Starting next week I will be giving two series of lectures for postgraduate students at the university here. Both of these are introductory-level courses with one covering things like small oscillations in bound systems and the other talking about radiations from and fields due to moving charges.
I think this will be an important event for me, firstly because teaching postgraduate courses is interesting given the scope of topics that can be covered; there is a depth to all discussions that is rarely seen in undergraduate courses, for example. But discussing physics at this level also requires a firm grasp of its concepts which I will not delude myself into thinking I have. There are people who understand this far better than me, so I look at this opportunity as a way of improving myself.
Understandably, this is also something to be nervous about and I am. But, at the same time, I am excited too. I spent the last couple of days planning these lectures excessively only to end up realising that one can never plan enough, and one need not. I think having a wireframe of sorts to hug while leaving the actual lecture open-ended is the best approach. But then again I am guilty of often going so far off track that I forget where I started and this, in the frame of scheduled lectures, is less advisable than in, say, casual discussion. Therefore, a wireframe: it affords structure while not being restrictive.
Interestingly, Chad Orzel (whose writing I have quoted on many an occasion before) recently wrote a timely piece for Forbes in which he names vector calculus, differential equations, and linear algebra as the must-haves in a physicist’s toolkit. I agree for the most part. As someone who majored in solid state physics I would also toss Fourier transforms into the list, but then I suppose every branch would have its own little additions to make. These three, however, are certainly universal.
What I have found over time is that physics has an underlying pattern to it. We generalise things in a way that makes most other things specific cases of the general example and tweak necessary variables to get results under specific conditions. Oscillators are good examples of this. And the three tools (as I would call them) help solve the equations that would set up these problems. While the translation often goes from real world to mathematical model to mathematical solution to physical re-modelling, it really comes down to making a given problem look somewhat like any one of a number of previously known solutions and going from there. Whether this is a trick or some clever puzzle-solving technique is debate for another day, but this is a fair, even if crude, description of how things work. Of course some (or many) may disagree with me and in most cases I am sure they know better than me.
In my lectures, this is what I want to make clear to students as well. Far too many people try and fail to find immediate impact from theoretical (or even experimental) physics in everyday life. In classical physics this would be a more realistic expectation. Enter the realms of quantum mechanics or relativity and this becomes much harder. It is not impossible to find an effect, and it is a lie to say there is no effect whatsoever on everyday life; it just requires some far-sightedness, an ability to imagine and to look decades into the future. (Things boasting immediate impact, I would argue, which are often nowhere near as fascinating as the ideas of physics, can be found in engineering and medicine.) But once you recognise that a lot of problems are various manifestations of the same thing, it becomes easier to appreciate physics. It also becomes easier to see how much work still needs to be done.
Admittedly, my views may be simplistic and less-informed than those of my more knowledgeable peers, but this is where I stand now. I look at my own lectures as having two layers: the first which explains this belief in how physics is done, and the second which talks about the actual physics prescribed for the lectures. Neither can do without the other, because one informs and the other offers perspectives. I hope I can live up to this as well as, at the end of the day, my own expectations. But most of all I hope I can pique the interest of at least one of my listeners enough to make their love of physics last a lifetime. ❖