Comparison of measurements

We should study completely about measurements and units before the study of physical terms that is often used in our real life because physics is mostly concerned with measurements.

For the introduction of sizes and measurements that was done by humans, it is given some examples of measured things.

Our Milky Way Galaxy is roughly 100,000 light years in diameter, and our nearest sister galaxy, the Andromeda Galaxy, is located roughly 2.5 million light years away. There are probably more than 100 billion (10to the power of 11) galaxies in the observable universe.

Typical galaxies range from dwarfs with as few as ten million (10 to the power of 7) stars up to giants with one trillion (10to the power of 12) stars, all orbiting the galaxy's center of mass. Thus, a very rough estimate from these numbers would suggest there are around one sextillion (10to the power of 21) stars in the observable universe;

A typical star has a mass of about 2×1030 kg, which is about 1×1057 atoms of hydrogen per star. A typical galaxy has about 400 billion stars so that means each galaxy has 1×1057 × 4×1011 = 4×1068 hydrogen atoms. There are possibly 80 billion galaxies in the Universe, so that means that there are about 4×1068 × 8×1010 = 3×1079 hydrogen atoms in the observable universe. But this is definitely a lower limit calculation, and it ignores many possible atom sources such as inter galactic gas.

The electron is by far the least massive of these particles at 9.11 × 10−31 kg, with a negative electrical charge and a size that is too small to be measured using available techniques. Protons have a positive charge and a mass 1,836 times that of the electron, at 1.6726 × 10−27 kg, although this can be reduced by changes to the energy binding the proton into an atom. Neutrons have no electrical charge and have a free mass of 1,839 times the mass of electrons, or 1.6929 × 10−27 kg. Neutrons and protons have comparable dimensions—on the order of 2.5 × 10−15 m, although the 'surface' of these particles is not sharply defined.

For the measurements done in physics, it was already formulated many methods. But all of those methods are formulated based on the principle of units and dimensions.

For instance, to measure the size of any curved path, it will be taken a small rope or thread would be placed on the curve. The measurement will give the nearest value of the length of the curve though there are some practical mistakes.

These measurements using ropes and thread are the very basic ideas that gave the technic of measurements using fixed physical objects. To measure all the physical things we need some fixed reference objects in our physical world.

Only if the measurements are done in terms of some fixed reference things [Units], it can be easily measured to any desired value. And those measurements can be easily converted various system of reference using elementary arithmetic operations.

Converting process can only be done using Units

Otherwise it is a collapse in Physics.

For example if there are 10 apples cost 105 rupees then how much will cost for 3 apples.

To solve this problem, first it should be found the cost of one apple and then it will be multiplied by 3 to get the desired cost.

It will be calculated simply like below,

            10 apples         for        100 rupees

            10 * 1 apples   for        100 rupees

            1 apple            for        100/10 rupees

            1 apple            for        10 rupees

            3* 1 apples      for        3* 10 rupees

            3 apples           for        30 rupees                    

Thus any measurements can be calculated for the value of unity of the object and it will be converted to any desired value.

Similarly all physical measurements will be done for unity as it is convenient to use it in many real life situations.

            So let it be started with length. It is already known that length is the measurement of amount of size and numbers are used to represent these amounts. But numbers doesn’t give any information about the size of the amount. The amount can take any size. 

If you simply say 5, 12, 10, 8 and 8 then it will give no information about any amount or any size. As it is just the numbers, it is inadequate and useless.

 But if you say 5 apples or 12 boxes or 10 kilometer or 8 kilograms or 8 hours then it gives the real physical meaning. Here the terms apples, boxes, kilometer, kilogram and hours gives meaning for the sentence and it acts as a reference for those sentences. That why they are called the units.

To describe any unit, first it should be clearly understood that what a reference is. 

Reference is nothing but the process of comparing something using a fixed common thing.

And that common thing is called the Unit. All the units are just the tools for the comparing process.

The need of reference is simple and can be illustrated simply as given below,

Two lines of different lengths are given below,

How it could be remembered the two sizes of the given two different lengths in our mind?

How it can be remembered, if it was given more than two lengths at one time?

 Comparison was made to solve this problem of lengths. We found a way to compare all types of lengths using a common length.

We used some fixed length to describe all the other lengths.   

Here in the above case you can say either,

The larger length is one and half times the smaller length or

The smaller length is 2/3 times the larger length.

For the case of two or more given lengths, we will take a common length in those lengths and we will compare other lengths with the fixed one.

But the same common thing will not happen for all the people. One person will take the bigger length as the fixed and the other one will take the smaller length as the fixed one. It needs not to be the same fixed reference length for all the people. Various people will use various common lengths as the reference.

To avoid these confusions, scientist created the international system of units. It was called SI units and now used worldwide.

They made common amounts to measure all types of various physical quantities. And the common amounts defined with the greater accuracy and precision.

Thus SI Units were formulated for most of the physical quantities and it has seven base units and many derived units.  

Some of the units are…

Unit for length is meter

Unit for time is second

Unit for mass is kilogram…etc.

Meter is the common amount and its size denoted using numbers and for some special amounts it is used the following prefixes like milli, deci, deca, kilo, etc.

The use of unity is that we can use unity to represent large amounts by simply multiplying the desired number with that unity value.  In the length illustration, unity value is one meter and to represent a large quantity like kilometer we will multiply the number 1000 with that unity.

If we want to specify 10 times the meter then we will multiply 10 with meter. Similarly we can represent any amount. It is like representing number 1000 as 1000 * 1. Unity is common for all.

It is similar to the problem of finding the required cost of 3 apples using the cost of one apple.   

And finally now, we are able to measure many natural things using our knowledge of comparison with units.

Finally it should be registered a word about unity that

 Unity is similar to an atom in a complex object that consisted of many atoms and molecules. It may be taken a single atom as a unit and we can measure the whole size in terms of number of atoms

as         1 apple equal some x number of atoms and                          

            1 banana is equal to some y number of atoms

since they are just the tool of comparison [where the number of atoms is the unit used here].

The molecular structure of objects was given above. In that structure a single atom is similar to the notion of the units.