Susana Prieta, a good Facebook friend of mine, asked me: “So, Vishu Menon can you explain e=mc^2 to me in easy to understand terms.”
This is Einstein’s equation that relates energy content and mass of any body (which Einstein qualified as inertial body, but all bodies that we shall ever encounter are inertial bodies. The equation means that energy and mass are interchangeable. Multiply mass by a certain number, you get energy. As simple as that.
There are two ways of explaining this crucial equation that changed the history of the world and led to the development of fission and fusion type nuclear bombs that will forever threaten the existence of the world. If you would like an analytical derivation of the equation and are good at mathematics, (only higher secondary mathematics will do), you could look up a lucid explanation by clicking this link. I am supposing that your question calls for a qualitative rather than quantitative analysis of the equation. Hence I do not propose to re-invent the mathematical wheel and waste your time.
So let us examine what the equation means to a common person like you and me.
E in this equation is total energy contained in a substance, any substance under consideration. It excludes the kinetic energy, ½ mv2 stored by a body in motion, but since that energy is relatively negligible in the numbers we deal with, its effect can be ignored.
Energy is measured in the unit of Joules. If the meaning of that unit is not clear, a Joule is the amount of energy that can deliver 1 Watt of electricity for one second. Thus 1000 Joules can give 1000 Watts per second; 3,600,000 Jule Kilowatt-hour of electricity to you. This is slightly more than the Unit you pay for when you consider the line losses during delivery of electricity to your house.
M is mass of the body. We will consider it in kilograms. (KG)
C is a constant. Although it is taken into account as the speed of light during the derivation of the equation, for us it is a constant number – 299,792,000. Further for simplicity, we will take this to be 300 million metres per second. Hence c2 would be 90,000 million million or 90,000,000,000,000,000 – a huge number, a constant.
Let us take one kilogram of a substance – any substance, say the timid but volatile hydrogen gas.
If somehow, we could completely split the single nucleus (one proton) of that hydrogen atom, then you could derive enough energy to deliver 90,000,000,000,000,000 Watts per second. Or 25 million million watt-hours per hour or supply sufficient energy to a town of 25, million factories at 1000 kilowatts per hour to an industrial town!
Of course, it is not possible by any known means within our technology to break up hydrogen proton and release all its energy at one go. However, our sun produces helium by fusing (fusion method, which is another way of releasing energy as we shall see below). The remainder of energy is radiated into space as free energy in the form of electromagnetic waves (including heat and light) to space, a small fraction of which that hits our planet makes life possible. Stars more powerful than our sun actually produce more massive substances including iron, gold and the very fissile substances like Uranium, Thorium and Plutonium.. This process is known as Stellar Nucleo-synthesis, first postulated by that enigmatic scientist-cum-science-fiction writer, Fred Hoyle (1915-2001).
On our own earth, there are substances such as Uranium and Plutonium that are more amenable to fission or fusion (respectively). These substances can be made to release massive amounts of free energy when they are enriched to near-purity. The secret in creating a nuclear bomb lies mainly in the process of enrichment. We will not go into the process of breaking up the protons to release energy,, but let me paraphrase (with changes to suit our civilized non-male-centric concept of morality) an analogy by the great Einstein himself.
Suppose there lives a rich woman who hides all her wealth. Nobody, not even her daughters, know how much she has, or if she holds any wealth at all. Now when she is in the process of dying, she realizes there is no point in hiding her wealth. So, she decides to give them away to her two daughters. Let us say she has five quantities of wealth. She allocates two quantities to her elder daughter, two to the younger one, and, realizing that she would be questioned at the Pearly gates, bequeaths the remaining small portion for public charity. If her wealth was all in bags of energy, then the remaining one bag bequeathed to the public is free energy. This, roughly, is the fission process.
If you somewhat modify this fantasy and imagine that two parents of a single daughter decide to bequeath all their wealth (in packets of energy) to the daughter, then, too, there is some left behind which goes to public as free energy. This is the fusion method. The so-called Hydrogen bomb uses the fusion method. In this kind of bombs, Hydrogen isotopes are made to fuse under extremely high temperature.
Look at our numbers above, Even if you divide that 90×10^15 joules is divided into five parts and only one of those parts is released in the atmosphere as free energy (largely heat, light and higher-frequency waes such as X-rays and Gamma rays), imagine the calamity that one Kg of a substance called Uranium 235 (92 protons, 143 neutrons as against one proton in Hydrogen)) can generate. The Little Boy, the atomic bomb that was dropped over Hiroshima had 64 kilograms of that fissile material! If you have the time, calculate the energy in Joules that it could have released if each kilogram contains 4255 followed by 20 zeroes of atoms.
Now you know the reason why during his pensive moods Einstein regretted publishing the equation in 1905 which led to the destruction of two cities in 1945 and someday, if you continue to have presidents like Trump and Putin, might destroy our entire human habitation.
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