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I've heard (and after googling for a while, found) that the only difference between matter and anti-matter is simply charge. This bothers me when it comes to the neutron. Matter and anti-matter annihilate when they come together, so in the case of the neutron, what we'd have is just two neutrons coming together; that shouldn't result in anything like a positron and electron- the neutrons are exactly the same!

I can think of two solutions to my doubt. 1) There are other 'subtler' (not so commonly mentioned) differences between matter and anti-matter that would differentiate between a neutron and anti-neutron. 2) Maybe the reason the neutron and anti-neutron annihilate is that the quarks they are made from change (instead of having two down and one up quark, the anti-neutron would have two anti-down and one anti-up quark?). This seems like the most logical explanation to me, although it's kind of strange; the individual quarks would 'do the annihilation', not the neutron itself. Is this what's going on?

Sorry for my ignorance- I know almost nothing about the subject of anti-matter (or particle physics, or even barely any QM unfortunately).

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the only difference between matter and anti-matter is simply charge

Nope. All "quantum numbers" reverse for them. In particular, for the example you consider, there's Baryon number, which is different for baryons and anti-baryons, and in particular, for a neutron and its anti-particle, an antineutron. It is in fact possible to differentiate between the two, in spite of the fact that both of them have identical mass and zero charge. This is by studying what they decay into - their decay products are different. While a neutron decays into a proton, electron and an anti-nuetrino (you probably know that the process is called beta decay), the decay modes of an antineutron would have antiproton, positron and neutrino as the daughter species. The two cases CAN be experimentally distinguished.

So, your possible solution 1 for the doubt is correct:

There are other 'subtler' (not so commonly mentioned) differences between matter and anti-matter that would differentiate between a neutron and anti-neutron.

Actually, if you take into account the quark content for the neutron and anti-neutron, even explanation no. 2 is correct. The two explanations aren't independent, see the baryon number definition (in terms of quark content) in the first link of the answer.

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