Killamajig: Biggus: Molecular adhesion technology, I should think. A post-scarcity society capable of matter/energy conversion can accomplish remarkable things.
tl;dr Star Trek is a fantasy setting; your answer is "magic described with science words".
Anonymous2: @Killamajig: I think Biggus Dickus wasn't wondering how the badges stick to their bodies, but more likely why the hell they would wear them at all during sex.
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tl;dr Star Trek is a fantasy setting; your answer is "magic described with science words".