‘Month of Equations’: What Does Mass-Energy Equivalence Really Mean?

October 3: Mass-Energy Equivalence

mass-energy equivalence
Mass Energy Equivalence

Meaning of Equation:

 Anything having mass has an equivalent amount of energy and vice- versa. In other words, mass is a concentrated form of energy.

Arose originally from the special theory of relativity, the mass-energy equivalence equation as a consequence of what Einstein proposed in his paper in November 1905 titled ” Does the inertia of a body depend upon its energy content?”  This equation known as Einstein’s mass-energy equivalence means that the total energy of an object is the sum of rest mass energy stored in an object and the kinetic energy of an object. In other words, we may say that any object that has some form of energy has an equivalent form of mass associated with it.

In order to understand this, let’s consider a simple example of two of your friends who look like the popular cartoon characters – Laurel and Hardy (or Motu-Patlu in the Indian version). If both of them are running towards you with the same velocity, who will be more difficult for you to stop and bring to rest? Yes, the answer is right, it will be more difficult to stop the friend who is more like Hardy (Motu).

Previous in Series: What does the Kepler’s Third law really mean?

Let us go to the basic definition of inertia- the inherent ability of a body depends upon its mass that tends to oppose a change in its state of rest or motion. So who do you think has more inertia- yes !! you are again right. Your Hardy like friend has more inertia because it is difficult to stop him as his body opposes a change from its state of motion to sate of rest. So, is this inertia a consequence of its kinetic energy due to motion? Will the body have less inertia if it would be at rest? So, is the mass increased when the object has increased energy?

We can understand this physical concept by considering an object in motion. The object will keep on gaining energy and hence, increasing its speed until it attains the speed of light. However, the speed of light is the maximum it can achieve no matter how much energy it absorbs, so, the object moving at the speed of light has a constant speed but it may keep on gaining energy and momentum.

This can be possible only if the mass of the object is increasing and hence, the concept of relativistic mass comes into picture where mass varies with the energy and momentum gained by an object which is given by gamma times the intrinsic mass or the rest mass and hence the expression of total energy being equal to gamma time rest mass multiplied by speed of light squared.

This Mass-Energy Equivalence relation has another aspect too-  Anything having mass has an equivalent amount of energy associated with it.

It is indeed very intriguing to know that every object whose intrinsic property is mass has an enormous amount of energy stored in it. So how much is this energy? Well,  let us see:

Consider a small playing marble whose mass is 20 grams. According to Einstein’s equation, the amount of concentrated energy stored in it shall be 20*10^(-3) kg times the speed of light squared. So the amount of energy stored in a 20 g marble shall be: 1.8*10^15 Joules.

How much energy is this?

Let me draw your attention towards a fact that the energy that can be released by one Megaton of a nuclear weapon is around 4.8 *10^15 Joules- and that is about the energy stored in a 20-gram object !!!

The question is then why is there so much havoc about a nuclear weapon and not a small marble? Because in order to harness all of the energy stored as a mass in the object, the matter needs to be combined with antimatter and undergo annihilation. So. until we do not encounter any anti-matter nearby us, we need not be afraid of any concentrated energy stored in the matter that we see in our day to day lives.

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