Suppose you are a student of engineering—say, of mechanical engineering or materials engineering (of perhaps even of computer engineering). You are taking a course on statistics or experimental methods, and your professor has suggested that you could easily create an interesting experimental apparatus: you could build a physical, particles-based model that illustrates the kind of process lying at the roots of the normal distribution. In other words, you could construct Galton’s board [^]. The professor happens to mention this point in your class only in the passing.
And so, on the next weekend, you go out shopping to the (Hindi) “junaa/chor bazaar” (English: flea market), get a few round rubber pieces, a discarded carom board, and a few ball-bearing balls. You affix the round rubber pieces onto the carom board following that Pascal’s triangle kind of arrangement. At the bottom, you affix a few wooden batten strips so as to collect the rolling balls into the compartmentalized collection bins. In the experiment, you would let the balls roll from the top of the triangle via an input channel, and after they have finished bumping into those various rubber pieces, and then rebounding and rolling down, you collect these balls into those various collection bins at the bottom. As the number of rows and the number of balls goes on increasing, the relative fractions of the balls cumulatively collected in the bottom bins tends towards the normal distribution [^].
Then, you think of an idea. You realize that what the mathematics requires is not this entire physical apparatus in all its physicality, but only certain quantitative aspects of it: the number of balls passing through the different places. And, focusing on the input and output of the system, you decide that the number of balls passing through the input channel at the top and the output channels at the bottom is all you are interested in.
Therefore, you think of some simple spring-loaded hammer-and-bell arrangement (or, on second thoughts, just some simple chiming cylinders of the Feng Shui sort) such that, whenever a ball rolls down through a given channel (input or output), it triggers a bell into chiming. To distinguish the various channels, you arrange to have each bell produce a different musical note. The advantage of this arrangement is that you don’t have to observe a ball as it goes rolling through your apparatus. You can simply hear it the moment it enters the apparatus, and you can hear its collection into each of the distinctive collection bins. Therefore, the only record that you need to keep is that of the musical notes: the input note, and the various output notes, say, Saa, Re, Ga, Ma… etc. (To the Western readers: Do, Re, Mi… or C, D, E…(with the appropriate sharps or flats as necessary)).
You demonstrate your working model in the class. Every one is impressed. Yes, even the professor. Not just him, but in fact, even the girls! They all have liked this idea of the bells…
Once the demonstration is over, as you head back to the hostels whistling, you find yourself toying with some ideas: would it be possible for you to collect all those appreciative glances coming from all those girls together, and use the collection to buy that super-bike with that oil-cooled twin-cylinder engine. … You continue walking, whistling happily over the bell idea…
Just then, you run into this budding physicist who lives in the adjacent hostel block. … He is a bit senior to you. You have always thought that a “wilting intellectual” would be a much more fitting term, but in this moment at least, that one seems to be an unnecessary kind of a detail if not a digression…
This guy—the budding etc. physicist—always carries an expression that is a linear combination of the following orthonormal components: (i) sleepy, (ii) sullen, (iii) dazed, (iv) abstract, (v) disturbed, and (vi) smug. The scalar multipliers along the individual dimensions do change more or less randomly, but the expression vector is always observed to span this six-dimensional space, you know by now. There is no change in the dimensionality of the space as it approaches you, not even on this bright, breezy and cool afternoon, you notice.
By now, you have had enough time to conclude that girls’ appreciative glances won’t buy you that bike. But even this realization wouldn’t hamper your aforementioned mood of utter joy and swelling confidence. You could solve any problem in the world, you are absolutely certain. Even a physicist’s problem. … Even a quantum physicist’s problem….
And so, you decide not to ignore the physicist the way you normally do. Instead, you approach him and offer if you could be of any help to him. … The expression vector collapses from (i) + (iv) + (vi) to mostly (v). “I am interested in resolving the riddles of QM, you know,” you tell him. The expression vector undergoes some very rapid changes, and then settles down to (v) + (vi). … “Drop by my lab, tomorrow,” he asks you. And, without a single further word, walks away. The expression vector now, you guess, is: (ii) + (iii) + (iv). But neither (v) nor (vi) makes too big a presence in the linear combination. Not bad, you say to yourself… It is yet another affirmation that this is a great day, you conclude.
* * * * * * * * * * * * * * *
Next day, you land up in his laboratory in the physics department. His prof is a big shot. And, young. It was only in the last semester that he had joined here on a contract position, after a very successful post-doc at one of top five US schools. He has also managed to bring in a lot of funding and contacts with him, as he came. His lab has acquired some brand new equipment for some new quantum experiments; the equipment has cost millions. The funds even came from the alumni association, you know. …
Your friend isn’t exactly the local guru in the lab—his aspiration is to be a theoretical physicist. But no one objects to his hanging around in the lab—every one knows that the prof may be a big shot, but because he is so young and has arrived only on a contract position, he can’t possibly arrange for separate, cosy, air-conditioned cabins for his theoretical physics students. And therefore, this friend of yours has no option but to make do with an old wooden desk, one that is covered with that government-green felt cloth (but without the glass on its top). The desk is placed in a side-corner in this otherwise new and swanky lab. Even as the two of you settle down at his desk, no one in the lab seems to notice your presence—your own, or, for that matter, even that of your friend! No greetings, no inquiring glances, not even raised eyebrows—nothing. They seem to carry on business as usual….
Your friend steps out to grab a cup of coffee, and then, as you get a bit restless, you try chatting with a few lab folks. There is a shade of respect for you as they come to know that you are a student of that engineering department. The campus-wide workshop [/lab resource/computer centre] comes under your department. In between their daily routine in the lab, they answer your queries about the lab and your friend. “No, we don’t understand the theory he is working on all that well,” they say, “but no matter, he just can’t be a very successful theorist, to be sure,” they tell you in a matter-of-fact tone. “Not a single experiment has yet gone wrong since he began sitting here,” they explain. … And no, they wouldn’t at all mind showing you how their equipment works.
There is a thick, black, metallic table with a lot of regularly drilled holes, serving as some kind of a platform, quite a few dazzlingly shiny steel bars/columns/tubes, looking glasses, flanges complete with gaskets, nuts and bolts, precision-built black enclosures, electronics, and wires, and also a couple of high-end workstations with 24″ monitors.
“What happens,” the lab fellows explain to you, “is that there is this central box in the middle of it all. There is a single quantum source—well not, single quantum, it actually is a stream, but the rate is so low that there is statistically very low chance that more than one quantum could be in the length of the box at any given instant of time. The stream of the statistically single quanta enters the box from this side. Then, there are these seven detectors on the other side. As the detectors detect the quanta, they generate a very small signal. We use this big imported amp, and a high-end data acquisition system, to capture these quantum events of interest to us, and the cables feed the data into these computers here.” They then show you the GUI of the software program. “Here, you see these seven circles in this GUI? Each circle represents one detector. For convenience, the circles carry different colours, in the VIBGYOR sequence. Whenever a detector event occurs, the circle lights up momentarily. It also adds the event to this large, terrabyte database that we maintain. Yes, we also do daily data backups. The software automatically shows you the fractions detected in the various detectors.”
“And what distribution is it? It looks something like the bell curve,” you wonder aloud.
“Wow! You know that, too, huh? … Well, yes, it is the normal curve,” they affirm in delight.
“And, what is inside that box?” you ask.
“That is an invalid question!” Your friend has returned, with only one cup of coffee—the one he is sipping from. All the friendly lab folks somehow begin to disperse in no time, and you follow your friend back to his desk.
Your friend resumes the discussion. He proceeds to cite the Solvay conference, the Bell inequalities, Schrodinger’s dead+alive cat, the EPR debate, Dirac’s anti-matter bubbles, the Stern-Gerlach experiment, the Bohr-Einstein debates, and so on and so forth. All of which proves, he says, that you cannot raise a question like that.
“We can talk meaningfully only of the observable quantum events.”
“That means, the lighting up of those seven VIBGYOR circles?”
Your friend ignores your interjection, and continues. “We can talk meaningfully only of the observable quantum events. But not of what can be there inside that box. That is just a hidden-variables nonsense. But hidden variables, by definition, cannot at all be observed. Ever. Hence, they can have no place in a theory of physics.”
He continues: “Quantum mechanics is a complete theory, an accurate theory. It has been experimentally tested for accuracy to the levels of one part in 1000(followed by many more zeroes), and it has always been found that the theory always gives results that are in complete agreement with the experiment.”
At this point of time, there is an increase in the dimensionality of the expression space; it has now acquired an additional dimension of “triumphant,” and the all the other scalar multipliers have become zero. You know that it is time to leave.
You decide to check out some books from the library before getting back to your hostel. At night, you begin to read them. You also do a lot of Web browsing, well into very late night. You are nowhere.
One day turns into one week, the one week turns into many weeks, then months, then years, and you still are nowhere. But you keep at it—at least intermittently. And then, finally, some realization descends on you. You switch on your computer, log in to your blogging account, and start writing a blog post.
* * * * * * * * * * * * * * *
The Copenhagen Interpretation:
The quantum shows the particle character as it enters the box. It shows a field character once in the box. The field collapses into a particle at the time of detection at one of those seven detectors. Thus, when the quantum is not observed, it exists as a field; when it is observed, it exists as a particle. This is called the Field-Particle Duality.
We cannot arrange the experimental apparatus of the triangular box in such a way that we could simultaneously observe both the field and the particle characters. This is called the Complementarity Principle.
We cannot ever hope to come to know how the quantum collapse occurs—how a field, an entity that is continuously spread over the entire triangular domain, suddenly localizes to a discretely observed particle, i.e., a spatially discontinuous entity or phenomenon.
There is an inherent uncertainty as to which detector a given quantum will hit. This is called the Uncertainty Principle.
However, the relative fraction of the times that quanta will be detected at a given detector, can be mathematically predicted, even if such a prediction can only be in the probabilistic terms.
The math [sic] is the same as the Newtonian gravity field + the theory of bifurcation points, apart from, of course, the theory of probability.
Quantum mechanics refutes the classical idea that we can measure anything with as much precision as we like. The Uncertainty and the Complementarity Principles in fact imply much more.
The idea is not just that we don’t know how the field-collapse occurs; it is that we cannot ever come to know anything about it. The nature of the empirical facts thrown up by quantum mechanics is like that. Quantum mechanics places a limitation on human knowledge, by introducing uncertainty at its most fundamental level.
All that fields vs particles is humbug. It’s a bunch of baloney. Real quantum does not behave that way at all. Real quantum is a particle. Yes, you got it right. This is what we know about quantum mechanics: The real quantum is a particle. But it’s bizarre! You have to construct those nice jazzy diagrams. In this case, the quantum undergoes these processes: a quantum goes from one place to another under the gravity field, or a quantum is absorbed and re-emitted with some momentum. There are many paths that a quantum can take. But there are no gears, ratchets and wheels. It’s all abstract. The 19th century physicists thought with all those mechanical gears and wheels and nails and collisions. But Maxwell got it right. He realized that there are no gears or nails. Maxwell was a smart guy. Also Pascal. Pascal also was a very, very smart guy. He was a mathematician. Pascal’s mathematical triangle is the abstract scheme which quanta somehow follow. There are many paths between different nodes of the Pascal triangle. Let us label the one node in the first row of the Pascal triangle as A, the two nodes in the second row as B1 and B2, those in the third row as C1, C2, C3, and so on and so forth. There are many paths and you have to sum up the quantum’s motion along each of them. For example, suppose there are only three rows. So, there are only a 3-factorial number of nodes: i.e., six in all. And you can connect these six nodes via all these tiny little arrows. And, so, in case there are only three rows to the triangle, you end up with these paths:
A -> B1 -> C1
A -> B1 -> C2
A -> B2 -> C2
A -> B2 -> C3
Of course, as the number of rows increases, the number of paths increases too. The factorial function is like that. It blows up. We spend seven years teaching our graduate students the necessary math [sic] so that they can calculate how these little quanta behave. But the essentials of that abstract mathematical process are very, very simple. I am sure my friend Smriti [/Kiran/Shazia/Shaina/…] can understand it. I thank her for inviting me here. Now, assuming that the path-lengths between the adjacent nodes in those paths are constant, then, the probability that the quantum will arrive at a detector, say, C2, can be calculated by taking the number of paths that have C2 as the final letter (2 here), and dividing it by the total number of paths (4 here). So, the probability in this case is 50.00…% You can calculate the probability to as much precision as you like: just keep on adding the recurring 0! Yes, you can do that. That is a neat trick which I learnt from my high-school teacher.
But no one understands quantum mechanics. Yes, a quantum is a particle. But it is nothing like a classical particle. It is quantum particle. No one understands what it means. No one can understand what it means. What this quantum particle actually does in that triangular box is, it goes over all those paths, before it is detected at any of the detectors. And so, you have to sum over all the paths. That is the way nature has chosen to do her book-keeping. Even if there is only a single quantum, you still have to take all the paths in your calculations. All the paths obtained by joining all those tiny little arrows. So, a single quantum simultaneously goes over the first path, the second path, the third path, etc. How it manages to be every where at the same time? That is something we don’t understand. No one understands. No one can understand. It’s not a classical particle. A classical particle follows only one path at a time. But a quantum particle goes over all the paths at the same time. This is called superposition. But it’s not an ordinary superposition. It is the quantum superposition. And you can calculate the probabilities with it…
And you can build a quantum machine. There is a lot of room at the bottom—in fact, the room goes on becoming bigger and bigger as you go down and further down the Pascal triangle. But, no one understands how this triangular box “really” works. No one ever can.
* * * * * * * * * * * * * * *
The Many Worlds Interpretation:
The essential confusion is about the measurement problem or the field-function collapse, and the probabilistic nature of the detection events.
Therefore, the only valid answer can be that when you conduct a quantum experiment and detect a quantum at a detector, say at C2, this detection event happens in our world. However, there also are other worlds. The mathematical Hilbert space is big enough to contain many worlds! It contains our physical world, as well as every other possible physical world. Let us be polite to all these worlds. In the above example of a Pascal’s triangle of 3 rows, the Hilbert space contains six worlds. As Feynman ingeniously pointed out, as the number of rows increases, the number of physical worlds contained in the mathematical Hilbert space goes up dramatically.
Suppose a quantum goes from row A to B to C following the path: A -> B1 -> C2. But in the process of the quantum going from A to B1 rather than B2, the entire universe branches into a second world. The quantum has gone from A to B1, but this occurrence has happened only in our world. But there is another world in which it actually has gone from A to B2. Even though we cannot observe it, ever. It exists. Hilbert space can be proved to contain it. And similarly, for every branching occasion and every branched out world.
And, let us all be polite: please don’t tell me that there can be only one world. I acknowledge and in fact in my work I encourage the idea that you might have a philosophically interesting idea there. But there are many worlds. And, this idea sounds very plausible even if it may not be immediately compelling, because there are no hidden variables in this theory, and yet everything is deterministic. So, there have to be many worlds. At least, many physicists take very favourably to this idea.
After all, physics is the most fundamental and most abstract science. Computer scientists may think they are the only ones to do the abstract thinking. But they are wrong. When they model the searching and sorting algorithms, they may construct what they call an abstract tree. They may show all the branches and the leaves of this tree data structure at the same time. But, their theories still are not sufficiently abstract. They still insist on telling you that the actual computer actually traverses the tree via only a single pathway at a time—depth-first, or breadth-first, or whatever-first. So, in that sense, they do make a distinction between what is only potentially traversed and what is actually traversed. And, it is this distinction that compels them to have this entire tree only in one world. If they were to think more abstractly, if they were to use the insights of quantum mechanics, they would realize that all the various branches of the tree are actually traversed quite at the same time, but in different worlds.
We the physicists think about the most fundamental principles. We therefore have to be most abstract. And, mathematical. Mathematics is fundamental to physics. Therefore, the Hilbert space is more fundamental than the physical world; it contains all the possible physical worlds. We thus are in logic forced to insist that all the branches and leaves of the tree are physically traversed at the same time. That’s quantum mechanics for you. But simultaneous traversals require many different worlds.
Ergo, there are many worlds. Just the way computer scientists use an entire tree even if only one pathway would be traversed, similarly, we use the entire multiplicity of the physical worlds hidden in the Hilbert space, even if the events occurring only in our world would be observed. This is another reason why we like the MWI: it helps simplify our calculations—apart from, of course, fully satisfactorily solving the measurement problem and the probabilistic nature of quantum phenomena. So what if it takes many worlds! How does that pose a problem?
* * * * * * * * * * * * * * *
A note on a more serious note: The above-discussed analogy is entirely classical, even though it does help pin-point the quantum idiocy to such an astounding extent. In case you don’t know QM, do not let yourself think that the above analogy is what QM is really like. In particular, the system evolution here occurs via the classical Newtonian gravity and momentum exchange, not according to Schrodinger’s equation, and there are no phases here—there are no interference effects. Similarly, in the Feynman interpretation, for a quantum system, depending on the context, the accounting might have to include the additional two paths: A + B1 + C3 and A -> B2 -> C1 paths. So, the analogy as given above remains entirely classical. Even if it helps bring out the quantum idiocy—I mean, not the idiocy of science popularizers, but that of physicists themselves—to this recognizable an extent.
* * * * * * * * * * * * * * *
A Song I Like:
(Hindi) “mila hai kisi kaa jhoomka…”
Music: Salil Choudhary
Singer: Lata Mangeshkar
[Guess I will not bother with this post much further, though, as usual, a chance exists that I might come back and streamline things a bit. The world is quantum.]