Now I am become Bohmianism

1. About the title of this post:

Just before this Diwali, I had tweeted that I had made a resolution. The tweets went like this:

Let me note the text portions of these tweets (just in case I delete these some time later or so).

3:29 PM 13 Nov. 2020:

This year, Pune directly went from the monsoon air to the Diwali air. We seem to have tunnelled through the October heat!

3:55 PM, 13 Nov. 2020:

#Deepavali #Diwali #deepavali2020 #Diwali2020

[Diya lamp emoji, 3 times]

This is the *third* straight Diwali that I go jobless.

3:56 PM, 13 Nov. 2020:

My Diwali Resolution:

“Be a Bohmian (https://www.google.com/search?q=Bohmian+mechanics)

[Yes, there are going to be the usual New Year’s Resolutions according to the Western calender too!]

Alright.

We will come to the “tunnelling” part later. Also, the tweet related to my jobless-ness. [If the Indian IT industry has any sense of shame left at all, they would have prevented this circumstance. But more on this, too, later.]

For the time being, I want to focus on the last tweet, and say that, accordingly:

Now I am become Bohmianism.

As to the quaint grammar used in the expression, first consult this Wired article [^], also the Q&A at the Quora [^].

As to why I use “Bohmianism” instead of “a Bohmian”: Well, to know that, you have to understand Sanskrit. If you do, then refer to the Gita, Chapter 11, verse 32, the compound phrase “कालोऽस्मि” (“kaalo smi”). I just tried to keep a similar grammatical form. … But let me hasten to add that I am not a Sanskrit expert, and so, going wrong is always a possibility. However, I also think that here I have not.

Hence the title of this post.

Now, going over to the Bohmianism i.e. the Bohmian mechanics proper…


2. Material on the Bohmian mechanics (BM):

The following is a partial list of papers and other material on BM that I have downloaded. I am giving you the list in a roughly chronological order. However, my reading isn’t going to be in any particular order. I have not read them all yet. In fact, I’ve just got going with some them, as of now.

Also note, I expect that

  • Some of this material might have become outdated by now
  • I may run into some other related topics as my studies progress

Alright. On to the list…


2.1 Student theses:

Antony Valentini (1992) “On the pilot-wave theory of classical, quantum and subquantum physics,” Ph.D. Thesis, International School for Advanced Studies, Trieste

Caroline Colijn (2003) “The de Broglie-Bohm causal interpretation of quantum mechanics and its application to some simple systems,” Ph.D. Thesis, University of Waterloo.

Paulo Machado (2007) “Computational approach to Bohm’s quantum mechanics,” Ph.D. Thesis, McMaster University

Jeff Timko (2007) “Bohmian trajectories of the two-electron helium atom,” Master’s Thesis, University of Waterloo

Leopold Kellers (2017) “Making use of quantum trajectories for numerical purposes,” Master’s Thesis, Technische Universität München


2.2. Code:

Dane Odekirk (2012) “Python calculations of Bohmian trajectories,” GitHub, 12 December 2012. https://github.com/daneodekirk/bohm


2.3. Papers:

C. Philippidis, C. Dewdney and B. J. Hiley (1978) “Quantum interference and the quantum potential,” https://www.researchgate.net/publication/225228072

Berthold-Georg Englert, Marlan O. Scully, Georg Sussmann and Herbert Walther (1992) “Surrealistic Bohm trajectories,” Z. Naturforsch. 47 a, 1175–1186.

Robert E. Wyatt and Eric R. Bittner (2003) “Quantum mechanics with trajectories: quantum trajectories and adaptive grids,” arXiv:quant-phy/0302088v1 11 Feb 2003

Roderich Tumulka (2004) “Understanding Bohmian mechanics: A dialogue,” Am. J. Phys., vol. 72, no. 9, September 2004, pp. 1220–1226.

D.-A. Deckert, D. Dürr, P. Pickl (2007) “Quantum dynamics with Bohmian trajectories,” arXiv:quant-phy/0701190v2 13 May 2007

Guido Bacciiagaluppi and Antony Valentini (2009) “Quantum theory at the crossroads: Reconsidering the 1927 Solvay conference,” Cambridge UP, ISBN: 9780521814218 arXiv:quant-ph/0609184v2 24 Oct 2009 [Note: This is actually a book.]

M. D. Towler and N. J. Russell (2011) “Timescales for dynamical relaxation to the Born rule,” arXiv:1103.1589v2 [quant-ph] 27 Sep 2011

Michael Esfeld, Dustin Lazarovici, Mario Hubert, Detlef Dürr (2012) “The ontology of Bohmian mechanics,” preprint, British Journal for the Philosophy of Science

Travis Norsen (2013) “The pilot-wave perspective on quantum scattering and tunneling,” m. J. Phys., vol. 81, no. 4, April 2013, pp. 258–266. arXiv:1210.7265v2 [quant-ph] 9 Jan 2013

Travis Norsen (2013) “The pilot-wave perspective on spin,” arXiv:1305.1280v2 [quant-ph] 10 Sep 2013

Kurt Jung (2013) “Is the de Broglie-Bohm interpretation of quantum mechanics really plausible?,” Journal of Physics: Conference Series 442 (2013) 012060 doi:10.1088/1742-6596/442/1/012060

Samuel Colin and Antony Valentini (2014) “Instability of quantum equilibrium in Bohm’s dynamics,” Proc. R. Soc. A 470: 20140288. http://dx.doi.org/10.1098/rspa.2014.0288

W. B. Hodge, S. V. Migirditch and W. C. Kerr (2014) “Electron spin and probability current density in quantum mechanics,” Am. J. Phys., vol. 82, no. 7, July 2014, pp. 681–690

B. Zwiebach (2016) “Lecture 6,” Course Notes for MIT 8.04 Quantum Physics, Spring 2016.

Basil J. Hiley and Peter Van Reeth (2018) “Quantum trajectories: real or surreal?,” Entropy vol. 20, pp. 353 doi:10.3390/e20050353

Oliver Passon (2018) “On a common misconception regarding the de Broglie-Bohm theory,” Entropy vol. 20, no. 440. doi:10.3390/e20060440


2.4. Advanced papers:

Asher Yahalom (2018) “The fluid dynamics of spin,” Molecular Physics, April 2018, doi: 10.1080/00268976.2018.1457808. https://www.researchgate.net/publication/324512014, arXiv:1802:09331v1 [physics.flu-dyn] 3 Feb 2018

Siddhant Das and Detlef Dürr (2019) “Arrival time distributions of spin-1/2 particles,” Scientific Reports, https://doi.org/10.1038/s41598-018-38261-4

Siddhant Das, Markus Nöth, and Detlef Dür (2019) “Exotic Bohmian arrival times of spin-1/2 particles I—An analytical treatment,” arXiv:1901.08672v1 [quant-ph] 24 Jan 2019


2.5. Nonlinearity in the Bohmian mechanics:

To my surprise, I found that a form of non-linearity has been found to come up in the Bohmian mechanics too. I am sure it must have come as a surprise to many others too. [I will comment on this aspect quite some time later. For the time being, let me list some of the papers/presentations I’ve found so far.]

Sheldon Goldstein (1999) “Absence of chaos in Bohmian dynamics,” arXiv:quant-ph/9901005v1 6 Jan 1999

S. Sengupta, A. Poddar and P. K. Chattaraj (2000) “Quantum manifestations of the classical chaos in an undamped Duffing oscillator in presence of an external field: A quantum theory of motion study,” Indian Journal of Chemistry, vol. 39A, Jan–March 2000, pp. 316–322

A. Benseny, G. Albareda, A. S. Sanz, J. Mompart, and X. Oriols (2014) “Applied Bohmian mechanics,” arXiv:1406.3151v1 [quant-ph] 12 Jun 2014

Athanasios C. Tzemos (2016) “The mechanism of chaos in 3-D Bohmian trajectories,” Poster Presentation, https://www.researchgate.net/publication/305317081

Athanasios C. Tzemos (2018) “3-d Bohmian chaos: a short review,” Presentation Slides, RCAAM, Academy Of Athens

Athanasios C. Tzemos (2019) “Quantum entanglement and Bohmian Mechanics,” Presentation Slides 17 July 2019, RCAAM of the Academy of Athens

Klaus von Bloh (2020) “Bohm trajectories for the noncentral Hartmann potential,” Wolfram demonstration projects, https://www.researchgate.net/publication/344171771 (August 2020)

G. Contopoulos and A. C. Tzemos (2020) “Chaos in Bohmian quantum mechanics: a short review,” arXiv:2009.05867v1 [quant-ph] 12 Sep 2020


3. What happens to my new approach?

It was only yesterday that a neat thing struck me. Pending verification via simulations, it has the potential to finally bring together almost all of my research on the spinless particles. I’ve noted this insight in the hand-written journal (i.e. research notebook) that I maintain. I will be developing this idea further too. After all, Bohmians do study mainstream quantum mechanics and other interpretations, don’t they?

Due to the RSI, the simulations, however, will have to wait further. (The status is more or less the same. If I type for 2–3 hours, it’s easily possible that I can’t do much anything for the next 2–3 days.)

OK. Take care and bye for now.


A song I like:

(Hindi) देखा ना हाय रे सोचा ना (“dekhaa naa haay re sochaa naa”)
Singer: Kishore Kumar
Music: R. D. Burman
Lyrics: Rajinder Krishan

[Another song I used to love in my high-school days—who wouldn’t? … And, of course, I still do! A good quality audio I found is here [^]. I had not watched this movie until about a decade ago, on a CD (or may be on the TV). I’ve forgotten the movie by now. I don’t mind giving you the link for the video of this song; see here [^]. (In any case, it’s at least 3 orders of magnitude better than any so-called Lyrical Video Saregama has released for any song. The very idea of the Lyrical is, IMO, moronic.)]

 

 

Updates: RSI. QM tunnelling time.

Yes, the correct spelling of the word in the title is “tunnelling” (with a double “l”): [^].


1. Update on my RSI:

1.1. RSI :

The RSI has been waning for a few days by now. However, I am not sure if I should therefore begin my QM simulations or not. Going by how the RSI had immediately reverted its course about 8–10 days ago or so, I’ve decided to take it easy for now. This blog post itself is a “test-case” of sorts—to see how the RSI reacts.

1.2. Not quitting QM, but…:

I still have not begun simulations. It’s only after simulations that I would be able to judge whether to quit QM for a long while, or to write a paper on my new approach.

Writing documentation/paper only after conducting some simulations, might look like a lack of confidence on my part on the theoretical side. … Yes, as of now, this much is true. … Yes, by now, I’ve gathered together enough ideas about the 3D + spin with the new approach, but some elements are still to be worked through, especially those concerning the spin.

QM is complex. There is a pun here, but it was not intended. QM is complicated. And, very unintuitive. That’s why, building a completely new approach is difficult. It takes time, and thinking, and re-thinking.


2. Tunnelling time for quantum mechanical particle(s):

See the Quanta Magazine article “Quantum tunnels show how particles can break the speed of light” [^].

On 2020.10.26, I had noted on Twitter [^] that:

“This is actually a scenario that’s tough to get right. Wolchover’s coverage is v. good, but the intricacies themselves are such that I, for one, don’t have that feeling of being on top of it. Need to re-read.

A topic that rarely makes it to pop-sci level QM. Good they covered it”

Since then, I’ve re-read this Quanta Mag article some “two and a half” times.

I’ve also browsed through Prof. Aephraim Steinberg’s Web site in general (after a gap of may be 2–3 years), and his group’s page on quantum tunnelling in particular [^]. [I ignored his spelling mistake concerning “tunnelling”.]

I then rapidly looked through the arXiv version [^] of their July 2020 Nature paper [^]—the one which was covered in the above mentioned Quanta Mag article.

For the time being, let me note these comments (without explaining them):

2.1. Details of the experiment are quite complicated:

Understanding the details (even the more important ones) of this experiment is going to take a while.

2.2. But there is a video which explains the essential ideas behind this experiment:

A highly simplified version of this experiment is relatively straight-forward to understand. See this excellent German-language video with English subtitles [^] (which I found mentioned in Steinberg’s Twitter feed).

As to the video: I guess I had understood the points that have been covered in the video, and then a slight bit more too, right on the first reading of the Quanta Mag article (i.e., when I made the above mentioned tweet). However, I still had a lot of doubts / questions related to the specifics of the experimental setup. I still do.

My study of this work continues. Oh, BTW, I’ve downloaded quite a bunch of papers, including about the Hartman effect [^], e.g. this one [ (PDF) ^]. (Hartman, the first to publish the calculations even if they sounded very implausible to others due to their poor understanding of the relationship of QM and relativity principles, was an engineer!)

2.3. A SciAm article by Anil Ananthswamy:

Right as I was writing this post, I ran into Anil Ananthaswamy’s SciAm post: “Quantum tunneling is not instantaneous, physicists show” [^]. … Looks like it came in July 2020, but I had, somehow, missed it!

The Quanta Mag article covers a more comprehensive territory. It goes over the experiments done before Steinberg’s to a greater depth. In contrast, Ananthswamy’s article focuses more on Steinberg’s work, and is easier to understand. So, on the second thoughts, go through this article first.

2.4. Steinberg’s experiment is truly outstanding:

I think that Steinberg’s idea of using the Larmor precession for experimentally determining the tunnelling times is neat, exceptionally neat. Just how exceptionally neat?

Well, I still don’t understand the QM spin the way I would really like to (and that’s because I don’t know the relativity theory). It is for this reason that I request you to take my judgment with a pinch of salt.

Yet, within this explicitly stated limitation of my understanding, I still think that it would be reasonable enough to say that:

This experiment could easily get nominated for a physics Nobel.

Reason:

In my opinion, this experiment is more outstanding than the famous series of experiments on testing QM entanglements, as by Aspect, Freedman and Clauser, and by others [^].

If the grapevine (i.e. opinions publicly expressed around the time of announcement of physics Nobels, over so many years by now) is anything to go by, then it’s reasonable to say that the Bell experiments must have been nominated for the physics Nobel.

If you want to know why I think the quantum tunnelling time experiment is more outstanding than the Bell test experiments, then I will try to give my reasons, but at some other time. I have to look after my wrist! Plus, I think the matter is very straight-forward. There is no room in the Copenhagen interpretation to even define something like a tunnelling time. There. Right there you have something to begin with. Also try to understand the idea behind the so called “weak measurement” experiments, and the particular advantages they bring.

2.5. The relevance of the tunnelling time experiments to my research:

Faster than light (FTL) speeds for the tunnelled particle should not surprise anyone. I don’t know why some physicists make an issue out of it.

In any case, assuming a simplified and abstract description of this experiment (as in the video mentioned above), I can say that:

My new approach  

    • is perfectly comfortable with FTL tunnelling,
    • predicts finite speeds, i.e., denies instantaneous action at a distance (IAD) for propagation of massive particles even in its present (non-relativistic) formulation.

That’s why I like this experiment. I was, in fact, looking for something on the “time taken” side, though I had somehow missed this particular experiment until the Quanta Mag ran the story.

It would be fun to develop my new approach to the point that it becomes possible to do a simulation of this experiment—at least a schematic version of it.

2.6. Should they pursue Bohmian mechanics for their simulations?

Steinberg’s group seems to have used the Bohmian mechanics for their simulations in the past. I think it’s not a good idea. See the next section.


3. Bohmian mechanics is flawed at a very basic level:

In general, by now, I have come to a definite conclusion that the Bohmian mechanics (BM) has a deep flaw in it—right at its most basic level.

So as to not stress my wrist a lot, let’s pursue this discussion in the next post (after a few days or a week).

In the meanwhile, go through this paper [^] by Prof. Travis Norsen. It’s a very well written paper; very easy to understand. It explains BM very clearly. In fact, it explains BM so clearly, in such a simplifying way, that it ends up defeating its very purpose! The author’s unstated goal here, I think, was to show that BM is reasonable. That must be the reason why he wrote this paper. But precisely because it’s so well written, you do get to understand BM very quickly. Which, in turn, makes spotting the flaws of BM so much the easier!

If you know the mainstream QM formalism well enough (especially its postulates), and if you have already thought a bit about the QM measurement problem (i.e., the “Process 1” according to von Neumann’s description of it [^]), then, it is possible to spot the essential weakness of the Bohmian mechanics just by reading only the first section (titled “Introduction”) of Norsen’s paper!

In a way, that’s why I appreciated this paper so much. In the past, I had tried to understand BM on 4–5 different occasions. But each time, I had to give up my attempt pretty soon, because I couldn’t understand the ideas like: the maths of the BM potential (after starting from geometrical optics), the physical source (if any) of that potential, etc.. … Somehow, I had not looked into this paper by Norsen all this while—the one which makes it all so easy to  understand!

So, go through this paper. We will discuss the weakness of the BM the next time. (If you know QM and are too short of patience to wait until the next post, then send me an email or leave a comment below, and I will give you an exactly one-line answer to you.)

BTW, Norsen has another paper that seeks to explain the QM spin in terms of BM; see it here [^]. I haven’t gone through it as yet, but if possible, I will try to cover it in the next post too. Or, if not in the next post, then at some other time when I discuss the QM spin.


4. My plans for the immediate future:

It was only yesterday that I began typing something in LaTeX (as in contrast to merely surfing the ‘net or tweeting). The typing was mostly a copy-paste job, plus some typing of equations in LaTeX. I pursued this activity for a couple of hours yesterday. Guess there wasn’t any noticeable worsening of the RSI today.

So, let me now try taking some notes on QM, or writing something further on my new approach to QM, or writing some Python code, from today onwards. I will be proceeding cautiously; I will not be exceeding 2–3 hours of typing per day, at least initially (over the coming few days). Let’s see how things progress.

OK, take care and bye for now.


A song I like:

(Marathi) तुझ्याच साठी कितीदा (“tujhyaach saaThee kiteedaa”)
Lyrics: N. G. Deshpande
Music: Shrinivas Khale
Singer: Krishna Kalle

[ Credits happily listed in a random order.

There are certain songs for which it doesn’t quite feel apt to say “I like this song” [so much, etc.]. A better way instead is to say this: There are some song such that, by showing how creativity and beauty can be combined with simplicity, they become some kind of a reference point for you—not just in the development of your tastes in music, but also in allowing you to grasp certain concepts like “culture” itself. And thus, it can be said that these songs have had a formative influence on you.

As far as I am concerned, this is one of such songs. I consider myself lucky to have been born at such a time that songs like these not only were being made but also were popular—at least, popular enough.

(And no, unlike many Indians/Maharashtrians who are high on culture and all, my reference points aren’t restricted to the Indian classical or semi-classical music alone. And, the set of my reference points doesn’t over-emphasize the devotional songs either. Et cetera. In fact, my referents haven’t been restricted to just the Indian songs either (as many of you might have gathered by now). …But then, matters like these is another story. Remind me some other day, when my wrist is in a better condition.)

A good quality audio for this song, appearing as a part of a collection, is here [^]. A link for a stand-alone version is here [^].

]


History:
— 2020.11.08 15:39 IST: Published
— 2020.11.09 00:53 IST: Very minor revisions/additions. Am done with this post now.
— 2020.11.10 12:08 IST: Added a couple of links for the Hartman effect.

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.

Addendum on 2019.06.06:

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