Back when I was working at Imperial — I forget exactly, mid 00's most likely — the not-so-far from retirement Prof G gave a sort of career summary seminar. First up was a photo of some men wearing suits and ties.
“Here's a picture of some undergraduates”, he said. Because, of course, he’d started at the beginning of his university days, and things were different back then, and had changed over the decades.
Indeed, as not so few of us might have experienced, the town where I grew up once was more or less separated — along the main road at least — from the rest of the suburban connurbation by a few bits of farmland — not so much, as it happened, but some. Of course, even before I left those patches were filled in, and has continued to ever spread further in the few available directions left to it.
And back in the day, physics was different too. Years ago, I recall reading a historical article in Physics Today — or was it Physics World? It told of how calculations were typically approached back in the Renaissance, or some similar period. Apparently doing things using ratios of whatever properties were relevant was the thing to do; and perhaps that sort of thing made a lot of sense when measuring devices were less reliable, and physical constants defined in a rather vaguer way than you would like.
But at the time of reading, unsurprisingly, I was struck by how bizarre that seemed; even more so than the suits and ties of … at least those in the vicinity of the pre-doctoral Mr G … 60’s undergraduates. Sure, ratios are handy every now and again, but using them everywhere? The whole methodology just seemed as weird and opaque as a typical page in a facsimile of Newton's Principia. It’s interesting to see how differently things were presented back then. What is going on with those diagrams? Aren't diagrams supposed to be helpful?
'Indeed, even more recent work, such as Maxwell's original papers on electromagnetism, which do not even have the familiar notation — that is the div and curl, and vectors — div and curl) given to us by Heaviside are hard work. Every component along each of the x, y, z axes is given on its own, and not just because you are in some simplified plane-polarized, propagating along z model. The whole 3D — or should that be 4D — thing.
Still, at least with Maxwell's formulation you could see the electric and magnetic components them as fields, properties that varied in space and time, and which you could manipulate accordingly.
Ah, fields. Nowadays the notion of "field" is dominant, across classical and quantum domains — you know, gravitational fields, quantum field theory, electric and magnetic fields, and innumerable other scalar, vector, and tensor fields — even if there are some who insist trying to convince us of the prospects for using cellular automata, or to introduce us to category theory (whatever the hell that is). And some of the approaches to generalisations of GR or trying to bootstrap spacetime from nothing are pretty weird as well.
Even Maxwell’s equations these days are often condensed from four vectorial equations to two using differential forms: just dF=0, and dH=J. Not that you can do much practical work with such elegance, since in the end in order to hack out a result it often comes down to vector components in a defined reference frame, but the drift to even more abstract notations is apparently quite persistent.
It would seem, then, if history is any guide, that even those fields — which we are nowadays so used to thinking in terms of — might well fall out of fashion as the dominant approach to representing physical quantities or theories.
So one can perhaps now imagine some future historian of science, after showing ancient videos of anachronistically dressed undergraduates and dubiously constructed experimental equipment — all shining stainless steel, vacuum pumps, and sapphire windows, or whatever — doing a detailed tour of various approaches to representing physical quantities.
And then while finishing up, whilst gesturing at the n-dimensional typocon clouds that constitute their current state of the art in physics literature, they will say:
“and all this ... used to be fields”