Math and physics: what should you know or learn?

When reading this blog and/or my papers on ResearchGate, you may wonder what kind of mathematical framework you need to appreciate the finer details. We ourselves were asked by fellow proponents of the kind of local and realist interpretation of QM that we are pursuing to look at Clifford or space-time algebra (STA). Well… We looked at it as part of our farewell to this weird pastime of ours, and we documented our response in our very last RG paper on physics, math and (a)symmetries in Nature. If you struggle with the question above, then our answer will probably make you happy: there is no need to learn fancy math to understand easy physics. 🙂

Post scriptum (10 November 2024): As for the “farewell” part of this – I swear – very last paper on all of this weird stuff, it is probably a bit too harsh – but then it is what it is. Let me say a few things about it for the benefit of the would-be student or the starting amateur physicist. Should you study modern physics? I do not think so now, but then I also know that one cannot help oneself when it comes to satisfying some curiosity on fundamental questions. So it probably does not really matter what I advise you to do or not do. I can only say what I write below.

When I started this intellectual journey – what’s this quantum stuff all about? – decades ago, and especially when I got serious about it back in 2013, I had never expected that what happened would happen. No. I’ve always been a good student, and so I expected to sail smoothly through the required math and the intricacies of relativistic mechanics and all of the subtleties of electromagnetic theory – which sort of happened – and, then, to sail through the wonderful world of quantum electrodynamics, quantum field theory and – ultimately – quantum chromodynamics (or let’s call it high-energy physics now) in pretty much the same way.

The latter part did not happen. At each and every page of Feynman’s third volume of Lectures – the ones I was most interested in: on quantum mechanics – I found myself jotting down lots of questions. Questions which took me days, weeks or even years to solve, or not. Most of these questions led me to conclude that a lot of what is there in these Lectures are nothing but sophisms: clever but false arguments aimed at proving the many ad hoc hypotheses that make up the Standard Model. I started to realize the Standard Model is anything but standard: it is just a weird collection of mini-theories that are loosely connected to one another – if connected at all! I started buying more modern textbooks – like Aitchison’s and Hey’s Gauge Theories, which is apparently the standard for grad students in physics – but that did not help. I got stuck in the first chapter already: this Yukawa potential – or the concept of a non-conservative nuclear force itself – did not make sense to me. Not only in an intuitive way: the logic and the math of it does not make sense, either!

Fortunately, I reached out and wrote to non-mainstream researchers whose ideas resonated with me. For example, I will be eternally grateful to Dr. Vassallo for his suggestion to read Paolo Di Sia’s paper on the nuclear force, in which he provides heuristic but good arguments showing the nuclear force might just be a dynamic electromagnetic dipole field. So then I found myself in the business of deconstructing the idea of a strong force. A deeper historical analysis of all these new strange quantum numbers and new quantum conservation laws led to the same: I started looking at sensible suggestions to explain what happens or not in terms of electromagnetic disequilibrium states – developing my own fair share of such suggestions – rather than irrationally or uncritically swallowing the idea of hypothetical sub-nuclear particles on which you then load all kinds of equally hypothetical properties.

While I thought I was doing well in terms of pointing out both the good as well as the bad things in Feynman’s Lectures, I suffered from the weirdest thing ever: censorship on the Internet. Some strange caretaker of Feynman’s intellectual heritage apparently used the weight of his MIT-connection to take down substantial parts of many of my blog posts, accusing me of “unfair use” of this 1963 textbook. Unfair use? Over-use, perhaps, but unfair? All was nicely referenced: when you want to talk about quantum physics, you need some reference textbook, right? And Feynman’s Lectures are – or were, I would say now – the reference then. It was ridiculous. Even more so when he went as far as asking YouTube to strike a video of mine. YouTube complied. I laughed: it took me ten minutes or so to re-edit the video – a chance to finally use all that video editing software I have on my laptop 🙂 – and then put it back online. End of problem.

Case closed? I am not sure. I am a pretty cheerful guy, but I am also quite stubborn when I think something isn’t right. So I just carried on and shrugged it all off thinking this would only boost my readership. It probably did, so: Thank You, Mr. Gottlieb! 🙂 But things like that are hurtful. In any case, that doesn’t matter much. What matters is that things like that do reinforce the rather depressing and very poor perception of academic physics that a Sabine Hossenfelder now (very) loudly talks or – should I say: rants? – about: the King of Science is in deep trouble, and there is no easy way out.

So, what is my conclusion then? I am happy I found the answers I was looking for: there is a logical explanation for everything, and that explanation has been there for about 100 years now: Max Planck, Albert Einstein, H.A. Lorentz, Louis de Broglie, Erwin Schrödinger, Arthur Compton and then some more geniuses of those times have probably said all one can say about it all. And it makes sense. In contrast, I feel the past fifty years of mainstream research were probably nothing more than a huge waste of human intellect. Am I right? Am I wrong? Only the future can tell. To be frank, I am not too worried about it.

I may add one anecdote, perhaps. I did talk to my own son six or seven years ago about what he’d like to study. He was most interested in engineering, but we did talk about the more fundamental study of physics. I told him to surely not study that. In his first year of his Master’s degree, he had to do one course in quantum physics. We walked through it together, and he passed with flying colors. However, he also told me then he now fully understood why I had told him to surely not go for theoretical studies in physics: it just does not make all that much sense. If you would happen to be very young and you want to study something useful, then go for applied science: chemistry, biology or – when you are really smart – engineering or medicine. Something like that. If you want to do physics, go join CERN or something: they probably value engineers or technicians more than theorists there, too! 🙂

Personal note: As for myself, I wanted to study philosophy when I was about 15 years old (so that’s 40 years ago now). I did that eventually, but in evening classes, and only after I did what my good old dad (he died from old age about twenty years ago) then told me to do: study something useful first. I was not all that good with math, so I chose economics. I did not regret that. I even caught up with the math because the math – including statistical modeling! – that you need to understand physics is pretty much what you need in econometric modeling too. So I’ll conclude with a wise saying: all’s well that ends well. 🙂