E = MC2: PART 1: What should we understand from it ?

You will find lot of articles about this equation on the internet. This is my attempt to put in my own words, what I have understood out of this revolutionary phenomenon called E = MC²

E = MC²: The most famous equation from Albert Einstein as a part of his work on 'Theory of Relativity'. In this equation relating Mass and Energy, E stands for 'Energy ', M for 'Mass' and C for the 'Speed of light in vacuum'. One of the simplest and tersest equations ever formulated but in the world of Physics, it has unleashed an impact inversely proportional to its size. But what does it really mean?

Section A :

Lets look at each of these terms E, M and C:

What is 'mass' ? Every matter, object or a thing has mass. But what is 'Matter' ? - 'Matter' is anything that is made up of atoms and molecules (matter is not just the things we see. Air or oxygen or any other gas is also 'matter'). Anything - solid, gaseous or liquid - which takes up space and has volume is 'matter'. And 'Mass' is a measure of how much matter there is in that object/body/thing.

What is 'energy'? Some of the common forms of energy that we know are 'thermal' and 'light'. When you burn coal, you release enough 'thermal energy' to heat water or cook a meal. When steam is pressurized at high speed, it has enough 'kinetic energy' to rotate a turbine. Water stored in dams has enough 'potential' energy. In addition to this it gains enough 'kinetic energy' when it flows down from a significant height. This energy enables it to rotate turbines and produce electricity.

What is 'C (Speed of Light in vacuum)' ? - Light is an electromagnetic wave just like xrays or microwaves, or radiowaves that transmit data between wireless devices like cellphones or waves those that bring songs to our radios from far off radio stations. All these waves are part of something called 'electromagnetic spectrum' and *all* electromagnetic waves have the same certain 'speed of travel'. Remember that light takes about 8 minutes to reach from sun to the earth? 'Light' also is one type of electromagnetic radiation which can be seen in different colors unlike xrays or other radiowaves. The fact is that 'Light' (just like any other electromagnetic waves) travels at a speed of 3, 00,000 Kilometers/second (in vacuum) . So when we talk about speed of light in vacuum it is actually speed of any kind of electromagnetic radiation in vacuum.

How do they fit in the equation E = MC² ? The equation really means that 'matter contains energy' (even when the matter is not moving) . Before Einstein’s time, the assumption was that energy can be exhibited by a body only when it is moving or when it is emitting some form of radiation like heat or light. A body at rest is simply a piece of matter with zero energy. Einstein dared to change this thinking. He proposed that matter is a chunk of mass with dormant energy trapped inside it even when it is *not* moving. When the mass moves, it has kinetic energy in addition to this trapped energy. Fine - mass has energy. But how much energy ? The energy trapped in a matter (in which 'M' is the measure of the mass) is equal to: 'M' multiplied by C² ( square of the value of C).

Universe is made up of Active energy (kinetic energy, heat, light and other electromagnetic radiations) and Passive energy (which is in form of 'Mass' or 'Matter'). One meaning of the equation E = MC² is that Mass and Energy are inter-convertible. When Einstein proposed this idea the world was not really ready to digest it. How can something that can be visualized and weighed, be converted into energy which in its most forms is not visible to the naked eye? Inter-convertibility also meant that energy can be converted to mass. How was that possible? And what has 'speed of Light' got to do with Mass and Energy? E, M and C - all were well understood terms at the time when Einstein formulated this equation in 1905 as a part of his work on ‘Theory or Relativity’. Also, relating mass and energy was not a new thing when Einstein started working on his theory. But it took a genius like him to knit these terms together in a simple and exact equation.

Talking of inter-convertibility between mass and energy, one should try to understand this conversion with the same ease as the conversion between feet and meters, or between kilograms and pounds. It’s very easy to visualize a system which measures a distance with either ‘feet’ or ‘meters’. A Meter-long distance can be broken down into 100 equal units (centimeters) or 3.3 equal units (feet). 1 meter is approximately 3.3 feet. So 3.3 is a constant called the ‘conversion factor’. Applying the same logic to mass and energy conversion, C²> (a scalar constant) is the conversion factor between E and M. But unlike 'distance', E and M are still fundamentally different things, and far too distinct from each other to undergo any kind of conversion amongst themselves. But Einstein disagreed. He said that they are just two manifestations of the same phenomenon.

If we analyze this equation from a different angle, it suggests that the sum of all the mass and energy in the universe is *constant*. Or another way to put it is - out of the total energy contained in the universe, some is present in form of active energy and remaining is in form of mass or matter and that mass can change into energy and vice versa.

Section B :

Let’s go back to the first fact - Mass contains energy equal to M X C². How much energy is that really? Let’s consider an example. The most common unit to measure energy is 'Joule'. 1 Joule of energy is what is required to lift up a small fruit in your hand. So how much energy does 1 gram of mass (matter) have? 1 gram of matter at rest has following amount of energy as per the equation E = MC² (C is approximately equal to 3, 00,000 Kilometers/second. Remember, 1 Kilometer = 1000 meters)

Energy in 1 gram of mass = 0.001 Kg X 300000 Km/s X 300000 Km/s = 90000000000000 Joules (or 90 TeraJoules)

To get an idea of the magnitude of this energy, consider following two scenarios:

- 90 Tera Joules is equal to 25000 Megawatt-hrs. This means converting 1 gram of mass completely into energy would fulfill the power requirement of city of Pune (Population: around 37 lacs or 3.7 million) for an entire month, and that too without any load shedding :)

- 'Little Boy', the nuclear bomb dropped over Hiroshima in 1945 had a yield of around 15 Kilo tons of TNT. That amounts to approximately 63 TeraJoules. The bomb contained 64 kilograms of uranium, of which only 0.6 grams were converted into energy. And how many people were killed? About 1.4 lac (or 140000).

That’s the sense of massiveness, magnificence, vastness that this equation has unleashed upon mankind. As of yet there is no means to extract 100 percent energy from mass. But mankind is hoping that it becomes a reality in future. The research is costly but it needs to be done, given that natural resources and fuels are fast depleting. It could one day open doors to cleaner energy. May be in future we could have a technology - where at one end of a fission reactor, you put in a raisin and on the other get energy enough to light up New York City (Population – around 20 million or 2 crores) for a day. You may say that this idea will forever stay as pure fiction, but so was the perception about cell phones in 80s when we used to watch Captain Clark of Star Trek series talking to his folks through a hand-held wireless device.

Part 2: Conversion of Mass to Energy / Energy to Mass

Authored by: Mandar Garge