Wave Watching

A few years back I found oceanographer Mirjam Gleesmer’s blog ‘Wave Watching’:

https://mirjamglessmer.com/wave-watching/

which is just what it says: a fascinating and insightful blog about watching waves – and what we can learn from doing so, not only about waves but about what they traversed, reflected off, diffracted around, broke over…

It spoke to me particularly because I was then watching waves almost obsessively: ripples on puddles, waves on our local lake, splashes from moorhens and coots and ducks on the canal; sea waves, coastal waves, every kind of wave. I wouldn’t quite say it risked losing me friends but people certainly got used to walking on and eventually looking back surprised to see me stopped staring at some interesting wave phenomenon.

Although I became interested in those sorts of waves they weren’t the source of my interest: radio wave were. I’ve studied and worked with waves a lot: it’s a foundation topic in physics and electronics, and I’ve worked on sound waves, ultrasound, radio waves and quantum waves – curiously though, my only real exposure to studying water waves was at school where we had some new-fangled ‘ripple tanks’ for the then innovative Nuffield Science project which emphasised experimentation and practical learning over theory.

The reason I was interested in radio waves was for my work in Radio Wave Imaging: using radio waves to probe, and make images of, the human body – and specifically to find and characterise cancer within it. I’d worked with ultrasound imaging for some years before that, but ultrasound is easy: the waves are small and basically just reflect off things so it is a bit like radar: you point at the thing and send a beam to it, then analyse the reflection. Radio waves are even more like radar because they actually are radar – Radio Detection And Ranging: but for medical imaging they’re not – I know, it’s confusing, but that’s the whole point, and is why I was interested in Wave Watching.

OK, let me rewind and try to explain. Waves, to a physicist,  are really easy – they’re S-shaped curves that travel out, reflect off or turn around something, and go off in another direction. It’s easy to calculate their shape, how it changes, where they go – using first-year university undergraduate  physics. They are beautiful precisely because their mathematical expression is so neat. The first-year physics student’s waves are springs and strings: and radio waves are just like sort of springs in the ether (yes, I do know there is no ether but I’m allowed poetic licence…). Water waves, like Mirjam’s ocean waves, aren’t so easy – water is heavy, and sticky, wind is capricious, shallows and beaches and rocks get in their way and change them and make them complex.

Radio waves are very simple: there are four concise equations that govern them: and despite generations of students fearing Maxwell’s Equations as the most horrifically complicated things they ever had to learn, those equations really are simple. Beautiful, too – they are carved into a wall at the University of Warsaw. They relate the magnetic field B to the electric field E: hence electromagnetism (geddit?..). I won’t go into the horrors that they conceal (we call it ‘simplifying’…) but basically they are similar to the equations that govern water waves – indeed any kind of wave – because they say:

1)      A changing electric field creates a magnetic field

2)      A changing magnetic field creates an electric field

I explained these in a Royal Institution maths masterclass once, to primary school children, and a 10-year old girl came up to me afterwards and put it much better than I had: “so this pushes it this way, and that makes the other push it back that way, and that makes this push it this way again?’ – which is about right, actually. The electric field creates a magnetic field, that creates an electric field, that creates … and so we get a self-sustaining push-me-pull-you effect that is a classic wave. Never mind, it doesn’t matter, we can solve the equations, that is all that matters practically: at least in very special circumstances.

So here, in radio wave imaging – radar in the human body – I can model, through precise and well-known equations, exactly how the radio waves propagate: how they are reflected, scattered, refracted, slowed, attenuated. Everything is under my control through the magic of equations: and armed with this god-like knowledge I can work out – ‘image’ - , by working the equations backwards, what the waves reflected off and what they  passed through.

There are three regimes of waves – three situations in which our equations work: big, small, and in-between. Big waves are easy: if a wave is very big compared to the thing it hits or passes through, then it’s really very little affected. This is not entirely true -  tides are humongously big (long) waves but at least around the convoluted coast of Britain they are notoriously hard to model – but let that lie for now. Small waves are even easier: they just reflect off big things – a bit like light waves, which we are used to seeing as ‘rays’ – straight lines of wave direction that reflect or refract in quite simple ways. (‘Simple’ is doing a lot of work here…). In-between waves are horrendous: you can’t model them as unaffected like the big waves, you can’t model them as straight lines of propagation like small waves, so you have to work out the equations, which get a bit complicated – but still, are possible (I would say ‘simple’ but I only do that to intimidate other physicists when I’m talking about it).

In Radio Wave Imaging we are not trying to model the waves but – as in Mirjam’s blog – to work out, by observing the waves, what they hit and passed through. The fact that the equations get complicated doesn’t hurt much – it just makes the working out complicated – because we can still solve the equations, it just takes a lot of working out. We’re not so lucky as Mirjam, though, because our waves are invisible so we can’t actually watch them: instead, we can measure them but that isn’t the same. If you look down on sea waves, for instance, you see the waves – their shape, how they travel – but the radio engineer can’t: what we can do is to measure the wave over time at a certain point. It’s a bit like watching an angler’s float ride over the waves on a lake, measuring how high the float is over time: we get a sort of picture of the wave but it’s a picture of it over time – at a point in space – rather than its shape at one time. There’s a crucial distinction here, that deserves a whole blog post of its own, between a wave’s shape in space and a graph of its height in time at one point in space: but let’s not go there. All we need to recognise is that we can’t see our radio waves, we can only measure them in a restricted way. From those measurements, we can work out what happened to the wave: what it hit, how it was reflected, what it passed through, how it was slowed, how it was attenuated: and so we can make our model – our ‘image’-  of those things (in our case of medical imaging, an image of the human body and any cancers it might sadly contain).

The problem I was facing, at that time – and still now – was that my invisible radio waves didn’t seem to behave as they ‘should’: the equations, beautifully ‘simple’ as they are, didn’t image what I ‘knew’ (what I thought…) was there. When that happens, the next steps are ‘obvious’ – and ‘simple’ – you identify factors you might have ignored or dismissed, and include those in the equations, which become more complicated, more difficult, but still hopefully tractable.

The problem was (still is..) that even so my invisible waves don’t seem to behave as they ‘should’: and to an experimental physicist like me, if things don’t behave as they ‘should’ then it is the ‘should’ that is in question, not the empirical behaviour. Something is missing from my model: maybe a lot of things are missing – maybe all the models are wrong because they miss something important. Which is how I ended up watching waves.

I can’t see my radio waves, so I can’t truly ‘visualize’ how they behave. ‘Visualize’ is a loaded word that we use carelessly in engineering: in the current case it means ‘model’ – I make a ‘visual’ model of what I ‘think’ is happening – and that isn’t the same as seeing what ‘really’ happens. (My ‘quotation’ marks are proliferating but that is because my unsureness is showing…). What I can do, though, is to watch other waves – to try to see behaviour that might give me a clue as to what it is that I am missing – and that is how I came to be Wave Watching.

I now love wave watching for itself: it is beautiful – calming, absorbing, fascinating, interesting. I see phenomena in water waves that I thought were abstract: diffraction (waves rounding a rock and washing out in all directions from it, or passing through a gap between water lilies and radiating out in all directions; waves becoming perfectly circular as they spread out far enough from the splashing mess made by a duck; waves interacting from different directions, cancelling or reinforcing to form complex but recognisable patterns; waves bent by shallow water that slows them; waves reflected or scattered from rocks and pebbles. And it’s a good thing I love it for itself, because sad to say I have not found the solutions I was looking for – but that’s OK because I retired so it’s up to someone else now.