SI Units Explained with Worked Examples

 

 

 

Home

 Site Map

 
The Base Units
 Amount (mol)
 Electric current (A)
 Length (m)
 Luminosity (cd)
 Mass (kg)
 Temperature (K)
 Time (s)
 
Other

 SI Derived Units

 
E = mc2 Explained
Special Relativity

 

 

 

 
  Time

Of the seven quantities measured by the SI base units time is by far the most mysterious. The SI unit of time, the second, symbol s, is easy enough to define, but time itself can only be defined in reference to other quantities. As we will see, time isn't even the steady thing that it seems to be, but can change rate depending on speed and mass.
 

Time is what stops everything from happening all at once

The traditional measurement of time is based on the length of a day. We split the day into hours, minutes and seconds. This is eminently sensible and something so obvious that we don't give it much thought. How, though, would we describe a second to an alien? It's no good saying that it's 1/60th of a minute, or 1/86400th of a day. The alien won't know what a minute or Earth day is either.

Aliens aside, using the day as a measurement also has its problems. One day is the time taken for the Earth to complete a rotation on its axis, but, importantly, the time it takes changes very slightly over long periods. Every few years a second needs to be added to the year to compensate for the Earth's rotation very gradually slowing down, caused mostly by the Moon's mass pulling on the Earth. Clearly, if we want the second to be a precise measurement we need to find something else to base it on.

It wasn't until the invention of atomic clocks, which work by measuring properties of certain atoms, that a really precise measurement of the passing of time became possible. The second was defined in 1967 as:
 

The duration of 9,192,631,770 periods of the radiation corresponding between the two hyperfine levels of the ground state of the caresium-133 atom.

In short, this means that the vibrations of a particular type of atom are observed and counted. The vibrational rates of atoms are incredibly precise and so allow for much more accurate measurements of time than any other system.

That much, then, is straightforward. Time is measured in seconds and we use the vibrational rate of a certain kind of atom to define exactly how long a second is. For most purposes that's good enough and we don't need to say any more about it. However, it's interesting to note that time can, under certain circumstances, change and so flow at a different rate.

When an object moves, any object at any speed, its internal clock slows down. This is sometimes summed up as "moving clocks run slow":
 

Clocks slow down when moving

If this is true why don't we notice our wristwatch slowing down when on the bus? The answer is that even though the watch will have slowed down it's by such a tiny amount that it's not noticeable. We need to be moving much, much faster before the effects become apparent and even then something else very strange needs to be taken into account.

The speed of light is close to 300,000 km a second and is the fastest thing there is. Moving as fast as a beam of light we could travel seven and a half times around the world every second. It's only at speeds comparable to this that the effects of time dilation, the slowing down of clocks, become apparent. For example, if we move at about 90% of the speed of light our clocks, including our body clocks, will slow down by about half. If we could travel at 99.999% of the speed of light our clocks would come to a virtual standstill.

I mentioned that there was something else that was very strange about this. If we moved at very high speeds our clocks would slow down, but only relative to external observers, i.e. people watching from a platform which is stationary relative to the moving object. They would see the occupants of such a high speed platform, such as a rocket, moving very slowly. Likewise, the occupants of the rocket would see the observers as moving very quickly. Their clocks are measuring time differently to one another based on their relative speeds. This is the basis of Einstein's famous theory of relativity and you can read more about it, together with worked examples, by clicking here or on the picture of Einstein:

Click for Einstein's Relativity

 


 

The mole The ampere The metre The candela The kilogram The kelvin The second