A wish. Looking for a couple of suitable post-docs. Covid-19 in India.

1. A wish…

I wish there were a neat, scholarly, account of the early development regarding the relativity theory. …

… There are tons of material on the topic, but not a single one seems to be to my liking…. I mean, even while rapidly browsing through so many of them, they all seem to fall short—rather, so awfully short. Reason: Most, if not all of them, seem intent on deifying Einstein, and / or, the primacy of maths over physics. [Did I cover all the eigenbases? May be not. So, let me add.] … The worst of them spend themselves out on promoting the idea that coming up with good but radical ideas in physics is all about getting lucky in some day-dreaming involving some mathematical ideas. 

OTOH, The “model” for the book which I have in mind here is something like what Prof. Malcolm Longair has done for QM; see his book: “Quantum concepts in physics: an alternative approach to the understanding of quantum mechanics.” [^].

… High time someone should have undertaken a similar effort. But unfortunately, it’s entirely lacking.

… The wish isn’t without purpose. The more I study the quantum mechanical spin, the more I realize the handicap which I have of not having already studied the relativity theory.

I can always postpone the fully consistent description, following my new approach, for the QM spin. [No one / no organization has ever sponsored my research. [Though, they all are hell bent on “following up” on me.]]

However, now that I have developed (what I believe to be) a good, basic, ontology for the QM phenomena, I have begun to see a promising pathway, at least from the viewpoint of a basic ontology, from a non-relativistic description of QM to a relativistic one—I mean the special relativistic one.


2. Looking for a couple of suitable post-docs…

Another possibility I am toying with, currently, is this:

Over a considerable period of time, say over a year or so, to build a series of Python/C++ scripts/programs that illustrate the classical EM in action, but following my new ontological ideas. These ideas are for the Maxwell-Lorentz EM, but I do anticipate that these would provide the easiest pathway to integrating the Special Relativity with the non-relativistic QM.

The trouble is: I will have to get into the FDTD algorithmics too, and I don’t have the time to do it. (In case you didn’t know, when it comes to EM, the best technique is FDTD.)

Wish I had a competent post-doc—actually two—working simultaneously with me! Right now!!

One could build the above-mentioned FDTD applets, but following the way I want them to be built.

The other one could work on “FEM-ization” of my FDM code (i.e., for the He atom, done with my new approach, and yet to be published). Once he is done, he could explore doing the same with FDTD (yes of course!), and compare and contrast the two. The FEM-ization of my FDM code won’t be very highly demanding, in the sense, people have done the finite elements formulation for the helium atom, and also have implemented it in code—decades ago… But of course, they did so following the mainstream QM. It would be a fun for the post-doc to implement it using the ideas I will be proposing—shortly.

Then, both could work on the ideas for the relativistic QM. … The pace of the work would depend on what they bring to the table, and how they perform.

Fallout? If you are a smart PhD in the concerned areas, I need not provide even a hint about it…


3. Status update on my QM research:

Currently, I am typing a set of notes on the topic of the quantum mechanical angular momentum, including the spin. For the time being, I am mostly following Dan Schroeder’s notes (which I mentioned in the post before the last, here [^]). Once done, I don’t mind uploading these notes—for proofreading by you the potential post-docs. [Who else?]

While typing these notes, it has become once again very clear to me—crystal clear, in fact—as to how my “theory” for the QM spin (following my new approach) falls short. … So short, in fact. … My “theory” doesn’t just look awfully arbitrary; it is so.

All in all, don’t expect the same kind of confidence from me for the spin-related aspects as for the spin-less ones. I mean, in the upcoming document on my new approach.


4. Back to the potential post-docs:

Exciting enough?

If yes, drop me a line. Especially, if you are working with Google / similar company. I gather they officially allow you some fraction of your official time for your own hobby projects too…


5. If you are someone young and enthusiastic, say from the Pune city and all (and in general, from India):

They have relaxed the curbs. However, I have a word of advice for you.

Don’t step out unless absolutely necessary, and if so doing, take all the precautions.

It’s just a matter of a few months now…

…BTW, I am also thinking whether the government shouldn’t relax the enforced gap of three months in between the first and the second dose for the jabs. … There are circumstantial matters which indicate that a gap in between two to three months might be ideal; that three months might be too long a period. (Actually, this matter had struck me right on the day that the Central Government increased the gap from 6 weeks to 12 weeks in one, single, move. …However, at that time, I had thought it prudent to wait and watch. Now, I think I can—nay, should—share my opinon. … I also have some other points about these matters, but these are not so important. I will sure mention these as and when it becomes necessary to do so.)


In the meanwhile, you all take care, and bye for now…


A song I like:

(Hindi) ज़िंदगी आ रहा हूँ मैं… (“zindagi aa rahaa hoon main…”)
Lyrics: Javed Akhtar
Music: Hridaynath Mangeshkar
Singer: Kishore Kumar

[

Credits happily listed in a random order. A good quality audio is here [^]. … Although I haven’t seen this movie, recently I watched the video for this song, and found that I enjoyed it too. A good quality video is here [^].

… I always loved this song, esp. the tune and the arrangement / orchestration. … And of course, Javed Akhtar’s awesome lyrics. … Well, yes, Kishore does sound, at places in this song, just a slight bit… and how shall I put it?… He doesn’t sound as if he were in his best frame of singing, here. His voice sounds a bit too “broad”, and perhaps heavy, and even a bit “tired” perhaps? as if he were straining a bit?…  Even then, of course, being Kishore, he does manage to pull a great job. [It’s just that, knowing Kishore, one wants to note this aside… I know, hair-splitting, it is. … Can’t help. … Sometimes.]

… [BTW, if you are young and dynamic and result-oriented etc.: The guy in this video is Sonam Kapoor’s dad. He used to be young. Once upon time. Me too. [Though I never ever had the hair-style he displays here. A lot of my class-mates did, mostly following The “Bachchan”. Not me. […Yeah, I know.]]

… All the same, all that you’ve to do now is to wait for just a few more months, that’s all… 2021 isn’t a meme on Twitter the way 2020 was. Nevertheless, in India, we have to wait. So, just listen to songs like this for just a wee bit more. … I can tell you, from experience: The scenery, esp. the Sahyaadri’s, does stay great also well until January / February next year. (And if you really love Sahyaadri’s, well, they are there, forever…)

…So there.]

…And if you are new to this song, see if you too like it…

Take care and bye for now…

]

 

The singularities closest to you

A Special note for the Potential Employers from the Data Science field:

Recently, in April 2020, I achieved a World Rank # 5 on the MNIST problem. The initial announcement can be found here [^], and a further status update, here [^].

All my data science-related posts can always be found here [^].


0. Preamble/Preface/Prologue/Preliminaries/Whatever Pr… (but neither probability nor public relations):

Natalie Wolchover writes an article in the Quanta Magazine: “Why gravity is not like the other forces” [^].

Motl mentions this piece in his, err.. “text” [^], and asks right in the first para.:

“…the first question should be whether gravity is different, not why [it] is different”

Great point, Lubos, err… Luboš!

Having said that, I haven’t studied relativity, and so, I only cursorily went through the rest of both these pieces.

But I want to add. (Hey, what else is a blog for?)


1. Singularities in classical mechanics:

1.1 Newtonian mechanics:

Singularity is present even in the Newtonian mechanics. If you consider the differential equation for gravity in Newtonian mechanics, it basically applies to point-particles, and so, there is a singularity in this 300+ years old theory too.

It’s a different matter that Newton got rid of the singularities by integrating gravity forces inside massive spheres (finite objects), using his shells-based argument. A very ingenious argument that never ceases to impress me. Anyway, this procedure, invented by Newton, is the reason why we tend to think that there were no singularities in his theory.

1.2 Electrostatics and electrodynamics:

Coulomb et al. couldn’t get rid of the point-ness of the point-charges the way Newton could, for gravity. No electrical phenomenon was found that changed the behaviour at experimentally accessible small enough separations between two charges. In electrostatics, the inverse-square law holds through and through—on the scales on which experiments have been performed. Naturally, the mathematical manner to capture this behaviour is to not be afraid of singularities, and to go ahead, incorporate them in the mathematical formulations of the physical theory. Remember, differential laws themselves are arrived at after applying suitable limiting processes.

So, electrostatics has point singularities in the electrostatic fields.

Ditto, for classical electro-dynamics (i.e. the Maxwellian EM, as recast by Hendrik A. Lorentz, the second Nobel laureate in physics).

Singularities exist at electric potential energy locations in all of classical EM.

Lesson: Singularities aren’t specific to general relativity. Singularities predate relativity by decades if not by centuries.


2. Singularities in quantum mechanics:

2.1 Non-relativistic quantum mechanics:

You might think that non-relativistic QM has no singularities, because the \Psi field must be at least C^0 continuous everywhere, and also not infinite anywhere even within a finite domain—else, it wouldn’t be square-normalizable. (It’s worth reminding that even in infinite domains, Sommerfeld’s radiation condition still applies, and Dirac’s delta distribution most extremely violates this condition.)

Since wavefunctions cannot be infinite anywhere, you might think that any singularities present in the physics have been burnished off due to the use of the wavefunction formalism of quantum mechanics. But of course, you would be wrong!

What the super-smart MSQM folks never tell you is this part (and they don’t take care to highlight it to their own students either): The only way to calculate the \Psi fields is by specifying a potential energy field (if you want to escape the trivial solution that all wavefunctions are zero everywhere), and crucially, in a fundamental quantum-mechanical description, the PE field to specify has to be that produced by the fundamental electric charges, first and foremost. (Any other description, even if it involves complex-valued wavefunctions, isn’t fundamental QM; it’s merely a workable approximation to the basic reality. For examples, even the models like PIB, and quantum harmonic oscillator aren’t fundamental descriptions. The easiest and fundamentally correct model is the hydrogen atom.)

Since the fundamental electric charges remain point-particles, the non-relativistic QM has not actually managed to get rid of the underlying electrical singularities.

It’s something like this. I sell you a piece of a land with a deep well. I have covered the entire field with a big sheet of green paper. I show you the photograph and claim that there is no well. Would you buy it—my argument?

The super-smart MSQM folks don’t actually make such a claim. They merely highlight the green paper so much that any mention of the well must get drowned out. That’s their trick.

2.2 OK, how about the relativistic QM?

No one agrees on what a theory of GR (General Relativity) + QM (Quantum Mechanics) looks like. Nothing is settled about this issue. In this piece let’s try to restrict ourselves to the settled science—things we know to be true.

So, what we can talk about is only this much: SR (Special Relativity) + QM. But before setting to marry them off, let’s look at the character of SR. (We already saw the character of QM above.)


3. Special relativity—its origins, scope, and nature:

3.1 SR is a mathematically repackaged classical EM:

SR is a mathematical reformulation of the classical EM, full-stop. Nothing more, nothing less—actually, something less. Let me explain. But before going to how SR is a bit “less” than classical EM, let me emphasize this point:

Just because SR begins to get taught in your Modern Physics courses, it doesn’t mean that by way of its actual roots, it’s a non-classical theory. Every bit of SR is fully rooted in the classical EM.

3.2 Classical EM has been formulated at two different levels: Fundamental, and Homogenized:

The laws of classical EM, at the most fundamental level, describe reality in terms of the fundamental massive charges. These are point-particles.

Then, classical EM also says that a very similar-looking set of differential equations applies to the “everyday” charges—you know, pieces of paper crowding near a charged comb, or paper-clips sticking to your fridge-door magnets, etc. This latter version of EM is not the most fundamental. It comes equipped with a lot of fudges, most of them having to do with the material (constitutive) properties.

3.3 Enter super-smart people:

Some smart people took this later version of the classical EM laws—let’s call it the homogenized continuum-based theory—and recast them to bring out certain mathematical properties which they exhibited. In particular, the Lorentz invariance.

Some super-smart people took the invariance-related implications of this (“homogenized continuum-based”) theory as the most distinguished character exhibited by… not the fudges-based theory, but by physical reality itself.

In short, they not only identified a certain validity (which is there) for a logical inversion which treats an implication (viz. the invariance) as the primary; they blithely also asserted that such an inverted conceptual view was to be regarded as more fundamental. Why? Because it was mathematically convenient.

These super-smart people were not concerned about the complex line of empirical and conceptual reasoning which was built patiently and integrated together into a coherent theory. They were not concerned with the physical roots. The EM theory had its roots in the early experiments on electricity, whose piece-by-piece conclusions finally came together in Maxwell’s mathematical synthesis thereof. The line culminated with Lorentz’s effecting a reduction in the entire cognitive load by reducing the number of sub-equations.

The relativistic didn’t care for these roots. Indeed, sometimes, it appears as if many of them were gloating to cut off the maths from its physical grounding. It’s these super-smart people who put forth the arbitrary assertion that the relativistic viewpoint is more fundamental than the inductive base from which it was deduced.

3.4 What is implied when you assert fundamentality to the relativistic viewpoint?

To assert fundamentality to a relativistic description is to say that the following two premises hold true:

(i) The EM of homogenized continuaa (and not the EM of the fundamental point particles) is the simplest and hence most fundamental theory.

(ii) One logical way of putting it—in terms of invariance—is superior to the other logical way of putting it, which was: a presentation of the same set of facts via inductive reasoning.

The first premise is clearly a blatant violation of method of science. As people who have done work in multi-scale physics would know, you don’t grant greater fundamentality to a theory of a grossed out effect. Why?

Well, a description in terms of grossed out quantities might be fine in the sense the theory often becomes exponentially simpler to use (without an equal reduction in percentage accuracy). Who would advocate not using Hooke’s law as in the linear formulation of elasticity, but insist on computing motions of 10^23 atoms?

However, a good multi-scaling engineer / physicist also has the sense to keep in mind that elasticity is not the final word; that there are layers and layers of rich phenomenology lying underneath it: at the meso-scale, micro-scale, nano-scale, and then, even at the atomic (or sub-atomic) scales. Schrodinger’s equation is more fundamental than Hooke’s law. Hooke’s law, projected back to the fine-grained scale, does not hold.

This situation is somewhat like this: Your 100 \times 100 photograph does not show all the features of your face the way they come out in the original 4096 \times 4096 image. The finer features remain lost even if you magnify the 100 \times 100 image to the 4096 \times 4096 size, and save it at that size. The fine-grained features remain lost. However, this does not mean that 100 \times 100 is useless. A 28 \times 28 pixels image is enough for the MNIST benchmark problem.

So, what is the intermediate conclusion? A “fudged” (homogenized) theory cannot be as fundamental—let alone be even more fundamental—as compared to the finer theory from which it was homogenized.

Poincaré must have thought otherwise. The available evidence anyway says that he said, wrote, and preached to the effect that a logical inversion of a homogenized theory was not only acceptable as an intellectually satisfying exercise, but that it must be seen as being a more fundamental description of physical reality.

Einstein, initially hesitant, later on bought this view hook, line and sinker. (Later on, he also became a superposition of an Isaac Asimov of the relativity theory, a Merilyn Monroe of the popular press, and a collage of the early 20th century Western intellectuals’ notions of an ancient sage. But this issue, seen in any basis—components-wise or in a new basis in which the superposition itself is a basis—takes us away from the issues at hand.)

The view promulgated by these super-smart people, however, cannot qualify to be called the most fundamental description.

3.5 Why is the usual idea of having to formulate a relativistic quantum mechanics theory a basic error?

It is an error to expect that the potential energy fields in the Schroedinger equation ought to obey the (special) relativistic limits.

The expectation rests on treating the magnetic field at a par with the static electric field.

However, there are no monopoles in the classical EM, and so, the electric charges enjoy a place of greater fundamentality. If you have kept your working epistemology untarnished by corrupt forms of methods and content, you should have no trouble seeing this point. It’s very simple.

It’s the electrons which produce the electric fields; every electric field that can at all exist in reality can always be expressed as a linear superposition of elementary fields each of which has a singularity in it—the point identified for the classical position of the electron.

We compress this complex line of thought by simply saying:

Point-particles of electrons produce electric fields, and this is the only way any electric field can at all be produced.

Naturally, electric fields don’t change anywhere at all, unless the electrons themselves move.

The only way a magnetic field can be had at any point in physical space is if the electric field at that point changes in time. Why do we say “the only way”? Because, there are no magnetic monopoles to create these magnetic fields.

So, the burden of creating any and every magnetic field completely rests on the motions of the electrons.

And, the electrons, being point particles, have singularities in them.

So, you see, in the most fundamental description, EM of finite objects is a multi-scaled theory of EM of point-charges. And, EM of finite objects was, historically, first formulated before people could plain grab the achievement, recast it into an alternative form (having a different look but the same physical scope), and then run naked in the streets shouting “Relativity!”, “Relativity!!”.

Another way to look at the conceptual hierarchy is this:

Answer this question:

If you solve the problem of an electron in a magnetic field quantum mechanically, did you use the most basic QM? Or was it a multi-scale-wise grossed out (and approximate) QM description that you used?

Hint: The only way a magnetic field can at all come into existence is when some or the other electron is accelerating somewhere or the other in the universe.

For the layman: The situation here is like this: A man has a son. The son plays with another man, say the boy’s uncle. Can you now say that because there is an interaction between the nephew and the uncle, therefore, they are what all matters? that the man responsible for creating this relationship in the first place, namely, the son’s father cannot ever enter any fundamental or basic description?

Of course, this viewpoint also means that the only fundamentally valid relativistic QM would be one which is completely couched in terms of the electric fields only. No magnetic fields.

3.6. How to incorporate the magnetic fields in the most fundamental QM description?

I don’t know. (Neither do I much care—it’s not my research field.) But sure, I can put forth a hypothetical way of looking at it.

Think of the magnetic field as a quantum mechanical effect. That is to say, the electrostatic fields (which implies, the positions of electrons’ respective singularities) and the wavefunctions produced in the aether in correspondence with these electrostatic fields, together form a complete description. (Here, the wavefunction includes the spin.)

You can then abstractly encapsulate certain kinds of changes in these fundamental entities, and call the abstraction by the name of magnetic field.

You can then realize that the changes in magnetic and electric fields imply the c constant, and then trace back the origins of the c as being rooted in the kind of changes in the electrostatic fields (PE) and wavefunction fields (KE) which give rise to the higher-level of phenomenon of c.

But in no case can you have the hodge-podge favored by Einstein (and millions of his devotees).

To the layman: This hodge-podge consists of regarding the play (“interactions”) between the boy and the uncle as primary, without bothering about the father. You would avoid this kind of a hodge-podge if what you wanted was a basic consistency.

3.7 Singularities and the kind of relativistic QM which is needed:

So, you see, what is supposed to be the relativistic QM itself has to be reformulated. Then it would be easy to see that:

There are singularities of electric point-charges even in the relativistic QM.

In today’s formulation of relativistic QM, since it takes SR as if SR itself was the most basic ground truth (without looking into the conceptual bases of SR in the classical EM), it does take an extra special effort for you to realize that the most fundamental singularity in the relativistic QM is that of the electrons—and not of any relativistic spacetime contortions.


4. A word about putting quantum mechanics and gravity together:

Now, a word about QM and gravity—Wolchover’s concern for her abovementioned report. (Also, arguably, one of the concerns of the physicists she interviewed.)

Before we get going, a clarification is necessary—the one which concerns with mass of the electron.

4.1 Is charge a point-property in the classical EM? how about mass?

It might come as a surprise to you, but it’s a fact that in the fundamental classical EM, it does not matter whether you ascribe a specific location to the attribute of the electric charge, or not.

In particular, You may take the position (1) that the electric charge exists at the same point where the singularity in the electron’s field is. Or, alternatively, you may adopt the position (2) that the charge is actually distributed all over the space, wherever the electric field exists.

Realize that whether you take the first position or the second, it makes no difference whatsoever either to the concepts at the root of the EM laws or the associated calculation procedures associated with them.

However, we may consider the fact that the singularity indeed is a very distinguished point. There is only one such a point associated with the interaction of a given electron with another given electron. Each electron sees one and only one singular point in the field produced by the other electron.

Each electron also has just one charge, which remains constant at all times. An electron or a proton does not possess two charges. They do not possess complex-valued charges.

So, based on this extraneous consideration (it’s not mandated by the basic concepts or laws), we may think of simplifying the matters, and say that

the charge of an electron (or the other fundamental particle, viz., proton) exists only at the singular point, and nowhere else.

All in all, we might adopt the position that the charge is where the singularity is—even if there is no positive evidence for the position.

Then, continuing on this conceptually alluring but not empirically necessitated viewpoint, we could also say that the electron’s mass is where its electrostatic singularity is.

Now, a relatively minor consideration here also is that ascribing the mass only to the point of singularity also suggests an easy analogue to the Newtonian particle-mechanics. I am not sure how advantageous this analogue is. Even if there is some advantage, it would still be a minor advantage. The reason is, the two theories (NM and EM) are, hierarchically, at highly unequal levels—and it is this fact which is far more important.

All in all, we can perhaps adopt this position:

With all the if’s and the but’s kept in the context, the mass and the charge may be regarded as not just multipliers in the field equations; they may be regarded to have a distinguished location in space too; that the charge and mass exist at one point and no other.

We could say that. There is no experiment which mandates that we adopt this viewpoint, but there also is no experiment—or conceptual consideration—which goes against it. And, it seems to be a bit easier on the mind.

4.2 How quantum gravity becomes ridiculous simple:

If we thus adopt the viewpoint that the mass is where the electrostatic singularity is, then the issue of quantum gravity becomes ridiculously simple… assuming that you have developed a theory to multi-scale-wise gross out classical magnetism from the more basic QM formalism, in the first place.

Why would it make the quantum gravity simple?

Gravity is just a force between two point particles of electrons (or protons), and, you could directly include it in your QM if your computer’s floating point arithmetic allows you to deal with it.

As an engineer, I wouldn’t bother.

But, basically, that’s the only physics-wise relevance of quantum gravity.

4.3 What is the real relevance of quantum gravity?

The real reason behind the attempts to build a theory of quantum gravity (by following the track of the usual kind of the relativistic QM theory) is not based in physics or nature of reality. The reasons are, say “social”.

The socially important reason to pursue quantum gravity is that it keeps physicists in employment.

Naturally, once they are employed, they talk. They publish papers. Give interviews to the media.

All this can be fine, so long as you bear in your mind the real reason at all times. A field such as quantum gravity was invented (i.e. not discovered) only in order to keep some physicists out of unemployment. There is no other reason.

Neither Wolchover nor Motl would tell you this part, but it is true.


5. So, what can we finally say regarding singularities?:

Simply this much:

Next time you run into the word “singularity,” think of those small pieces of paper and a plastic comb.

Don’t think of those advanced graphics depicting some interstellar space-ship orbiting around a black-hole, with a lot of gooey stuff going round and round around a half-risen sun or something like that. Don’t think of that.

Singularities is far more common-place than you’ve been led to think.

Your laptop or cell-phone has of the order of 10^23 number of singularities, all happily running around mostly within that small volume, and acting together, effectively giving your laptop its shape, its solidity, its form. These singularities is what gives your laptop the ability to brighten the pixels too, and that’s what ultimately allows you to read this post.

Finally, remember the definition of singularity:

A singularity is a distinguished point in an otherwise finite field where the field-strength approaches (positive or negative) infinity.

This is a mathematical characterization. Given that infinities are involved, physics can in principle have no characterization of any singularity. It’s a point which “falls out of”, i.e., is in principle excluded from, the integrated body of knowledge that is physics. Singularity is defined not on the basis of its own positive merits, but by negation of what we know to be true. Physics deals only with that which is true.

It might turn out that there is perhaps nothing interesting to be eventually found at some point of some singularity in some physics theory—classical or quantum. Or, it could also turn out that the physics at some singularity is only very mildly interesting. There is no reason—not yet—to believe that there must be something fascinating going on at every point which is mathematically described by a singularity. Remember: Singularities exist only in the abstract (limiting processes-based) mathematical characterizations, and that these abstractions arise from the known physics of the situation around the so distinguished point.

We do know a fantastically great deal of physics that is implied by the physics theories which do have singularities. But we don’t know the physics at the singularity. We also know that so long as the concept involves infinities, it is not a piece of valid physics. The moment the physics of some kind of singularities is figured out, the field strengths there would be found to be not infinities.

So, what’s singularity? It’s those pieces of paper and the comb.

Even better:

You—your body—itself carries singularities. Approx. 100 \times 10^23 number of them, in the least. You don’t have to go looking elsewhere for them. This is an established fact of physics.

Remember that bit.


6. To physics experts:

Yes, there can be a valid theory of non-relativistic quantum mechanics that incorporates gravity too.

It is known that such a theory would obviously give erroneous predictions. However, the point isn’t that. The point is simply this:

Gravity is not basically wedded to, let alone be an effect of, electromagnetism. That’s why, it simply cannot be an effect of the relativistic reformulations of the multi-scaled grossed out view of what actually is the fundamental theory of electromagnetism.

Gravity is basically an effect shown by massive objects.

Inasmuch as electrons have the property of mass, and inasmuch as mass can be thought of as existing at the distinguished point of electrostatic singularities, even a non-relativistic theory of quantum gravity is possible. It would be as simple as adding the Newtonian gravitational potential energy into the Hamiltonian for the non-relativistic quantum mechanics.

You are not impressed, I know. Doesn’t matter. My primary concern never was what you think; it always was (and is): what the truth is, and hence, also, what kind of valid conceptual structures there at all can be. This has not always been a concern common to both of us. Which fact does leave a bit of an impression about you in my mind, although it is negative-valued.

Be advised.


A song I like:

(Hindi) ओ मेरे दिल के चैन (“O mere, dil ke chain”)
Singer: Lata Mangeshkar
Music: R. D. Burman
Lyrics: Majrooh Sultanpuri

[

I think I have run the original version by Kishore Kumar here in this section before. This time, it’s time for Lata’s version.

Lata’s version came as a big surprise to me; I “discovered” it only a month ago. I had heard other young girls’ versions on the YouTube, I think. But never Lata’s—even if, I now gather, it’s been around for some two decades by now. Shame on me!

To the n-th order approximation, I can’t tell whether I like Kishor’s version better or Lata’s, where n can, of course, only be a finite number though it already is the case that n > 5.

… BTW, any time in the past (i.e., not just in my youth) I could have very easily betted a very good amount of money that no other singer would ever be able to sing this song. A female singer, in particular, wouldn’t be able to even begin singing this song. I would have been right. When it comes to the other singers, I don’t even complete their, err, renderings. For a popular case in point, take the link provided after this sentence, but don’t bother to return if you stay with it for more than, like, 30 seconds [^].

Earlier, I would’ve expected that even Lata is going to fail at the try.

But after listening to her version, I… I don’t know what to think, any more. May be it’s the aforementioned uncertainty which makes all thought cease! And thusly, I now (shamelessly and purely) enjoy Lata’s version, too. Suggestion: If you came back from the above link within 30 seconds, you follow me, too.

]

 

 

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.