# If atoms never “physically” touch each others, then how does matter-antimatter annihilation happen?

It is known that matter and antimatter annihilate each others when they "touch" each others. And as far as I know, the concept of "touching" as our brain gets it is not true on the atomic level since atoms never really touch each others but only get affected by different forces.

If this is true, then when does the annihilation really happen ? Does it happen when two atoms are affected by each others repulsion force for example ?

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I am not sure what does "physically 'touch'" mean. Matter-antimatter annihilation does not have to involve atoms, like $e^+ + e^- \rightarrow 2 \gamma$. They are described by the fields. If their fields (wavepackages) come together, then the scattering (matter-antimatter annihilation) happens –  user26143 Aug 10 '13 at 12:48

You should not think a particle as point like. Classically, the probability of two point like particles colliding with random location and velocity is 0, that is why you said it never happens.

However, at quantum mechanical level, these particle are described by wavefunction. It means that there is spreading in its spatial location, say 0.1nm (the minimum spreading is guaranteed by Hiesenberg uncertainty principle). The probability of annihilation can therefore be calculated by the overlap of these wavefunction and their interaction. This overlap is the meaning of "touching" in some sense.

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"You should not think a particle as point like." Apparently, not everybody agrees: "As far as we know the electron is a point particle." –  bright magus Jul 23 at 16:44
It can be (and is) simultaneously true that electrons scatter like point-particles (down to $10^{-18}\,\mathrm{m}$ experimental precision) and that their bound wave-function gives significant probability to distances on order of $10^{-10}\,\mathrm{m}$. –  dmckee Jul 23 at 19:22

When one is in the micro level of particles one has to stop thinking classically, i.e. with terms we have developed from our macroscopic observations.

"Touch" at the particle level can be defined as "interaction". Our feeling of touch actually does involve the electromagnetic interactions, we touch with the field of the molecules in our hand the field of the other objects, and this touching involves the exchange of force carrying virtual particles, i.e. particles which do not have definite mass but retain their quantum numbers characterizing them.

There is a precise mathematical description given graphically by the Feynman diagrams:

The diagram translates one to one with integrals that give the probability of this interaction happening. The exchanged electron in this diagram( or positron, depending on how one reads this) is virtual, it does not have definite mass.

Then the closer the e+ and e- are to each other the larger the probability that the scattering will result to an annihilation. So annihilation happens according to the probability of interaction.There are higher order exchanges but they give much smaller probabilities.

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There is no proven interpretation about what 'really' physically happens in subatomic level, only mathemathical expressions and heuristic pursuit explanations.

The mechanical explanation of what 'happens' will vary according to what theory you are focusing, but no theory for now can fully satisfactory explain the entire subatomic universe, so its safe to say that we dont know yet how the 'touching' really works.

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What do you mean by a "proven interpretation"? –  user26143 Aug 10 '13 at 14:07
I meant a interpretation that doesnt have flaws and works in every studied level. –  eJunior Aug 10 '13 at 14:29
Then what's wrong with QFT? –  user26143 Aug 10 '13 at 14:47
For one thing, there is no explanation how gravity fits the model, and it fails to explain how the energy can possibly emmerge from nothing, supersymmetry hasnt gotten any proof yet after decades of study. There are LOTs of theoretical explanations derived from the theory that doesnt relly on empirical evidence. Im not saying its wrong just maybe incomplete, but the point is QFT in essence is just the mathemathical expressions behind it, and most theories derived from it that try to explain 'reality' dont relly on evidence, just creativity trying to explain why the equations are what they are. –  eJunior Aug 10 '13 at 15:22
@eJunior Interpretation is not science. Interpretation is to understanding as philosophy is to science. We have solid science on QFT and have even developed technologies (scanning tunneling microscopes, quantum computers, etc.) which take advantage of our well-founded understanding of it. –  KidElephant Jul 23 at 17:15