I have written about all things physics for a long time - mainly on my blog, since 2012 – but I have never been quite satisfied with the result: Too boring for experts, not exciting and popular science-y enough for the 'educated public'. I think the reason was my hidden agenda, an agenda not even obvious to myself.
I wrote about phenomena and subfields I had just immersed myself and (re-)learned about, either because this was very remote from what kind of physics I use on a daily basis, or just because I was concerned with some aspect of it but wanted to complement that with 'more theory' for the fun of it.
In spite of that, I tried to keep a style that somewhat resembles your typical 'science communications', but that was most likely to no avail. Re-reading my old blog posting I don't read so much about 'the physics' as about my own learning process. Or I remember what I actually wanted to write about, but did not – in order to violate the pop-sci agenda - so the result was something in between a learner's notes and sketches of ideas for popular presentations. For example, I (re-)learned Quantum Field Theory after all the news about the Higgs particle and LHC. Both my experimental and theoretical background was in condensed matter physics, so it really took me a while to map what I learned about so-called Second Quantization and many body systems (described in a non-relativistic way) onto your typical QFT introduction that started with Noether's Theorem and Lorentz transformations. Now in order to drive that point home (in a blog posting), to explain what was so interesting for me, I would have had to introduce all those concepts to a lay audience which I considered futile. Or I was just too lazy to learn more LaTex or too hesitant to use equations at all. I noticed, I got on all sorts of tangents when I tried to run a series on QFT – I did exactly what I did not like myself about popular texts on theoretical physics: Pontificate on more or less palpable metaphors about fields and waves, but not being able to really explain anything above a certain threshold of abstractness.
I gave up on my series before I could 'explain' what interested me most: How forces translate into the exchange of virtual particles and how I actually knew about the 'Higgs field giving particles mass' without knowing any more: I had learned about Andersen's mechanism in solid state physics, and Ginzburg-Landau theory of superconductivity. Perhaps that would have been a great example of symmetry breaking and that infamous sombrero hat potential typically used in pop-sci articles about the Higgs field?
I absolutely know that this may sound totally opaque – which is the reason why I only write about it here, on my website in that forgotten corner of the web, rather than trying to turn this into a blog post. Here, I follow my stream of consciousness and don't bother anybody on social media with it. There, I try to be somewhat entertaining and useful.
But even here, I try to write about something that somebody somewhere might be able to relate to, and here 'the internet' comes to rescue: For better or for worse, no matter how seemingly unique, special, and eclectic your hobbies and professional specializations, are – there is somebody somewhere on the net who indulges in the same combination of stuff. So, yes: It seems there is a growing community of hobbyist physics enthusiasts who feel the same and who 'practice' physics in the same way: Professionals with a STEM background who seriously learn about physics in their spare time, like R;&D managers writing textbooks about undergraduate physics or introductions about Quantum Field Theory. Like the IT server admin or the management consulting who write blog posts about what they have (re-)learned in their sparse spare time. Like the retired IT specialists who returns to what they originally studied – physics. Like me, who has an education mainly in applied condensed matter physics and who works as a consulting engineer and IT consultant.
From a down-to-earth perspective, this hobby can be worthwhile and useful: I noticed that it sharpens the mind, even if I don't use that physics and math directly on a daily basis. It's this effect that is makes the hackneyed saying about the 'analytical skills' of physics majors true. However, there is a caveat: Yes, physicists may be good at any corporate job, but I think not to lose you 'analytical edge' you need to practice the skills that originally shaped your mind. I don't know about research in psychology, so this is just my personal anecdotal experience. Living the corporate, inbox- and interrupt-driven work-style and having your mind scattered and distracted my social media does not help. There was a time in my life when I got up at 4:00 AM every day to re-learn physics, starting with Feynman's Physics Lectures. Surprisingly, that investment was well spent. I felt, my IT security concepts become crisper, more concise, and better – and it took me less time to compile them; So the ROI was great.
What triggered this article is my prime example of useful mathematical: While I had some background in QFT there was one subfield in physics I had missed completely: the theory called 'most beautiful', even by sober authors Landau and Lifshitz – the theory of General Relativity (GR). I had specialized in solid state physics, lasers, optics, and high-temperature superconductors, and GR was not a mandatory subject.
But I wanted at least to understand a bit about current research and those issues with not being able to unify quantum (field) theory and relativity. And I can relate to poor consumers of my feeble attempts at pop-sci physics: When I read popular physics books, I enjoy them as long as I have some math background - although I feel sometimes flowery metaphors make it more difficult to recognize something you actually know in terms of math. But when you would have to use new mathematical concepts you cannot understand the metaphors at all. Digression: So it baffles me when people like articles about Black Hole, the universe, and curved spaces but complain about not perfectly comprehensible explanations of more mundane physics and engineering. I believe the reason is that you 'need not' understand worm-holes etc.; so can just relax and scroll through the story, much like watching an illogical science-fiction movie. But mechanical engineering and simple thermodynamics feels like you 'should know it' and 'try a bit harder to understand it', and so it brings back memories of school and tests.
But as I said, there might be small community of people who genuinely want to learn, despite – or because of!! – the so-called hard aspects: Going through mathematical derivations again and again, and banging your head against the wall, until suddenly you understand. Which is a reward in itself, a feeling that's hard to share, and could and should not be shared anyway – in an act of subversive protest against our culture of craving for attention and 'likes'.
So for this community I'd like to share the resources I have picked for learning General Relativity: A set of free resources, each one complete and much more than just 'lecture notes'. Each of them also represents a different philosophy and pedagogical style, and I believe physics is learned best by using such a diverse set of resources.
One can debate endlessly, if and how to introduce the mathematical foundations used in some subfield in theoretical physics. As a physics major, you learn analysis and linear algebra before tackling its applications in physics and/or some mathematical tools are introduced as you go (Hello, Delta function!). I think it does not make such a difference in relation to the first courses in theoretical physics, e.g. learning about vector analysis before or in parallel to solving Maxwell's equations.
I feel it is more difficult the more advanced the math and the physics get, as you have to keep a lot of seemingly abstract concepts in mind, before you finally are presented with what 'you actually use that'. But maybe it is just me: Different presentations of GR seem 'more different to me' than different presentations of special relativity and electromagnetism.
In GR you can insist on presenting a purely mathematical and rigorous introduction of mathematical foundations first – your goal being to erase all false allusions and misguided 'intuitive' mental connections. Thinking about vectors in a 3D 'engineering math' way might harm your learning about GR just as too creative science writing might put false metaphors in your mind.
On the other hand, you could start from our flat space (our flat spacetime) and try to add new concepts bit by bit, for example trying to point out what curvature in 4D spacetime means for curvature in the associated 3D space, and what we might be able to measure.
Some authors use a mixed approach: They starting with a motivational chapter on experiments, photons in an elevator, and co-ordinate transformations in special relativity … and then they leave all that for a while to introduce differential geometry axiomatically … until they are back to apply this something tangible … until more mathematical concepts are again needed.
Sean Carroll does the latter in his Lecture Notes on General Relativity, that are actually much more than notes. He also published a brief No-Nonsense Introduction to GR that serves as a high-level overview, and he manages to keep to his signature conversational tone that makes his writings to enjoyable. Perhaps – if this was the only literature used – the mixed presentation plus digressions into special topics and current questions in physics would be a bit confusing.
But I was still searching for video lectures to complement any written text. A few years ago, I have not found any comprehensive self-contained course, but in 2015 this series of lectures was published, recordings from an event called the Heraeus Winter School on Gravity and Light 2015 – marking the 100th anniversary of Einstein's publication of GR. A nostalgic factoid I found most intriguing: The central lecture of the course by Frederic P. Schuller was given in the very lecture hall at my Alma Mater (Johannes Kepler University of Linz in Austria – JKU) that I received my education in Theoretical Physics, by Heisenberg's last graduate student Wilhelm Macke. Tutorial sheets and video recordings of tutorial sessions can be found on the conference website.
Schuller focuses on the math first, and this was really enlightening and helpful after I used other resources based on mixed intuitive physics and math. The Youtube channel of the event also has recordings of Tutorial sessions, and I found some versions of brief lecture notes. I think this is a must – and unfortunately often overlooked or downplayed in the world of free 'MOOCs'- In order to learn math really, you need to do problems and you absolutely have to walk through every single step of every derivation. It is tempting to just skip the boring proof in a text (that you thought you understood), and it is even more deceptive to watch science videos and believe you understood something. So thanks a lot to my former university to make this course available to the public.
But I was still curious if you can do without manifolds and stuff – without cheating – and I think I found the master of the genre. And again it is a signal from the past (my past): I had looked things up in Landau/Lifshitz Course of Theoretical Physics when I worked at the university. But as the 10 volumes were quite expensive I never bothered to purchase them later. Recently I jumped with glee: Due to whatever quirk in copyright law, the Internet Archive made 9 of 10 volumes available, and I downloaded them all. Browsing through table of contents I noticed that GR was actually explained in volume 2, The Classical Theory of Fields. I am totally smitten by their style, too: Elegant, terse, detached. Much like Dirac's Principles of Quantum Mechanics. And I don't agree with those who say that the explanations are too terse: Landau and Lifshitz try to stay to tangible physics, and they use math in an ingenious way, mathematicians might call it sloppy (like: 'dividing' by differentials to yield a derivative). For that reason, one should consult other resources as well, but I think LL's GR is self-contained.
These books and videos will keep with busy for a while. I also try to interlace it with a bit of QFT again, e.g. by reading Dirac's version of it. My goal for next year is to complete first courses on GR, recapitulate what bit of QFT I learned in 2013/14, and then tackle an actual former specialty again: Re-learning about theories of superconductivity, with an emphasis about how these methods are also used in particle physics.
It might be dangerous thing to announce such grand plans on the web. But next year might be a busy one business-wise, and need to braze myself accordingly.