How did the Dirac equation predict antimatter?

[daveed9]

Hi I'm curious,

how did the dirac equation predict the existence of anti matter? what was the mechanism that made physicists believe it existed?

Thank you

 

[Fra]

Not trying to give an accurate description of history but in short if you take Newtons mechanics (E = P^2/2m) and plug in the QM operators(E -> ih-bar d/dt etc), you get the schrödinger equation. It's nonrelativistic QM.

If you instead try to make a relativistic QM, one might try ( E^2=(pc)^2 + (mc2)^2), that gives you the so called klein gordon equation.

Then the problem is how to find a sound interpretation the negative energy solutions of the equation, that did not involve twisted stuff like "particles going backwards in time etc".

Then various interpretations came up.

By a change of variables, one can transform the klein gordon second order eq to a first order dirac equation. Anothre interesting thing here is that the so called spin of the two views are different. The klein gordon supposedly describes a spinless particle. This makes the relation to the equation for a half integer spin more interesting. In this limited context, the plain transformation between klein gordon and dirac is somewhat interesting.

So one could say it was the problem of coming up with a consistent interpretation relativistic quantum mechanics, lead to the idea of antiparticles.

/Fredrik

 

[merryjman]

Right, Fra's explanation is good. To clarify a simple point: when dealing with the electron from a quantum and relatavistic viewpoint, Dirac found that some solutions to his equations were just like electrons but with negative energy. At that time, they had no reason to believe "antimatter" existed, but here it was, staring them in the face - the new theory demanded it. I believe that at first Dirac envisioned a "hole" in a sea of electrons which behaved like a positively charged particle. Decades later, evidence was found for actual antimatter particles.

 

[CompuChip]

I believe that at first Dirac envisioned a "hole" in a sea of electrons which behaved like a positively charged particle.

And actually, we still use the idea of the Dirac sea in our modern physical theories.