Revising the Metric System


Relationship between the new SI units (image produced using the igraph package of R)

On May 20, a major redefinition of SI (metric) units comes into force. In particular, the second, metre, ampere, mole, kilogram, kelvin, and candela will be defined as follows:

The second (unit of time)

As it is now, the second will be defined using ultra-precise caesium clocks. Specific microwave radiation from caesium atoms is defined to have a frequency of exactly 9.192 631 770 GHz. That is, counting 9,192,631,770 waves will take exactly one second.

The metre (unit of length)

As it is now, the metre will be defined using the speed of light, which is defined to be exactly 299,792,458 metres per second. That is, the metre is the distance travelled by light in one 299,792,458th of a second (where the second is defined as above).

The ampere (unit of electric current)

The definition of the ampere (amp) has been greatly simplified, taking account of the connection between electricity and electrons. The ampere is a coulomb of electric charge flowing past a given point per second, and the charge on a single electron is now defined to be 1.602 176 634 × 10−19 coulombs. Thus an ampere is about 6,241,509,074 billion electrons flowing past a given point in a second.

As a consequence of this new definition, two important natural constants which used to have defined values (the permeability of free space and the permittivity of free space) now have experimentally determined ones. This will require rewriting pretty much every physics and electrical engineering textbook.

The mole (unit of amount of substance)

The mole represents Avogadro’s number of atoms, molecules, or other particles. Previously, Avogadro’s number was defined to be the number of carbon atoms in 12 grams of pure carbon-12. It is now defined to be exactly 6.022 140 76 × 1023.

The kilogram (unit of mass)

Until 2019, the kilogram was defined by the mass of a specific metal cylinder held in Paris. This has been felt to be unsatisfactory for many years. The current definition uses the fact that the energy of a light photon (in joules) is its frequency times Planck’s constant h, which is defined to be exactly 6.626 070 15 × 10−34.

In practice, a Kibble balance will be used to measure weights by balancing them against an electrically produced force. Units derived from the kilogram include:

  • The newton (unit of force): the force needed to accelerate 1 kilogram at a rate of 1 metre per second squared
  • The pascal (unit of pressure): 1 newton of force per square metre
  • The joule (unit of energy): the energy used in applying a force of 1 newton over a distance of 1 metre
  • The watt (unit of power): 1 joule of energy per second
  • The volt (unit of electric potential): the amount of electric potential across a resistance producing 1 watt of heat per ampere of current
  • The ohm (unit of electrical resistance): the resistance which produces 1 ampere of current when 1 volt of electric potential is applied

See also what NIST has to say about the kilogram.

The kelvin (unit of temperature)

Temperature in degrees Celsius was originally measured on a scale with 0 °C being the freezing point of water and 100 °C the boiling point (at standard pressure). The lowest possible temperature turned out to be absolute zero, −273.15 °C. In 1954, the two fixed points on the scale were changed to −273.15 °C (0 kelvins) and the triple point of water, 0.01 °C (273.16 kelvins).

This definition proved unhelpful for calibrating thermometers intended for very high temperatures, and the current definition uses the fact that the average translational kinetic energy (in joules) of a moving atom of a monoatomic ideal gas is (3/2k T, where T is the temperature of the gas in kelvins, and the Boltzmann constant k is defined to be exactly 1.380 649 × 10−23.

The candela (unit of luminous intensity in a given direction)

The definition of the candela remains what it has been, except that it is influenced by the change in definition of the kilogram (and hence the watt). A light source that emits monochromatic yellowish-green light at a frequency of 540 THz (roughly 555 nm wavelength) is taken to emit 683 lumens per watt, and a light source that uniformly radiates 1 candela in all directions has a total luminous flux of 4π lumens (the constant 683 reflects the human ability to perceive light). The lux is a lumen per square metre.

The dream

When the metric system was first introduced, the metre was defined in terms of the world (1/10,000,000 of the distance between the Equator and the North Pole, measured via Paris). Today, the metric system carries that philosophy to its ultimate conclusion, with all units except the candela defined in terms of the universe. Five of the units are defined in terms of fundamental physical constants: the speed of light (first measured by Rømer in 1676), the charge on the electron (first measured directly by Robert A. Millikan in 1909), the Avogadro constant (measured several ways by Jean Perrin around 1910), and the Planck and Boltzmann constants (first defined by Max Planck around 1900).

The redefined metric system is a little difficult to grasp without understanding modern physics, but fortunately most of us will just keep on using exactly the same measurement instruments as we have done for years.


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2019 in science so far

This year in science so far (click to zoom). Clockwise from top left:


Hello again, little tree-kangaroo


The Wondiwoi tree-kangaroo (detail of an illustration by Peter Schouten)

National Geographic recently reported an interesting story about the Wondiwoi tree-kangaroo (Dendrolagus mayri). Until recently, this arboreal marsupial was known only from a single specimen collected in the Wondiwoi Peninsula of West Papua in 1928. It was thought to be extinct, and was listed on the “25 most wanted lost species” at lostspecies.org. But when an amateur expedition visited the dense mountain forests of the Wondiwoi Peninsula, there it was, living happily in the trees. A good-news story from the animal kingdom, for once.

Surprised to find kangaroos living in trees? There are a number of related species that do this, in the rainforests of New Guinea and northern Australia. In fact, members of the kangaroo family live in a range of different habitats (the rock-wallaby would be a less dramatic example).


New Horizons status check

The New Horizons spaceprobe, having given us some lovely pictures of Pluto in 2015, is on its way to the Kuiper belt. But what is the Kuiper belt? Named after Dutch-American astronomer Gerard Kuiper, the Kuiper belt is much like the asteroid belt, but much larger, about 15 times further out from the Sun, and far less well understood.

Initially, New Horizons is headed for the rock, or perhaps pair of rocks, (486958) 2014 MU69, which NASA has nicknamed Ultima Thule. The space probe is due to reach it on January 1st (which will be just short of 13 years after its launch). Currently, New Horizons is 6,360,000,000 km or 5.9 light-hours from Earth, and has recently completed a course-correction manoeuvre.


Midwestern Solar Challenge

On June 3, two of the top Cruiser-class solar cars held a Midwestern Solar Challenge, racing south from St Paul, MN to Ames, IA. The teams were:

Race news

Scoring

Here is my (totally informal) scoring of the race (see the chart below):

  • Person-kilometres is the race distance times the average number of people carried (which I believe was 4 for PrISUm and 2 for UMNSVP). The first coloured bar shows this, scaled so that 100% is the highest value.
  • Energy input is the number of charges (1, in this case) times battery size. The second coloured bar shows this, scaled so that 100% is the highest value (this bar points downward, because smaller is better).
  • The third coloured bar shows the ratio of these numbers, scaled so that 80% is the highest ratio.
  • We add on (in grey) the practicality scores (I’m estimating 9 for PrISUm and 7 for UMNSVP), scaled so that 20% is the highest practicality.
  • This gives final scores of 100 for PrISUm and 82 for UMNSVP. Congratulations, PrISUm!
  • But will PrISUm still have the advantage when it needs to carry passengers uphill?


Solar Car Racing Status Check #3

In solar car racing news, 29 teams are registered for the American Solar Challenge (ASC) in July. Scrutineering for this race begins on July 6, track racing on July 10, and the road race runs from July 14 to July 22. I am maintaining a detailed information page and teams list for this race. Five teams are attending with cars that raced at WSC 2017 (including one Australian team), although these cars will require adjustment to satisfy ASC rules. Seven other teams had existing cars (including one Russian team). The remaining teams have been building new cars.


ETS’s beautiful new car, Éclipse X, was unveiled on 16 May (picture credit)

Recently unveiled cars for the ASC include Missouri S&T (18 April), Poly Montreal / Esteban (23 April), Georgia Tech (24 April), and ETS Quebec / Eclipse (16 May). A couple of teams have (very sadly) dropped out, while many other teams are frantically working on their cars. Iowa State University (PrISUm) and the University of Minnesota are holding a practice mini-race on June 3 (with cars on display at the Science Museum of Minnesota the day before). Full details on all teams and latest news here.


Many ASC teams are frantically working on their cars – AppState is shown, and they plan to reveal their car on June 22 (picture credit)

The Albi Eco Race was held on May 25 and 26. Bochum won with their SolarWorld GT, while Dokuz Eylül University / Solaris came second, and Polytech Clermont-Ferrand / Bélénos third. Details here.


Albi Eco Race cars (picture credit)

Fourteen teams have registered so far for the 24 hour iLumen European Solar Challenge (iESC) at Circuit Zolder in Belgium (September 19 to 23), and Twente will be defending their title there. World champions Nuon might also attend (with an old car). I am maintaining an information page and teams list for this race as well. See also the official iESC social media at  


Circuit Zolder seen from above (imagery: Landsat, solar car photo: Bochum, chart: Scientific Gems). Sunset/sunrise and the phase of the moon are correct for the date

Preparations are also continuing for the SASOL Solar Challenge in South Africa (September 22 to 30). Defending champions Nuon and Japanese team Tokai will attend this event, along with local teams, such as North-West University, Tshwane University of Technology, the University of Johannesburg, Vaal University of Technology, Central University of Technology, and the University of Cape Town.