce whatever it is that the mainstream QM predicts. Given this conclusion I have drawn about this approach, I did think that the above-quoted portion was a bit misleading.

The main text of the article then proceeds to more accurately point out the actual problem (i.e., the way Prof. Tomas Bohr apparently sees it):

“… the dividing-wall thought experiment highlights, in starkly simple form, the inherent problem with de Broglie’s idea. In a quantum reality driven by local interactions between a particle and a pilot wave, you lose the necessary symmetry to produce double-slit interference and other nonlocal quantum phenomena. An ethereal, nonlocal wave function is needed that can travel unimpeded on both sides of any wall. [snip] But with pilot waves, “since one of these sides in the experiment carries a particle and one doesn’t, you’ll never get that right. You’re breaking this very important symmetry in quantum mechanics.””

But isn’t the pilot wave precisely ethereal and nonlocal in nature, undergoing instantaneous changes to itself at all points of space? Doesn’t the pilot theory posit that this wave doesn’t consist of anything material that does the waving but is just a wave, all by itself?

…So, if you think it through, people seem to be mixing up two separate issues here:

1. One issue is whether it will at all be possible for any real physical experiment done up with the bouncing droplets to be able to reproduce the predictions of QM or not.
2. An entirely different issue is whether, in Bohr’s dividing-wall thought-experiment, the de Broglie-Bohm approach actually predicts something that is at a variance from what QM predicts or not.

These two indeed are separate issues, and I think that the critics are right on the first count, but not necessarily on the second.

Just to clarify: The interference pattern as predicted by the mainstream QM itself would undergo a change, a minor but a very definite change, once you introduce the middle dividing wall; it would be different from the pattern obtained for the “plain-vanilla” version of the interference chamber. And if what I understand about the Bohmian mechanics is correct, then it too would proceed to  produce exactly the same patterns in both these cases.

With that said, I would still like to remind you that my own understanding of the pilot-wave theory is only minimal, mostly at the level of browsing of the Wiki and a few home pages, and going through a few pop-sci level explanations by a few Bohmians. I have never actually sat down to actually go through even one paper on it fully (let alone systematically study an entire book or a whole series of articles on this topic).

For this reason, I would rather leave it to the “real” Bohmians to respond to this fresh argument by Prof. Tomas Bohr.

But yes, a new argument—or at least, an old argument but in a remarkably new settings—it sure seems to be.

How would the Bohmians respond?

If you ask me, from whatever I have gathered about the Bohmians and their approach, I think that they are simply going to be nonchalant about this new objection, too. I don’t think that you could possibly hope to pin them down with this argument either. They are simply going to bounce back, just like those drops. And the reason for that, in turn, is what I mentioned already here in this post: their pilot-wave is both ethereal and nonlocal in the first place.

So, yes, even if Wolchover’s report does seem to be misguided a bit, I still liked it, mainly because it was informative on both the sides: experimental as well as theoretical (viz., as related to the new thought-experiment).

In conclusion, even if the famous experiment does not doom this (Bohmian) alternative to the quantum weirdness, the basic reason for its unsinkability is this:

The Bohmian mechanics is just as weird as the mainstream QM is—even if the Bohmians habitually and routinely tell you otherwise.

When a Bohmian tells you that his theory is “sensible”/“realistic”/etc/, what he is talking about is: the nature of his original ambition—but not the actual nature of his actual theory.

To write anything further about QM is to begin dropping hints to my new approach. So let me stop right here.

[But yes, I am fully ready willing from my side to disclose all details about it at any time to a suitable audience. … Let physics professors in India respond to my requests to let me conduct an informal (but officially acknowledged) seminar on my new approach, and see if I get ready to deliver it right within a week’s time, or not!

[Keep waiting!]]

Regarding other things, as you know, the machine I am using right now is (very) slow. Even then, I have managed to run a couple of 10-line Python scripts, using VSCode.

I have immediately taken to liking this IDE “code-editor.” (Never had tried it before.) I like it a lot. … Just how much?

I think I can safely say that VSCode is the best thing to have happened to the programming world since VC++ 6 about two decades ago.

Yes, I have already stopped using PyCharm (which, IMHO, is now the second-best alternative, not the best).

No songs section this time, because I have already run a neat and beautiful song just yesterday. (Check out my previous post.) … OK, if some song strikes me in a day or two, I will return here to add it. Else, wait until the next time around. … Until then, take care and bye for now…

[Originally published on 16 October 2018 22:09 hrs IST. Minor editing (including to the title line) done by 17 October 2018 08:09 hrs IST.]