Measurements and Units

Measurements and Units

Why do we need Measurements?

The purpose for why measurements exist in physics is to find patterns in nature. Since physics is a science of understanding how nature works, It also involves knowing how everything is connected and what are the relationship between things.
But it’s easy to find correlation between things and call it a pattern. The webpage called Spurious Correlations has a list of correlation between random stuff that should not corelate. But in physics we need an objective way to define the existence of such patterns. That’s where measurements come in the picture.
As an example we know metal expands on heating and contracts on cooling. This is a pattern, a relationship, between the length and temperature of the rod. But this raises the following questions:

Note that these are not the only questions that can be asked. You may come up with more. But once we have an answer to these questions we can can start making a scientific model trying to explain why heating expands metal. We can then apply the scientific method to these models and make falsifiable predictions and if the model passes a test, it becomes a theory.

But all of these start with measurements.
Now the example above explains the relevance of measurement from the perspective of physics. But we use measurement in our day to day lives for various reasons. But all measurements directly or indirectly arises due to dependence and interaction of things. Like if you cook more food you will need to add more salt. And the amount of salt added is proportional to the amount of food cooked. If it’s not in proportion it will either have less salt or become salty. But it will not taste right.

Physical Quantities

Lets start with asking the following questions:

To answer these questions lets look at a few everyday things that can be measured and ones that cannot be measured. We will look at one example of each. Let’s start with the height of a person.

There are various ways of measuring heights, the most common way we know of in the present day and age is by using a meter scale, or a measuring tape. But imagine if you did not have measuring instruments. You can still compare heights between two people using the span of your hand (I will discuss why using someone’s hand measuring heights isn’t a good idea in a future post). But the key point to focus on is you have a property called height and it can be measured with a ruler or the span of someone’s hand. These properties that are associated with objects are called physical quantities. And it is physical quantities that can be measured.
It must be noted here that not all objects have all physical quantities. Gases do not have length.
And not all physical quantities are physical in nature, so may not me able to touch it . A good example would be brightness of light. Brightness is a physical quantity that can be measured but light is not a solid, liquid or a gas. So physical quantities are not limited to physical objects. But must be understood as properties that certain objects or systems or a phenomenon might have.

There are also objects that cannot be quantitively measured. Like emotions. More specifically even if you come up with a method to compare emotions, it will not be objective. If asked “Which is taller, an adult giraffe or a baby elephant?” everyone will agree that an adult giraffe is taller. and more specifically if you have a method to measure height, you can tell exactly how tall the giraffe is compared to an elephant.
But if I asked you “Which creature is more scary, a spider or a cat?” You would get different answer depending on who you ask. While one says the spider is scary. Another would say the cat, a third might say both are scary and someone else would say both are not scary at all.
Now, lets assume for a moment everyone agrees a spider is scarier than a cat. There is no objective was to measure fear. You cannot say a spider is 2.5 times more scarier than a cat. So Fear is not a physical quantity. There maybe many more examples like this.
Having said this, scientist are always trying to expand our knowledge and a few may have come up with an objective systems to measure certain emotions but I’ll leave that as an exercise for you to research on.

Units

Now that we understand physical quantities lets look at units. And to understand unit we need to understand the method of measurement first.

Imagine you are stranded on an island with a dog who we’ll call Fluffy. Fluffy is cute and friendly and well trained and will respond to commands you give. This will make the experiment easier to perform. Now imagine that you need to find how much is Fluffy’s mass and that your life depends on this information. (In common everyday language we would ask: how much does he weigh?)
Now you manage to use the bark of trees and fibres from plants to make a good weighing scale. But you do not have an assortment of weights to measure Fluffy’s true mass. But you notice there are coconuts lying around and you find a bunch of coconuts that have the same mass (you can use your weighing balance to do this. Now that you have a collection of coconuts of equally weighing mass, you can use these coconuts to measure the mass of Fluffy. and lets call the mass of one coconut 1 “cocomas”. And yes I made up the word “cocomas”.

Every every physical quantity there is a certain amount that we set as reference. Then any measurement is only a comparison of physical quantities to these references. These fixed amount or references for each physical quantities are called a units. Each physical quantity has its own units.
As an example, for the physical quantity called length, we have a certain prescribed reference length that we call 1meter.
Meter is the unit for the physical quantity we call Length
So when someone says they are 1.52 m tall. What they actually mean is they are 1.52 times longer than this reference length called meter.

This Wikipedia page has a list of physical quantities and their corresponding units.