I'm sort of annoyed by the notion that "you can't prove a negative". It's true when we're talking about empirical evidence, but it's only a specific case of "you can't prove anything". There's nothing at all special about negatives. It's just that at no point can we ever say "Well, that's it, our confidence in this belief is now 100%" (even though we can get damned close). Of course, sometimes people say "proved" to mean "supported by evidence to the point that all reasonable people should believe it". In that case, you can prove negatives just fine.
I think that the "can't prove a negative" thing must originate from the subtler "it's hard to confirm the null hypothesis", but even that one isn't a hard rule, so long as you have lots of statistical power.
I think that the "can't prove a negative" thing must originate from the subtler "it's hard to confirm the null hypothesis", but even that one isn't a hard rule, so long as you have lots of statistical power.