Bitcoin creates problems for two theories that attempt to explain why a new fiat money might gain traction and continue to have value - the Regression Theorem and chartal theory of money.
In order to delve into these two theories, here's some data on the debut of bitcoin as a currency that should help out. Back in March 2010, someone tried to offer bitcoin for pizza in but never managed to get a bid. Later in May a bitcoin user named Laszlo finally managed to trade 10,000 BTC for a pizza. Given that the pizza was worth $40, this valued bitcoin at around a half-a-cent each. But even before the famous pizza exchange there were trades going at the Bitcoin Market, a formal bitcoin exchanges. The first published trade from late April involved 1000 coins at 0.003, a princely sum of $3. Back in October 2009 New Liberty Standard began publishing an exchange rate based off the electricity cost of generating bitcoin, though there is no indication of how much trade was actually done.
The thinking behind Ludwig von Mises's regression theorem is that people's expectations "regress" into the past. An intrinsically worthless fiat token (like US dollars or bitcoin) trades at a positive value because it had a positive value yesterday, and it had a positive value yesterday because it did the day before. This regression continues until day 1 of the fiat money's debut. What on day 1 might have generated the positive value necessary to initiate this chain of cause and effect? Mises's answer: the token wasn't a money on day 1, it was already being traded for its non-monetary value. This initial positive value provides the seed that eventually leads to the phenomenon of fiat money. Along the way the money could lose its non-monetary use -- a gold linked currency could be decoupled from gold -- but it will continue to have a positive value.
Bitcoin challenges Mises's Regression theorem because bitcoin never had an initial non-monetary use. They are just bytes. You can't eat them, wear them, or decorate with them.
There are three ways you can proceed with this.
1. Actually, bitcoin did have an initial non-monetary use so the regression theorem still applies. In its initial form bitcoin was valued as a sign of geekiness, a demonstration of one's devotion to technology. Based on this initial non-monetary value, a Misesian progression could proceed. This explains why seemingly valueless bitcoin was eventually accepted in payment for a pizza and why it continues to be valued as money today.
2. No, Bitcoin never had a non-monetary use. It's intrinsically worthless. It's a ponzi scheme. In the short term, people can irrationally bid up the price to some non-zero amount. But in the long term the logic of the regression theorem requires that the price of Bitcoin fall to zero.
3. The regression theorem is wrong.
The second theory that Bitcoin challenges is the chartal theory of Georg Frederich Knapp. The chartal theory of money says that a fiat money gains value because a government places an obligation on its subjects (say a tax) that can only be discharged by payment of those fiat tokens. This generates a demand for the tokens so that they trade at a positive value in the market.
The obvious challenge to this theory is that bitcoin has emerged spontaneously. No government asks that its taxes or bonds be paid in bitcoin. Yet bitcoin is a positively valued money token.
You can go a few ways with this.
1. Bitcoin isn't money, it's purely anomalous. The chartal theory doesn't have to explain it. Bitcoin will fall to zero.
2. Chartalism is wrong.
3. The chartal theory of money can describe a few types of fiat money, and some monetary phenomena, but shouldn't be expected to explain other types of fiat money or phenomena.
I think both theories cut the cake in a way that prevents them from seeing from a better vantage point. They treat money as a noun, not an adjective. The problem with treating money as a noun is that it implies that somewhere along the line of its development, bitcoin crossed some invisible line from being a money to a non-money.
If you think of money as an adjective, then "moneyness" becomes the lens by which you view the problem. From this perspective, one might say that Bitcoin always was a money. A degree of moneyness was attached to it from the moment the first bitcoin user realized that their bitcoins could traded to another user for something else. Bitcoin's moneyness would have only increased as bitcoin became involved in more and more transactions.
If you treat money as an adjective, the regression theorem and chartalist theory are irrelevant. Whether moneyness gets attached to a fiat token issued by the government to discharge taxes, or whether it gets attached to an object valuable for religious or industrial purposes, is unimportant. The degree of liquidity - or moneyness - is the variable of interest.