By far the most famous equation in the whole history of humanity is this little gem here: E = mc2. It stands among the great achievements of humankind, be it in literature, politics, science, the arts or design. It has all the attributes to be the top rockstar of equations. It’s easily recognisable but at the same time it’s not easily understood by the masses. Most people might read it as a relationship between energy and matter but that’s wrong. Others might fail to interpret what the ‘c’ and the ‘2’ stand for. Granted it’s not as straightforward as 1 + 1 = 2 but, still, it’s worth knowing what it means for the sole reason that without this interesting fact of nature (that E and m are equivalent), there would be no life as far as we know it. Just for that simple fact alone, I think it’s important that we appreciate this equation and its implications. We have to thank Albert Einstein for bringing this beautiful jewel to light for it does shine brighter than all the stars put together.
So what does E = mc2 stand for? E represents energy, m is for mass and c denotes the speed of light in vacuum. Fine, that’s how we read it but what does it actually mean? It tells us that this thing we call ‘energy’ and this thing we call ‘mass’ are actually equivalent, that they are the two faces of the same coin, that you can go from one to the other (granted it’s not easy but it’s possible), and that a small amount of mass is sufficient to give a large amount of energy due to the large value of the square of the speed of light.
It’s easy to mistake ‘mass’ for ‘matter’ because, as far as we can tell, in our constant interaction with matter, we cannot distinguish one from the other. We are made of matter and we know, we feel, that we have some weight (and therefore some mass), there is substance in us, there is stuff, we are material, physical objects. The chair we sit on, the spoon in our hand, the water we drink, all of the material stuff we interact with every day, has this thing we call mass or weight, whether they’re heavy or not. So for us it’s easy, it’s normal to think of matter as being the same as mass. And that’s fine, we can live with that. We can go about our daily business without this knowledge of matter not being the same as mass and we’ll be fine. But we cannot let this misconception distort the most beautiful equation. Even if it’s true that every material stuff has mass, it is not necessarily true that if something has mass then it must be a material stuff. There are things, physical entities, that have mass yet cannot be deemed to be matter.
This leads us to ask what mass is. Mass is the property of a physical entity which impedes its state of rest or motion. That is, if something is at rest then to make it move one has to overcome its inertia. If that same thing is moving then to make it move faster or slower, again one has to put some effort to change that state. This resistance to change one’s state is inertia and mass is that quantity which represents inertia. The more massive, the bigger the inertia.
There is another way to describe mass and it has to do with the force of gravity. Now that might seem like a circular argument because whatever has mass also exerts a force of gravity and whatever exerts a force of gravity must also have mass. True, this looks like a circular argument. But if we take the analogy of a magnet, as example, then a magnet is a thing which has this magnetic field around it which can either attract or repel other magnets and only magnets would feel the influence of that force in the field. Likewise, mass is this property of a thing which interact with a gravitational field. So two masses would attract each other through the mutual influence of their gravitational field.
So, we have two approaches towards understanding mass. One has to do with inertia and is therefore known as inertial mass. The other has to do with gravity and is known as gravitational mass. Newton and, later, Einstein have shown that these two ‘definitions’ of mass are equivalent.
Now, why should anything possess this quantity called ‘mass’ in the first place? Well, for this we have to look at something called the Higgs boson. In a previous blog, called Higgs, I’ve explained this. For now, let’s carry on with understanding the world’s most famous equation.
Light, for example, is something which is immaterial, it doesn’t constitute of matter, yet it has mass. We know for a fact and we’ve verified that light has mass because it can be influenced by a gravitational field. There is this observed phenomenon called gravitational lensing whereby light from a distant star or galaxy can be ‘bent’ or distorted on its way to our telescopes as it passes near massive stars or other massive celestial objects. Also, the fact that even light can be completely absorbed into a black hole is proof that it has mass.
Mass, whether it’s a very subtle concept or not, is at the heart of Einstein’s well known equation. Everything that possesses mass also possesses an equivalent amount of energy. How much exactly? Well, take the speed of light, multiply that by itself and then multiply that quantity by the amount of mass. The speed of light, in vacuum, has a value of about 300 000 000. Square this number and you get a value of 90 000 000 000 000 000. now, consider a litre of water, it has a mass of 1 kg. This means that if we were to convert that litre of water into energy, we would end up with 90 000 000 000 000 000 joules of energy. How significant is that? That would be enough to keep an average bulb in your house lit for about 70 million years! Now imagine what we could do with so much energy if just a litre of water is enough to keep a bulb alight for a million times our average lifespan. If only we could harness all this energy from mass then we would have all the energy we’ll ever need. But things aren’t that simple. Converting mass into energy is, well, quite a demanding task.
The most common place where this energy-mass conversion occurs is at the heart of stars. Inside them there are the right conditions for such extreme reactions to happen and convert mass into energy. We cannot just get energy out of mass, we have to put in some energy to get something out of it. It is, as far as we can tell, the most efficient form of harnessing energy. However, it has its disadvantages as well whereby not only is it good to have an efficient source of energy but it is more important to ensure that this system of energy production is safe and economically viable. As yet, we still haven’t found a way to make nuclear fusion worthwhile. Nuclear fusion is the reaction in which nuclei of atoms fuse together to form heavier elements and release energy in the process. This happens all the time inside stars, our Sun included. The nucleus of hydrogen atoms merge together to eventually form the nucleus of helium atoms. Hydrogen is the simplest and lightest of chemical elements. Next up is helium. So hydrogen atoms turn into helium and other, heavier, chemical elements through the process of nuclear fusion. This process carries on and on and this is how the Sun (and other stars) are able to burn so bright. The Sun is essentially a big ball of burning helium gas. In fact, the Greek god of the Sun is called Helios and you can already see the connection between this divine character and the chemical element we named helium. If you add the mass of four hydrogen nuclei together you get a little more than the mass of a helium nucleus. The difference in mass can be accounted for by the release of energy resulting from that fusion process. For us to sustain what would essentially be the core of a star within our mundane laboratories is so far very challenging. I ‘m not saying that it’ll be impossible for us to be able to produce energy using nuclear fusion but for us to reach that technological possibility will take some time and effort. If we do reach that stage in our technological evolution then it would be such a giant leap forward for our species. We claim that taming fire was a big jump forward for our species but this would be a glimmer compared to our mastering the technology of nuclear fusion. We would, quite literally, be holding the heart of the stars in the palm of our hands.
But this is mere speculation. For now, what we have to content with is the knowledge that without the basic equivalence between energy and mass, lighter chemical elements would not be able to give rise to heavier ones, stars would not be shining, more complex would not be formed, and life, life which is essentially an amalgamation of complex chemicals sustained by the energy from the Sun, would not be possible anywhere in the Universe, let alone here on our home planet. Plants, which are at the base of the food chain, depend directly on the energy from the Sun to be able to photosynthesise their nutrients, releasing the oxygen vital for our existence. The energy from the Sun is a by-product, an after thought if you will, of the nuclear reaction going on inside it. This energy comes directly from the merging masses of the particles in the guts of the stars. What Einstein has achieved is to be able to give us a clue as to how this energy can be accounted for. And the simplicity of his equation is a wonderful example of how elegant the Universe is in its workings even though the processes might appear complex to us.
To state that E = mc2 is a beautiful equation only in its mathematical form is to miss the point that the concept it encapsulates is at least as potent as the nuclear reactions going on inside stars, and to release its true meaning is more powerful than the energy required to sustain life. We cannot overestimate its importance.