Ontologies in physics—6: A basic problem: How the mainstream QM views the variables in Schrodinger’s equation

1. Prologue:

From this post, at last, we begin tackling quantum mechanics! We will be covering those topics from the physics and maths of it which are absolutely necessary from developing our own ontological viewpoint.

We will first have a look at the most comprehensive version of the non-relativistic Schrodinger equation. (Our approach so far has addressed only the non-relativistic version of QM.)

We will then note a few points concerning the way the mainstream physics (MSMQ) de facto approaches it—which is remarkably different from how engineers regard their partial differential equations.

In the process, we will come isolate and pin down a basic issue concerning how the two variables \Psi and V from Schrodinger’s equation are to be seen.

We regard this issue as a problem to be resolved, and not as just an unfamiliar kind of maths that needs no further explanation or development.

OK. Let’s get going.


2. The N-particle Schrodinger’s equation:

Consider an isolated system having 3D infinite space in it. Introduce N number of charged particles (EC Objects in our ontological view) in it. (Anytime you take arbitrary number of elementary charges, it’s helpful to think of them as being evenly spread between positive and negative polarities, because the net charge of the universe is zero.) All the particles are elementary charges. Thus, -|q_i| = e for all the particles. We will not worry about any differences in their masses, for now.

Following the mainstream QM, we also imagine the existence of something in the system such that its effect is the availability of a potential energy V.

The multi-particle time-dependent Schrodinger equation now reads:

i\,\hbar \dfrac{\partial \Psi(\vec{R},t)}{\partial t} = - \dfrac{\hbar^2}{2m} \nabla^2 \Psi(\vec{R},t) + V(\vec{R},t)\Psi(\vec{R},t)

Here, \vec{R} denotes a set of particle positions, i.e., \vec{R} = \lbrace \vec{r}_1, \vec{r}_2, \vec{r}_3, \dots, \vec{r}_N \rbrace. The rest of the notation is standard.


3. The mainstream view of the wavefunction:

The mainstream QM (MSMQ) says that the wavefunction \Psi(\vec{R},t) exists not in the physical 3-dimensional space, but in a much bigger, abstract, 3N-dimensional configuration space. What do they mean by this?

According to MSQM, a particle’s position is not definite until it is measured. Upon a measurement for the position, however, we do get a definite 3D point in the physical space for its position. This point could have been anywhere in the physical 3D space spanned by the system. However, measurement process “selects” one and only one point for this particle, at random, during any measurement process. … Repeat for all other particles. Notice, the measured positions are in the physical 3D.

Suppose we measure the positions of all the particles in the system. (Actually, speaking in more general terms, the argument applies also to position variables before measurement concretizes them to certain values.)

Suppose we now associate the measured positions via the set \vec{R} = \lbrace \vec{r}_1, \vec{r}_2, \vec{r}_3, \dots, \vec{r}_N \rbrace, where each \vec{r}_i refers to a position in the physical 3D space.

We will not delve into the issue of what measurement means, right away. We will simply try to understand the form of the equation. There is a certain issue associated with its form, but it may not become immediately apparent, esp. if you come from an engineering background. So, let’s make sure to know what that issue is:

Following the mainstream QM, the meaning of the wavefunction \Psi is this: It is a complex-valued function defined over an abstract 3N-dimensional configuration space (which has 3 coordinates for each of the N number of particles).

The meaning of any function defined over an abstract 3ND configuration space is this:

If you take the set of all the particle positions \vec{R} and plug them into such a function, then it evaluates to some single number. In case of the wavefunction, this number happens to be a complex number, in general. (Remember, all real numbers anyway are complex numbers, but not vice-versa.) Using the C++ programming terms, if you take real-valued 3D positions, pack them in an STL vector of size N, and send the vector into the function as an argument, then it returns just one specific complex number.)

All the input arguments (the N-number of 3D positions) are necessary; they all taken at once produce the value of the function—the single number. Vary any Cartesian component (x, y, or z) for any particle position, and \Psi will, in general, give you another complex number.

Since a 3D space can accommodate only 3 number of independent coordinates, but since all 3N components are required to know a single \Psi value, it can only be an abstract entity.

Got the argument?

Alright. What about the term V?


4. The mainstream view of V in the Schrodinger equation:

In the mainstream QM, the V term need not always have its origin in the electrostatic interactions of elementary point-charges.

It could be any arbitrary source that imparts a potential energy to the system. Thus, in the mainstream QM, the source of V could also be gravitational, magnetic, etc. Further, in the mainstream QM, V could be any arbitrary function; it doesn’t have to be singularly anchored into any kind of point-particles.

In the context of discussions of foundations of QM—of QM Ontology—we reject such an interpretation. We instead take the view that V arises only from the electrostatic interactions of charges. The following discussion is written from this viewpoint.

It turns out that, speaking in the most fundamental and general terms, and following the mainstream QM’s logic, the V function too must be seen as a function that “lives” in an abstract 3ND configuration space. Let’s try to understand a certain peculiarity of the electrostatic V function better.

Consider an electrostatic system of two point-charges. The potential energy of the system now depends on their separation: V = V(\vec{r}_2 - \vec{r}_1) \propto q_1q_2/|\vec{r}_2 - \vec{r}_1|. But a separation is not the same as a position.

For simplicity, assume unit positive charges in a 1D space, and the constant of proportionality also to be 1 in suitable units. Suppose now you keep \vec{r}_1 fixed, say at x = 0.0, and vary only \vec{r}_2, say to x = 1.0, 2.0, 3.0, \dots, then you will get a certain series of V values, 1.0, 0.5, 0.33\dots, \dots.

You might therefore be tempted to imagine a 1D function for V, because there is a clear-cut mapping here, being given by the ordered pairs of \vec{r}_2 \Rightarrow V values like: (1.0, 1.0), (2.0, 0.5), (3.0, 0.33\dots), \dots. So, it seems that V can be described as a function of \vec{r}_2.

But this conclusion would be wrong because the first charge has been kept fixed all along in this procedure. However, its position can be varied too. If you now begin moving the first charge too, then using the same \vec{r}_2 value will gives you different values for V. Thus, V can be defined only as a function of the separation space \vec{s} = \vec{r}_2 - \vec{r}_1.

If there are more than two particles, i.e. in the general case, the multi-particle Schrodinger equation of N particles uses that form of V which has N(N-1) pairs of separation vectors forming its argument. Here we list some of them: \vec{r}_2 - \vec{r}_1, \vec{r}_3 - \vec{r}_1, \vec{r}_4 - \vec{r}_1, \dots, \vec{r}_1 - \vec{r}_2, \vec{r}_3 - \vec{r}_2, \vec{r}_4 - \vec{r}_2, \dots, \vec{r}_1 - \vec{r}_3, \vec{r}_2 - \vec{r}_3, \vec{r}_4 - \vec{r}_1, \dots, \dots. Using the index notation:

V = \sum\limits_{i=1}^{N}\sum\limits_{j\neq i, j=1}^{N} V(\vec{s}_{ij}),

where \vec{s}_{ij} = \vec{r}_j - \vec{r}_i.

Of course, there is a certain redundancy here, because the s_{ij} = |\vec{s}_{ij}| = |\vec{s}_{ji}| = s_{ji}. The electrostatic potential energy function depends only on s_{ij}, not on \vec{s}_{ij}. The general sum formula can be re-written in a form that avoids double listing of the equivalent pairs of the separation vectors, but it not only looks a bit more complicated, but also makes it somewhat more difficult to understand the issues involved. So, we will continue using the simple form—one which generates all possible N(N-1) terms for the separation vectors.

If you try to embed this separation space in the physical 3D space, you will find that it cannot be done. You can’t associate a unique separation vector for each position vector in the physical space, because associated with any point-position, there come to be an infinity of separation vectors all of which have to be associated with it. For instance, for the position vector \vec{r}_2, there are an infinity of separation vectors \vec{s} = \vec{a} - \vec{r}_2 where \vec{a} is an arbitrary point (standing in for the variable \vec{r}_1). Thus, the mapping from a specific position vector \vec{r}_2 to potential energy values becomes an 1: \infty mapping. Similarly for \vec{r}_1. That’s why V is not a function of the point-positions in the physical space.

Of course, V can still be seen as proper 1:1 mapping, i.e., as a proper function. But it is a function defined on the space formed by all possible separation vectors, not on the physical space.

Homework: Contrast this situation from a function of two space variables, e.g., F = F(\vec{x},\vec{y}). Explain why F is a function (i.e. a 1:1 mapping) that is defined on a space of position vectors, but V can be taken to be a function only if it is seen as being defined on a space of separation vectors. In other words, why the use of separation vector space makes the V go from a 1:\infty mapping to a 1:1 mapping.


5. Wrapping up the problem statement:

If the above seems a quizzical way of looking at the phenomena, well, that precisely is how the multi-particle Schrodinger equation is formulated. Really. The wavefunction \Psi is defined on an abstract 3ND configuration space. Really. The potential energy function V is defined using the more abstract notion of the separation space(s). Really.

If you specify the position coordinates, then you obtain a single number each for the potential energy and the wavefunction. The mainstream QM essentially views them both as aspatial variables. They do capture something about the quantum system, but only as if they were some kind of quantities that applied at once to the global system. They do not have a physical existence in the 3D space-–even if the position coordinates from the physical 3D space do determine them.

In contrast, following our new approach, we take the view that such a characterization of quantum mechanics cannot be accepted, certainly not on the grounds as flimsy as: “That’s just how the math of quantum mechanics is! And it works!!” The grounds are flimsy, even if a Nobel laureate or two might have informally uttered such words.

We believe that there is a problem here: In not being able to regard either \Psi or V as referring to some simple ontological entities existing in the physical 3D space.

So, our immediate problem statement becomes this:

To find some suitable quantities defined on the physical 3D space, and to use them in such a way, that our maths would turn out to be exactly the same as given for the mainstream quantum mechanics.


6. A preview of things to come: A bit about the strategy we adopt to solve this problem:

To solve this problem, we begin with what is easiest to us, namely, the simpler, classical-looking, V function. Most of the next post will remain concerned with understanding the V term from the viewpoint of the above-noted problem. Unfortunately, a repercussion would be that our discussion might end up looking a lot like an endless repetition of the issues already seen (and resolved) in the earlier posts from this series.

However, if you ever suspect, I would advise you to keep the doubt aside and read the next post when it comes. Though the terms and the equations might look exactly as what was noted earlier, the way they are rooted in the 3D reality and combined together, is new. New enough, that it directly shows a way to regard even the \Psi field as a physical 3D field.

Quantum physicists always warn you that achieving such a thing—a 3D space-based interpretation for the system-\Psi—is impossible. A certain working quantum physicist—an author of a textbook published abroad—had warned me that many people (including he himself) had tried it for years, but had not succeeded. Accordingly, he had drawn two conclusions (if I recall it right from my fallible memory): (i) It would be a very, very difficult problem, if not impossible. (ii) Therefore, he would be very skeptical if anyone makes the claim that he does have a 3D-based interpretation, that the QM \Psi “lives” in the same ordinary 3D space that we engineers routinely use.

Apparently, therefore, what you would be reading here in the subsequent posts would be something like a brand-new physics. (So, keep your doubts, but hang on nevertheless.)

If valid, our new approach would have brought the \Psi field from its 3N-dimensional Platonic “heaven” to the ordinary physical space of 3 dimensions.

“Bhageerath” (भगीरथ) [^] ? … Well, I don’t think in such terms. “Bhageerath” must have been an actual historical figure, but his deeds obviously have got shrouded in the subsequent mysticism and mythology. In any case, we don’t mean to invite any comparisons in terms of the scale of achievements. He could possibly serve as an inspiration—for the scale of efforts. But not as an object of comparison.

All in all, “Bhageerath”’s deed were his, and they anyway lie in the distant—even hazy—past. Our understanding is our own, and we must expend our own efforts.

But yes, if found valid, our approach will have extended the state of the art concerning how to understand this theory. Reason good enough to hang around? You decide. For me, the motivation simply has been to understand quantum mechanics right; to develop a solid understanding of its basic nature.

Bye for now, take care, and sure join me the next time—which should be soon enough.


A song I like:

[The official music director here is SD. But I do definitely sense a touch of RD here. Just like for many songs from the movie “Aaraadhanaa”, “Guide”, “Prem-Pujari”, etc. Or, for that matter, music for most any one of the movies that the senior Burman composed during the late ’60s or early ’70s. … RD anyway was listed as an assistant for many of SD’s movies from those times.]

(Hindi) “aaj ko junali raat maa”
Music: S. D. Burman
Singer: Lata Mangeshkar, Mohammad Rafi
Lyrics: Majrooh Sultanpuri


History:
— First published 2019.10.13 14:10 IST.
— Corrected typos, deleted erroneous or ill-formed passages, and improved the wording on home-work (in section 4) on the same day, by 18:29 IST.
— Added the personal comment in the songs section on 2019.10.13 (same day) 22:42 IST.

 

 

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

0. Preliminaries:

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

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

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

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

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

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

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

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

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


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

2.1. Context: QM involves IAD:

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

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

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

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

OK. Enough of setting up the context.

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

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

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

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

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

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

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

2.3 Implication for the RNGs:

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

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


3. The MVLSN principle, and its epistemological basis:

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

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

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

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

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

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

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

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


4. To conclude my main argument here…:

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

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

Go ahead, try it.


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

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

The issue here is somewhat like asking this question:

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

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

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

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

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

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

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

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


6. Aaronson’s further points:

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

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

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

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

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

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

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

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

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

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

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

My two cents.


Addendum on speed limits and IAD:

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

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

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

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

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


A song I like:

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

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

 


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

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

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

 

Determinism, Indeterminism, Probability, and the nature of the laws of physics—a second take…

After I wrote the last post [^], several points struck me. Some of the points that were mostly implicit needed to be addressed systematically. So, I began writing a small document containing these after-thoughts, focusing more on the structural side of the argument.

However, I don’t find time to convert these points + statements into a proper write-up. At the same time, I want to get done with this topic, at least for now, so that I can better focus on some other tasks related to data science. So, let me share the write-up in whatever form it is in, currently. Sorry for its uneven tone and all (compared to even my other writing, that is!)


Causality as a concept is very poorly understood by present-day physicists. They typically understand only one sense of the term: evolution in time. But causality is a far broader concept. Here I agree with Ayn Rand / Leonard Peikoff (OPAR). See the Ayn Rand Lexicon entry, here [^]. (However, I wrote the points below without re-reading it, and instead, relying on whatever understanding I have already come to develop starting from my studies of the same material.)

Physical universe consists of objects. Objects have identity. Identity is the sum total of all characteristics, attributes, properties, etc., of an object. Objects act in accordance with their identity; they cannot act otherwise. Interactions are not primary; they do not come into being without there being objects that undergo the interactions. Objects do not change their respective identities when they take actions—not even during interactions with other objects. The law of causality is a higher-level view taken of this fact.

In the cause-effect relationship, the cause refers to the nature (identity) of an object, and the effect refers to an action that the object takes (or undergoes). Both refer to one and the same object. TBD: Trace the example of one moving billiard ball undergoing a perfectly elastic collision with another billiard ball. Bring out how the interaction—here, the pair of the contact forces—is a name for each ball undergoing an action in accordance with its nature. An interaction is a pair of actions.


A physical law as a mapping (e.g., a function, or even a functional) from inputs to outputs.

The quantitative laws of physics often use the real number system, i.e., quantification with infinite precision. An infinite precision is a mathematical concept, not physical. (Expect physicists to eternally keep on confusing between the two kinds of concepts.)

Application of a physical law traces the same conceptual linkages as are involved in the formulation of law, but in the reverse direction.

In both formulation of a physical law and in its application, there is always some regime of applicability which is at least implicitly understood for both inputs and outputs. A pertinent idea here is: range of variations. A further idea is the response of the output to small variations in the input.


Example: Prediction by software whether a cricket ball would have hit the stumps or not, in an LBW situation.

The input position being used by the software in a certain LBW decision could be off from reality by millimeters, or at least, by a fraction of a millimeter. Still, the law (the mapping) is such that it produces predictions that are within small limits, so that it can be relied on.

Two input values, each theoretically infinitely precise, but differing by a small magnitude from each other, may be taken to define an interval or zone of input variations. As to the zone of the corresponding output, it may be thought of as an oval produced in the plane of the stumps, using the deterministic method used in making predictions.

The nature of the law governing the motion of the ball (even after factoring in aspects like effects of interaction with air and turbulence, etc.) itself is such that the size of the O/P zone remains small enough. (It does not grow exponentially.) Hence, we can use the software confidently.

That is to say, the software can be confidently used for predicting—-i.e., determining—the zone of possible landing of the ball in the plane of the stumps.


Overall, here are three elements that must be noted: (i) Each of the input positions lying at the extreme ends of the input zone of variations itself does have an infinite precision. (ii) Further, the mapping (the law) has theoretically infinite precision. (iii) Each of the outputs lying at extreme ends of the output zone also itself has theoretically infinite precision.

Existence of such infinite precision is a given. But it is not at all the relevant issue.

What matters in applications is something more than these three. It is the fact that applications always involve zones of variations in the inputs and outputs.

Such zones are then used in error estimates. (Also for engineering control purposes, say as in automation or robotic applications.) But the fact that quantities being fed to the program as inputs themselves may be in error is not the crux of the issue. If you focus too much on errors, you will simply get into an infinite regress of error bounds for error bounds for error bounds…

Focus, instead, on the infinity of precision of the three kinds mentioned above, and focus on the fact that in addition to those infinitely precise quantities, application procedure does involve having zones of possible variations in the input, and it also involves the problem estimating how large the corresponding zone of variations in the output is—whether it is sufficiently small for the law and a particular application procedure or situation.

In physics, such details of application procedures are kept merely understood. They are hardly, if ever, mentioned and discussed explicitly. Physicists again show their poor epistemology. They discuss such things in terms not of the zones but of “error” bounds. This already inserts the wedge of dichotomy: infinitely precise laws vs. errors in applications. This dichotomy is entirely uncalled for. But, physicists simply aren’t that smart, that’s all.


“Indeterministic mapping,” for the above example (LBW decisions) would the one in which the ball can be mapped as going anywhere over, and perhaps even beyond, the stadium.

Such a law and the application method (including the software) would be useless as an aid in the LBW decisions.

However, phenomenologically, the very dynamics of the cricket ball’s motion itself is simple enough that it leads to a causal law whose nature is such that for a small variation in the input conditions (a small input variations zone), the predicted zone of the O/P also is small enough. It is for this reason that we say that predictions are possible in this situation. That is to say, this is not an indeterministic situation or law.


Not all physical situations are exactly like the example of the predicting the motion of the cricket ball. There are physical situations which show a certain common—and confusing—characteristic.

They involve interactions that are deterministic when occurring between two (or few) bodies. Thus, the laws governing a simple interaction between one or two bodies are deterministic—in the above sense of the term (i.e., in terms of infinite precision for mapping, and an existence of the zones of variations in the inputs and outputs).

But these physical situations also involve: (i) a nonlinear mapping, (ii) a sufficiently large number of interacting bodies, and further, (iii) coupling of all the interactions.

It is these physical situations which produce such an overall system behaviour that it can produce an exponentially diverging output zone even for a small zone of input variations.

So, a small change in I/P is sufficient to produce a huge change in O/P.

However, note the confusing part. Even if the system behaviour for a large number of bodies does show an exponential increase in the output zone, the mapping itself is such that when it is applied to only one pair of bodies in isolation of all the others, then the output zone does remain non-exponential.

It is this characteristic which tricks people into forming two camps that go on arguing eternally. One side says that it is deterministic (making reference to a single-pair interaction), the other side says it is indeterministic (making reference to a large number of interactions, based on the same law).

The fallacy arises out of confusing a characteristic of the application method or model (variations in input and output zones) with the precision of the law or the mapping.


Example: N-body problem.

Example: NS equations as capturing a continuum description (a nonlinear one) of a very large number of bodies.

Example: Several other physical laws entering the coupled description, apart from the NS equations, in the bubbles collapse problem.

Example: Quantum mechanics


The Law vs. the System distinction: What is indeterministic is not a law governing a simple interaction taken abstractly (in which context the law was formed), but the behaviour of the system. A law (a governing equation) can be deterministic, but still, the system behavior can become indeterministic.


Even indeterministic models or system designs, when they are described using a different kind of maths (the one which is formulated at a higher level of abstractions, and, relying on the limiting values of relative frequencies i.e. probabilities), still do show causality.

Yes, probability is a notion which itself is based on causality—after all, it uses limiting values for the relative frequencies. The ability to use the limiting processes squarely rests on there being some definite features which, by being definite, do help reveal the existence of the identity. If such features (enduring, causal) were not to be part of the identity of the objects that are abstractly seen to act probabilistically, then no application of a limiting process would be possible, and so not even a definition probability or randomness would be possible.

The notion of probability is more fundamental than that of randomness. Randomness is an abstract notion that idealizes the notion of absence of every form of order. … You can use the axioms of probability even when sequences are known to be not random, can’t you? Also, hierarchically, order comes before does randomness. Randomness is defined as the absence of (all applicable forms of) orderliness; orderliness is not defined as absence of randomness—it is defined via the some but any principle, in reference to various more concrete instances that show some or the other definable form of order.

But expect not just physicists but also mathematicians, computer scientists, and philosophers, to eternally keep on confusing the issues involved here, too. They all are dumb.


Summary:

Let me now mention a few important take-aways (though some new points not discussed above also crept in, sorry!):

  • Physical laws are always causal.
  • Physical laws often use the infinite precision of the real number system, and hence, they do show the mathematical character of infinite precision.
  • The solution paradigm used in physics requires specifying some input numbers and calculating the corresponding output numbers. If the physical law is based on real number system, than all the numbers used too are supposed to have infinite precision.
  • Applications always involve a consideration of the zone of variations in the input conditions and the corresponding zone of variations in the output predictions. The relation between the sizes of the two zones is determined by the nature of the physical law itself. If for a small variation in the input zone the law predicts a sufficiently small output zone, people call the law itself deterministic.
  • Complex systems are not always composed from parts that are in themselves complex. Complex systems can be built by arranging essentially very simpler parts that are put together in complex configurations.
  • Each of the simpler part may be governed by a deterministic law. However, when the input-output zones are considered for the complex system taken as a whole, the system behaviour may show exponential increase in the size of the output zone. In such a case, the system must be described as indeterministic.
  • Indeterministic systems still are based on causal laws. Hence, with appropriate methods and abstractions (including mathematical ones), they can be made to reveal the underlying causality. One useful theory is that of probability. The theory turns the supposed disadvantage (a large number of interacting bodies) on its head, and uses limiting values of relative frequencies, i.e., probability. The probability theory itself is based on causality, and so are indeterministic systems.
  • Systems may be deterministic or indeterministic, and in the latter case, they may be described using the maths of probability theory. Physical laws are always causal. However, if they have to be described using the terms of determinism or indeterminism, then we will have to say that they are always deterministic. After all, if the physical laws showed exponentially large output zone even when simpler systems were considered, they could not be formulated or regarded as laws.

In conclusion: Physical laws are always causal. They may also always be regarded as being deterministic. However, if systems are complex, then even if the laws governing their simpler parts were all deterministic, the system behavior itself may turn out to be indeterministic. Some indeterministic systems can be well described using the theory of probability. The theory of probability itself is based on the idea of causality albeit measures defined over large number of instances are taken, thereby exploiting the fact that there are far too many objects interacting in a complex manner.


A song I like:

(Hindi) “ho re ghungaroo kaa bole…”
Singer: Lata Mangeshkar
Music: R. D. Burman
Lyrics: Anand Bakshi

 

 

Wrapping up my research on QM—without having to give up on it

Guess I am more or less ready to wrap up my research on QM. Here is the exact status as of today.


1. The status today:

I have convinced myself that my approach (viz. the idea of singular potentials anchored into electronic positions, and with a 3D wave-field) is entirely correct, as far as QM of non-interacting particles is concerned. That is to say, as far as the abstract case of two particles in a 0-potential 1D box, or a less abstract but still hypothetical case of two non-interacting electrons in the helium atom, and similar cases are concerned. (A side note: I have worked exclusively with the spinless electrons. I don’t plan to include spin right away in my development—not even in my first paper on it. Other physicists are welcome to include it, if they wish to, any time they like.)

As to the actual case of two interacting particles (i.e., the interaction term in the Hamiltonian for the helium atom), I think that my approach should come to reproduce the same results as those obtained using the perturbation theory or the variational approach. However, I need to verify this part via discussions with physicists.

All in all, I do think that the task which I had intended to complete (and to cross-check) before this month-end, is already over—and I find that I don’t have to give up on QM (as suspected earlier [^]), because I don’t have to abandon my new approach in the first place.


2. A clarification on what had to be worked out and what had to be left alone:

To me, the crucial part at this stage (i.e., for the second-half of March) was verifying whether working with the two ideas of (i) a 3D wavefield, and (ii) electrons as “particles” having definite positions (or more correctly, as points of singularities in the potential field), still leads to the same mathematical description as in the mainstream (linear) quantum mechanics or not.

I now find that my new approach leads to the same maths—at least for the QM of the non-interacting particles. And further, I also have very definite grounds to believe that my new approach should also work out for two interacting particles (as in the He atom).

The crucial part at this stage (i.e., for the second half of March) didn’t have so much to do with the specific non-linearity which I have proposed earlier, or the details of the measurement process which it implies. Working out the details of these ideas would have been impossible—certainly beyond the capacities of any single physicist, and over such a short period. An entire team of PhD physicists would be needed to tackle the issues arising in pursuing this new approach, and to conduct the simulations to verify it.

BTW, in this context, I do have some definite ideas regarding how to hasten this process of unraveling the many particular aspects of the measurement process. I would share them once physicists show readiness to pursue this new approach. [Just in case I forget about it in future, let me note just a single cue-word for myself: “DFT”.]


3. Regarding revising the Outline document issued earlier:

Of course, the Outline document (which was earlier uploaded at iMechanica, on 11th February 2019) [^] needs to be revised extensively. A good deal of corrections and modifications are in order, and so are quite a few additions to be made too—especially in the sections on ontology and entanglement.

However, I will edit this document at my leisure later; I will not allocate a continuous stretch of time exclusively for this task any more.

In fact, a good idea here would be to abandon that Outline document as is, and to issue a fresh document that deals with only the linear aspects of the theory—with just a sketchy conceptual idea of how the measurement process is supposed to progress in a broad background context. Such a document then could be converted as a good contribution to a good journal like Nature, Science, or PRL.


4. The initial skepticism of the physicists:

Coming to the skepticism shown by the couple of physicists (with whom I had had some discussions by emails), I think that, regardless of their objections (hollers, really speaking!), my main thesis still does hold. It’s they who don’t understand the quantum theory—and let me hasten to add that by the words “quantum theory,” here I emphatically mean the mainstream quantum theory.

It is the mainstream QM which they themselves don’t understood as well as they should. What my new approach then does is to merely uncover some of these weaknesses, that’s all. … Their weakness pertains to a lack of understanding of the 3D \Leftrightarrow 3ND correspondence in general, for any kind of physics: classical or quantum. … Why, I even doubt whether they understand even just the classical vibrations themselves right or not—coupled vibrations under variable potentials, that is—to the extent and depth to which they should.

In short, it is now easy for me to leave their skepticism alone, because I can now clearly see where they failed to get the physics right.


5. Next action-item:

In the near future, I would like to make short trips to some Institutes nearby (viz., in no particular order, one or more of the following: IIT Bombay, IISER Pune, IUCAA Pune, and TIFR Mumbai). I would like to have some face-to-face discussions with physicists on this one single topic: the interaction term in the Hamiltonian for the helium atom. The discussions will be held strictly in the context that is common to us, i.e., in reference to the higher-dimensional Hilbert space of the mainstream QM.

In case no one from these Institutes responds to my requests, I plan to go and see the heads of these Institutes (i.e. Deans and Directors)—in person, if necessary. I might also undertake other action items. However, I also sincerely hope and think that such things would not at all be necessary. There is a reason why I think so. Professors may or may not respond to an outsider’s emails, but they do entertain you if you just show up in their cabin—and if you yourself are smart, courteous, direct, and well… also experienced enough. And if you are capable of holding discussions on the “common” grounds alone, viz. in terms of the linear, mainstream QM as formulated in the higher-dimensional spaces (I gather it’s John von Neumann’s formulation), that is to say, the “Copenhagen interpretation.” (After doing all my studies—and, crucially, after the development of what to me is a satisfactory new approach—I now find that I no longer am as against the Copenhagen interpretation as some of the physicists seem to be.) … All in all, I do hope and think that seeing Diro’s and all won’t be necessary.

I also equally sincerely hope that my approach comes out unscathed during / after these discussions. … Though the discussions externally would be held in terms of mainstream QM, I would also be simultaneously running a second movie of my approach, in my mind alone, cross-checking whether it holds or not. (No, they wouldn’t even suspect that I was doing precisely that.)

I will be able to undertake editing of the Outline document (or leaving it as is and issuing a fresh document) only after these discussions.


6. The bottom-line:

The bottom-line is that my main conceptual development regarding QM is more or less over now, though further developments, discussions, simulations, paper-writing and all can always go on forever—there is never an end to it.


7. Data Science!

So, I now declare that I am free to turn my main focus to the other thing that interests me, viz., Data Science.

I already have a few projects in mind, and would like to initiate work on them right away. One of the “projects” I would like to undertake in the near future is: writing very brief notes, written mainly for myself, regarding the mathematical techniques used in data science. Another one is regarding applying ML techniques to NDT (nondestructive testing). Stay tuned.


A song I like:

(Western, instrumental) “Lara’s theme” (Doctor Zhivago)
Composer: Maurice Jarre