I learnt last year that quantum systems are essentially linear because the mathematics that physicists have found can describe quantum-mechanical phenomena contain only linear terms. Effects add to each other like 1 + 1 = 2; nothing gets out of control in exponential fashion, at least not usually. I learnt this by mistake in an article published in 1998 when I was trying to learn more about the connection between the Riemann zeta function and ‘quantum chaos’. This is to say that physicists take for granted several concepts – many of which might even be too ‘basic’ for them to have to clarify to a science reporter – that the reporter may only accidentally discover.
“Classical systems are, roughly speaking, defined by well-bounded theories and equations, most of which were invented to describe them. But the description of quantum systems often invokes concepts and mathematical tools that can be found strewn around many other fields of physics.” This impression was unexpectedly disorienting when it first struck. After many years, I realised that the problem lies in my (our?) schooling: I learnt concepts in classical physics in a way that closely tied them to other things I was learning at the same time. Could that be why complicated forms of Euclidean geometry come up at the same time as optics, and vector algebra at the same time as calculus? But it also strikes me that quantum systems lend themselves more readily to be described by more than one theory because of the significant diversity of effects on offer.
The edge of physics is a more wonderful place than the middle because there’s a lot of creativity at work at the edge. This statement is very true for classical physics but vaguely at best for quantum physics. One reason is the diversity of effects: a system that is intractable in statistical mechanics might suddenly offer glimpses of order and predictability when viewed through the lens of quantum field theory. More than a few problems require ‘goat solutions’ – a personal term for an assumption thrown in to make a problem amenable to solving in such a way that the solution doesn’t retain any effects of the assumption (reason for the choice of words here). In some instances, physicists’ assumptions have brought the Iron Man films to mind: the assumptions are in the realm of the fantastic, but are still bound by a discipline that prevents runaway imagination.
Researchers who use the tools of mathematical physics seem to take mathematical notation for granted. Statements of the following form may seem simple but actually pack a lot of information: “Consider a function f(x, y) of the form Σ xip where p is equal to dy/dt in some domain…” (an obviously made up example). I’m all the more spooked when I encounter symbols whose names themselves are beyond me, like ζ or Π, or when the logarithms make an appearance. We need to acknowledge the importance of being habituated to these terms. To a physicist who has spent many years dealing with that operation, a summation might mean a straightforward accumulation of certain effects, but in my mind it always invokes a series of complex sums. I don’t know what else to visualise.
Only a small minority of physicists in India can talk in interesting ways about their work. They use interesting turns of phrase, metaphors borrowed from a book or a play, and sometimes contemplate what their and/or others’ work is telling them about the universe and our place in it. I don’t know why this is rare.