There's absolutely an actual economy backing a fiat currency, and it is essential, otherwise the military cannot be funded effectively, but you can't force the use of a fiat currency without a military. It's not possible, in my mind. You either belong in a union of countries that share the same currency (e.g., Euro), each of which relies more or less in the military of the other, or you issue your own fiat currency, which will inevitably be used to fund the military, and then the military, when needed to defend the nation or attack other nations, will defend the fiat currency.