• Ch-1: Introduction to Physics
  • 1.1: What is Physics?
  • 1.3: Units

Introduction to Physics

1.1 What is Physics?

Physics is dynamic. It has evolved through ages as our understanding of nature has increased, and will continue to evolve as we continue our endeavour to understand nature better. The various laws of physics that were formulated in different times were the nice and elegant(not necessarily the best) approximations that physicists used to relate the obtained experimental findings. As we gain new experiences, we modify these laws to account for our new findings. Thus, we should always remain motivated and remember that there is always possibility of a new insight, and perhaps it might come from us!

1.3 Units

To measure is to compare. We all have heard this. However abstract comparisons like larger/smaller, hotter/colder or brighter/darker cannot always take us far. We then need to quantify the comparison. For this, we take measurements with respect to a presumed standard body and express the measurement in multiples of this standard body. This standard body is then called a unit.

It is important to realise that this unit can actually be anything arbitrary. To appreciate this let's see this amazing story:

Ravi's Water-Bottle Dillema

Once upon a time, in a quiet town nestled between hills and fields, lived a diligent boy, Ravi. He owned a little shop that sold all kinds of things.

One day, the local Town School decided to have a fun event for the kids. The principal announced a competition of water bottles! And promised to award tickets to the Brand New Super-Duper City Amusement Park🎢, to the student who would bring the largest bottle!. So Hari, our school boy, determined to win this event, called Ravi's shop and asked for the largest bottle to be sent by courier. Indeed, the stakes were very high.

Ravi, exactly knew, this was his best chance to shine. He at once called the courier company to send a courier boy and the courier boy arrives in his van.

Ravi has two water-bottles, a normal blue one and a larger purple one. All the shops in the town sell the blue bottle, but only Ravi has the large purple bottle. To enquire about the cost of transport, Ravi shows the two bottles to the courier boy:

Ravi: "Hey man, how much will it cost to transport this purple bottle?"

The Courier Boy: "Sir, the cost of transport depends on the length of the bottle. I am seeing this purple bottle for the first time. But I have seen the blue bottle, and our company charges Rs. 12 for this. So if this purple bottle was twice the length then it would cost you Rs. 24."

Ravi: "Oh I see"

Ravi takes the purple bottle and tries to compare it to the blue bottle. He first holds the blue bottle's bottom end with the bottom end of purple bottle. Then making a mark on the purple bottle where the top of the blue bottle reached tries to take measurement again. But he observes that the purple bottle falls short this time. So it's clear that the purple bottle is larger than the blue bottle but is shorter than twice the length of the blue bottle.

But then how do we know the exact height of the purple bottle?

Ravi sees a pencil nearby. He wonders if he could use this pencil as a unit and take measurements. He measures the blue bottle with this pencil and finds that the blue bottle is exactly 3 pencil units. He then measures the purple bottle and finds it is 5 pencil units.

So he concludes that that if the 3-pencil unit blue-bottle is charged Rs. 12 then the company charges Rs. 4 for each pencil-unit of length. Thus, the purple bottle will cost him 5 ྾ Rs. 4 = Rs. 20 to transport. 

The Courier Boy: "Sir, you are a genius! You used this pencil as a standard unit of length!"

Measurement using Pencil Unit

fig 1: Ravi's method of measuring the length using the pencil as a standard unit

Pg-3

Radian & Steradian:

The book mentions them to be supplementary 'units' in the SI system. However this classification has now got a few modifications. The interested reader may further inquire this on his own. I will duly update with a separate post on these special units.

Invariability, Availability and Maintenance of Units:

The book writes that often, the methods involved in defining and maintaining standard values are not straightforward. We may question why. Also, since we mentioned that a unit can be anything arbitrary, we should just be able to select anything, shouldn't we? There's a problem, however.

Consider Ravi's story again. In the story, we saw at last that Ravi & Hari argued because Hari found the purple bottle to be 4 pencil units using his pencil. This issue was resolved when we realized that they were using different units.

Suppose they continue to use their pencils for writing and thus sharpen them a few times. When Hari measures the bottle, he finds it to be 5 pencil units. When Ravi measures it, he finds it to be 6 pencil units w.r.t. his pencil. Both of them understand that the problem is due to the reduced size of their pencils, but now how do they confirm that this bottle is indeed the original bottle and not replaced by an identical shorter bottle by a clever friend? In fact, in this situation, there is no way to explain to anyone else what the original 5-pencil-unit-length bottle meant!

With the original standard unit damaged, our ability to define anything using it is also lost. This explains the importance of defining standard units that are least prone to damage and can remain unchanged over years & years. It also explains why extensive care is taken to maintain these units once they have been defined.

The maintenance part is eliminated if we use constants already present in nature to define our standard units. Nature then does its job to keep them unchanged. Ravi may be able to redefine his pencil unit using his 3-pencil-unit blue bottle, but we can never be sure that its length has remained unchanged. Its length may also have been affected by wear and tear.