units, standards and dimensions a look at the international system of units

UNITS, STANDARDS and DIMENSIONS

A look at the International System of Units

MEASUREMENTS• “To measure” means “to compare a

value” (of length, mass, time) “to a standard.”

• It is impossible to measure without comparing; the very act of measuring involves laying an instrument beside the object and reading off of the instrument – that is, comparing the object to the instrument.

The Art of Measuring

• Measurements and measuring instruments are all based on a standard – an object or prescription to which all other measurements are compared.

• Each standard has, in turn, a unit and a dimension related to it. The unit is the label given to it, and the dimension is what the standard measures.

UNIT, STANDARD and DIMENSION

STANDARD: the physical object, DIMENSION: what it such as this one. measures (for example,

length or mass)UNIT: the label given to thestandard; what measurementsare measured in. “block”

“block” as a standard of lengthDIMENSION: length

UNIT: “block”, abbreviated bl.

“block” This line is 6 bls(“blocks”) long

“block” as a standard of volume

DIMENSION: volume UNIT: “block”, abbreviated bl.

“block” This object has a volume of 4 bls.

“block” as a standard of massDIMENSION: mass UNIT: “block”, abbreviated bl.

“Smiley” weighs 2 bls. “block”

“block”

“block” as a standard of timeSome standards are “prescriptions” – little recipes to figure out the standard. For example, one “block” of time could be defined as the time taken by gamma-rays to travel from one end to the directly opposite end of the block:DIMENSION: time UNIT: “block”, abbreviated bl.

gamma-ray enters 1 “block”

gamma-ray leaves

The 4 desirable characteristics of a STANDARD

For a standard to be useful, it must “pass” 4 tests. It must be:1. UNIVERSAL – agreed upon by the world;2. EASILY AVAILABLE – must be reproducible with

a minimum of difficulty;3. IMMUTABLE – does not change appreciably

over a long period of time;4. PRECISE – the best of the best; the “cream of

the crop”.

CAUTION!

Standards are IMMUTABLE, not IRREPLACEABLE!

These standards…… are chosen in International Conferences, held currently about 4 years apart, in France.• The first conference was held in 1889.• The most recent one was held in 2011. • As of 10 August 2012, there are 56 Member States

of the BIPM, and 37 Associate States and Economies of the General Conference.

• At these conferences, standards are reviewed and, if needed, replaced by more accurate (precise) ones.

The SI system of units and standards

• SI stands for Système International d'Unités, which is French for International System of Units.

• In 1960, the 11th General Conference on Weights and Measures (Conférence Générale des Poids et Mesures – CGPM), adopted the 6 fundamental standards, units and dimensions.

• A seventh fundamental standard, unit and dimension was adopted by the 14th CGPM in 1971.

WHERE ARE THEY?• The master standards are kept in Sègres, near

Paris, France.• The original ones where actual objects. They

“evolved” to match the precision of current measurements.

• There are 7 fundamental standards, units and dimensions (also called base units and dimensions). All other units and dimensions can be determined from these 7, and are called “derived” units and dimensions.

SI systemFundamental Dimensions

1. Length

Fundamental Units

1. Meter (m)

SI systemFundamental Dimensions

1. Length2. Mass

Fundamental Units

1. Meter (m)2. Kilogram (kg)

SI systemFundamental Dimensions

1. Length2. Mass3. Time

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)

SI systemFundamental Dimensions

1. Length2. Mass3. Time4. Electric Current

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)

SI systemFundamental Dimensions

1. Length2. Mass3. Time4. Electric Current5. Temperature

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)5. Kelvin (K)

SI systemFundamental Dimensions

1. Length2. Mass3. Time4. Electric Current5. Temperature6. Luminescence

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)5. Kelvin (K)6. Candela (cd)

SI systemFundamental Dimensions

1. Length2. Mass3. Time4. Electric Current5. Temperature6. Luminescence7. Amount of substance

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)5. Kelvin (K)6. Candela (cd)7. Mole (mol)

This system is also called MKS…Fundamental Dimensions

1. Length2. Mass3. Time4. Electric Current5. Temperature6. Luminescence7. Amount of substance

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)5. Kelvin (K)6. Candela (cd)7. Mole (mol)

…or MKSA system.Fundamental Dimensions

1. Length2. Mass3. Time4. Electric Current5. Temperature6. Luminescence7. Amount of substance

Fundamental Units

1. Meter (m)2. Kilogram (kg)3. Second (s)4. Ampere (A)5. Kelvin (K)6. Candela (cd)7. Mole (mol)

Sometimes…

… people refer to this system as the “metric system”. Well, although metric units are used (meaning multiples of ten), this is NOT an official name for it.

Make a note of these:

1. Units with “capital letters” are those named after famous scientists;

2. The SI unit for mass is the only one with a prefix;

3. The only standard still an object is the mass standard;

4. The last fundamental dimension to be added was “amount of substance.”

So, what are the standards?

Fundamental Dimensions1. Length

Fundamental Standards1. The metre is the length of the

path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

NOTE: both metre (British) or meter (US) are correct forms of the unit. Here, definitions of the standards were taken directly from the Conference publications, hence the form “metre.”

Outdated Length Standards• On 19 March 1791 the metre was theoretically defined

as being equal to the ten millionth part of one quarter of the terrestrial meridian.

• In 1799, a bar of 90% Pt – 10% Ir (a special metal alloy) was constructed to match the definition of the “metre” above.

Outdated Length Standards

• In 1960, the metre was defined as the length equal to 1 650 763,73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 (86Kr) atom.

• In 1983, the meter was defined based on the speed of light.

So, what are the standards?

Fundamental Dimensions1. Length 2. Mass

Fundamental Standards1. The metre is the length of

the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

2. A cylindrical block of 90% Pt - 10% Ir (metal alloy) kept in vacuum, under triple bell jars, and controlled conditions.

The Die-hard Mass Standard

So, what are the standards?Fundamental Dimensions

3. Time

Fundamental Standards

3. Duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 (133Cs) atom.

The Atomic Clock• The USNO (United States Naval Observatory) is in charge

of keeping the official time in the US.• It relies on 44 atomic clocks – 31 Cesium and 13 Hydrogen

masers – whose times are averaged and reported. Thus the master clock is an average of 44 atomic clocks!

• These clocks are distributed over 20 environmentally controlled clock vaults, to ensure their stability. By automatic inter-comparison of all clocks every 100 seconds, the USNO time scale can be computed which is not only reliable but also extremely stable. Its rate does not change by more than about 100 picoseconds (0.000 000 000 1 seconds) per day from day to day.

What do Atomic Clocks look like?

(below) Hydrogen maser aser

(above) Cesium clock

What Time Is It?

• To get the standard time from the Master Clock of the US Naval Observatory, go to:

http://tycho.usno.navy.mil/estclock.html

So, what are the standards?Fundamental Dimensions

3. Time

4. Electric current

Fundamental Standards

3. Duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 (133Cs) atom.

4. Constant current maintained in two straight parallel ideal conductors of infinite length, 1 metre apart in vacuum, that produces between them a force of 2 x 10–7 N/m.

So, what are the standards?

Fundamental Dimensions5. Temperature

Fundamental Standards5. Fraction 1/273.16 of the

thermodynamic temperature of the triple point of water.

So, what are the standards?

Fundamental Dimensions5. Temperature

6. Luminescence

Fundamental Standards5. Fraction 1/273.16 of the

thermodynamic temperature of the triple point of water.

6. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

So, what are the standards?

Fundamental Dimensions7. Amount of substance

Fundamental Standards7. The mole is the amount of

substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12 (12C).

NOTE: This is the most recent standard added to the list.

REMEMBER THIS!!!!

• Units and Dimensions have a one-to-one correspondence!

• What that means is that, if you know the unit, you know the dimension, and therefore, which quantity is being measured.

• This translates into you being able to figure out what variables are present in a word problem, which is a HUGE step in solving the problem.

VERY IMPORTANT!!!1. UNITS AND DIMENSIONS MUST MATCH.

2. YOU CAN ONLY COVERT BETWEEN UNITS MEASURING THE SAME DIMENSION.

FOR EXAMPLE, YOU CAN CONVERT YARDS TO METERS, BUT NEVER TO SECONDS.

3. ONLY LIKE DIMENSIONS CAN BE ADDED OR SUBTRACTED.

FOR EXAMPLE, YOU CAN ADD TWO LENGTHS, BUT NOT A LENGTH AND A SPEED.

DID YOU KNOW THAT…• … metrology is the science of measurements?• … a degree in metrology takes about 2 years to earn,

and pays very well?• … the Bureau of Weights and Measures constantly

checks measuring instruments that are used to sell goods to people to make sure they deliver what they sell? Check, for instance, the gas pumps at your favorite gas station for a silvery metal stamp with the date of the last inspection. This is your assurance that when you pay for one gallon of gas, that is exactly what you get.

Current Issues in Metrology• Did you know that the kilogram standard has

“lost weight”? It has – 50 µg – and it also has people a little baffled!

• The current electric current, amount of substance, luminescence and mass standards are about to be “outlawed”? They are scheduled to be replaced by standards based on some fundamental Physics constants, by as early as 2014!

THE END

Lilian Wehner ©