The first place to start is with the most famous equation in all of physics, Einstein's E=MC². What this equation is telling us is that energy and mass are two forms of the same thing, and are proportional to each other: the energy (E) of a particle is the product of its mass (M) and the speed of light squared (C²). So, how does this explain the basic mass of an atom?
As you'll know, all atoms are made up of electrons, and nucleons (protons and neutrons). As electrons have a negligible mass in comparison to the nucleons, we can say that the mass of an atom is determined by the nucleus of the atom, which is probably something you'll have learnt in your GCSE science lessons. The link between E=MC² and the mass of an atom becomes more obvious when you consider what's going on inside of the nucleus of the atom: you have a bunch of positively charged protons packed in very close together. According to electromagnetism, the similarly charged protons should repel, but instead they're held together by another of the four fundamental forces*, called the Strong Nuclear Force, . The SNF does a certain amount of work to overcome the repulsive electromagnetic forces, thus keeping the nucleus together. It's somewhat like pushing two magnets together - you have to put energy in to make the repulsive ends of magnets touch. This energy used to keep the nucleus together is called the "rest energy" of an atom, as it exists even when the particle is at absolute rest, and given that energy and mass are the same thing, the atom therefore has to have a "rest mass", which would be the rest energy divided by C².
One place where it's useful to think of mass and energy like this is in a phenomena called "pair production". If an electromagnetic wave has enough energy, it can spontaneously create a pair of a particle and its antimatter counterpart. Using energy-mass equivalence, we can predict what waves will produce what pairs of particles, as the energy of the wave has to be equal to or greater than the mass of the particle and antiparticle produced.
So, where does the Higgs Boson come in to all of this? Well, all I've done so far is explain how the mass of more complicated nuclei is calculated, which is all well and good, unless you want to know why the more fundamental particles have any mass at all. The answer to this question was suggested almost fifty years ago by a number of scientists, including Peter Higgs. They suggested that fundamental particles gain energy (and therefore mass) through their interactions with the Higgs field, which permeates all of space. As different particles travel through the Higgs field, they interact differently with higgs bosons, the bosonic (force carrying) particle of the Higgs field, and thus gain different amounts of mass.
So, I'll leave it at that for this post. Sorry for the lack of posts recently, I've been busy with university applications and the like, and with the first term of my A2s. I was inspired to write this post after the events that occurred at a UCL lecture on relativity I went to. In the lecture, someone asked how the rest mass of a particle was calculated, and he didn't know, so after the lecture I went up to him and explained how I thought you calculated the rest mass, and he thought it sounded about right, and yeah.
Thanks for reading as ever,
GM ^^
(*the others being gravity, electromagnetic, and weak nuclear force)
