Sunday 7 May 2017

Relatively Relative

We (humanity), have invented many ways to measure things, but what is it that we are really doing when we measure something?

To explore this question, we start by drawing a dot on a blank paper. How big is that dot? To find out we would probably compare it with something that has dimensions outside of the paper like a ruler or the size of the paper itself. Within the paper surface though, there is no indication of the size of the dot. If we draw a figure next to this dot, suddenly we can define the dimensions of this new shape by the number of dots that fit into it. We see that size has meaning when compared to something else, but not before.

Similar to this, a single object cannot be measured as moving in any way. Motion has to be relative to something else for it to have meaning. If we add another object, we can measure the distance with which these two objects have moved towards or away from each other (or rotated in relation to eachother). We would of course have to measure this movement with the length of one of the objects involved in the system though unless we had something with which to compare.

What about measurements not based on distance? Time comes to mind and just as before, it would not have meaning without comparing it to something. If all events are happening randomly, there is no way we can use to tell someone how long something is taking. What we have to do in this case, is to add something repetitive or predictable. Then we will have something to anchor our time measurements on. Something like the recurring seasonal changes or the rotation of the earth making the sun set. We can start thinking in comparative terms, like "this usually takes about as long as this sand takes to get to the bottom of this container".

After having something to base our measurement on, we can create a unit of measurement by naming this measurement something, e.g. "...and there we rested for 3 sands before moving on...". This would then have to become a standard among the people with whom we want to be able to communicate using relative measurements to this unit. If we meet other groups who compare things differently we would have to define conversions and have tedious discussions on who's unit is better. One unit may even be more convenient for a certain situation but not for another.

Today, we have scientific definitions of units that define exactly what they mean based on natural laws, but we cannot get away from the fact that somewhere deep down they are still just comparisons. Luckily we do not have to worry about those exact definitions to use the units in normal life. If we did, then I missed celebrating my 10^18th period of the radiation corresponding to the transition between the two hyperfinelevels of the ground state of the caesium 133 atom, and that would be sad...