Related article at Bitcoin Magazine:
Is bitcoin money? To most readers the answer will be a resounding yes, but to many people, including former Federal Reserve Chairman Alan Greenspan, the answer is less clear. Indeed, one of the things holding back the adoption of cybercurrencies such as bitcoin is that they do not conform with traditional ideas about money.
Read the rest of the article here: https://bitcoinmagazine.com/21616/quantum-theory-money-value/

So my take on this is that we do need a new theory of money, based on the idea that money is fundamentally dualistic, with real/virtual properties that both complement and contradict one another, rather like the wave/particle properties of matter in quantum physics. The theory works well for cybercurrencies because it explains how a currency can boot itself up and attain value without being backed either by precious metal or the state.

Here's the abstract:
A quantum theory of money and value
The answer to the question “what is money?” has changed throughout history. During the gold standard era, money was seen as gold or silver (the theory known as bullionism). In the early 20th century, the alternative theory known as chartalism proposed that money was a token chosen by the state for payment of taxes. Today, many economists take an agnostic line, and argue that money is best defined in terms of its function, e.g. as a neutral medium of exchange. This paper argues that none of these approaches adequately describe the nature of money, and proposes a new theory, inspired by non-Newtonian physics, which takes into account the dualistic real/virtual properties and complex nature of money. The theory is applied to the example of the emergence of cybercurrencies.

The full paper is here: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624371

Agree with all of these, what I'm not clear on is whether bitcoin needs to be backed by electricity (since it is backed by the other things). I understand that the mining process puts a price on the blockchain and is a security feature, but on the other hand it is wasteful of electricity! So is this there just so that bitcoin will be backed by something real (i.e. electricity and computational power)? Is it necessary? And could other approaches that require less energy (e.g. Litecoin, proof-of-stake) work just as well?

People's perceptions are shaped by theories of money. For example Alan Greenspan said: "I do not understand where the backing of Bitcoin is coming from. There is no fundamental issue of capabilities of repaying it in anything which is universally acceptable, which is either intrinsic value of the currency or the credit or trust of the individual who is issuing the money, whether it's a government or an individual." So he is making a judgement about Bitcoin because it does not conform to the traditional idea that money needs to be backed either by intrinsic value (e.g. gold) or by a centralized issuer (e.g. the state).
Agree there is a lot of theorizing about money, but not much of it applies very well to Bitcoin ... Also, money is something that is completely missing from most economic models (e.g. Stephanie Kelton: "Money, debt and finance don’t even fit into many economic models)" which is another sign that the theories aren't working.

Yes, "backed by the state" is losing some of its prestige! The paper came out of a book I'm doing about money. The data points are events that were not available to anyone writing about this even a decade ago - the emergence of Bitcoin and other cybercurrencies.

Agree with the first part, but scarcity itself does not make Bitcoin into money. I would say it does have backing, not by something physical such as gold, or by the state, but by its expanding network of users.

True but some would say Bitcoin is too specialized at the moment to be considered a medium of exchange, see e.g. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2434194
But I think the problem is that the medium of exchange doesn't define what money is, it is more a description of what money does. Which is one reason we need a new theory ...

Conventional theories of money assume that money is backed by precious metal (the theory known as bullionism) or by the state (chartalism) but Bitcoin is backed by neither. Economists also often define money as anything that serves as a medium of exchange, but Bitcoin isn't much good at that either (so far, at least). So does that mean Bitcoin is not money, or is the problem with these theories?
I have posted a paper on this question here, comments/responses appreciated: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624371