Every particle has its antiparticle, which is an exact copy of itself with opposite charge. Sometimes antiparticles have special names, like the positron, the anti-particle of the electron. Sometimes those names are boring: the muon has the anti-muon, the neutrino has the anti-neutrino and so on. Because particles and antiparticles are equal in all aspects except for charge, they can annihilate: when they meet, they vaporize into a bunch of photons, at least two of them. A classic example of this is electron-positron annihilation, which happens when an electron bumps into a positron.
Antiparticles were predicted for the first time by Paul Dirac. Dirac’s suggestion was a bit weird: he thought we live in a sea of negative-energy particles and that positrons are “holes” in that sea. Nowadays we have abandoned the idea of a negative-energy sea, but the positron has stayed with us. So what is a positron exactly? One way to look at it is as an electron going back in time. This was a favorite of Richard Feynman, though other physicists may tell you that positrons are just regular, positively-charged particles and that’s that. I will stick to the “going back in time” picture because it is way cooler. To understand how this work, we need to know a bit about how quantum particles work,
Quantum particles come with a timer on them. You can imagine it as a tiny clock that spins as time passes. How fast this clock spins is related to the energy of the particle: a high-energy particle’s clock will spin faster. In quantum mechanics we call this the “phase” of the particle and it is an abstract mathematical property, but you can imagine it as a clock and you won’t be far from the truth. What happens when the energy is negative? It turns out the clock spins the opposite way. So negative energy is really related to how this particle moves in time, just like momentum is related to how it moves in space. By convention, positive momentum tells us a particle moves to the right; by convention, positive-energy particles move towards the future, whereas the other ones do so towards the past.
So what will a particle travelling back in time do? Exactly the opposite as one that travels forward. If, for example, the electron is attracted to a proton, then the positron will be repelled. Which means that the positron appears, to all intents an purposes, as an exact copy of the electron with positive charge.
Do anti-particles have negative mass?
Antiparticles do not have negative energy. If they did, when they annihilated with an electron there would be nothing left. Instead, we get photons with a combined energy of roughly twice the mass of an electron. However, is it possible that anti-particles have negative mass?
The short answer is we don’t know. Gravity is really hard to probe at small distances, because any other force is way, way stronger. So there is no way, for now, to measure the gravitational force between, say, an electron and a positron. If anti-particles did have mass, they would attract each other and be repelled by regular particles. The fact that anti-particles have positive energy would point to the fact that they also need to have positive mass, if you believe in Einstein’s theory. Like everything in physics, we won’t know until we do the experiment.