# How units were defined?

I was wondering how we humans can be sure that one meter is one meter and that one second is one second. Nowadays, except for the Kilogram, all other units are well defined using highly accurate techniques (frequency of atoms vibrations or stuff like that). But at the end all units are kind of related to each other and the definition of each unit is based on a combination of other units. There must be some viable sources that have constant measurable values that we used to define the basic units. What is those sources?

To explain more let's start with the meter. From wikipedia, the definition is: 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. So here it is clear that the definition of a meter relies on the accuracy of how we define a second.

Now let's look at the second:

the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

How is this period calculated? The sensor has probably some equations that imply transformations using other units like Kg etc...

Where does this loop stops?

EDIT:

I think I was a little bit mistaken. Not all units are directly related and there is 3 totally independent units which are : Time (second), Temperature (kelvin) and Mass (kilogram). Time and Temperature are well defined but Kilogram is still unclear. Every existing unit can be transformed into a combination of those three. It means that all units based on Kilogram are not absolute.

• Your question is unclear to me. Are you asking if there are some physical manifestation of basic units, like there is for the kilogram? – BMS Jul 3 '14 at 5:59
• I edited my question. I hope it is clearer now. – Mehdi Jul 3 '14 at 6:05

In short, up until now, the $kg$ was arbitrary, but now people are trying to define it based on universal constants

There is a ongoing process to try and link all the units to universal constants. This has been done already for the second (using Cesium) and the meter (using the speed of light in a vacuum)

However, the kilogram is a little less straightforward. An interesting read is SI units revision proposal. It proposes to link the kg to the Plank constant $h$, but also to link Kelvin $K$ to the Stefan-Boltzman constant $k$ and more of these constructions.

The idea is that these universal constants are the only things in the world that will never change (hence 'constant'), and these constants should be the only things on which the units should be based.

The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. How is this period calculated? The sensor has probably some equations that imply transformations using other units like Kg etc...

The number of periods of anything isn't calculated, it's counted, at least in principle. To count them, yes you might have to use technical equipment which uses other known principles to operate, but in the end it's just counting. The operation of this equipment could use some non-standard definitions of units, so lang as they accurately count.

• I meant how the period is calculated and not how the number of periods is counted. But I see now that a second is defined as a convention of counting level transitions in cesium. This means that the only units we are sure of are time and distance and their combinations, and temperature also. Everything else is still not absolute because of the Kilogram. – Mehdi Jul 3 '14 at 6:23

Talking about a "viable" source, we can talk about time, as in how long does it take to go from my place to the grocery store? 10 minutes by bicycle. How long does it take from LA to Boston? 0.04 light seconds, or 4 car hours, or 5 weeks on a boat, etc.

So we see that we can use time to define other units, not to mention we really do use time to define many other units.

• Unfortunately most of the units are based on the Kg and it is still not well defined nowadays. – Mehdi Jul 3 '14 at 6:25
1. In the SI there are 7 independent base units: meter, kg, second, ampere, kelvin, mole, candela.
2. Many people think that the last 3 (kelvin, mole, candela) should not be base units, and they have good points for each case.
3. Some theoretical physicists think there are even fewer base units, of which I am not convinced yet.
4. All base units are "random", (9192631770 periods is random and 1 period is random).
5. All other units are "derived units" and therefore no longer random (given the base units), (well, almost all other units).
6. The choice of base quantities (e.g. which quantities are selected for the base units) is also random. For example it would be possible to choose the coulomb as a base unit instead of the ampere.
7. The concept of base units is not very important in the real world. It is interesting for fundamental reasons, though.
8. In many fields of physics it is common to calculate in "natural units" which are supposed to be less random. One can argue that the atomic unit of charge, e, is less random than the coulomb. However, since we don't really understand why e has the value it has, it can also be considered random. In the end it depends on the definition of "random".
9. More important is that a system of unit is "coherent". This allows for simple formulae.