Some comments on QM and CM—Part 2: Without ontologies, “classical” mechanics can get very unintuitive too. (Also, a short update.)

We continue from the last post. If you haven’t read and understood it, it can be guaranteed that you won’t understand anything from this one! [And yes, this post is not only long but also a bit philosophical.]


The last time, I gave you a minimal list of different ontologies for physics theories. I also shared a snap of my hurriedly jotted (hand-written) note. In this post, I will come to explain what I meant by that note.


1. In the real world, you never get to see the objects of “classical” mechanics:

OK, let’s first take a couple of ideas from Newtonian mechanics.

1.1. Point-particles:

The Newtonian theory uses a point particle. But your perceptual field never holds the evidence for any such an object. The point particle is an abstraction. It’s an idealized (conceptual-level) description of a physical object, a description that uses the preceding mathematical ideas of limits (in particular, the idea of the vanishingly small size).

The important point to understand here isn’t that the point-particle is not visible. The crucial point here is: it cannot be visible (or even made visible, using any instrument) because it does not exist as a metaphysically separate object in the first place!

1.2. Rigid bodies:

It might come as a surprise to many, esp. to mechanical engineers, but something similar can also be said for the rigid body. A rigid body is a finite-sized object that doesn’t deform (and unless otherwise specified, doesn’t change any of its internal fields like density or chemical composition). Further, it never breaks, and all its parts react instantaneously to any forces exerted on any part of it. Etc.

When you calculate the parabolic trajectory of a cricket ball (neglecting the air resistance), you are not working with any entity that can ever be seen/ touched etc.—in principle. In your calculations, in your theory, you are only working with an idea, an abstraction—that of a rigid body having a center of mass.

Now, it just so happens that the concepts from the Newtonian ontologies are so close to what is evident to you in your perceptual field, that you don’t even notice that you are dealing with any abstractions of perceptions. But this fact does not mean that they cease to be abstract ideas.


2. Metaphysical locus of physics abstractions, and epistemology of how you use them:

2.1. Abstractions do exist—but only in the mind:

In general, what’s the metaphysics of abstractions? What is the metaphysical locus of its existence?

An abstraction exists as a unit of mental integration—as a concept. It exists in your mind. A concept doesn’t have an existence apart from, or independent of, the men who know and hold that concept. A mental abstraction doesn’t exist in physical reality. It has no color, length, weight, temperature, location, speed, momentum, energy, etc. It is a non-material entity. But it still exists. It’s just that it exists in your mind.

In contrast, the physical objects to which the abstractions of objects make a reference, do exist in the physical reality out there.

2.2. Two complementary procedures (or conceptual processings):

Since the metaphysical locus of the physical objects and the concepts referring to them are different, there have to be two complementary and separate procedures, before a concept of physics (like the ideal rigid body) can be made operational, say in a physics calculation:

2.2.1. Forming the abstraction:

First, you have to come to know that concept—you either learn it, or if you are an original scientist, you discover/invent it. Next, you have to hold this knowledge, and also be able recall and use it as a part of any mental processing related to that concept. Now, since the concept of the rigid body belongs to the science of physics, its referents must be part of the physical aspects of existents.

2.2.2. Applying the abstraction in a real-world situation:

In using a concept, then, you have to be able to consider a perceptual concrete (like a real cricket ball) as an appropriate instance of the already formed concept. Taking this step means: even if a real ball is deformable or breakable, you silently announce to yourself that in situations where such things can occur, you are not going to apply the idea of the rigid body.

The key phrases here are: “inasmuch as,” “to that extent,” and “is a.” The mental operation of regarding a concrete object as an instance of a concept necessarily involves you silently assuming this position: “inasmuch as this actual object (from the perceptual field) shows the same characteristics, in the same range of “sizes”, as for what I already understand by the concept XYZ, therefore, to that extent, this actual object “is a” XYZ.

2.2.3. Manipulation of concepts at a purely abstract level is possible (and efficient!):

As the next step, you have to be able to directly manipulate the concept as a mere unit from some higher-level conceptual perspective. For example, as in applying the techniques of integration using Newton’s second law, etc.

At this stage, your mind isn’t explicitly going over the defining characteristics of the concept, its relation to perceptual concretes, its relation to other concepts, etc.

Without all such knowledge at the center of your direct awareness, you still are able to retain a background sense of all the essential properties of the objects subsumed by the concept you are using. Such a background sense also includes the ideas, conditions, qualifications, etc., governing its proper usage. That’s the mental faculty automatically working for you when you are born a human.

You only have to will, and the automatic aspects of your mind get running. (More accurately: Something or the other is always automatically present at the background of your mind; you are born with such a faculty. But it begins serving your purpose when you begin addressing some specific problem.)

All in all: You do have to direct the faculty which supplies you the background context, but you can do it very easily, just by willing that way. You actually begin thinking on something, and the related conceptual “material” is there in the background. So, free will is all that it takes to get the automatic sense working for you!

2.2.4. Translating the result of a calculation into physical reality:

Next, once you are done with working ideas at the higher-level conceptual level, you have to be able to “translate the result back to reality”. You have to be able to see what perceptual-level concretes are denoted by the concepts related to the result of calculation, its size, its units, etc. The key phrase here again are: “inasmuch as” and “to that extent”.

For example: “Inasmuch as the actual cricket ball is a rigid body, after being subjected to so much force, by the laws governing rigid bodies (because the laws concern themselves only with the rigid bodies, not with cricket balls), a rigid body should be precisely at 100.0 meter after so much time. Inasmuch as the cricket ball can also be said to have an exact initial position (as for a rigid body used in the calculations), its final position should be exactly 100 meter away. Inasmuch as a point on the ground can be regarded as being exactly 100 meter away (in the right direction), the actual ball can also be expected, to that extent, to be at [directly pointing out] that particular spot after that much time. Etc.

2.3: A key take-away:

So, an intermediate but big point I’ve made is:

Any theory of classical mechanics too makes use of abstractions. You have to undertake procedures involving the mappings between concretes and abstractions, in classical mechanics too.

2.4. Polemics:

You don’t see a rigid body. You see only a ball. You imagine a rigid body in the place of the given ball, and then decide to do the intermediate steps only with this instance of the imagination. Only then can you invoke the physics theory of Newtonian mechanics. Thus, the theory works purely at the mental abstractions level.

A theory of physics is not an album of photographs; an observation being integrated in a theory is not just a photograph. On the other hand, a sight of a ball is not an abstraction; it is just a concretely real object in your perceptual field. It’s your mind that makes the connection between the two. Only can then any conceptual knowledge be acquired or put to use. Acquisition of knowledge and application of knowledge are two sides of the same coin. Both involve seeing a concrete entity as an instance subsumed under a concept or a mental perspective.

2.5. These ideas have more general applicability:

What we discussed thus far is true for any physics theory: whether “classical” mechanics (CM) or quantum mechanics (QM).

It’s just that the first three ontologies from the last post (i.e. the three ontologies with “Newtonian” in their name) have such abstractions that it’s very easy to establish the concretes-to-abstractions correspondence for them.

These theories have become, from a hindsight of two/three centuries and absorption of its crucial integrative elements into the very culture of ours, so easy for us to handle, they seem to be so close to “the ground” that we have to think almost nothing to regard a cricket ball as a rigid body. Doesn’t matter. The requirement of you willingly having to establish the correspondenc between the concretes and abstractions (and vice versa) still exists.

Another thing: The typical application of all the five pre-quantum ontologies also typically fall in the limited perceptual range of man, though this cannot be regarded as the distinguishing point of “classical” mechanics. This is an important point so let me spend a little time on it.

Trouble begins right from Fourier’s theory.


3. “Classical” mechanics is not without tricky issues:

3.1. Phenomenological context for the Fourier theory is all “classical”:

In its original form, Fourier’s theory dealt with very macroscopic or “every day” kind of objects. The phenomenological context which gave rise to Fourier’s theory was: the transmission of heat from the Sun by diffusion into the subterranean layers of the earth, making it warm. That was the theoretical problem which Fourier was trying to solve, when he invented the theory that goes by his name.

Actually, that was a bit more complicated problem. A simpler formulation of the same problem would be: quantitatively relating the thermal resistance offered by wood vs. metal, etc. The big point I want to note here is: All these (the earth, a piece of wood or metal) are very, very “everyday” objects. You wouldn’t hesitate saying that they are objects of “classical” physics.

3.2. But the Fourier theory makes weird predictions in all classical physics too:

But no matter how classical these objects look, an implication is this:

The Fourier theory ends up predicting infinite velocity for signal propagation for “classical” objects too.

This is a momentous implication. Make sure you understand it right. Pop-sci writers never highlight this point. But it’s crucial. The better you understand it, the less mysterious QM gets!

In concrete terms, what the Fourier theory says is this:

If you pour a cup of warm water on ground at the North pole, no doubt the place will get warmer for some time. But this is not the only effect your action would have. Precisely and exactly at the same instant, the South pole must also get warmer, albeit to a very small extent. Not only the South Pole, every object at every place on the earth, including the cell phone of your friend sitting in some remote city also must get warmer. [Stretching the logic, and according a conduction mode also to the intergalactic dust: Not just that, every part of the most distant galaxies too must get warmer—in the same instant.] Yes, the warming at remote places might be negligibly small. But in principle, it is not zero.

And that’s classical physics of ordinary heat conduction for you.

3.3. Quantum entanglement and Heisenberg’s uncertainty principle are direct consequences of the same theory:

Now, tell me, how intuitive was Fourier’s predictions?

My answer: Exactly as unintuitive as is the phenomenon of quantum entanglement—and, essentially, for exactly the same ontological-physical-mathematical reasons!

Quantum entanglement is nothing but just another application of the Fourier theory. And so is Heisenberg’s uncertainty principle. It too is a direct consequence of the Fourier theory.

3.4. Another key take-away:

So, the lesson is:

Not all of “classical” mechanics is as “intuitive” as you were led to believe.

3.5. Why doesn’t any one complain?

If classical physics too is that unintuitive, then how come that no one goes around complaining about it?

The reason is this:

Classical mechanics involves and integrates a conceptually smaller range of phenomena. Most of its application scenarios too are well understood—even if not by you, and then at least by some learned people, and they have taken care to explain all these scenarios to you.

For instance, if I ask you to work out how the Coriolis force works for two guys sitting diametrically opposite on a rotating disco floor and throwing balls at each other, I am willing to take a good bet that you won’t be able to work out everything on your own using vector analysis and Newton’s laws. So, this situation should actually be non-intuitive to you. It in fact is: Without searching on the ‘net, be quick and tell me whether the ball veers in the direction of rotation or opposite it? See? It’s just that no pop-sci authors highlight issues like this, and so, no philosophers take notice. (And, as usual, engineers don’t go about mystifying anything.)

So, what happens in CM is that some expert works out the actual solution, explains to you. You then snatch some bits and pieces, may be just a few clues from his explanation, and memorize them. Slowly, as the number of such use-cases increases, you get comfortable enough with CM. Then you begin to think that CM is intuitive. And then, the next time when your grandma asks you how come that motorcyclist spinning inside the vertical well doesn’t fall off, you say that he sticks to the wall due to the centrifugal force. Very intuitive! [Hint, hint: Is it actually centrifugal or centripetal?]

OK, now let’s go over to QM.


4. The abstract-to-concretes mappings are much more trickier when it comes to QM:

4.1. The two-fold trouble:

The trouble with QM is two-fold.

First of all, the range of observations (or of phenomenology) underlying it is not just a superset of CM, it’s a much bigger superset.

Second: Physicists have not been able to work out a consistent ontology for QM. (Most often, they have not even bothered to do that. But I was talking about reaching an implicit understanding to that effect.)

So, they are reduced to learning (and then teaching) QM in reference to mathematical quantities and equations as the primary touch-stones.

4.2. Mathematical objects refer to abstract mental processes alone, not to physical objects:

Now, mathematical concepts have this difference. They are not only higher-level abstractions (on top of physical concepts), but their referents too in themselves are invented and not discovered. So, it’s all in the mind!

It’s true that physics abstractions, qua mental entities, don’t exist in physical reality. However, it also is true that the objects (including their properties/characteristics/attributes/acctions) subsumed under physics concepts do have a physical existence in the physical world out there.

For instance, a rigid body does not exist physically. But highly rigid things like stones and highly pliable or easily deformable things like a piece of jelly or an easily fluttering piece of cloth, do exist physically. So, observing them all, we can draw the conclusion that stones have much higher rigidity than the fluttering flag. Then, according an imaginary zero deformability to an imaginary object, we reach the abstraction of the perfectly rigid body. So, while the rigid body itself does not exist, rigidity as such definitely is part of the natural world (I mean, of its physical aspects).

But not so with the mathematical abstractions. You can say that two (or three or n number of) stones exist in a heap. But what actually exists are only stones, not the number 2, 3, or n. You can say that a wire-frame has edges. But you don’t thereby mean that its edges are geometrical lines, i.e., objects with only length and no thickness.

4.3. Consequence: How physicists hold, and work with, their knowledge of the QM phenomena:

Since physicists could not work out a satisfactory ontology for QM, and since concepts of maths do not have direct referents in the physical reality as apart from the human consciousness processing it size-wise, their understanding of QM does tend to be a lot more shaky (the comparison being with their understanding of the pre-quantum physics, esp. the first three ontologies).

As a result, physicists have to develop their understanding of QM via a rather indirect route: by applying the maths to even more number of concrete cases of application, verifying that the solutions are borne out by the experiments (and noting in what sense they are borne out), and then trying to develop some indirect kind of a intuitive feel, somehow—even if the objects that do the quantum mechanical actions aren’t clear to them.

So, in a certain sense, the most talented quantum physicists (including Noble laureates) use exactly the same method as you and me use when we are confronted with the Coriolios forces. That, more or less, is the situation they find themselves in.

The absence of a satisfactory ontology has been the first and foremost reason why QM is so extraordinarily unintuitive.

It also is the reason why it’s difficult to see CM as an abstraction from QM. Ask any BS in physics. Chances are 9 out of 10 that he will quote something like Planck’s constant going to zero or so. Not quite.

4.4. But why didn’t any one work out an ontology for QM?

But what were the reasons that physicists could not develop a consistent ontology when it came to QM?

Ah. That’s too complicated. At least 10 times more complicated than all the epistemology and physics I’ve dumped on you so far. That’s because, now we get into pure philosophy. And you know where the philosophers sit? They all sit on the Humanities side of the campus!

But to cut a long story short, very short, so short that it’s just a collage-like thingie: There are two reasons for that. One simple and one complicated.

4.4.1. The simple reason is this: If you don’t bother with ontologies, and then, if you dismiss ideas like the aether, and go free-floating towards ever higher and still higher abstractions (especially with maths), then you won’t be able to get even EM right. The issue of extracting the “classical” mechanical attributes, variables, quantities, etc. from the QM theory simply cannot arise in such a case.

Indeed, physicists don’t recognize the very fact that ontologies are more basic to physics theories. Instead, they whole-heartedly accept and vigorously teach and profess the exact opposite: They say that maths is most fundamental, even more fundamental than physics.

Now, since QM maths is already available, they argue, it’s only a question of going about looking for a correct “interpretation” for this maths. But since things cannot be very clear with such an approach, they have ended up proposing some 14+ (more than fourteen) different interpretations. None works fully satisfactorily. But some then say that the whole discussion about interpretation is bogus. In effect, as Prof. David Mermin characterized it: “Shut up and calculate!”

That was the simple reason.

4.4.2. The complicated reason is this:

The nature of the measurement problem itself is like that.

Now, here, I find myself in a tricky position. I think I’ve cracked this problem. So, even if I think it was a very difficult problem to crack, please allow me to not talk a lot more about it here; else, doing so runs the risk of looking like blowing your own tiny piece of work out of all proportion.

So, to appreciate why the measurement problem is complex, refer to what others have said about this problem. Coleman’s paper gives some of the most important references too (e.g., von Neumann’s process 1 vs. process 2 description) though he doesn’t cover the older references like the 1927 Bohr-Einstein debates etc.

Then there are others who say that the measurement problem does not exist; that we have to just accept a probabilistic OS at the firmware level by postulation. How to answer them? That’s a homework left for you.


5. A word about Prof. Coleman’s lecture:

If Prof. Coleman’s lecture led you to conclude that everything was fine with QM, you got it wrong. In case this was his own position, then, IMO, he too got it wrong. But no, his lecture was not worthless. It had a very valuable point.

If Coleman were conversant with the ontological and epistemological points we touched on (or hinted at), then he would have said something to the following effect:

All physics theories presuppose a certain kind of ontology. An ontology formulates and explains the broad nature of objects that must be assumed to exist. It also puts forth the broad nature of causality (objects-identities-actions relations) that must be assumed to be operative in nature. The physics theory then makes detailed, quantitative, statements about how such objects act and interact.

In nature, physical phenomena differ very radically. Accordingly, the phenomenological contexts assumed in different physical theories also are radically different. Their radical distinctiveness also get reflected in the respective ontologies. For instance, you can’t explain the electromagnetic phenomena using the pre-EM ontologies; you have to formulate an entirely new ontology for the EM phenomena. Then, you may also show how the Newtonian descriptions may be regarded as abstractions from the EM descriptions.

Similarly, we must assume an entirely new kind of ontological nature for the objects if the maths of QM is to make sense. Trying to explain QM phenomena in terms of pre-quantum ontological ideas is futile. On the other hand, if you have a right ontological description for QM, then with its help, pre-QM physics may be shown as being a higher-level, more abstract, description of reality, with the most basic level description being in terms of QM ontology and physics.

Of course, Coleman wasn’t conversant with philosophical and ontological issues. So, he made pretty vague statements.


6. Update on the progress in my new approach. But RSI keeps getting back again and again!

I am by now more confident than ever that my new approach is going to work out.

Of course, I still haven’t conducted simulations, and this caveat is going to be there until I conduct them. A simulation is a great way to expose the holes in your understanding.

So take my claim with a pinch of salt, though I must also hasten to note that with each passing fortnight (if not week), the quantity of the salt which you will have to take has been, pleasantly enough (at least for me), decreasing monotonically (even if not necessarily always exponentially).

I had written a preliminary draft for this post about 10 days ago, right when I wrote my last post. RSI had seemed to have gone away at that time. I had also typed a list of topics (sections) to write to cover my new approach. It carried some 35+ sections.

However, soon after posting the last blog entry here, RSI began growing back again. So, I have not been able to make any substantial progress since the last post. About the only things I could add were: some 10–15 more section or topic names.

The list of sections/topics includes programs too. However, let me hasten to add: Programs can’t be written in ink—not as of today, anyway. They have to be typed in. So, the progress is going to be slow. (RSI.)

All in all, I expect to have some programs and documentation ready by the time Q1 of 2021 gets over. If the RSI keeps hitting back (as it did the last week), then make it end-Q2 2021.

OK. Enough for this time round.


A song I like:

[When it comes to certain music directors, esp. from Hindi film music, I don’t like the music they composed when they were in their elements. For example, Naushad. For example, consider the song: मोहे पनघट पे (“mohe panghat pe”). I can sometimes appreciate the typical music such composers have produced, but only at a somewhat abstract level—it never quite feels like “my kind of music” to me. Something similar, for the songs that Madan Mohan is most famous for. Mohan was a perfectionist, and unlike Naushad, IMO, he does show originality too. But, somehow, his sense of life feels like too sad/ wistful/ even fatalistic to me. Sadness is OK, but a sense of inevitability (or at least irromovability) of suffering is what gets in the way. There are exceptions of course. Like, the present song by Naushad. And in fact, all songs from this move, viz. साथी (“saathi”). These are so unlike Naushad!

I have run another song from this movie a while ago (viz. मेरे जीवन साथी, कली थी मै तो प्यासी (“mere jeevan saathee, kalee thee main to pyaasee”).

That song had actually struck me after a gap of years (may be even a decade or two), when I was driving my old car on the Mumbai-Pune expressway. The air-conditioner of my car is almost never functional (because I almost never have the money to get it repaired). In any case, the a/c was neither working nor even necessary, on that particular day late in the year. So, the car windows were down. It was pretty early in the morning; there wasn’t much traffic on the expressway; not much wind either. The sound of the new tires made a nice background rhythm of sorts. The sound was very periodic, because of the regularity of the waviness that comes to occur on cement-concrete roads after a while.

That waviness? It’s an interesting problem from mechanics. Take a photo of a long section of the railway tracks while standing in the middle, especially when the sun is rising or setting, and you see the waviness that has developed on the rail-tracks too—they go up and down. The same phenomenon is at work in both cases. Broadly, it’s due to vibrations—a nonlinear interaction between the vehicle, the road and the foundation layers underneath. (If I recall it right, in India, IIT Kanpur had done some sponsored research on this problem (and on the related NDT issues) for Indian Railways.)

So, anyway, to return to the song, it was that rhythmical sound of the new tires on the Mumbai-Pune Expressway which prompted something in my mind, and I suddenly recalled the above mentioned song (viz. मेरे जीवन साथी, कली थी मै तो प्यासी (“mere jeevan saathee, kalee thee main to pyaasee”). Some time later, I ran it here on this blog. (PS: My God! The whole thing was in 2012! See the songs section, and my the then comments on Naushad, here [^])

OK, cutting back to the present: Recently, I recalled the songs from this movie, and began wondering about the twin questions: (1) How come I did end up liking anything by Naushad, and (2) How could Naushad compose anything that was so much out of his box (actually, the box of all his traditional classical music teachers). Then, a quick glance at the comments section of some song from the same film enlightened me. (I mean at YouTube.) I came to know a new name: “Kersi Lord,” and made a quick search on it.

Turns out, Naushad was not alone in composing the music for this film: साथी (“saathee”). He had taken assistance from Kersi Lord, a musician who was quite well-versed with the Western classical and Western pop music. (Usual, for a Bawa from Bombay, those days!) The official credits don’t mention Kersi Lord’s name, but just a listen is enough to tell you how much he must have contributed to the songs of this collaboration (this movie). Yes, Naushad’s touch is definitely there. (Mentally isolate Lata’s voice and compare to मोहे पनघट पे (“mohe panghat pe”).) But the famous Naushad touch is so subdued here that I actually end up liking this song too!

So, here we go, without further ado (but with a heartfelt appreciation to Kersi Lord):

(Hindi) ये काैन आया, रोशन हो गयी (“yeh kaun aayaa, roshan ho gayee)
Singer: Lata Mangeshkar
Music: [Kersi Lord +] Naushad
Lyrics: Majrooh Sultanpuri

A good quality audio is here [^].

]


PS: May be one little editing pass tomorrow?

History:
— 2020.12.19 23:57 IST: First published
— 2020.12.20 19:50 IST and 2020.12.23 22:15 IST: Some very minor (almost insignificant) editing / changes to formatting. Done with this post now.

 

 

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.

Entanglement, nonlocality, and the slickness of the MSQM folks

Update: See at the end of this post.


0. Context

This post began its life as a comment to Roger Schlafly’s blog post: “Smolin preaches nonlocality nonsense” [^]. However, at 7000+ characters, my comment was almost twice the limit (of 4k characters) there. So, I decided to post my reply here, as a separate entry by itself.

I assume that you have read Schlafly’s post in toto before going any further.


1. Schlafly’s comments:

Schlafly says:

“Once separated, the two particles are independent.”

The two particles remain two different entities, but their future dynamics also remains, in part, governed by a single, initial, entangling, wavefunction.

“Nothing you do to one can possibly have any effect on the other.”

The only possible things you can do to any one (or both) of the entangled particles necessarily involves their shared (single) wavefunction.

Let me explain. Let’s begin at the beginning.


1. System description and notation:

Call the two entangled particles EP1 and EP2.

If you want to imagine two different things physically being done to the two EPs, then you have to have at least two additional particles (APs) with which these EP’s eventually interact. APs may be large assemblages of particles like detectors; EPs are regarded as simple single particles, say two electrons.

Imagine a 1D situation. Initially, the EPs interact at the origin of the x-axis. Then they fly apart. EP1 goes to, say, +1000.0 km (or lightyears), and EP2 goes to -1000.0 km (or lightyears). Both points lie on the same x-axis, symmetrically away from the origin.

To physically do something with the EP1, suppose you have the additional particle (detector) AP1 already existing at 1000.0 +\epsilon km, and similarly, there is another AP2, exactly at -1000.0 - \epsilon km, where \epsilon is a small distance, say of the order of a millimeter or so.

Homework 1: Check out the distance from the electron emitter to the detector in the single-particle double-slit interference experiments. Alternatively, the size of the relevant chamber inside a TEM (transmission electron microscope).

The overall system thus actually has (and always had) four different particles, and in the ultimate analysis, they all have always had a single, common, universal wavefunction. (Assume, there is nothing else in the universe.)

But for simplicity of talking, we approximated the situation by eking out a two-particle entangled wavefunction for the EPs—just to get the discussion going.

All MSQM (mainstream QM) people blithely jump to and forth between abstractions in this way—between two abstractions of having basically different scopes. That’s not the trouble. The trouble is: They never tell you exactly when they are about to do that.

OK. Now, think of the 4-particles system-wavefunction as being built from four different 1-particle wavefunctions (via an appropriate linear superposition of all the appropriate product-states of the four 1-particle wavefunctions, with the proviso that the resulting single wavefunction must have enough generality, and that it obey the appropriate exchange-operator rules etc.).


2. The sense in which entangled particles approach independence—in their interactions with the other particles:

Each 1-particle wavefunction has an anchoring point in space.

[MSQM people never tell you that. [Google on “anchoring of” “potentials” or “wavefunctions” in the context of QM.]]

Each such a wavefunction very rapidly drops off in intensity from its anchoring point, so as to satisfy the Sommerfeld radiation condition. …May be there is a generalization of this principle for the many-particle situations; I don’t know. But I know that if the system-wavefunction has to be square-normalizable, then some condition specifying a rapid decay over space is what Sommerfeld the nature ordered.

[MSQM people never remind you of such a condition in any such contexts to you. [Google!]]

So, the 1-particle wavefunction for AP1 affects EP1 far, far more than it affects EP2. Similarly, the 1-particle wavefunction for AP2 affects EP2 far, far more that it affects EP1.

Homework 2: Find the de Broglie wavelength for an electron, and for a typical detector. Work it out on your own. Don’t cheat [^][^] !

In this sense, sure, what AP1 does to EP1 (and vice-versa) has overwhelmingly greater effect than what it does to EP2 (and vice-versa).

So, what Schlafly says (“Nothing you do to one can possibly have any effect on the other”) does have a certain merit to it, but only in a limiting and approximate (“classical-like”) sense.

In a certain limiting sense, the AP1 \Leftrightarrow EP1 and AP2 \Leftrightarrow EP2 interactions do approach full independence.

To use the language that the MSQM people typically use, the reason put forth is that AP1 and AP2 never directly interacted with each other.

Actually, they all always had interacted with all the others—but in this case, only dimly so. So, as we would say to describe the same point: Due to the Sommerfeld radiation condition, AP1 \Leftrightarrow AP2 interaction always was, remains, and assuming that they don’t leave their fixed positions at \pm 1000.0 km so as to go nearer to each other, it will also always remain, very negligibly small.


3. The entangled particles’ dynamics continues to be influenced from the initial entanglement:

However, note that as EP1 and EP2 travel from the origin to their respective points (to their respective positions at \pm 1000.0 km), this entire evolution in their states (consisting of their “travel”s/displacements) occurs at all times under an always continuing influence of the same, initial, 2-particle entangled part of, the 4-particle system wavefunction—its deterministic time-evolution (as given by the Schrodinger equation).

Since the state evolution for both EP1 and EP2 was guided at each instant by the same 2-particle entangled part of the same wavefunction, the amount of distance does not matter—at all.

Even if their common entangled wavefunction initially has almost a zero strength at the distant points \pm 1000.0 km away, once EP1 and EP2 particles begin moving away from the origin, their states evolve deterministically (obeying the time-dependent Schrodinger equation). As they approach the two \pm 1000.0 km points respectively, the common wavefunction’s strength at these two points accordingly increases (and the strength of that portion of the same wavefunction which lies in the space near the origin progressively decreases). That’s because the common entangling part of the system wavefunction, is composed from two 1-particle wavefunctions, one each for EP1 and EP2, and each of these two 1-particle wavefunction has the respective current positions of EP1 and EP2 as their reference (or anchoring) point. Why? Because the potential energy has a singularity in their current point positions, that’s why.

So, all in all, yes, the nature of what EP1 can at all do in its interaction with AP1 is still, in part, being governed by the deterministically evolved state of the initial, single, 2-particle entangling wavefunction. [That’s how even the MSQM folks put it. Actually, it’s a 2-particle part of the 4-particle system wavefunction.]

So, the net result at the +1000.0 km point is that, when seen in an approximate manner, EP1 seems to be interacting with AP1 (or, AP1 with EP1) in a manner that seems to be completely independent of how  EP1 interacts with AP2 and EP2—i.e., there is almost no interaction at all.

Similarly, the net result at the -1000.0 km point is that, when seen in an approximate manner, EP2 seems to be interacting with AP2 (or, AP2 with EP2) in a manner that seems to be completely independent of how  EP2 interacts with AP1 and EP1—i.e., there is almost no interaction at all.


4. The paradox we have to resolve:

We thus have two apparently contradictory ways of summarizing the same situation.

  • Since the two EPs have gone so farther apart, and since AP1 and AP2 never “interacted” strongly with each other (or with EP1 and EP2), therefore, EP1’s behaviour should be taken to be “independent” of EP2’s behaviour, when they are at the \pm 1000.0 km points. Their behaviour should have nothing in common.
  • Yet, since EP1 and EP2 were initially entangled, and since both their respective state-evolutions were governed by the common, single wavefunction entangling them, therefore, their behaviour must also have something in common.

Got it?

How do we resolve this paradox?


5. What kind of things actually happen:

Suppose the interaction of AP1 with EP1 is such that we can say that it is EP1’s spin-property which gets measured by AP1.

Here, imagine an assemblage of a large number of particles, acting as a spin-detector, in place of AP1. (We will continue to call it a single “particle”, for the sake of simplicity.)

Suppose that the measurement outcome happens to be such that EP1’s spin is measured at AP1 to be “up” with respect to a certain z-axis (applicable to the entire universe).

Now, remember, measurement is a probabilistic process. Therefore, the correct statement to make here is:

If (and when) AP1 measures EP1’s spin, the outcome is one (and only one) of the two possibilities: either “up”, or “down.”

In other words, it is always possible that EP1 interacts with AP1, and yet, the action of EP1’s spin influencing some large-scale configuration changes within AP1 (an event which we call “measurement”) never actually comes to occur. This is possible to. However, if a measurement does occur, then the outcome is one and only one of those two possibilities.

Now suppose, to take the description further, that AP1 does indeed end up measuring EP1 spin. (That is to say, suppose that such a thing comes to occur as a physical fact, an irreversible change in the universe.)

Assume further—for the sake of pedagogic simplicity—that the EP1’s spin is measured to be “up” (and not “down”).

Suppose further that the interaction of AP2 with EP2 is such that we can say that it is EP2’s spin which is the property that gets measured by AP2—if there at all occurs a measurement when EP2 is near or at AP2. Again, remember, measurement is a probabilistic process. The correct statement now to make is:

If (and when) AP2 ends up measuring EP1’s spin, then, since the EP1 and EP2 are entangled, the outcome at the -1000.0 km point has to be: “down” (because we assumed that EP1’s spin was measured as “up” at the +1000.0 km point).

Note, the spin of EP2 is certain to be measured “down” in our case—provided it at all gets measured during the interaction of EP2 with AP2.

But note also that since AP2’s state is not entangled with AP1’s (they were too far away to begin with), just because AP1 does end up measuring EP1’s spin (as “up”) does not mean that AP2 will also necessarily measure EP2’s spin at all—despite the interaction they necessarily go through. (All four particles are, in reality, interacting. Here, AP2 and EP2, being closer, are interacting strongly.)


6. The game that the MSQM people play (with you):

Now, the whole game that MSQM (mainstream QM) physicists play with you is this.

They don’t explain to you, but it is true, that:

The fact

“AP1 interacted with EP1 to measure its spin state”

does not necessitate the conclusion

“AP2 must also measure the spin-state of EP2 in the same experimental trial“.

The latter is not at all necessary. It does not have to physically take place.

If so, then what can we say here? It is this:

But if (and when) AP2 does measure the spin-state (and no other measurable) of EP2, then the measured spin will necessarily be “down”.

The preceding statement is true.

This is because angular momentum conservation implies that if any one of the spins is measured as “up”, then the other has to get measured as “down”. This necessity is built right in the way the single entangling wavefunction is composed from the two 1-particle wavefunctions. It is the property of the initial entangling wavefunction that it has zero net spin-angular momentum. It gets reflected also in the measured read-outs with equal probability if two measurements at all take place at symmetrically far away points, so that the local patterns of the common wavefunction themselves must be symmetrically opposite. (Only a symmetrically opposite pair of 1-particle wavefunctions can together conserve angular momentum for the 2-particle entangling wavefunction.)

The slickness of MSQM people consists of refusing to make you realize that the common (entangling) wavefunction must, of necessity, arise from such symmetry conditions as just mentioned, and that it must also evolve perfectly preserving this symmetry throughout the Schrodinger evolution. Further, their slickness consists of making you believe that if AP1 does indeed physically measure EP1’s spin as “up”, then AP2 is also mandated to physically end up measuring EP2’s spin, in each and every trial.


7. How the MSQM people maintain their slickness, while presenting experimental data:

When they do experiments, they actually send entangled particles apart, and measure their respective spins at two equal distance apart and similarly tilted detector-positions.

What their raw data shows is that when the AP1 measures EP1 to be in the “up” state, AP2 may not always show any measurement outcome at all. Also, for all other three possibilities. (AP1 says “down”, nothing at AP2. AP1 says nothing, AP2 says “up”. AP1 says nothing, AP2 says “down”.)

What the MSQM folks do is, effectively, to simply drop all such observations. They retain only those among the raw data-points which have one of the two results:

  • EP1 actually measured (by AP1) to have the spin “up”, and EP2 actually measured (by AP2) to have the spin “down” in a single trial, or
  • EP1 actually measured (by AP1) to have the spin “down”, and EP2 actually measured (by AP2) to have the spin “up” in some other, single, trial.

So, their conclusion never do highlight the previously mentioned four possibilities.

No, they are not doing any data-fudging as such.

The data they present is the actual one, and it does support the theory.

But the as-presented data is not all the data there is—it’s not all there is to these experiments. And, so, it is not the complete story.

And, the part dropped-out of the final datasets sure tells you more about demystifying entanglement than the part that is eventually kept in does. It is this same—mystifying—data that gets presented in conferences, summarized in textbooks and pop-sci articles (including those on the Quanta Magazine site), and of course, in the pop-sci books (by all authors writing on this subject [Google (verb)!]).

Just hold the above discussion in mind, and see how it straightens out everything.


8. Summary of what we saw thus far:

A measured value is decided only in an act of measurement—if any measurement at all occurs during the ongoing interaction of a particle and a detector.

The respective probabilities for each of the two possible outcomes (in the spin “up” or “down” type of two-state situations) have already been decided by the deterministic time-evolution (the Schrodinger-evolution) of the initial, 2-particle entangling, part of the 4-particle system wavefunction.

If the AP1 detector is oriented to measure EP1’s spin as “up” with a P % probability, then EP2’s spin is necessarily “shaped” by the same wavefunction as to be inclined to be measured by AP2 as “down”, with the same P % probability—provided that:

  1. AP2 was in all respects identical to AP1 (including their orientations—say, placed in an exact mirror-symmetrical arrangement), and
  2. AP2 does at all end up measuring EP1. It might not, always.

Existence of an entanglement between EP1 and EP2 does not necessitate that if AP1 measures the spin-property of EP1 (w.r.t. a certain axis), then AP2 for the corresponding EP2 (coming from the same trial) must also measure the spin-property of EP2 (w.r.t to the same axis).

But if AP2 undergoes a measurement process too, then the outcome is determined, due to the commonality of the single entangling wavefunction (including the spinor function) which is shared by EP1 and EP2. And it works out as: if the first is “up”, the second must be “down”, or, vice versa.

 


Note: I am not sure if I noted in the NY resolutions post or not. But I’ve decided that I may not add a songs section every time—but sure enough I will, if one is somewhere at the back of the mind.

This topic is not difficult, but it is intricate. Easy to make typos. Also, very easy to make long-winding statements, not find the right phrases, ways of expression, metaphors, etc. So, I think I should come back and revise it after a few days. I should also give titles to the sections and all … But, anyway, in the meanwhile, do feel free to read.


History:

— 2020.01.03 12:15 IST: Initial posting.
— 2020.01.03 13:44 IST: Correction of typos, misleading statements. Addition of section titles, and a further section on the comparison with classical diffusion systems.
— 2020.01.03 15:33 IST: Added the section: “One last comment…”.
— 2020.01.03 17:03 IST: Further additions/corrections. Now am going to leave this post in this shape for at least a couple of days or more. But looks like it’s mostly done.
— 2020.01.04 14:18 IST: Nope. In simplifying everything as much as possible, it seems to me that I ended up getting off the track, and thus wrote something which is, I now think, was wrong. The error was confined to section 9.

The wrong part was important. I will have to look into the maths involving the spin property once again (and in fact learn more about it and many-particle systems in general), and further, I will have to integrate it with my new approach. Only then would I be able to come back on this point. It may take me quite some time to finalize such an integration, may be weeks, may be months.

My plan all so far was to leave the spin property of QM systems alone, and present the new approach only for spin-less systems. (That’s what I did in the Outline document too.) Yet, yesterday, somehow, I got tempted at covering the spin and the new approach together, right on the fly, and ended up writing a bit inadvertently adopting an ensembles-based interpretation. I thus sounded a bit too much like the Bohmian approach than what my approach actually should be like. (I know it from some other points of view that there are going to be important differences in my approach and the Bohmian one.)

All this, I realized, completely on my own, without any one prompting me or providing any feedback (not an indirect one, say as through the “follow-up” sort of channels), only this morning. So, I am deleting what earlier was the section 9.

The section 10 was not wrong as such. But its contents were prompted only by the topic covered in section 9. That’s why, though section 10 was essentially correct, I am also deleting it. I will cover both their topics in future.

In case any one is at all interested in having the original (erroneous) version of this post (with sections 9. and 10.), then I could share it. Feel free to approach me via an email or a comment.

As to any other errors/ambiguities/ill-expositions, I will let them be. I am done with this post. Time to move on.