The Riddle of Metrology: Part 2

In the previous blog post, I introduced what I will refer to as the traditional realist view of measurement. According to this view, the goal of measurement is to reveal the true value of a physical quantity.

The "true value" means simply the value that the quantity would be found to have, if we were to do a perfect measurement on it.

At first glance, this seems like the most natural idea in the world -- what else could measurement possibly mean? However, when you look below the surface, there are some troubling assumptions lurking behind this seemingly obvious idea. First let me explain what these assumptions are, then I will say what is troubling about them.

In the first place, this view assumes that the world is inherently numerical. For instance, imagine we wish to measure the temperature of a bath in degrees Celsius; traditional realism says that the bath temperature really has some true value, — say 40 degrees Celsius — which is just the value we would get if we were to measure it with a perfect thermometer.

(The particular number depends on what units we are using, of course, but the important point is that the measured quantity is indeed a quantity: something that comes already equipped with the structure of a number, that is to say, something that by its very nature can be added, substracted, divided and multiplied).

Consequently, the uncertainty expressed by the error bars on our instruments takes on a specific interpretation, namely, it represents our degree of ignorance about the true value, due to imperfections in the measuring instrument or imperfect control over the conditions under which it was used.

Secondly, thinking of the world as being made up of quantities that are already numerical leads us naturally to think of measurement as a process that transforms one number into another: namely it takes the true value as input and produces a measurement result as the output. Since no actual measurement is perfect, the process will introduce errors, which according to Traditional Realism explains why the final result can be different from the true value.

Drawing upon Claude Shannon's influential work on information theory, we see that in order to make sense of this view of measurement, it is essential that both the input and the output of the measurement process must already be expressed in symbolic language, in this case as numbers. Then measurement is treated as being fundamentally equivalent to information transmission over what Shannon called a "noisy channel".

So, what is wrong with this view?

From a philosophical standpoint, the main problem is that the true values which are supposed to exist "out there" and which describe reality as it truly is, cannot be known to us even in principle.

For one thing, when we are constructing (say) thermometers, we do not have any independent way of checking their accuracy against the true temperature, because that would require us to already possess a perfect thermometer. The problem is not just that real thermometers are imperfect, it is much deeper: for even if one of our thermometers happened to be a perfect thermometer, we have no way of finding this out.

A common response to this argument is that we have a theory (in this case thermodynamics) which tells us how to build instruments that can measure the true temperature. However, this reply is circular because in order to develop the theory of thermodynamics, we first needed to have sufficiently accurate thermometers to provide the data against which to check the theory.

Historically, measurement instruments and the theories that describe how they work seem to develop in tandem, each one providing support for the other, in a way that seems oddly circular, but nevertheless works extremely well.

Indeed, reading the history of metrology, I couldn’t help thinking of that famous quiz from a late 1800's physics schoolbook: Why can not a man lift himself by pulling up on his bootstraps?

The job for any serious philosophy of metrology is to explain why this seemingly self-referential process works so well in practice. According to traditional realism, it shouldn't work at all! This is perhaps the most damning case against the traditional interpretation: it seems unable to make sense of why metrologists do what they actually do, and why their methods seem to work so well.

Traditional realism as I have characterized it here is of course just a "straw man": an extreme view not really endorsed by many people, but criticizing can still be an instructive excercise because it delimits the outlines of a more complex and nuanced idea.

Traditional realism is an exaggeration of what could perhaps be called "scientific realism", which says -- loosely speaking -- that there is a world out there that exists independently of our information-gathering activities, and our theories of physics serve as approximate (but never perfect) representations of what that world is like (as well as what it would be like if we were not around to observe it).

It is possible to articulate an interpretation of measurement that fits with scientific realism in this broad sense. (If you would like to see an example of how this can be done, I highly recommend the book Measurement Across the Sciences, one of the major reference texts we have been studying in this project).

Nevertheless, in order to rescue some notion of realism in metrology without suffering the drawbacks of traditional realism, the role of true values in metrology needs to be significantly weakened. And indeed, although the term "true value" still appears in the official vocabulary of metrologists, in practice it is a largely useless concept.

For instance, another reference textbook for metrologists, "the Guide to the expression of Uncertainty in Measurement" (known fondly to metrologists as the “GUM”— perhaps because it is the metaphorical glue that holds metrology together?) states that in order to work out the uncertainty of a result, it is only necessary to consider "the observed (or estimated) value of a quantity and the observed (or estimated) variability of that value".

In particular, according to the GUM, there is no need to consider the "true value", which in any case is an "idealization" that is "unknowable" in principle.

But if measurement is not about revealing to us the true values that quantities already had before our measurements, then how should we think about it? In the next blog post I will introduce a new way of thinking about measurements that we have adopted as the starting point for thinking about metrology in this project. It is called the coherentist approach.