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 + 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”.]
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.
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.
- is perfectly comfortable with FTL tunnelling,
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.)
— 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.