Some thoughts on ecology, evolution and economics

Taking the measure of nature

The Kibble balance.

The Système Internationale (or SI) offers a coherent and standard way of measuring nature. It is based on seven standard units for time, length, mass, electric current, temperature, brightness and amount of substance. This fussy, academic world has been roiled by passionate debate about the very idea of measurement. Rather than allowing units like the second (1.157 x 10-5 days) to define our world, a meeting in Versailles this November will propose to base all measurement on a set of universal constants such as the speed of light. The difference is slight, since these constants will still be defined in the familiar units of seconds, metres and kilograms, yet fundamental, since there will no longer be observable standards like the Grand K – the internationally recognized object that represents the unit of mass.  These universal constants define the fabric of our universe yet, except for one of them, they are not measured in pure units. They are conversion ratios of two or more of the fundamental units.


The exception to the rule is the heartbeat of atomic clocks,the frequency of light emitted by Cesium.  This frequency replaces the rotation of the  earth as the defining aspect of time.  Being much shorter – a hundred million times shorter –  than a second and much more reliable than our wobbly earth, the frequency allows a great deal of precision.


The speed of light was made famous by Einstein in his equation E=mc2, where c is the speed of light. It is constant in a vacuum.  Light can cover around 3 cm in one tick of an atomic clock’s frequency and, again. provides a very precise way of measuring length.


The next constant is the electrical charge of a single electron, the basic building block of electrical current. A wire that sees 679 million electrons flow through it in the time it takes for a Cesium frequency has a current of 1 ampere. The amp, as it is affectionately known, helps define a whole world of standard electrical units.


The chemist’s dozen or the mole is the next constant.  It is a ratio of the number of atoms in a sample to its mass .  It is calibrated by 12C, the ordinary kind of carbon with six protons and six neutrons. A mole is the number of 12C atoms in 12 grams. It is an exceedingly large constant, being a 6 with 23 digits after it.  It allows chemists to get the right proportions of reagents with different atomic weights.


The remaining units all depend on a very curious constant called Planck’s constant.  It is the ratio between the energy of light and its frequency.  Energetic radiation, like X rays, have very high frequencies and low energy radiation, like radio waves, have very low frequencies. This constant comes in handy because its units are in kilograms per metre2 per second or Joule-seconds.  Planck’s constant has been estimated  very precisely by something called a Kibble balance, which measures the energy it takes to support a given mass. In the new SI system, a kilogram will be defined by the Cesium frequency, Planck’s constant and the speed of light.  This is rather confusing, since none of these things seem to have anything to do with mass.  What is important to realize is that mass is most relevant to our lives in determining the force (mass X acceleration) or energy (force X length) needed to move it around. By providing a conversion ratio between energy and time (the inverse of frequency), Planck’s constant allows us to measure mass more precisely and reliably than the Grand K could allow.


Boltzmann’s constant is a conversion ratio between the average energy of particles in a gas and the temperature of the gas. This allows us to define a single degree Kelvin (or Celsius) in terms of the Cesium frequency, Planck’s constant and Boltzmann’s constant.  This provides more precision than could be achieved by basing temperature on the measured values of the Triple point of water.


Luminous efficacy is the final constant in the proposed system. It is the only one that is defined in terms of what humans can perceive. Of course, there wouldn’t be much point in developing units of brightness for wavelengths that humans cannot see, like infrared!  So luminous efficacy defines the conversion of energy into light in the lime green range- right in the middle of the visible spectrum. You can calculate the value of one candela (originally based on the light of one candle) from the luminous efficacy constant, Planck’s constant and the Cesium frequency.

Measurement is ultimately the comparison of two things, one of which is taken to be a standard.  I am comforted by the idea that our measurements will soon be based on constants that can be observed anywhere in the universe and I marvel at the elegance of the proposed solution.  I am also relieved that we won’t have to learn a whole new system of units!