The meaning of life in 15 pages ! Or… Well… At least a short description of the Universe… Not sure it helps in sense-making. 🙂
Post scriptum (25 March 2021): Because this post is so extremely short and happy, I want to add a sad anecdote which illustrates what I have come to regard as the sorry state of physics as a science.
A few days ago, an honest researcher put me in cc of an email to a much higher-brow researcher. I won’t reveal names, but the latter – I will call him X – works at a prestigious accelerator lab in the US. The gist of the email was a question on an article of X: “I am still looking at the classical model for the deep orbits. But I have been having trouble trying to determine if the centrifugal and spin-orbit potentials have the same relativistic correction as the Coulomb potential. I have also been having trouble with the Ademko/Vysotski derivation of the Veff = V×E/mc2 – V2/2mc2 formula.”
I was greatly astonished to see X answer this: “Hello – What I know is that this term comes from the Bethe-Salpeter equation, which I am including (#1). The authors say in their book that this equation comes from the Pauli’s theory of spin. Reading from Bethe-Salpeter’s book [Quantum mechanics of one and two electron atoms]: “If we disregard all but the first three members of this equation, we obtain the ordinary Schroedinger equation. The next three terms are peculiar to the relativistic Schroedinger theory”. They say that they derived this equation from covariant Dirac equation, which I am also including (#2). They say that the last term in this equation is characteristic for the Dirac theory of spin ½ particles. I simplified the whole thing by choosing just the spin term, which is already used for hyperfine splitting of normal hydrogen lines. It is obviously approximation, but it gave me a hope to satisfy the virial theorem. Of course, now I know that using your Veff potential does that also. That is all I know.” [I added the italics/bold in the quote.]
So I see this answer while browsing through my emails on my mobile phone, and I am disgusted – thinking: Seriously? You get to publish in high-brow journals, but so you do not understand the equations, and you just drop terms and pick the ones that suit you to make your theory fit what you want to find? And so I immediately reply to all, politely but firmly: “All I can say, is that I would not use equations which I do not fully understand. Dirac’s wave equation itself does not make much sense to me. I think Schroedinger’s original wave equation is relativistically correct. The 1/2 factor in it has nothing to do with the non-relativistic kinetic energy, but with the concept of effective mass and the fact that it models electron pairs (two electrons – neglect of spin). Andre Michaud referred to a variant of Schroedinger’s equation including spin factors.”
Now X replies this, also from his iPhone: “For me the argument was simple. I was desperate trying to satisfy the virial theorem after I realized that ordinary Coulomb potential will not do it. I decided to try the spin potential, which is in every undergraduate quantum mechanical book, starting with Feynman or Tippler, to explain the hyperfine hydrogen splitting. They, however, evaluate it at large radius. I said, what happens if I evaluate it at small radius. And to my surprise, I could satisfy the virial theorem. None of this will be recognized as valid until one finds the small hydrogen experimentally. That is my main aim. To use theory only as a approximate guidance. After it is found, there will be an explosion of “correct” theories.” A few hours later, he makes things even worse by adding: “I forgot to mention another motivation for the spin potential. I was hoping that a spin flip will create an equivalent to the famous “21cm line” for normal hydrogen, which can then be used to detect the small hydrogen in astrophysics. Unfortunately, flipping spin makes it unstable in all potential configurations I tried so far.”
I have never come across a more blatant case of making a theory fit whatever you want to prove (apparently, X believes Mills’ hydrinos (hypothetical small hydrogen) are not a fraud), and it saddens me deeply. Of course, I do understand one will want to fiddle and modify equations when working on something, but you don’t do that when these things are going to get published by serious journals. Just goes to show how physicists effectively got lost in math, and how ‘peer reviews’ actually work: they don’t.