E = MC2: PART 2: Converting Mass to Energy / Energy to Mass

Continued from Part 1 ....

It’s easy to get examples of mass being converted to energy. When you burn coal into ash, you are using up the binding force (which holds the ‘molecules’ of that substance together) to get energy. You are releasing the energy that is holding up atoms and molecules together. Molecules break down and atoms recombine to form new molecules of resulting byproducts. Weight of byproducts after burning process is lesser than that of original coal. This is nothing but mass converted to energy. The amount however is extremely minute with respect to original mass of coal. On the other hand when you trigger nuclear fission you are basically breaking down the atom (nucleus) of an element and converting some atomic (nuclear) mass into energy. The mass of the nucleus before fission is slightly more than the sum of the masses of the separated elements of the nucleus. The difference is what got converted to energy. In other words, this energy is dormantly trapped inside the nucleus, and as long as it stays trapped, it shows up as that 'differencial' mass.

Nuclear reactors and nuclear bombs work on this principal of 'nuclear fission'. However, for the same original mass, the percentage of mass converted to energy is much higher in case of nuclear fission than conventional ways like burning fuels. Hence fission process has much higher yields. The process of fusion is also associated with mass-to-energy conversion. When you fuse two atoms (protons) of hydrogen to form helium, the united protons together weigh less than the sum of individual protons. The difference is converted to energy. 'Hydrogen' (or thermo-nuclear) bomb works on the same principle and so does the Sun of our solar system.

But it’s hard to imagine processes where pure energy gets converted into mass or matter. What is Matter? Matter in its simplest form means - protons, neutrons (and electrons because they also have mass, although minuscule). Protons and neutrons form the nucleus and electrons are moving around the nucleus. These three act as building blocks in making up atoms, which in turn make up molecules that make up different elements and compounds. If you pull out a proton (or a neutron or an electron) from a nitrogen atom and replace it with a proton (or a neutron or an electron) from an oxygen atom or any other element’s atom - Nitrogen would still remain Nitrogen. Hence matter boils down to protons, neutrons and electrons.

When the big bang happened approximately 13.7 billion years ago, all you had was energy (thermal and electromagnetic. Remember, light is electromagnetic radiation). That energy spread over and in bits and pieces, started getting converted into 'Matter' or 'Mass'. First Hydrogen was formed since it is the easiest one to be created when it comes to creating matter from scratch. Why easiest? Construct a nucleus with only one proton and you have Hydrogen atom. (That’s also the reason why Hydrogen is most abundant in universe). Then gradually other elements were created and chunks of these elements started grouping together to form different compounds and celestial bodies mainly stars and planets. So there you go - energy got converted to matter.

But where did that initial energy that triggered the big bang come from? The accepted answer is 'God'. But assuming that God also is made up of matter, how did he get created? I don’t know :)

I don’t think human quest would reach that far. But the Particle Accelerator experiment at CERN, is attempting to get closer to the time just after the big-bang. It aims to create a miniature big bang which will lead to creation of 'matter’ from scratch. But wait a minute. How would you create the big-bang without having enough energy to cause that big bang in first place ? Of course, you can’t create energy but can covert it from some matter, cant you? The CERN equipment will try to do exactly that. It will try to energize protons (which is matter in its simplest form) to travel at speeds close to that of light. These protons would then have enourmously high amount of energy. These high energy protons would be banged into each other to create a mini big-bang. So here, matter (protons) is being converted into energy (big bang) and that energy is expected to be converted back into new matter (or ‘mass’).

But one important thing is that big-bang will produce two types of matter - 'normal' matter as well as 'anti-matter'. Normal matter is positively charged. Antimatter as a matter of fact, is still ‘matter’ and has the same 'mass' as its corresponding matter, but has 'negative' electric charge. Yes, it is matter with mass that has ‘negative electric charge’. (Note - its ‘negatively charged’ and not 'negative' mass, which supposedly does exists. But its a totally different theory and no need to worry about it here). How can that be? Does mass have a charge? Yes. It does and we don’t usually have to worry about it, because the positive charge of the mass will be detectable only if there is a negatively charged mass in its vicinity and we don’t have any negatively charged matter around us. An electron (with negative charge of 1 electron-volt) will not let us know that it has a negative ‘electric’ charge unless we let a positive charge venture into its vicinity. And what happens when positive and negative ‘electric’ charges combine? ‘Nothing’ - may be a spark. The charges neutralize.

So what would happen when matter and anti-matter come together? No, not ‘nothing’ this time. Remember, we are dealing with masses (positive scalar quantities) with 'opposite' charges. The charges will neutralize but mass quantities will add up and annihilate to create ‘Pure Energy’. Union of matter and anti-matter will create energy with 100 percent efficiency (meaning 100 percent of matter gets converted to energy)

Thinking of the reverse process, we know that matter got created during big-bang 13.7 billion years ago. But does it also mean that equivalent amount of anti-matter was also got created under the rules of E=MC²?. That’s what scientists at CERN are assuming. A section of the scientific community has always believed that antimatter was also created with matter when big-bang happed. They conclude that anti-matter is somewhere out there far away in the universe, dormant like a sleeping dog but when you get closer to it, it would growl and pounce on you to cause total annihilation and creation of 'pure' energy. The other section of scientists disapprove this theory (of equivalent amount of anti-matter being present somewhere in the universe)

So you get the idea - how mass and energy are inter-convertible and how they are two different forms of the same thing? Einstein proposed this theory in 1905, but rest of the world took decades to grasp this revolutionary concept.

If you come so far, I believe you will be interested in knowing more about what has ‘Speed of Light’ got to do with this Energy and Mass conversion? If you are, please visit the following link:

Part 3: How is 'Speed of light' involved in the conversion ?

Authored by: Mandar Garge

E = MC2: PART 3: Why is 'Speed of Light' involved as the conversion factor?

...Continued from Part 2

This could be hard to explain. Its definitely not as easy as explaining why the conversion between meters and feet is ‘3.3’. But I will try my best. Remember, the equation E=MC² is a part of Einstein's work on his ‘Theory of Relativity’ and ‘C’ was a term pivotal to that theory. Einstein was particularly fascinated by Light, its speed, its properties. During his work on Theory of Relativity, it dawned upon him that C - the ‘Speed of Light’ (or an electromagnetic radiation) in vacuum has to be constant in all frames of reference (The fundamental basis of Theory of Relativity)

- The first assumption in his theory of relativity was that C, the speed of Light in vacuum, was always constant for observers in all frames of reference. So me, standing on earth (one frame of reference) and you travelling in a rocket at around 15-20 times speed of sound (second frame of reference), or our friend travelling at half the speed of light (third frame of reference) – all will measure the value of C to be the same (approximately 300,000 km/s).

- The second assumption was that laws of motion should apply the same way to all systems travelling at constant speed ‘relative’ to each. So if you are travelling at half the speed of light and I am at rest on earth, you can say that you are at rest in your spaceship and earth is travelling at half the speed of light. So we are travelling at constant speed ‘relative’ to each other and both can apply the laws of physics (for example Newton’s laws of motion) the same way in our own systems.

So C is the only thing that remains constant in all frames of references, the only thing that is ‘absolute’ with an ‘absolute’ value of 300000 km/s. Everything else is ‘relative’. For laws of motion to hold in all frames of reference (which measure C to be the same) – Time, Distance, Mass, Energy - have to adjust in order to maintain the constantness of C. Einstein proposed that, for a system moving at constant speed with respect to a system at rest – ‘Time’ would slow down, ‘Distance’ would be compressed, ‘Mass’ and ‘Energy’ would increase (with respect to the same terms measured in a system at rest). The “extent” by which time, distance, energy, mass differ in two systems moving ‘relative’ to each other – is determined by formulas - all of which contain the term ‘C²’.
For example assume that system is moving at a speed of 'V' m/s. Then as per equations of theory of relativity, the slowed-down time (t') of that system with respect to time (t) measured in system at rest is:

t' = t (1-V²/C²)^½

So as an example assume that you are travelling at 60 % the speed of light from point A to B, and I am at rest. If ‘I’ measure 10 minutes in my watch as your travel time from A to B in my frame of reference, then ‘I’ would measure 8 minutes (80 % of 10) in your watch which is operating in a system that is moving relative to my system at 60 % the speed of light. That means ‘time’ in your frame of reference, has slowed down, as observed from my frame of reference.

Based on the same principle, In order to keep C (Speed = distance/time) constant for both frames – distance (or length) must also reduce in value (compress). So if the spacecraft in which you are travelling is actually 10 meters long, I would see it compressed to 8 meters from my frame of reference (applying the same equation for distance). But you in your own frame of reference would measure yourself as 10 meters. Confused? The point is that time and distance that I measure in your system, are different than what I measure in my system.

It’s not important that you understand how Einstein arrived at these equations. What is important is the role played by the term ‘C²’. Apply the same logic to Energy. Yes you guessed it right. The difference between energies of the two systems moving relative to each other at constant speed must be having term ‘C²’ involved somewhere. Einstein figured out that when objects emit energy in form of heat, sound, light etc (or decay and emit radiations) they were actually losing mass. The form of energy being emitted was not important. So for purpose of calculation of this equation, Einstein considered a system where a body emitted light (radiation):

From frame of Reference of Object at Rest:

"Energy of an Object _{before emission} = Energy of that object _{after emission} + Energy emitted"

Then he applied the same equation for the frame of Reference that was moving with respect to object at Rest.

"Energy of a moving Object _{before emission} = Energy of that moving object _{after emission} + Energy emitted by moving object"

Then he compared the observations in the two systems for calculation of the emitted energy and arrived at a conclusion that - when a body emits energy 'K', its mass diminishes by an amount = K/C². This means the mass of the object depicts how much energy it contains.

This explanation is surely a very short excerpt. But the gist is that Einstein formulated E=MC² as part of Theory of Relativity where the term ‘C’ plays a pivotal role. The equation was proved decades later in 1938 when German scientists successfully carried out fission of uranium for the first time and found that the energy released during the fission due to loss of mass was exactly in line with this equation (A Swedish physicist named Lise Meitner was the one to prove this).

Even today most of the mankind doesn’t see what terrific revelation is hidden in this equation, but Einstein visualized it more than a century ago. What a revolutionary and mind-blowing concept it has been.

Authored by: Mandar Garge