# Nature of Physical Laws: The Basic NCERT Concept

In this article, we will be studying about the nature of laws in Physics. Their conservation (specifically- energy) and the connection of conservation with the symmetry of nature will also be discussed. The topic is much theoretical but researchers will find this interesting.

This article is in continuation to my previous article Fundamental Forces in Nature: The Basic NCERT Concept . In this article, we will study mainly the nature of physical laws: Their conservation and the connection of conservation with the symmetry of nature. So let's start:

## How Do Physical Laws Come into Existence?

Our universe is ordered in an intelligible way. Physicists explore the universe. The range of their exploration is extremely wide: particles that are smaller than the atoms in size to the stars that are very far away. In addition to finding facts by observations and experimentation, physicists attempt to discover the laws that summarize (often as mathematical equations) these facts. When a physical phenomenon governed by the different types of forces takes place several quantities change with time but some special quantities remain constant and such observation leads to the origin of conservative principles in Physics.
Example:-Suppose a ball is freely falling* to the ground. Some quantities such as velocity, displacement etc. change with time but mechanical energy (the sum of kinetic and potential energy) remains constant. And that's when we say mechanical energy is conserved under free fall.
*Free fall means the force acting on the ball is the only gravitational force, however in real conditions, air resistance also play a big role that is a type of friction force.
The example we studied follows the following general statement:
For motion under an external conservative force, the total mechanical energy of a body is a constant.
This law restricted for a conservative force should not be confused with the general law of conservation of energy of an isolated system (which is the First Law of Thermodynamics).

## Specifically to the Concept of Energy

The concept of energy is central to Physics. The expressions for energy can be written for every physical system.
When all forms of energy e.g., heat, mechanical energy, electrical energy etc., are counted, it turns out that energy is conserved.
This needs to be noted that the previous statement "For motion..............a constant" is valid for conservative forces but the general law of conservation of energy is valid for all types of forces, for any kind of transformation between different forms of energy and across all domains of nature: microscopic to macroscopic.
In the falling ball example, if we include the effect of air resistance during the fall and see the situation after the ball hits the ground and stays there, we can easily determine that mechanical energy is not conserved but general law of conservation of energy is still applicable as heat and sound energy is also produced that need to be taken into the account.
If we talk about the applications of this law, they are:
• Analysis of atomic, nuclear and elementary particle processes.

• In producing water electricity.

• Deeply applicable in our day-to-day activities

and much more..

### Einstein Theory: Mass Conservation to Energy Conservation

Until Einstein introduced his theory of relativity, mass conservation and energy conservation were treated separately, since the matter was thought to be indestructible. Law of conservation of mass is still used in general chemical reactions because there is just a simple rearrangement of the molecules. The energy required for destruction or production of significant mass is neither produced nor absorbed in general reactions. Because the theory of Einstein says:
E= mc2
through which we say mass m is equivalent to energy E and c is the velocity of light equal to 299792458 m/s or approximately 3x 108.
So according to it for the production 1gm of the molecule, the amount of energy required is
10-3x9x1016= 9x1013 Joules.
Now you can have some idea how big amount of the energy is that.
In nuclear reactions such transformations take place.

## Some Other Conservative Quantities and Applications of Their Conservation

There are many other conserved quantities like the energy in nature such as Linear Momentum and Angular Momentum etc. They are also conserved. The laws of their conservation can be derived from Newton's laws but they are applicable in all domains of nature even where Newton's laws are not applicable.
These conservation laws are very useful in general Physics' practices. It often happens that we cannot solve the full dynamics of a complex problem involving different particles and forces but still, these conservation laws provide useful results.
Example:-We may not know the complicated forces that act during the collision of two automobiles, yet momentum conservation law enables us to bypass the complications and help us predict or rule out the possible outcomes. With the help of conservation laws of energy and momentum, Wolfgang Pauli correctly predicted the existence of neutrino. This proves that these laws are very useful in Nuclear Physics too.

## Connection of Physical Laws with Symmetry of Nature

Conservative properties are deeply connected with the symmetry of nature. For example, an important observation is that these conservation and other universal laws do not change with time! It turns out that symmetry of nature with respect to translation(i.e. displacement) in time is equivalent to the Law of Conservation of Energy (meaning- simply, both remains the same with time). Likewise, space is homogenous and there(intrinsically) is no preferred location in the universe. to put it more clear, physical laws remains the same everywhere but it is possible that the phenomena may differ. For example, gravitation force on the moon is 1/6 (due to the less mass of the moon) that of the earth but the universal law of gravitation is applicable everywhere. To learn more about symmetry check: http://www.pnas.org/content/93/25/14256.full
This symmetry of laws of nature with respect to translation in space gives rise to the conservation of momentum. In the same way isotropy of space (no intrinsically preferred direction in space) underlies the law of conservation of angular momentum. Similarly, the other conservation laws (like charge and other attributes of symmetry) can be related to certain abstract symmetries. Thus symmetries play an important role in modern theories of fundamental forces in nature.
Here is the end of the first lesson of NCERT class-XI. You can read the whole chapter in with the help of following links-

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