# What barriers exist to prevent us from turning a baryon into a anti-baryon?

At present the only way we can produce anti-matter is through high powered collisions. New matter is created from the energy produced in these collisions and some of them are anti-matter particles such as positrons, anti-protons etc.

My question is, normal matter and anti-matter are so similar. They both appear to react to the fundamental forces in the same way. Is it conceivable that we could find a way of "switching" matter to become "anti-matter" through some low energy technique? E.g. find a way to flick a few "quantum switches" and voila your proton is now an anti-proton, ready for annihilation and limitless energy for humanity!

Would we be breaking a great deal of the fundamental laws of physics if this was found to be possible (i.e. should I give up now)?

Short answer: Give up now. Conservation of baryon number, lepton number, strangeness, charm, bottomness, and most importantly charge are making your job hard.

Long answer: I'm ignoring charge conservation issues from time to time; as its no fun if you take that into account

Well, not baryons or leptons. And we have conservation of charge in the way as well.

## Baryons

We have conservation of baryon number $$B=\frac{1}{3}(\text{number of quarks-number of antiquarks})$$, which has opposite values for particle-antiparticle pairs. The only way to convert a baryon to its antibaryon would be to bombard it with a different antibaryon with (negative) twice the baryon number (And twice the negative charge as well). And that would require energy (to create the antibaryon).

## Leptons

For leptons, we have conservation of lepton numbers $$L_e,L_{\mu},L_{\tau}$$. I doubt any reaction exists where a lepton becomes an antilepton, as leptons can only have lepton number $$\pm1$$, and particle reactions involve two reactants (IIRC). I'm not considering neutrino oscillations here; they make it possible to do stuff like this. The only naturally abundant neutrino is the electron one (maybe not naturally abundant, but easy to generate passively); unfortunately, it's got a very low energy. And the entire neutrino oscillation thing is still debated. Anyways, your neutrino source would be a beta-decaying substance; and there are different,easier ways to get energy from that.

## Mesons

It's easier for mesons, though there still are restrictions (conservation of charmness, topness, bottomness). Due to these restrictions, the only conversions possible would be for these mesons (and their antimesons): $$u\bar{d} (\pi^\pm),d\bar{t},u\bar{t}$$. The last one is anyways in a superposition with its antiparticle, so we get a total of two pairs of particle-antiparticle conversion reactions.

## Guage bosons

(I'm not sure if the gauge bosons can do such reactions)

## Analysis of feasability of mesons

Anyways, the antimatter=limitless energy is something rather overhyped. Over here, we have two possible candidates. $$d\bar{t}$$ isn't an everyday particle (Dunno if it's even been synthesized; top quarks are pretty hard to create, and Wikipedia has no data in its list of mesons), and anyways is pretty unstable. You'd have to pump in a bunch of energy to create it, and that defeats the purpose.

### Feasibility of pi-meson

$$u\bar{d}/\bar{u}d (\pi^\pm)$$ is interesting, as it's a common particle in nuclei. But it's bound inside (not exactly--its part of the virtual particle "sea", but that makes it worse), and decays pretty fast. So you'd have to break apart the atom (yes, you'd get energy from that, but not if you separate it into nucleons), "catch" a pi meson, convert it to an antiparticle by means of the "quantum switch", and collide it with another pi meson (alternatively, without the "quantum switch", you can just find an opposite pi-meson). And that will give you a tiny amount of energy as compared to your efforts. You would also need to supply some oppositely-charged particle to conserve charge. Making it more complicated.

## Conclusion

So nope, it's not a good energy source. It doesn't work for protons/neutrons/electrons; it only will work for two particles (one more if we consider neutrino oscillations). Neither of them is feasible. Stick to fission-fusion.

• Really fun mini-excercise to analyse the whole particlespace; even though charge conservation is in your way the whole time. – Manishearth Feb 24 '12 at 15:20
• Note that if the neutrinos are Majorana particles (a matter as yet unsettled), then a sufficient boost would serve to flip a neutrino to an anti-neutrino or vice versa. Secondly to say that pions are bound in a nucleus is, well, not actually wrong but imprecise. There is no pion valence content, it's all part of the sea. – dmckee --- ex-moderator kitten Feb 24 '12 at 17:28
• If we want to consider the sea, we have problems as it is. virtual particles as it is are useless for stuff like this; you'd have to pump energy to make them real. I guess nucleus pions are virtual particles as well, though. Regarding neutrinos, I hadn't thought about their oscillations. I'll write a note. – Manishearth Feb 25 '12 at 1:02
• That is not about neutrino oscillation (which preserve matterness), but about the distinction between Majorana and Dirac particles. Different issue – dmckee --- ex-moderator kitten Feb 25 '12 at 1:42
• @dmckee OK, didn't know that. I myself don't understand this stuff; feel free to edit it into the question if you want. – Manishearth Feb 25 '12 at 1:50

You would be going against all known particle physics knowledge.

Particles and antiparticles differ by quantum numbers that are immutable in the standard model, i.e. there are strict conservation laws or conservation laws governing interactions that have been proven to hold over and over again .

No such switch can exits, so give up or write science fiction,

As was emphasized right at the outset by Manishearth, the conservation of electric charge is probably the most serious constraint. So expecting the proton to turn into an antiproton is just about hopeless. However, in the Standard Model of particle physics, baryon number is not exactly conserved. More precisely, it is a symmetry of the classical theory, but it is violated by the quantum chiral anomaly. You can think of the baryon (say neutron) and the corresponding antibaryon as two minima of a potential with the same energy, but separated by a barrier. In order for the baryon to turn into the antibaryon, it has to tunnel through the barrier. The tunneling rate is very small. (At zero temperature, it is suppressed as $e^{-c}$ where $c$ is inversely proportional to the electroweak coupling and larger than 100.) Bad news.

Now a bit of theoretical hype. You were asking about turning matter into antimatter as a low-energy process. From the point of view of effective field theory, such a process must necessarily be strongly suppressed. Either it proceeds via the electroweak anomaly mentioned above, or it uses some new, unknown physics. There is no other way, since the Standard Model is extremely well tested in collider experiments. Every time new physics is involved, the probability for processes that it mediates will be suppressed by some power of $E/M$ where $E$ is the low energy and $M$ the mass scale of the new physics. Current experimental limits on new physics that violates conservation laws present in the Standard Model, such as the conservation of baryon or lepton number, are very strict, making the possible scale $M$ very high. In particular, if baryon number were violated by some new physics, it would lead to a decay of the proton into lighter particles. This has not been observed so far, and to appreciate how unlikely it is, note that the experimental lower bound on proton lifetime is currently some $10^{30}$ years.

• Brilliant answer Tomas! – Matt Luckham Feb 24 '12 at 23:19