“Why does E=mc²” Book Overview
Why does E=MC² and more importantly, why should we care? I’ll detail a book explaining just that by Brian Cox and Jeff Forshaw, whose names you may recognise. This equation, showing how the increased relativistic mass (m) of a body times the speed of light squared (c²) is equal to the kinetic energy (E) of that body, is perhaps the most famous thing associated with Albert Einstein, aside from the comical hair. The book is an informal and easy to understand guide for everyone by not only demonstrating the theory and proof of this equation but also the purpose with a familiar insight into the use of it into ordinary lives. The first half of the book derives (showing how Einstein reached the conclusion of) the theory, what energy is, how mass affects the energy and how on earth Einstein even linked something like the speed of light to it. The latter parts of the book show how this equation “underpins our understanding of the workings of the universe”. What is mass? Why is nuclear power the most efficient? Why do stars shine? Modern particle physics then follows, and the book concludes with the biggest effects and questions this (at first glance simple) equation and its relationship with the structure of space and time.
Space and time…what are they? One may imagine space as a desolate void of blackness and time as the tick of your watch. Einstein’s theory is a description of space and time and at the centre of THAT is the speed of light, the universe’s speed limit, almost exactly…300 thousand km per second, 8 minutes from the Earth to the Sun. However, it’s nowhere near infinite and so we can imitate this speed, such as the 27km hadron collider which accelerates objects to a fraction of a percentage of the speed of light. Space, however, is more complex. The example given about “moving in a plane” proves there is no such thing that was can detect as staying still in motion, as the person is moving relative to the plane and the plane moves in relation to the Earth and the Earth to the Sun etc. To pinpoint an area exactly would be with a three-dimensional grid which could extend out infinitely. There cannot be proof of absolute motion, as the ground may be moving in the exact opposite direction in the same speed in one way. Therefore, we can only talk in relativity, the plane moves relative to the ground, space has no obvious centre of movement. Motion is expressed as speed and speed can be measured in terms of time. The speed being the only immutable concept, the control variable, means there is no experiment which can prove absolute time.
Equations can reveal deep connections between quantities that are not immediately apparent from the results of the experiment (as well as let you predict the results of an experiment without conducting it), an example being Maxwell’s electric and magnetic fields, written because the equations were the only way to link the vast phenomena into a single unified set. The unapparent correlation between the two variables only existed when an extra piece was put into his equations not mandated by the experiments. Maxwell added the displacement current to keep mathematical consistency and so Maxwell’s equations predicted that “the ratio of strengths gives the speed of the waves”. Maxwell’s waves travelled at exactly 299,792,458 meters a second! The same as light! However, there was no talk about the speed of the source or the receiver. This was due to the belief that light travelled through a medium (a substance that makes possible the transfer of energy from one location to another, especially through waves).
Water waves can only exist in the presence of water etc and since light can travel through everything, even the vacuum in space, there must be a medium which is consistent everywhere, which scientists name “ether.” It’s strange stuff though, how everything can go through it without being impeded and so in 1881 A.Michelson and E.Morley devised an experiment measuring the speed of light at different times of year, to which there was no difference, showing inconclusive results and therefore Einstein abandoned the whole idea of ether for his theory. If we are to follow Maxwell’s equation, (imagine running alongside light from a torch) the light would still recede away from us at the same 300,000 km, an assertion that the speed of light is a constant in nature.
As said before, spacetime is a representation of the two linked and due to Occam’s razor (make the simplest hypothesis and gradually build it) Einstein’s equation demonstrates the connection between space, speed and time. This notation may already be recognised in distance over speed equals time, but the 4-dimensional view of actual spacetime is defined by Einstein’s equation. To spare you an extra 20 minutes, I’ll summarise and say the theory was formed based on directional vectors. Just as a vector can point north, it can also point in a spacetime direction. Any two points can be linked with virtual arrows in this concept, like the spacetime velocity vector which represents the 3D version in the 4D spacetime. And so, Einstein found the links.
This equation shows how mass is more than a measure of the stuff something contains, it’s also a measure of the latent energy stored within the matter. If unlocked, we have an enormous amount of energy “at our disposal”. The conversion of mass to energy happens everywhere, absorbing heat from fire and through things like nuclear power we can use this to our advantage. The everyday method of heating to take this harness this energy or the expensive nuclear fission for a huge amount of our energy. The conversion of mass to energy is not an exotic process and just like the firewood which turned to ash becoming lighter due to the energy escaping. The difference would be equal to the amount of energy discharged divided by the speed of light squared, which is what the formula shows.
The conversion is fundamental for everything in nature. The equation also explains how stars are formed, which greatly expands our knowledge of the universe and more practically it shows us how to harness nuclear power, neutrons are fired at the nuclei of uranium atoms, which causes the uranium to split into smaller atoms. The process of fission releases energy, as explained through the theory, which simultaneously describes how matter is just a “super concentrated form of energy” and so things can turn from one to the other. The most famous use of this equation, the biggest breakthrough, the thing which was the most reliant upon this equation was the atom bomb, and while this fusion and fission can be deadly, it can also greatly impact normal social lives.
So then. The particle physics and deep understanding of relativity theory extend beyond what I could convey within a few paragraphs, but I hope I’ve shone some light on the complicated world and discoveries of our scientists behind the scenes.
As a book overview, I hope to have given you just a flavour of how much this work of art is worth a read. You may now know some of why E=mc², and why we care about it. But for the other 99% of what I took from the book, you need to pick it up yourself.
Faaris Haque
Image Credits:
https://en.wikipedia.org/wiki/Four-dimensional_space
https://www.energy.gov/science/doe-explainsnuclear-fusion-reactions
