Standards and Units

In Physics, as in all of Science, we rely on Operational Definitions, what operation must we do--what steps do we need to carry out--to measure a quantity.

For example,

what is the distance between A and B?

We can measure that distance by placing a ruler, end to end, over and over again, between points A and B.

We may find some other method or operation that is easier or more convenient, but it will be equivalent to this simple operational definition. For instance, we might use a tape measurer because it is more convenient than physically laying small rullers end-to-end. But the value--the answer we get--will be the same.

For Mechanics, we need to measure length, mass, and time.

> the need for a standard

- trade or commerce

- general communications

> past standards

- "three dried barley corns" were defined as an English inch

- the king's arm span, from nose to forefinger, was defined as an English yard

- the length of the king's own, real, actual foot was defined as the French foot

> the "metric system" or, now, the International System of Units

- "SI" or Système International

- units needed for Mechanics

- length (meter)

- mass (kilogram)

- time (second)

- beyond Mechanics

- temperature (kelvin)

- electric current (ampere)

- light intensity (candela)

- amount of material (mole)


We might well define the meter as the distance between two carefully scribed marks on a block of metal.

This definition of the meter was used until 1960. In practice, such secondary standards are still in use. However, there is a problem with this type of standard,

Do we measure the "distance between the lines" from the center or an edge? Or, for that matter, how do we find "the edge"? How do you measure the size of a cloud?

From 1960 to 1983, a meter was defined as

1 650 763.73 wavelengths

of light emitted from Kr86 (krypton-86)

This has the effect of making the fundamental standard available to everyone.

In 1983, this standard was changed. One meter is now defined as the distance traveled by light in a vacuum during

This effectively defines the speed of light as exactly 299 792 458 m/s. (For convenience, we will usually take the speed of light to be c = 3.00 x 108 m/s). The speed of light (and the index of refraction) is different for different wavelengths (or colors) as light goes through a material like glass or plastic or water. This is why a spectrum is produced by a prism and why a rainbow is produced by raindrops. But, in a vacuum, all light, of all wavelengths, has the same speed, namely,

c = 299 792 458 m/s.


In SI, the basic fundamental standard of mass, the kilogram, is still defined in terms of the mass of a specific platinum-iridium cylender kept in very controlled conditions at the International Bureau of Weights and Measures at Sèvres, France, near Paris. Other countries have secondary standards that are all compared to this mass. In the US, our National Institute of Standards and Technology keeps the US standard in Gaithersburg MD or Boulder CO.


Astronomers have always been extremely accurate. In the 1675 the speed of light was measured by Ole Roemer because there was a discrepency in the times of eclipses of the moons of Jupiter!

For many years, time was defined in terms of the time required for Earth to rotate around the Sun or around its axis. In 1967, the second was defined in terms of atomic vibrations. Now one second is defined as the time required for

9 192 631 770 vibrations

of the radiation from a Cs133 (cesium-133) atom.

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Dimensional Analysis
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(c) Doug Davis, 2001; all rights reserved