# Why does antimatter and matter fuse to release energy even though they will cancel each other perfectly?

I have seen many physics people talk about antimatter as a evil twin of matter and when they come in contact with each other leave massive amount of energy instead of only void.

If antimatter and matter exactly opposite to each other why they should leave this enormous amount of energy? They should just cancel out each other leaving only blank space.

Why not positron(+) and electron(-) cancel each other out perfectly to leave nothing?

Please correct me if I am missing something.

• Both have positive energy and energy is conserved, i.e., the energy doesn't 'cancel out'. – Alfred Centauri Mar 10 '16 at 3:51
• What I am missing is the entry "evil twin" in the vocabulary of physics. :-) One thing is true: Mother nature doesn't treat both kinds of her children equally. For some reason that we don't quite understand, yet, she treats one kind ever so slightly preferentially. – CuriousOne Mar 10 '16 at 3:52
• "If antimatter and matter exactly opposite to each other why they should leave this enormous amount of energy?" (It has something to do with the Energy to Mass equivalency that Einstein worked out. E=MC^2). You can't erase mass without creating energy (and vis versa). – userLTK Mar 10 '16 at 3:57
• in fact you are missing all of modern physics understanding – anna v Mar 10 '16 at 6:27
• @All: Say we consider matter as just a form a energy, does antimatter a form of anti-energy/negative energy? If yes what is the by-product of fusion energy and anti-energy? – Xinus Mar 10 '16 at 10:23

They aren't complete opposites. They have the same (positive) rest mass (invariant mass) for instance. And since energy follows the equation

$$E=+\sqrt{(mc^2)^2+(\vec pc)^2},$$

they have the same (positive) energy when they have the same momentum. And further, since the momentum is squared they have the same (positive) energy when they have opposite momentums. And since their rest masses are the same, they have opposite momentum when their velocities are opposite.

Thus, in a frame where they have equal and opposite velocities, they end up with equal and opposite momentums, and they always have equal and opposite charge, but they have equal (positive) mass, equal (positive) rest energy, equal (positive) kinetic energy, and equal (positive) total energy.

The opposite charge is because they are antiparticles and always have opposite charges.

The equal rest energy is because they are antiparticles and so have the same (positive) rest mass (invariant mass). Both positive. Both equal.

The opposite momentum is because of the choice of frame.

The total energy is equal because they have the same mass $m$ and the same squared momentum $(\vec pc)^2$ so the same numbers go into the right hand side of

$$E=\sqrt{(mc^2)^2+(\vec pc)^2}.$$

The rest energy, $mc^2,$ is the same because they have the same rest mass, $m$.

The kinetic energy is the same because kinetic energy is $E-mc^2$ and the (total) energy, $E,$ is the same and the rest energy, $mc^2,$ is the same.

So they both have positive energy. It's like if you had a bank account that required a million dollar minimum balance. That's like your rest energy. As long as you keep the account you aren't spending that money. And as long as you have that mass (and are on shell like real particles are), then aren't giving up that rest energy becasue its the minimum energy you have.

The energy is $E=\sqrt{(mc^2)^2+(\vec pc)^2}$ and the smallest that can be is $mc^2$ and when the momentum is nonzero it only gets larger. When the momentum is very different than zero then the energy can get much larger.

But just like you can get that money by closing your account, you can spend that energy if you get rid of the mass. But the mass was intrinsic to the particle so that only happens when you get rid of the particle itself.

To do that you have to get rid of the electric charge. But you also have to get rid of the other charges, such as lepton flavor/species charges. For instance a muon (which has a large mass) could decay into an electron, a muon-flavored neutrino, and the anti-particle of an electron-flavored neutrino. The total electron-flavor is zero before and after (the electron-flavored neutrino has an equal electron flavor as the electron itself and antiparticles always have opposite charges). The total muon-flavor is one before and after. The electric charge is the same before and after (the muon and the electron have identical electric charge and the neutrinos have zero electric charge).

But the electron doesn't have a less massive lepton to decay into like the muon and tauon do. But the positron is the antielectron. It has opposite electric charge. And opposite flavor. So it does allow the electron to go away. It has its own positive mass (that equals the electron mass) and its own positive energy (which equals the electron energy in the zero momentum frame) and so when everything else cancels there is still some energy.

There are things that can still be different. For instance spin. So when they jointly decay into photons, the photons need to carry away the total energy, the total (vector) linear momentum, and the total spin (total angular momentum).

• In the frame you talked about where they have equal and opposite momentum when they fuse together will their kinetic energy/rest energy results into release of energy? I just want to know where this huge energy comes from. I am assuming momentum and electric charge cancel out completely. – Xinus Mar 12 '16 at 13:06
• Sorry I could not understand that equation [ I am not physics folk ]. I just have very much liking in the field of physics but chose softwares. Please help me understand. – Xinus Mar 12 '16 at 13:13
• One more thing , when you talk about negative momentum, is it mass or velocity opposite to each other? – Xinus Mar 12 '16 at 13:45
• @Xinus It's velocity that is opposite. – Timaeus Mar 12 '16 at 16:55
• @Xinus All the energy is released. The reason it is so huge is because the speed of light is so huge so the energy is really close to $mc^2$. So the particles always have this huge energy but only when they meet their antiparticle and go away is that energy released. Imagine a millionaire who works at a minimum wage got and only spends their paycheck. But when they meet their long lost twin, the millionaire spends all their money. They had lots of money all along but weren't sharing it. The particles have lots of energy all along, a very huge amount, but they don't share it usually. – Timaeus Mar 12 '16 at 17:00