After further and deeper studies of the Schrodinger formalism, I have now come to understand the exact position from which the physicists must be coming (I mean the couple of physicists with who I discussed the ideas of my new approach, as mentioned here [^])—why they must be raising their objections. I came to really understand their positions only now. Here is how it happened.
I was pursuing finding correspondence between the configuration space of the Schrodinger formalism on the one hand and the physical space on the other, when I run into this subtle point which made everything look completely different. That point is the following:
Textbooks (or lecture notes, or lecturers) don’t ever highlight this point (in fact, indirectly, they actually obfuscate it), but I came to realize that even in the cases like the QM harmonic oscillator (QHO), the Schrodinger formalism itself remains defined only on an abstract hyperspace—it’s just that in the case of the QHO, this hyperspace happens to be in nature, that’s all.
I came to realize that, even in the simplest case like the QHO the variable which appears in the Schrodinger equation does not directly refer to the physical space. In case of QHO, it refers to the change in the equilibrium separation between the centers of the two atoms.
Physicists and textbooks don’t mention this point, and in fact, the way they present QM, they make it look as if is the simple position variable. But in reality, no it is not. It can be made to look like a position variable (and not a change-in-the-interatomic-distance variable) by fixing the coordinate system to one of the two atoms (i.e. by making it a moving or Lagrangian coordinate system). But doing so leads to losing the symmetry in the motion of the two atoms, and more important, it further results in an obfuscation of the real nature of the issue. Mind you, textbook authors are trying to be helpful here. But unwittingly, they end up actually obfuscating the real story.
So, the variable whose Laplacian you take for the kinetic energy term also does not represent the physical space—not even in the simplest cases like the QHO.
This insight, which I gained only now, has made me realize that I need to rethink through the whole thing once again.
In other words, my understanding of QM turned out to have been faulty—though the fault is much more on the part of the textbook authors (and lecturers) than on the part of someone like me—one who has learnt QM only through self-studies.
One implication of this better understanding now is that the new approach as stated in the Outline document isn’t going to work out. Even if there are a lot of good ideas in it (Only the Coulomb potentials, the specific nonlinearity proposed in the potential energy term, the ideas concerning measurements, etc.), there are several other ideas in that document which are just so weak that I will have to completely revise my entire approach once again.
Can I do that—take up a complete rethinking once again, and still hope to succeed?
Frankly, I don’t know. Not at this point of time anyway.
I still have not given up. But a sense of tiredness has crept in now. It now seems possible—very easily possible—that QM will end up defeating me, too.
But before outright leaving the fight, I would like to give it just one more try. One last try.
So, I have decided that I will “work” on this issue for just a little while more. May be a couple of weeks or so. Say until the month-end (March 2019-end). Unless I make some clearing, some breaththrough, I will not pursue QM beyond this time-frame.
What is going to be my strategy?
The only way an enterprise like mine can work out is if the connection between the world of observations and the hyperspace formalism can be put in some kind of a valid conceptual correspondence. (That is to say, not just the measurement postulate but something deeper than that, something right at the level of the basic conceptual correspondence itself).
The only strategy that I will now pursue (before giving up on QM) is this: The Schrodinger formalism is based on the higher-dimensional configuration space not because a physicist like him would go specifically hunting for a higher-dimensional space, but primarily because the formulation of Schrodinger’s theory is based on the ideas from the energetics program, viz., the Leibniz-Lagrange-Euler-Hamilton program, their line(s) of thought.
The one possible opening I can think of as of today is this: The energetics program necessarily implies hyperspaces. However, at least in the classical mechanics, there always is a correspondence between such hyperspaces on the one hand and the space on the other. Why should QM be any different? … As far as I am concerned, all the mystification they effected for QM over all these decades still does not supply any reason to believe that QM should necessarily be very different. After all, QM does make predictions about real world as described in ! Why, even the position vectors that go into the potential energy operator are defined only in the space. …
… So, naturally, it seems that I just have to understand the nature of the correspondence between the Lagrangian mechanics and the mechanics better. There must be some opening in there, based on this idea. In fact my suspicion is stronger: If at all there is a real opening to be found, if at all there is any real way to crack this nutty problem, then its key has to be lying somewhere in this correspondence.
So, I have decided to work on seeing if pursuing this line of thought yields something definitive or not. If it doesn’t, right within the next couple of weeks or so, I think I better throw in the towel and declare defeat.
Now, understanding the energetics program better meant opening up once again the books. But given my style, you know, it couldn’t possibly be the maths books—but only the conceptual ones.
So, this morning, I spent some time opening a couple of the movers-and-packers boxes (in which stuff was still lying as I mentioned before [^]), and also made some space in my room (somehow) by shoving the boxes a bit away to open the wall-cupboard, and brought out a few books I wanted to read / browse through. Here they are.
The one shown opened is what I had mentioned as “the energetics book” in the background material document (see this link [^] in this post [^]). I am going to begin my last shot at QM—the understanding of the — issue, starting with this book. The others may or may not be helpful, but I wanted to boast that they are just a part of personal library too!
Wish me luck!
(And suggest me a job in Data Science all the same! [Not having a job is the only thing that gets me (really) angry these days—and it does. So there.])
BTW, I really LOL on the Record of 17 off 71. (Just think what happened in 204!)
A song I like:
(Hindi) “O mere dil ke chain…”
Singer: Kishor Kumar
Music: R. D. Burman
Lyrics: Majrooh Sultanpuri
Minor editing to be done
and a song to be added, tomorrow. But feel free to read the post right starting today.
Song added on 2019.03.10 12.09 AM IST. Subject to change if I have run it already.