## Thursday, March 18, 2010

### Holes and antiparticles

In the Theory of Relativity, there is a famous equation involving energy.
E = mc2
No, not that one!  That equation doesn't include kinetic energy.  Here's a more complete equation.
E2 = (mc2)2 + (pc)2
Okay, but if you don't know what all those letters mean, it's just a bunch of math gibberish.  For now, there is only one part of the equation which is important, the E2.  E is, of course, the energy.  But because we squared the energy, it could be negative or positive.  Just looking at the math, both the positive and negative energy solutions make just as much sense.

It may make mathematical sense, but is it real?

Let's go back to the early 1900s.  Einstein published Special Relativity Theory in 1905 and General Relativity Theory in 1915.  Quantum Mechanics became established in the mid-1920s.  If you read popular physics literature, you already know that there is a bit of a conflict between Relativity theory and quantum theory.  String Theory, for instance, is an attempt to combine the two.  But you have to be careful.  The conflict is between quantum theory and General Relativity.  Quantum theory and Special Relativity have already been combined.

One of the big steps towards combining the two occurred in 1928.  Paul Dirac formulated the Dirac Equation, which is basically a quantum version of the above equation.  As it happens, the Dirac Equation has the same issue: the energy can be positive or negative.  This issue was hard to ignore, because the theory predicted that particles would jump between the positive and negative energies.

So in 1929, Dirac proposed a solution called the Dirac sea.  The negative energies are real, but they're already filled up with a "sea" of particles.  As I explained before, it's not possible for two fermions to occupy the same state.  And in quantum theory, the possible energy levels are discrete, meaning you can count them one by one.  If all the negative energy levels are filled, then it's impossible for any more electrons to fall into the negative energy levels.

Each horizontal black line represents an energy level.  The higher the line, the higher the energy.  The red circles represent electrons which fill the levels.

What happens when you give the system a good kick, and one of those electrons in the Dirac sea jumps up to a positive energy?
We got two things out of that kick.  First, we got a brand new particle from nothing.  Second, we got a "hole", an empty energy level which would normally be filled.  The hole is not a particle per se, but a lack of a particle.  It has the opposite charge, opposite spin, opposite everything of a normal particle.  It even has the opposite energy, but since it's in a negative energy level, the opposite of a negative energy is a positive energy.

We can basically treat the hole as a new kind of particle, called an antiparticle.  If a particle is a fermion, then it must have a corresponding antiparticle.  The antiparticle has the opposite charge but the same energy.  The antiparticle of an electron is called a positron.

Antiparticles are awesome because you can create them with nothing but a kick of energy.  This is called pair production.  Also, if a particle and antiparticle meet, they can disappear, leaving energy in their place.  The technical term for this is annihilation.

Motivated by Dirac's new idea, the positron was discovered in 1932 by Carl D. Anderson, earning him the Nobel Prize in 1936.  Incidentally, the positron had been observed in 1923, but no one really knew what it was back then.

Positrons have real applications too.  The P in PET scan stands for positron.  First you inject a positron-emitting tracer into the subject, and then a device detects the positrons.  PET scans can do all sorts of useful things, like find tumors and image brains.  But, hey, don't give physicists all the credit, I'm sure engineers and doctors deserve some too.

Positrons are also a vital component of the positronic brains of sentient androids.

Clearly, antiparticles have many present and future applications.

Going back to our first question, is it real, or is it just math?  Are antiparticles really just holes in the Dirac sea?  Perhaps, but there are problems with the theory.  In most systems, there would be infinitely many energy states, going up higher and higher.  Therefore, there are also infinite negative energy states, going lower and lower.  Are we willing to accept that there is an infinite sea of particles filling those states all the way down?

And if we're talking about electrons (or any other charged particle), wouldn't that mean that a pure vacuum has an infinite charge?  Antiparticles clearly exist, but some of the other implications of the theory are just weird.  So how can the Dirac sea be real?

The answer, I'm afraid is not that satisfying.  Modern quantum theory interprets antiparticles as real particles all to themselves, rather than holes.  The theory is mathematically equivalent to the Dirac sea, and makes the same predictions.  But there isn't any sea anymore, as pretty as it was to look at.  Unfortunately, the goal of a physicist isn't always to make things pretty...

#### 1 comment:

chumbly said...

Well explained article - thanks.

My 2 cents worth is that the cosmos must at heart be digital. So can algorithms and register outputs through the Heisenberg area fit in to the 'vacuum'.

Digitally of course one can create as much matter as there are numbers - which is a lot. So somehow this matter & energy creation in a vacuum makes sense. But I would love to get a clear picture of what is going on.