March 2014: Explaining the Sub-atomic Octopus

LOM March 14 Figure 1I recall a Physics lesson where the teacher was describing the solar system model of the atom (see Figure 1). “Of course,” he said, “the big problem with this model is that accelerating charged particles emit gamma rays and thus lose energy.” Now this was news to me, but I can see why it would be a problem: if the electrons orbiting the nucleus kept losing energy because of these gamma rays they would go slower and slower until they dropped out of orbit and crashed into the nucleus. Similarly, in order to put something in orbit around the earth, it needs to be sent out of the atmosphere otherwise air resistance will cause it to lose energy and crash to earth. This, however, is not the Big Problem with the solar system model because the BIG PROBLEM with the solar system model is the nucleus. Look at it. Chock full of positive protons and neutral neutrons. Now, I don’t know if you’ve ever tried to hold the north poles of eight magnets together at the same time: it’s not easy, even for an octopus and yet this is the feat routinely accomplished by every atom of oxygen (Figure 2). Everything I was taught suggests that like charges repel and yet here are a bunch of like charges happily cosying up at the heart of every atom. That’s the Big Problem.

LOM March 14 Figure 2Not all Physicists accept the octopus model of the atom and the Standard Model of Particle Physics is generally preferred. It turns out that deep inside atoms there are three types of particles: Leptons, Quarks and Bosons.

Leptons: There are six types of Lepton including the electron. The other five leptons are, no doubt, fascinating but they do not come into this explanation (they are, no doubt, fascinating but sadly irrelevant (FBSI)). Before we move onto more exotic particles it’s important to note that electrons have an anti-particle: the positron. Electrons have charge -1 and positrons have charge +1 (they also have a quantity called spin which is FBSI). Particles and antiparticles are going to come into this explanation several times and so it’s worth giving them a proper think. The first thing to understand is that at the level of very tiny things (such as leptons) odd things can happen and the key equation to remember is that E=mc2 (E is energy, m is mass and c2 is a big number: this equation basically says that Energy is equal to mass). At this level energy is the same as mass: in fact, the mass of particles is often given in eV (electron Volts) which are a unit of energy.

Consequences of E=mc2 (don’t look at me: blame Einstein)

  1. When an electron hits a positron (or any particle hits its antiparticle) they are both annihilated and energy is given out because mass is Energy.
  2. If there is enough energy around then it can condense into an electron and a positron (or any particle and its anti-particle) because Energy is mass.
  3. Actually, even if there isn’t enough energy around a particle and an anti-particle can come into existence for long enough to do something so long as they get annihilated afterwards. These are called virtual particles and the time they can exist for depends on their mass due to the uncertainty principle (the bigger the mass, the quicker they have to disappear again). This happens partly because Energy is mass but mostly because Physics of the very small is quite strange.

LOM March 14 Figure 3Quarks: There are also six types (or flavours) of quarks. Sadly none of the flavours is “chocolatey” and the two we are interested are called “up” and “down”. Up quarks have charge +23 and down quarks have charge -1/3. Up quarks are lighter than down quarks. Both kinds of quark have spin (FBSI). There are also anti-quarks: anti-up quarks and anti-down quarks and they can do the same kinds of thing that leptons and anti-leptons do. Unlike leptons, quarks don’t hang around on their own. Two up quarks and a down quark will combine to make a proton (total charge 1) and two down quarks and an up quark combine to make a neutron (total charge 0). Quarks also come in three different colours. A quark can be red, green or blue (these are no more related to our idea of colour than the flavours of quarks are related to our idea of chocolate. The mental images are useful but are not meant to be taken literally). Anti-quarks can be yellow (anti-blue), magenta (anti-green) or cyan (anti-red) and any collection must combine to be a neutral colour (white). Therefore in any proton or neutron there will be one red quark, one blue quark and one green quark. Red light + blue light + green light = white light. Quarks can also come together in pairs of a quark and anti-quark so long as the colours match (e.g. a blue down quark and an anti-blue down anti-quark can team up); these are called mesons.

Bosons: Bosons are particles that allow quarks and leptons to interact with each other (bosons can also interact with themselves under the right conditions: FBSI). The first example to understand is how electrons repel each other. Physicists like to draw what are known as Feynmann diagrams at this point. Figure 4 shows two electrons approaching each other. A virtual photon travels from one to the other and as a result the electrons move off in opposite directions. Photons are a kind of boson that transmit the electromagnetic force. They have no mass or charge and they are their own antiparticle. Photons are the reason that electrons repel each other and they do generate a large force pushing protons in the nucleus apart.

LOM March 14 Figure 4The important thing to understand here is that the particle (a photon) moving from one electron to another allows the transfer of energy so that the particles settle down in a more comfortable (energetically favourable) state. The precise details of how strong a force is and whether it is attractive or repulsive are FBSI.

The other boson we are interested in is the gluon. This acts within particles such as protons and holds the quarks together. Gluons have no mass or charge but they do have colour: each gluon carries one colour and one anti-colour. Within a proton the quarks are constantly exchanging gluons and being held together by the resulting force. This affects the colours of the quarks. Figure 5 shows an example of an exchange between two quarks.

LOM March 14 Figure 5

If this is beginning to seem tricky then I sympathise. Fortunately there are no new particles or ideas to learn about: the force holding protons and neutrons together in the nucleus (the nuclear force) is a result of the exchange of gluons within the particles.
 

LOM March 14 proton neutron 1-3

  1. We can start with a proton and a neutron. For there to be a force between them we need a particle to move from one to the other. Quarks and gluons are unable to leave the particles because the strong force is so strong! Only colourless particles can escape.


     
  2. In the proton the green up quark can break into a green/anti-blue gluon and a blue up quark (there is still one quark and the colours still add up to the same green+anti-blue+blue=green).

     
  3. The proton can borrow energy from the universe to create a down quark and a down anti-quark. The gluon colours the quark green and the anti-quark anti-blue. LOM March 14 proton neutron 4-6

     
  4. The blue down quark and anti-blue anti-quark can now escape because between them they are colourless. The proton is still a proton. The particle moving between the proton and the neutron is a virtual meson (actually a pion FBSI).
     
  5. On arrival at the neutron the anti-blue anti-quark can annihilate the red quark and just leave the colours as a gluon: red/anti-blue. The blue down quark from the meson joins the neutron so it still has three quarks and colours that add together to make white.
     
  6. The red/anti-blue gluon can join to the blue up quark to make a red up quark. The proton and neutron have exchanged a particle and this means that there can be a force between them.

One interesting aspect of this force is that the meson has mass which means that a virtual meson can only exist for a small time because of the uncertainty principle. This means that the nuclear force can only operate over small distances (photons don’t have this problem and so the electromagnetic force has a theoretically infinite range – although it does drop off as the distance gets bigger.)

The nuclear force explains why the nucleus holds together despite the repulsion of all those positive forces (you may prefer the explanation of the sub-atomic octopus but sadly the large hadron collider has yet to find evidence of such a creature). It also explains (which the subatomic octopus does not) why as nuclei get bigger the proportion of neutrons increases (more nuclear forces are needed to overcome the repulsion). Unfortunately it does not explain why you can’t keep a nucleus stable by adding more and more neutrons to it (you can’t: if a nucleus has too many neutrons it is radioactive and gives off beta radiation). For this we need more bosons (called W and Z: FBSI) and another force: the weak nuclear force. That, however, is learning for another month.