The Riddle of Metrology: Part 1

When I tell people I work on quantum mechanics, their eyes light up. When I tell them I've lately been studying metrology, they look confused -- “you mean the weather?”

“No”, I say: “that's meteorology. Metrology is the science of measurement; like measuring mass in kilograms, or measuring time in seconds. The science of measuring quantities very precisely.”

About half-way through my explanation, the person's eyes glaze over, much as I imagine they would look if I said I was interested in financial accounting. The odd thing is, metrology is actually a fascinating subject. My introduction to metrology came when philosopher Harald Wiltsche (who is part of our collaboration) recommended I read Hasok Chang’s book Inventing Temperature. “It's really just the history of thermometers”, said Harald, “but man, it's a real page-turner!”

Only a few pages into the book, I was hooked. I lay awake at night seeing in my mind's eye images of Thomas Hutchins, huddled on top of a fort in Hudson's Bay in the winter of 1781 with only a few deer-skins sewn together to protect him from the lethal wind. Covered in snow, his eyes fixated on the bizarre apparatus in front of him: a bath of Mercury, now frozen solid around the sides of the container, with a thermometer -- a Mercury thermometer! -- carefully inserted into the middle portion of the bath where the surrounding Mercury was still a liquid. I imagined Hutchin's eyes beginning to freeze over as he stared at the instrument, making the first ever measurement of the freezing point of Mercury, by the ingenious trick of using Mercury itself.

I found myself wondering: why had nobody ever told me that thermometers were so interesting? And why aren't more of my colleagues in physics excited about metrology?

The answer to that question probably has to do with the very nature of metrology itself. Metrology is one of those peculiar sciences whose aim is actually to make itself invisible to the very people who depend on it the most. When we buy any sort of device that is used for measuring something —whether it be a kitchen scale, a thermometer, or a multimeter for measuring voltage and current — the device comes with a certification and a manual, which together tell us that so long as we use the device in the correct way, we can simply trust the numbers that it produces without needing to understand why we can trust them.

Measurement devices are produced in such a way that they have an almost magical quality: the consumer can blindly trust in the device. That is what makes it so useful.

The self-effacing nature of metrology means that the very processes which go into the design and manufacture of measuring instruments ensure that the people using those very instruments can remain perfectly ignorant of how they were made, including the very important question of why we can trust them to give us accurate readings of whatever it is we are using them to measure. Consequently, even physicists are largely ignorant of what goes on behind the scenes in order to produce the expensive equipment, such as lasers, atomic clocks, spectrometers, lenses, and so on, which they use to make precise measurements of physical quantities. When something “just works”, there surely can't be any deep philosophical problems with it. Right?

Well…

In his books and articles, Hasok Chang discusses a profound mystery right at the heart of metrology — a mystery that is completely invisible to everyone except those who study the history and philosophy of metrology itself.

The mystery is this: how can we ever know that our measuring instruments are measuring what we think they are, when the only means we have of checking them is by comparing them to other instruments?

Clearly, part of what gives us confidence in a measuring instrument is the fact that we have a theory which describes the quantity that we are trying to measure, and this theory tells us how to build instruments to measure that quantity. But looking closer this explanation turns out to be circular.

Theories do not just appear out of thin air, complete with a guarantee of truth: they begin as a set of messy, tentative competing hypotheses — little more than educated guesses and speculation by scientists — that are subsequently whittled down and refined into more precise theories by taking into account the evidence from measurements. But in order to create a proper theory of a physical quantity, it seems that you first need to have a way to measure that quantity!

There seems to be a chicken-and-egg problem between the dual processes of constructing instruments that measure a quantity, and proposing theories that define the quantity that we aim to measure.

Chang calls this the “problem of nomic measurement”. It is essentially the same problem that Bas van Fraassen calls “the problem of co-ordination” in his influential book Scientific Representation: Paradoxes of Perspective, and it has a long history going back to the writings of Poincaré, Reichenbach, and Mach.

Perhaps the most puzzling thing about the problem of nomic measurement is that it has apparently not impeded progress in metrology in the slightest. The reason is that, strange as it may sound, the various methods and techniques that metrologists use to establish the reliability and precision of their instruments do not seem to require us to know anything beyond what the instruments themselves are telling us.

In practice, metrologists have operational ways of knowing that certain instruments measure certain quantities, and for comparing the precision of different instruments among themselves. Of course it is natural to assume these methods work only because the measured values of quantities are accurate representations of the true values of those quantities that exist out there in the world — but how could we ever verify that?

In the next blog post in this series, I will discuss why this traditional idea has recently fallen out of favour, and explore the possibility of other ways to explain why the practices of metrology are so successful.