As you know, I was planning to write a post on the uniqueness of “the” solution of the simple, linear, partial differential diffusion equation. In particular, I was going to show that the Fourier-theoretical solution isn’t unique.
I have changed the plan. Not because my idea does not hold water, but simply because I am so confident that it does. It’s just a matter of writing it down in a more scholarly and somewhat mathematics-like manner. I may in fact write a journal paper-like article in the PDF format, run it through some maths professor at an IIT (probably IIT Bombay), and then publish it here, first. (Though mathematics-like, it will still avoid the use of words like “lemma.” No layman (including engineer/physicist) ought ever to use that term, in my very deeply considered opinion.)
Instead, there is this bit of a news that is very exciting, at least to me.
Before getting to it, let me tell you why I worry so much about the diffusion equation. I do, because, to my mind, the diffusion equation makes for a poor man’s quantum mechanics.
And, the exciting news is that a new experimental set-up to verify my QM proposal has occurred to me. Just about within the past half an hour. … It is that fresh.
I plan to post about it, almost simultaneously here and at my iMechanica blog, hopefully on the Christmas day (simply because it’s the first upcoming holiday that will allow me to pursue research, as in contrast to other official duties of being a (temporary, on contract) professor, such as grading the university examination papers.) Even then, you could expect this upcoming post to be rather incoherent/inchoate/in-India-like/etc. But, it will have something. If I can get researchers abroad to make some comments on it, then I am sure it will result into something that can be pursued in actual experimentation.
The idea occurred to me while I was trying to write my planned post on the uniqueness of the solution of the diffusion equation, but in completely non-technical terms. While trying to write something that any intelligent layman could understand, I tried to think of an example that clearly brings out the differences between different approaches to the diffusion equation—Fourier’s, Einstein’s (stochastic), and, say, those having arguments originating from numerical analysis methods (deterministic). While trying to make these differences as easy to grasp as possible, I started thinking of a simple experiment which any one could perform at home. … And, suddenly, the bulb lighted up, so to speak.
But as I said, let me have some free time so that I can write at least partly coherently about it.
In the meanwhile, there was a thoughtful comment that I received here on this blog, and I have replied it. It spells out my view of the “multi-verse” idea. Please browse it, here[^]. In particular, when I said “eject” in that reply, I was reminded of a certain scene from the movie: “Arthur;” check out between 0:53 to 0:57, here [^].
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