Who hasn’t heard the equation E=mc2? Very,
very few people. If you know only one scientific equation that would be it. We know
that Einstein came up with the equation and that it stems from the theory of
special relativity but many of us do not know what it really means or why it is important. Well, today we are going to learn together.
It again goes back to the photon which has no mass but has momentum. This is strange since momentum is all about velocity and mass. How then can
a photon exhibit momentum? The answer according to Einstein was to
equate the energy that makes up the photon to a specific quantity of mass. The way that Einstein proved this idea was to
think of a stationary box placed in the middle of space, a photon is inside the
box which due to its obvious momentum travels from side to side, the momentum
needs to be conserved so the box must also begin to move. If the photon hits the side of the box, the momentum is then transferred to the box and voila
the box again is made stationary. The one thing that we need to note is
that there are NO external forces acting upon our box and photon combo so
therefore the centre of mass must remain in the same spot the entire time (even
when the box moves). The only way to make sense of the immobile centre of mass
is to give the photon’s energy some sort of mass equivalence.
Alright, now let’s look at the math. (c= speed of light, v=velocity,
M=mass box, Δt = change in time, Δx= distance moved, E=energy or the photon,
L=length of box, m= mass of photon)
M(Δx/Δt) = E/c
Since the momentum of the photon is the speed of
light and the momentum of the box is its mass multiplied by the velocity and we know the momentum is conserved
we can make this general equation.
Next, if we say that the change in time equals the length of
the box divided by the speed of light then with some rearrangement and applying the idea
that the photon has mass (so we can calculate the centre of mass of our system), we can end up with this little equation: (since the centre of mass is the same
at the start and end of the experiment).
mL = MΔx
(If you want all the steps you can find them on this
website: http://www.adamauton.com/warp/emc2.html)
Let’s look more carefully at this equation; it proves that energy and mass essentially can be used to measure the same thing. By
this I mean that Einstein basically said mass was simply another form of energy
– mind you it is very, very, very concentrated energy. So, how does this relate
to nuclear energy? Well fission is the process by which neutrons are shot
towards the nuclei of atoms, this splits the atoms releasing energy and neutrons. At the end of the process if we were to actually calculate the mass of the
product it would be just a little bit less than the mass of the reactants –
this means that the mass went somewhere and Einstein proposed that it went to
energy. If the quantity of mass that is missing is so small why do we get
such large energy releases from nuclear bombs/power plants? this again can be
referred back to the equation E-mc2 ; since the speed of light is so
very large and then we take that number and square it; the result is A LOT of
energy produced. Think of it this way for every kilogram of mass the impact can
be equated to more than 40 megatons of TNT! That is a lot of energy. Take your weight in kilograms, if we could harvest all the energy inside you; you could
power millions if not billions of homes. However, if we were to try to release all the energy nuclear
fission would simply not work since it only releases a small amount of the
atoms mass and most of it remains in its original form of
protons/neutrons/electrons. Therefore we turn to other ways of releasing energy such as using antimatter; it has the same particles as matter but opposite charges. The sad thing is that
currently we need to actually use particle accelerators to produce antimatter
and it would take millions of years to produce very small quantities of it.
Special relativity is a theory that states with speed comes greater mass, essentially this explains how particle accelerators work
(accelerate protons to as close to the speed of light as possible and hit them
together – this smashing produces particles of greater mass than protons which
could be studies by scientist, Einstein’s equation being a large contributor
since it would give insight into these new particle masses.)
I know what you are waiting for - the grand atomic bomb. I
have already talked about the importance of the speed of light and how the
majority of the energy we see produced comes from the speed of light however we
have not looked at how this explains the atomic bomb. To do this we need to give
Einstein some credit since his theory made other scientists realize the atomic bombs
potential; however, the equation was not meant for destruction when it was first
published. The bombs were created by the process of a bunch of fission chain reactions
(called meltdown reactions: when there is a consistent flow of neutrons released hitting more and more
uranium atoms resulting in greater amounts of heat which melt everything surrounding
the uranium). If you didn’t already
grasp this the idea behind the bomb is to smash a bunch of uranium together in a
short amount of time to create a fast fission process. During World War II two
bombs were dropped containing the power of about 20 kilotons of TNT.
http://www.emc2-explained.info/Emc2/Fission.htm#.VivgwPmrSUk
http://www.theironsamurai.com/2015/08/28/word-is-worse-than-the-atomic-bomb-technical-writing-nightmare-quote/
http://www.theironsamurai.com/2015/08/28/word-is-worse-than-the-atomic-bomb-technical-writing-nightmare-quote/
