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### Measurement and the New SI Units

The SI units will be changing again in the next few years. You would think that choosing the units of measurement would be an unemotional topic, but as I recall from Canada’s, only partially successful attempt to convert to the metric system, that is far from the case. I remember one rather irrational editorial on the topic where the writer went on about how the changing  definition of the metre was an indication that the people behind the metric system did not know what they were doing. Since this was in an English Canadian paper, he blamed the problem on the French for having blown the original definition. Ignorance profound. The writer would probably have been surprised to learn that the inch is defined as 2.54 centimeters except, of course, in the US where there is a second inch (the surveyor’s inch) defined as 39.37 inches equal one meter.  Ah, the joy of traditional measurements. There are at least three different gallons in use, and as for barrels, there are more than you can shake a stick at. However, the petroleum barrel is defined as exactly 158.987294928 litres. I am sure you wanted to know that and don’t forget the last decimal point—the 8 is very important. As far as I can see, the only reason for using the traditional units is familiarity and yes, I still use the inch and foot, but also the kilometer. And I believe it’s also safe to say, that the generation born after the country officially switched, also does the same. That is the joy of living in a country that has half converted to metric.

Measurements tend to be of two types. One is pure numbers like the number of ducks in a row (or in a pond). The other type is the measurement of a number with a dimension. Here we need a standard to compare against; a length of six feet only make sense if we know what a foot is. In other words, we have a standard for it. Thus, the need to define units so different people can compare their results, and when we buy a hogshead of beer, we know how much we are getting.

Editorial writers will have another chance to rant in a few years as the General Conference on Weights and Measures is set to change the definitions of the basic metric or Standard International (SI) units again—this time, not the metre but the kilogram and other units. The history of how the definition of the units have changed over time is quite interesting, involving not just changing technology but also changing tastes. The original metre was defined in terms of the distance from the equator to the North Pole. But this could not be determined sufficiently accurately, so the standard was shifted to a physical artifact; a rod kept in Paris with two marks on it. This was then shifted to the wavelength of light from a certain atomic transition and finally, to fixing the speed of light. Similarly, for time, the second went from being defined in terms of the length of the day to being defined in terms of the frequency of an atomic transition. There is a trend from defining the units in terms of macroscopic quantities—the size of the earth, the length of day, the length of a bar—to microscopic quantities, or more specifically, atomic properties. There is a simple reason for this, namely that it is in atomic systems that the most accurate measurements can be made. Unfortunately, it also makes the unit definitions esoteric and detached form everyday experience. Everyone can identify with the length of a foot, but it is not immediately clear what the speed of light has to do with distance. Telling my daughter it takes five nanoseconds for light to travel from her head to her foot doesn’t do much for her. There is also a trend, partly aesthetic, towards defining the base units by fixing the fundamental constants of nature.

A fundamental constant of nature, like the speed of light, starts it life as something that relates two apparently unrelated quantities. In the case of the speed of light, it is time and distance. But then over time, it comes to be just a way of relating different units for measuring the same thing. Indeed, time units are sometimes used for distances and vise versa. This even happens in everyday life, such as when the distance from Vancouver to Seattle is given as three hours, meaning, of course, an average travel time. But in science, the relation is more definite and defining the metre in terms of the speed of light makes it explicit that the fundamental constant, the speed of light, is just a conversion factor from one set of units to another, from seconds to metres (1 metre = 3.3 nanoseconds).

The new proposal for the base SI units continues this trend of defining units by fixing fundamental constants. The degree Celsius is now defined in terms of the properties of water—the so called triple point. In the proposed new system, it will be defined by fixing a fundamental constant, the Boltzmann constant. The Boltzmann constant relates degrees to energy. At the microscopic level, i.e. in statistical mechanics, temperature is just a measure of energy and the new definition of the degree makes this explicit. Again, a fundamental constant turned to a conversion factor between different units—degrees and joules. The case of the kilogram is more subtle. It is currently defined by a physical artifact—the standard kilogram stored in Paris. The new proposal is to determine the kilogram by fixing the fundamental constant; Planck’s constant. This is another example of a fundamental unit becoming just a conversion factor between different units, in this case between time and energy units, or equivalently distance and momentum units.

As a theorist, this new set of units makes it nice for me as I like to use what are called natural units in my calculations. These are given by setting the speed of light (c), Planck’s constant (ħ), Boltzmann’s constant (k) and π all equal to 1 (OK, usually not π, but I did see that legitimately done once). An interesting side effect of the new units is that they all have exact conversion from these natural units. There is another set of natural units called Planck units which are defined in terms of the gravitational strength and the strength of the electromagnetic force. (In the proposed change, the charge of the electron is used to define the electromagnetic units.) Ultimately, those may be the most elegant units but we are nowhere close to having the technology to make them the bases of the SI units.

Naturally, any change of units has the naysayers coming out of the woods. One of the criticisms of the new units is that, since the fundamental constants are fixed by definition, we can no longer study their time dependence. To some extent, this is true. For example, with the current definition of the kilogram, Planck’s constant changes every time atoms are lost or gained by the standard kilogram. This change will be lost with the new units. This illustrates the absurdity of asking if a fundamental constant changes in isolation. All that is meaningful is if the constant has changed with respect to some other quantity with the same dimensions. The new choice of units makes this explicit, which is a good thing.

There is much more to the new choice of units than I can cover here and the interested reader is referred to the relevant web pages: http://www.bipm.org/en/si/new_si/ , http://royalsociety.org/events/2011/new-si/ , or http://en.wikipedia.org/wiki/New_SI_definitions .

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.