Antiparticle Mass: Dirac Equation & E=mc^2

[widderjoos]

I've heard that the dirac equation predicts antiparticles with negative energy. Since for particles at rest, E=mc^2, shouldn't antiparticle masses be negative? If this were true, it would explain a lot. I know there's probably a counter-example that if an electron and positron annihilated, they'd make a photon with a certain energy, but couldn't that energy have come from the momenta of the particles? Or are there non-relativistic experiments that rule out this possibility?

 

[bcrowell]

There is conclusive evidence that the inertial mass of antimatter is positive. Its gravitational mass is believed to be positive as well, but there is no conclusive experimental evidence: http://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter

 

[widderjoos]

Thanks for the reply, but doesn't there have to be something wrong with the equations or experiment for antimatter mass to be positive?

 

[mathman]

I've heard that the dirac equation predicts antiparticles with negative energy. Since for particles at rest, E=mc^2, shouldn't antiparticle masses be negative? If this were true, it would explain a lot. I know there's probably a counter-example that if an electron and positron annihilated, they'd make a photon with a certain energy, but couldn't that energy have come from the momenta of the particles? Or are there non-relativistic experiments that rule out this possibility?

Electron-positron annihilation produces two photons each which has the energy equivalent of the rest mass of the electron or positron (511 kev), possibly with a slight addition due to the momenta.


Also radioactive decay leading to positron emission wouldn't balance if the mass of the positron was negative.

 

[Kevin_Axion]

Also the equations that describe anti-particles in Quantum Field Theory don't effect the mass of the particle, only its charge. "Solutions of the Dirac equation contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amount of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower energy states so that, due to the Pauli exclusion principle no other electron could fall into them. Sometimes, however, one of these negative energy particles could be lifted out of this Dirac sea to become a positive energy particle. But when lifted out, it would leave behind a hole in the sea which would act exactly like a positive energy electron with a reversed charge. These he interpreted as the positron, and called his paper of 1930 A theory of electrons and positrons." - Wikipedia

 

[bcrowell]

Thanks for the reply, but doesn't there have to be something wrong with the equations or experiment for antimatter mass to be positive?

I think your interpretation of E=mc² is wrong. First off, let's take units with c=1, so it becomes E=m. Then E=m can be thought of as a special case of the relativistic relation E²-p²=m², where p is the momentum. Therefore it doesn't predict anything about the sign of m.

 

[widderjoos]

I think your interpretation of E=mc² is wrong. First off, let's take units with c=1, so it becomes E=m. Then E=m can be thought of as a special case of the relativistic relation E²-p²=m², where p is the momentum. Therefore it doesn't predict anything about the sign of m.

Ok, thanks everyone! I see what I'm doing wrong now.