MMT explains how fiat currencies work. My understanding is that the Austrian School of Economics would prefer going back to using Gold, or something equivalent (sound money). That is fine, but how would we get from fiat to sound money? There was a reason why the US Government broke the Gold Standard and declared the Dollar as fiat.

In any case, all such systems are human invented and can work in any way we collectively agree - there is no fundamental physics underpinning any economic system. All that actually matters is how a person can mediate with another person for resources they require or desire. We have used various forms of money for centuries to do this (and force of course), but it also happened before the concept of money was invented back in our distant past. The expert stone knapper trading with an expert hunter for example.