In this chapter, we will understand conservation laws in Physics. During any physical phenomenon governed by different forces, several physical quantities may change with time, but some special physical quantities remain constant with time. Such physical quantities are called “conserved quantities” of nature. A physical quantity is said to be conserved if its value does not change with time. In other words, if a physical quantity does not change when we go from one situation to another, we say it as the quantity to be conserved.
For example, an electric charge is a conserved quantity in nature. It means that electric charge can neither be created nor be destroyed, i.e. the net amount of electric charge in any system remains constant over time. It can only be transferred from one system to another. Other examples of conserved quantities are energy, mass, and momentum. The laws concerning to these conserved quantities are called conservation laws in physics.
Table of Contents
Definition of Conservation Laws in Physics
Conservation laws are those laws of nature that state some physical quantities are conserved, meaning that they are the same before and after an event or internal interaction. In other words, the laws which govern the conservation of some physical quantities in nature are called laws of conservation in physics. These laws are applicable to only isolated systems.
Scientists have performed a very large number of experiments to examine the conserved nature of physical quantities. In all the experiments, they proved the conserved nature of physical quantities beyond any doubt. However, conservation laws cannot be proved mathematically.
The conservation laws have a deep relationship with symmetries in nature. There are nearly 8 laws of conservation based on the symmetry principles in physics. They are as:
- Law of conservation of energy
- Law of conservation of mass
- Law of conservation of mass-energy
- Law of conservation of linear momentum
- Law of conservation of angular momentum
- Law of conservation of electric charge
- Law of conservation of baryon number
- Law of conservation of lepton number
Let’s understand a brief discussion of laws of conservation one by one in easy words.
Law of Conservation of Energy
This law states that energy can neither be created nor destroyed, but can only be transformed from one form into another. For instance, when an object is at a certain height from earth, it possesses only potential energy, not kinetic energy. But, when it falls down, the potential energy gradually transforms into kinetic energy and when the object is just to strike the ground, the energy is wholly kinetic. When it hits the ground, the kinetic energy changes into sound, heat, and mechanical energy, as shown in the below figure.
But it is found that the total mechanical energy remains constant at any instant in this process. Hence, the law of conservation of energy also states that the total energy in any system always remains the same. This is universal law, and the total energy of the universe remains unchanged.
Law of Conservation of Mass
This law states that the total mass of reactants is the same as the total mass of products in a chemical reaction. Only rearrangement of atoms takes place during the chemical reaction. But this law is approximately valid in the case of only chemical reaction. The law of conservation of mass was considered as a conservation law of nature until the advent of Einstein’s theory of relativity (energy-mass relation, E = mc2).
This is because earlier, it was assumed that matter is indestructible, meaning that matter can neither be created nor be destroyed. However, it still is an important principle used in the analysis of chemical reaction. Now this law is not regarded as a basic conservation law because mass and energy are considered as inter-convertible. Therefore, we have a law of conservation of mass-energy. Let’s understand it in simple words.
Law of Conservation of Mass-Energy
Albert Einstein discovered this law in 1905, which states that the mass of a system can be changed into energy and the energy of a system can be converted into mass, but the sum of mass and energy of the system remains constant. Einstein given this law using mass-energy relation, E = mc2, where m is the mass of a body and c is the speed of light in a vacuum. The principle of atomic and nuclear bomb is based on this mass-energy law, where mass gets converted to energy (or vice versa).
This is the energy which is released during the generation of nuclear power and nuclear explosion. In the case of nuclear reaction, mass is not conserved, but appears as energy. The annihilation of an electron and positron (positively charged electron) into two photons is another example of the conversion of mass into energy. In this process, mass is not conserved, but the total energy is conserved.
Law of Conservation of Linear Momentum
This law explains that the total linear momentum of a system in a given direction remains constant if no resultant external force acts on the system. i.e. the net external force acting on the system is zero. The total linear momentum refers to the vector sum of linear momentum of each particle in a system.
For instance, jet planes and rockets work on the principle of conservation of linear momentum. Another example of this law is the recoil of a gun.
Law of Conservation of Angular Momentum
This law explains that the total angular momentum of a system remains constant if no external torque acts on a system. For instance, planets revolving around the sun in elliptical orbits maintain their motion in the orbital plane because of conservation of angular momentum.
Law of Conservation of Charge
This law explains that the total electric charge of an isolated system remains constant if no external force acts on the system. For example, if we rub an ebonite rod with cat fur, the rod becomes negatively charged, and the fur becomes positively charged because some electrons are transferred from fur to the ebonite rod.
In this case, the negatively charged on the rod and positively charge on the fur both are equal in amount (say q). Thus, the total charge on the system (rod + fur) before rubbing was zero and the total charge on the system after rubbing = (+ q) + (- q) = 0, which verifies the law of conservation of electric charge.
Law of Conservation of Baryon Number
This law explains that when a nuclear reaction or a decay occurs, the sum of baryon numbers before the reaction or decay must be equal to the sum of baryon numbers after the reaction or decay. That is, the total number of baryon number remains constant (i.e. conserved) in any process.
Let us consider a decay: Λ → p + Π–
Here, the baryon number of Λ and p is +1 and the baryon number of Π– is zero. Hence, the baryon number before and after decay is +1. Therefore, this decay is allowed because the baryon number is conserved.
Law of Conservation of Lepton Number
This law explains that whenever a reaction or decay occurs, the sum of the electron-lepton numbers before the process must be equal to the sum of electron-lepton numbers after the reaction or decay. In other words, the total lepton number is always conserved in any particle reaction or decay.
Consider the decay of neutron: n → p + e– + ve
This decay is allowed because lepton number before the decay is zero and it is also zero (0 + 1 – 1 = 0) after the decay. However the following decay n → p + e– + ve is not allowed because the total lepton number of the product is 0 + 1 + 1 = 2, whereas the lepton number before the neutron decay is zero. Therefore, the law of conservation of lepton number does not allow this decay to occur.
