This post continues from my last post, here [^].
So, what’s the mental imagery that rushes to my mind when I think of the idea/concept: “Quantum Mechanics”?
Since I have thought about this topic for such a long time (certainly for more than two decades), as far as I am concerned, the picture has no problem immediately jumping to the surface of my mind. However, to write it down is going to take a lot of words, and so, it may not look like a readily available image to you. In any case, since the imagery is a bit complex, brace yourself for yet another long post. Certainly more than a thousand words!
Keep a fresh paper and a few color sketch-pens ready to draw the diagram as we go along.
What I imagine is basically a fake quantum system, because I don’t want my picture to be complicated by a lot of what I regard are the inessential details.
I basically imagine a two-atom system with a bond, in which the nuclei are, in the first stage at least, taken to be fixed in space. Thus, the entire quantum universe consists of only these particles: two positively charged massive nuclei (say two protons), two (or more) negatively charged lighter electrons, and a bunch of massless photons to establish the bond.
In the first version of my imagery, the system is in the time-independent ground state of the molecule. I then add an imagination of a time evolution from this ground state to an excited state, and then, the subsequent collapse back to the ground state. Thus, it’s not a single picture but a series of them.
For the static version of the ground state, using a blue sketch pen, put two blue dots some sizable distance apart near the center of a piece of paper. These blue dots—the nuclei—don’t move.
For the two electrons, take a red sketch pen and make a lot of red dots (of equal sizes) around the two blue dots. The local density of the red dots should be higher near the nuclei, and it should drop off to a negligible density near the edges of the paper. I declare myself that as the paper extends to the (other) end of the universe—and note, not “to” infinity—the dots go on decreasing in density. Yes, I believe in a spatially cyclic—closed and finite—universe. It’s my mental imagery, remember? [There are a lot of trees still left in the world, and new ones are always being planted. So, help yourself with another piece of paper, to draw your imagery. Here, we are concerned only with mine.]
I then take a sketch pen of any faint color, say grey, and add a lot of more dots. These are the virtual photons.
The classes of elementary particles in my mental quantum universe is thus exactly three: nuclei, electrons, and photons, that’s all. I could complicate it more, later. But before I could complicate it further, I know, I would have to get at least this version of the imagery right. And, I remain stuck up right there. That’s why, I regard mass of the massive particles (protons and electrons) as their intrinsic property—a possible compromise from the best possible quantum picture. It actually is a leftover from the Newtonian universe, but it’s OK by me.
The red dots together represent the specific position that any one of the two electrons is likely to occupy. In particular, although there are numerous red dots (and in the continuum limit an infinite number of these), at any given instant, a given electron is found only at one of these dots—the rest are indicative but unoccupied positions.
Note, in my picture, it does not matter which dot corresponds to which electron, even if I know that the electrons always are two separate (and spatially distinguished) entities. The specific positions of the red dots are immaterial; their local density taken together, however, does matter.
This point about the dots and their density has been implicitly well-understood by me, and so it doesn’t find too prominent a place in my imagery, but perhaps it is necessary to spell it out in greater detail. Here is a visualization aid for getting the density of the dots right. Write a Python + matplotlib program to draw such dots. Here is the algorithm. Say, divide the drawing surface (say of 15 X 15 cm extent) into a finite number of square cells (say 1 cm square each). Assume any suitable nonuniform distribution for the electron cloud. Remember, this is all a fake distribution. So anything convenient to you is OK. For instance, the distribution obtained by superposing two Gaussian distributions each of which is centered around one of the two nuclei. Or, the sinc function. Etc. Now, for any cell, you can use the assumed distribution to find out the local density of dots contained in it. In fact, you don’t even have to use the idea of cells; directly using the discrete space of pixels is enough: using a pseudo random number generator, write a program to light up a pixel with a dot such that the probability of its being lit up is proportional to the local distribution density there. Or, you may use the idea of cells thus: find out the density at each of the four corners of a given cell using the analytical expression for the assumed distribution, and then, using the simplest approximate bi-linear interpolation, determine the interpolated density, and then use it to probabilistically to light up the pixels. Finally, another method is to use the strength at the corners of the cell to first decide the number of pixels to light up in a cell, and then randomize the x- and y-coordinates (rather than the lighting up amplitude) for deciding the places where this precise number of dots will get lit up.
Repeat the selected algorithm over time, so that while the density of dots per cell remains constant, due to the changes in the specific random numbers generated, the specific pixels being lit up goes on changing. That’s what I mean by a distribution of dots that is proportional to probability. A specific realization of probabilities isn’t important; that’ the point.
It’s understood that the local density of dots gives you only the probability of finding an electron over that local volume. So, what I do is: I make any two red dots slightly brighter (or bigger, or highlighted via any other means, e.g., via encircling) than the other dots. That’s where the two electrons actually are, at any given instant of time, in my imagery. In the next instant, of course, they occupy some other instantaneous position of some other dot.
Now, an important question: How do the highlighted dots—the positions where the electrons really are—move?
In my imagery, they always move to one of the adjacent instantaneous positions for the neighboring un-highlighted dots. A highlighted dot (the actual position of the electron) never jumps over any one of the un-highlighted dots lying closest to it in its local neighborhood. In other words, IAD (instantaneous action at a distance) summarily goes out for a toss, in my imagery.
Hmmm… But how do the real electrons actually move, even if they move only in their local neighborhood over any given slice of time? … Enter those grey photons. Do I need to say more? Perhaps I do. After all, it’s my imagery.
Before going on to telling you a bit more about the photons themselves, I have to modify my imagery a bit. I now imagine that the edges of the paper represent a virtual end of the universe, and so, I apply a zero density Dirichlet condition on these edges. The sandbox is the universe, in short.
Next, I apply a conservation principle also to the number of photons. Yes, your friendly Nobel laureates go for a toss in my imagery. In my imagery, this happens mostly silently. However, I now recognize that in your imagery of my imagery, they perhaps don’t go out equally silently. They perhaps go out screaming “shame,” “shame,” “ignorance,” “ignorance,” etc. And, along with them go also your not so friendly physics professors at IISc Bangalore, not to mention those at the five old IITs (and all the new ones). (It’s my imagery, remember?) The total number of the small grey dots thus always remains constant.
Another thing. Photons can pass through each other; electrons and protons don’t. All the elementary particles—the nuclei, electrons and photons—are spatially definite; every particle of each kind is confined to a region of space. Which means, I can always point out to some region of paper and say: this given dot does not exist there—a given dot is not spread out everywhere. The existence condition acquires different binary values at a given position. If the particle exists here, it does not exist there. Vice versa.
This requirement does not rule out the possibility that the same place may be occupied by two particles. But, this provision is currently made only for the photons.
[In my current research (i.e. idle arm-chair thinking), I am re-examining this aspect—I am wondering if I can allow two electrons, or one electron and one proton, to occupy the same region of space or not. I am not throwing out the possibility out of the hand. But, the imagery as of now does not allow this possibility. BTW, I have a very, very good logic (very, very good, even to my unsatisfiable self) to think why photons should overlap but not protons or electrons, though I am sure I will keep re-examining the issue. And, no, I am not going to disclose the reasons either way—not until I write a paper on the topic. [evil grin.]]
What exactly are these photons like? Do they have a structure? Yes, or no? What is the difference between these greylings that are the virtual photons and the real photons?
Patience, people, patience. I certainly know the answers; it’s just that I don’t feel like jotting them down here and now, that’s all. [Yawn. Then, an evil grin.]
Do you still want me to narrate how the system evolves? Yes? No? [The evil grin is repeated; then, after a while, it is suppressed.]
OK. Let me be less evil. … You were asking for the difference between the virtual and the real photons, na? OK. Here is my (partial) answer: The similarity between the virtual photons and the real photons is that they both are real. They both exist in spatially delimited sense. The difference between them is that the virtual photons are incapable of altering a given eigen-state; instead, they help bring it into being in the first place. The real photons, in contrast, are those that are capable of changing the eigen-states. To see how, you have to expand the details of this simple imagery a bit more. However, the picture then becomes too complicated. In any case, these additional details is what I myself don’t recollect right in the first second; they come to me only in, say, the 3rd or the 5th second.
So, the rest of the QM is just details, maths, and applications, as far as I am concerned. The real quantum story ends here.
QM is, first and foremost, a theory of sequences of stable configurations of elementary building blocks of matter, and of the passage of matter through these various configurations. To my mind, QM is just that.
It’s, thus, the most elementary materials science. Even chemistry, if you wish. That’s what QM is to me. The mechanics part is only for calculations. QM becomes a branch of physics only because physics is able to supply the principles that allow you to perform the calculations.
But the real QM is only about configuration of matter.
A few remaining notes.
This picture of mine is both in accord with the established axioms of the mainstream theory, as well as at odds with the non-axiomatic but routine assumptions made in the theory.
Pick up any good introductory text on QChem or QM (McQuarrie’s or Levins, or Griffith’s are enough). Go through the list of axioms.
The picture I have here is not in conflict with any of these—the mainstream axioms themselves. Not in the basic sense of the terms they use, anyway. (Challenge for you: Show me one place in one axiom where there is a conflict.)
Yet, my picture also gloatingly insults many of the most mystically revered pillars of QM. These are the suppositions built, not by science popularizers, but by both the ordinary professors and the Nobel laureates of physics alike, including Feynman. Go through the above description once again, and find all of the points where I happily depart from this part of the mainstream tradition. Here is a partial list: spatially delimited elementary particles, specific locations and paths for particles, conservation of photons. … And, at least two more. Find them out. If you really know your Feynman, Dirac, Shankar, or even just Griffiths, you should have no difficulty completing this exercise.
* * * * * * * * * * * * * * *
A [Video of a] Song I Like
I am going to make an exception to my usual rules for this section, this time round. (i) I am going to repeat a song in this section—something I haven’t done so far, and, for that reason, (ii) I am going to make a reference to a video—not just the audio—of that song.
I have in mind, a YouTube video officially uploaded by Saregama, i.e., the recording/publishing company.
However, the thing is, as far as I know, the credits as noted by Saregama are wrong. The song, the music, and in fact even the choreography of the dance in the video—they all come from a single man who is not even passingly mentioned by Saregama, viz., the Nobel laureate Gurudeb Robindranath Thakur [hey Bongs, did I get that spelling right?]. Salil Chaudhary merely conducted the music; Hemant Mukherjee/Mukhopadhyaya [i.e. the Hindi film music composer and singer Hemant Kumar] merely sang the piece. [That is, as far as I know. If I am mistaken about any of these aspects, please do correct me.]
One more comment.
This is one dance you can never imagine as originating in any other land, and at any other time. It had to be in India, specifically, in British India, specifically in Bengal, and specifically after the Enlightenment spirit brought by the British had been readily integrated into the local culture by men who also were well-steeped in the best traditions of the ancient Indian culture. This instance of music and dance is a product of someone who was at the cross-roads of those two cultures. He was educated in the Western Enlightenment ideas, and yet he remained recognizably Indian in his soul. Ravindranath Tagore.
As far as the music part is concerned, you can detect a faint Western influence here: the idea of building a piece of music using a progression of chords subtly does find its way here. Thus, though the music is on the whole Indian, you can still detect a faint shade of the Western influence.
Yet, the dance movements here are very emphatically only Indian. The bodily movements are just too supple, just too fluid, either for the West, or for that matter, even for the rest of the East. They obviously are steeped into the traditional Indian culture. Yet, the movements here are too innovative to be merely “traditional;” compare them, after you watch the video, with any BharatnaaTyam or Kathak you saw recently.
The facial expressions of the dancers are only a bit reserved, not too much. These obviously come from the Indian “abhinaya” tradition. Yet, the expressions here drop out that overly dramatic part in the traditional “abhinaya.” The expressions here are, in fact, informal enough to be almost immediately recognizable even to the layman; they are almost of the simple, homely, kind. It’s this part that, by way of an example, serves to highlight the importance of facial expressions in dance. Compare the dancers here with any severely stern-faced, or at least unnecessarily formal-faced Western dancer—which means, most any Western dancer. In any tradition. Ballet, or otherwise. [And no, the expressions here aren’t mindless as in Gypsy or carnival traditions anywhere.]
To say that the dance here, overall, is graceful etc., is a complete waste of words; I have no desire to rush into the category of the eloquent dumb; not so soon anyway. So, let me point out the video to you. Except for just one more noting. Please allow me that.
All the dancers here—including the lead female—have a wheatish, nay, dark wheatish complexion. It’s beautiful.
To reveal a bit about me (it’s not at all a secret; all my friends have always known it): Keeping all other things constant or irrelevant, throughout my life, I have always found the dark wheatish complexion to be the most beautiful one. Even rivetingly so. Not as black as some of the Africans go, but a definitely dark tone, nevertheless. I have never had a fascination for the fair skin. A fair-skinned girl had to be exceptionally beautiful otherwise—in the structure of her face and body—before I could come involuntarily to describe her as being beautiful. Otherwise, using that adjective has been instinctively impossible for me. (No, I have never found either Aishwarya Rai or Madhuri Dixit very beautiful. They are OK, certainly not bad; the first one is passable as above average; the second one as much above average. But neither is ravishingly beautiful. Beauty, to me, is, say, Nandita Das, esp. her younger self. Also, the younger Sonali Kulkarni (the senior one, of course; realize, she alone has a dark complexion among the two).)
In this regard, my tastes have been so much at odds at the prevailing cultural norms in India that I have always felt being more than a bit out of place about it. [In my college days, I had to defend myself against the charge that I was being a maverick just for the heck of being one. At 50+, hopefully, no one levels that charge once again at me.]
It therefore was a very delightful surprise to me when I heard it from a highly respected Sanskrit scholar in Pune (himself a fair-skinned one, in fact, he was born in the Konkanastha Brahmin caste) that the standard of beauty in the ancient India has always included a dark skin tone. Also, relatively fuller (though not very thick) lips. Neither the fair skin, nor the European-thin lips. Rama was wheatish, and KrishNa was relatively even darker in skin color. Also, women like RukmiNi. She was dark-skinned, and was considered very beautiful. Sita was wheatish, too; she too was regarded as beautiful. But it’s the Sanskrit literature preexisting before all these Gods’ times which informs us that the standards were neither compromised nor even slightly modified for these Gods; instead, the existing standards of beauty themselves were merely applied while describing them. Indeed, Sita was regarded more as a smart or sharp-looking than as being very beautiful, whereas RukmiNi was regarded as a perfect example of the most beautiful. So, the standards themselves certainly preexisted all these Gods and Goddesses. They got scrapped sometime only later, perhaps much later; I don’t know precisely when. [It doesn’t have to be as late as the Brits; the Persian standard, too, carries a thing about the fair skin; it too regards a fair skin as being essential to beauty. And, the influence of the Persian standards predates the Mughals at least in some north-western and northern parts of India.]
… No, not all “saanwale” people are beautiful; most in fact are not. In particular, those with a very round face and thereby missing the cheek-bones cannot ever be beautiful—not at least to me: my mind automatically goes into a virtually interminable loop searching for features on such a face. E.g., the actress Sridevi. Below average. Or, Rekha, in her early, plumpy, days. Much below average. Or, Rekha, in her later, slimmer, and far better turned out version. Just about average (or, OK, slightly above that). To my mind, Moushumi Chatterjee would always beat them all very, very easily. (By them, I mean: Madhuri Dixit, Rekha, Aishwarya Rai, and Sridevi.) So, not all “saanwale” people are beautiful. But beautiful people invariably are “saanwaale”.
And, the sheer physical beauty is completely apart from factors such as that “spark” of brilliance or of life on a face, the air (or even the aura, if you wish), the habitual expressions, the manner of conducting oneself or the body language, etc. Here, I was talking only about the sheer physical aspects of beauty, its standards. [Gayatri Devi? Very impressive in looks, and with a very definite purity on the face. Also, good looking. But beautiful? Really beautiful? No, not quite. Beauty is something different than being merely impressive, imposing, or alluring. … Yes, I too could easily describe Gayatri Devi as a beautiful lady. But that’s only in the approximate sense of the term, not exact. That’s the point here.]
Anyway, to wrap up this discussion, so that’s another point about this video that I like—the distinctively Indian look of the dancers, including their beautiful (Hindi) “saanwalaa” skin tone. … And, that distinct touch of the early monsoons in the fields, which forms a very apt background for this video. … All in all, excellent!
OK. Let me not stretch your already far too stretched patience any further; the video is here [^]. Enjoy!
[I don’t know, but, may be, an update might be due. Or, a continuation of the QM topic into a third (and last) part in this series. Especially, if you raise some objections about it. I will check back tomorrow or the day after.]