OK, after a long hiatus (mainly due to viral fever and cough etc.), I am back into the game. This post of course continues from the previous one in this series, i.e., the very last one.
On 18 July 2019 I then posted the next two tweets, now about my new approach (as in the Outline document [^]):
3/4. My new approach is something like: Quanta as Discrete Sets for the States of Fields & Changes in Them. (Hard to form a neat short-form.) I’ve abandoned the idea of the spatially delimited quantum particles—whether photons (Einstein), or others too (Feynman).
4/4. Instead, I have singular potential () fields for protons and electrons. These fields are continuous at all points other than their instantaneous positions where they are singular. I also have the ever continuous as a physically existing attribute / characteristic of the background object. This is quite like how stress / strain are attributes of a continuum.
Looking back, I think that my coming out of the heavy influence of the Einstein–Feynman idea, viz., regarding a photon as a spatially discrete object, was truly a turning point for me. It was the best thing that happened to me.
While my thinking was my own, in retrospect, I think the following were truly helpful pointers in finally coming out of the influence of Einstein (and Feynman): (1) a systematic study of QM text-books like Griffiths, mostly done with a viewpoint of what it would take to computationally model Schrodinger’s equation—which I now took as just another differential equation, almost as if it had nothing to do with quantum phenomena. (2) The “Anti-Photon” paper by the Nobel laureate W. E. Lamb. (3) Some comments by some bloggers (like Roger Schlafly and Lubos Motl) who were critical of the spatially discrete nature of photon. (In fact, even Lamb’s paper was pointed out by someone posting a comment at some blog or physics forum.)
While my studies of textbook QM had begun much earlier (I have some margin-notes in my copy of Griffiths that are dated to October 2015), the turning away from the particles viewpoint mostly began much after my running into the “Anti-photon” paper by W. E. Lamb, Jr. [^], which was in November 2015.
Initially, I took Lamb’s paper with a view to refute it. (“Faith” gives you a lot of confidence.) Lamb’s paper anyway was written with a touch of humour. So, the temptation to outright refute it was even greater—I had this suspicion that since the author was employing humour, may be he didn’t mean to advocate that position very seriously, which in turn meant that the position had some weakness or so.
However, slowly, very slowly, I began to grant some kind of a respect to Lamb’s skepticism of this Einstein–Feynman view (of a spatially discrete nature for the photon). I also began to realize that Lamb wasn’t just a great experimentalist, he also had a great nose on the conceptual side of physics.
It was precisely around this same time (late 2015) that I finally decided to complete Griffiths’ text on QM.
Before turning to Griffiths, I had certain ideas of creating a computational model (or simulation) for generation and absorption of photons from material objects. [So, until late 2015, I was definitely still believing in photons as spatially discrete particles.]
For convenience in computational modeling, after evaluating a lot of other choices, in a moment of inspiration (at a “chaai Tapari” i.e. road-side tea-stall), I had finally decided to take the simplest possible material object: a single H atom for the emission of a photon, and another single H atom for its absorption. (This, I remember, was in early October 2015.)
Now, I wanted to know the specifics of how an isolated H atom might go from an excited state to a ground state, and how another H atom might go from the ground state to an excited state. The problem, as I saw it, was to relate these two transitions to the generation and absorption of a single photon that was spatially discrete.
My vague inspiration came from my studies of droplet formation and coalescence, a topic I was looking into because of my interest in the particles-based approaches in CFD. There was some good work done using LBM (lattice-Boltzmann method) and SPH etc. It formed a backdrop of sorts.
So, when one H atom transitions down from an excited state to the ground state, I had thought, it would be emitting a droplet of a photon, and this droplet would subsequently get absorbed by another H atom in its ground state. If Einstein and Feynman were right, the formation of such droplets must come out rather straight-forwardly from the simulations. All that I had to do was to look up the equations that described transitions of states, and fields adjustments internal to the emitter/absorber, and simulate them carefully. If I could do that, the droplets would be there for me to see!
I had thought that I would master this part (of finding the right equations to describe the transitions) using Griffiths book within, say, a couple of weeks or so. That’s how in late 2015, I had picked up my copy of Griffiths (which I had bought much earlier, in 2011 or so).
And then, slowly working through the text, I came to realize that the thing which I needed to understand and focus on first was not photons traveling in space but the electrons in the material objects.
Now, clearly, even if all that you want to simulate is just a single electron in a single H atom, you still have to first understand the layers and layers of the analysis. This solution is really hard, even horrendous (for someone who hasn’t solved PDEs of the similar kind in the past). I kept on dragging myself through the studies of this topic. … I couldn’t turn the pages as fast as I had anticipated I would be doing. But having to spend more time on the topic also meant that got used to having the continuum field strike me as the first object of QM—not those droplets of photons.
Mind you, until this time, I had not given up the droplet-like idea for the photon. But I had now grown familiar enough with the wavefunction formalism. Slowly, I began to appreciate the fact that contrary to my naive expectations, no one had described how a quantum jump (say in an energy eigenstate) begins and ends. Certainly, there were no simulations of such a thing either—which was a big surprise for me.
Next, I also wondering about the logic behind one electron travelling between two H atoms, say from a H atom to an H+ ion etc.
At this point, I asked myself a simple question: Why does the electron at all have to go from the stable H atom, and get absorbed into an H+ ion which can be quite some distance apart? Wouldn’t it be better for the electron to remain bonded to the local proton (nucleus)? … Answers were hard to come by. So, going with the textbooks, I again decided to re-focus back first on a single H atom, and the transitions that a single electron could undergo in its own energy eigenstates. (I could not deal with a single electron and two protons back then; I ran into the double-well potentials only some time later on.)
Also, since I was teaching an engineering thermodynamics course around this same time (II semester 2015, ME Thermo course, at GHRCEM), I naturally picked up the old habit of visualizing all systems first as isolated systems (because they were the simplest), and only then introducing any interactions between two or more such systems, thereby gradually increasing the complexity. Since QM systems too are, thermodynamically, just systems, I began working within the framework of isolated systems first and foremost. Thus, scattering wasn’t an interesting phenomena, but quantum jumps were. Interactions were best postponed because in QM they must occur via the fields, and fields-based interactions are always far more complex. [Isolated systems are especially convenient in studies of QM because their total energy always remains conserved—i.e., even if their Hamiltonian is not time-independent. [If you know QM, think about it for a moment.]]
In the process of thus first going for the simplest system possible, I also began doing away with every arbitrarily specified potential (be it gravitational, magnetic, or even electrostatic, as in the particle-in-the-box or quantum harmonic oscillator situations). Instead, I began visualizing the lone singularity of an electron for the field.
The energy content of an isolated system had to translate to something physical existing in each volume element making up the system. Since momenta were involved with the field, I realized, the nucleus would experience forces. To simplify simulation, it was better kept fixed. This in turn meant that I started visualizing some unspecified support forces arising for the nucleus, as the field changed in time. I began drawing the support symbol as in the FBDs (free body diagrams) of trusses and frames etc. Once drawing the support forces became a habit, it was easy enough to realize that the singular positions of electrons too would have local forces acting on them, and so, the electrons would have to be moving around the fixed nucleus in some way that was accessible to simulations.
… Also sometime in the process, I had spotted a similarity of the above-kind of a simplified model of QM of just one or two H atoms, and the molecular dynamics (MD) technique.
As to MD, I had already browsed through it for a long time, mainly because of my preoccupation with the particles-based approaches in CFD. Indeed, while teaching in Mumbai (back in 2014), I had written several small MD simulation programs in C++ and OpenGL. (I have lost them in a subsequent HDD crash.)
Now, though people don’t usually note it, I had noticed that that MD obviously involved a nonlinearity because the interatomic potentials were anchored into the relative separations of the atomic nuclei—and therefore, into their absolute positions. If this nonlinearity were not present, the MD simulation couldn’t show a liquid to solid state transition. MD was nothing but the 3-body problem gone on steroids.
Some time later, I transferred this insight (about anchoring of the potential and hence of the nonlinearity) from MD to QM, because by now, my QM had already done away with all the arbitrary potentials—I would entertain only those potential which arise from superposition of the singular potentials of the point-charges. By this time, I had come to forget all my original motivation about modeling the spatially discrete droplets of photons, my PhD time FAQ approach, and all that.
Indeed, by the time I came across a paper [(.PDF) ^] on 1D simulation of photon propagation by Prof. Martin Ligare [^], I had already come to drop the idea of visualizing a photon as some kind of a droplet (or even as a streak extended over length but of delimited cross section which begins protruding from the emitter atom and winds up at the absorber atom).
In any case, most of the essential ideas mentioned in the Outline document were already with me when I wrote this post [^] in February 2017. In contrast, if I check out an earlier post on QM [^], I think that many crucial ideas of the Outline document would be missing at that point of time. This fact also seems to match well with my memory, though I would continue cross-checking further. (I have kept a lot of hand-written notes, but right now they are lying behind layers of books in the more-or-less inaccessible cubboard.)
So, overall, the studies for the new approach (which means detailed textbook studies) began in late 2015, and was mostly complete by 2016-end or so. The first public offer to conduct a seminar on it was made in February 2017, see the linked post above.
Alright, enough. Given the nature of the rest of the tweets, commentary for them won’t be as personal, and so, it won’t be as lengthy. The explanations, if any, will be mostly technical and business-like. I will try to wrap up this exercise of moving the tweets over here at this blog ASAP, with the next post in this series coming in here may be right tomorrow or the day after.
(Hindi) “aye dil-e-naadaan”
Singer: Lata Mangeshkar
Lyrics: Jan Nisar Akhtar