# Matter Antimatter Equations

1. Sep 26, 2014

### Quarlep

How paul dirac find antimatter equation I guess It came this equation
E2=(pc)2+(mc2)2 than we pass
E2=(mc2)2
than E=mc2 and -E=mc2 isnt it ?

2. Sep 26, 2014

### Khashishi

Close. If we take the square root:
E = sqrt((pc)^2 + (mc^2)^2).
Dirac was looking for a way to express the square root as an operator, and came up with the idea of using matrices to represent the operation. But there were negative solutions for E, for the same reason as you gave, but all without dropping the term (pc)^2.

Dirac assumed that the negative solutions were already all filled up with some infinite sea of negative energy electrons. The "holes" in the negative electron energy levels behaved like positive energy positively charged electrons, e.g. positrons.

Really, Dirac's reasoning here isn't rigorously correct, but he did get the right prediction. To me, it seems he accidentally got the right prediction with a pretty bogus explanation.

3. Sep 26, 2014

### Khashishi

The problem with the idea is all these damned infinities. If there are infinite negative energy levels, all filled, then all the vacuum is filled with a negative infinity energy density, and negative infinite charge density. We have to pretend that this negative infinity all equates to zero vacuum energy, zero charge, and zero of everything else.

4. Sep 26, 2014

### Staff: Mentor

Hmmmm. Maybe. But a careful analysis shows the issues can be rectified.

But its bypassed these days in QFT where the creation operator is interpreted as the annihilation operator of antiparticles and conversely:
http://en.wikipedia.org/wiki/Antiparticle

The QFT approach is more elegant, since everything is treated as a field, but it turns out to be basically equivalent to Dirac's approach.

Thanks
Bill