It is often said that quantum physics is so weird that it is beyond our understanding. According to the great physicist Richard Feynman, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” John von Neumann said that “You don’t understand quantum mechanics, you just get used to it.” Niels Bohr described it as “fundamentally incomprehensible.”

As just one example of freakish quantum behaviour, light behaves in some respects as if it consists of waves – it can be made to produce interference patterns – but in other respects as if it is made of particles, known as photons. Neither the particle nor the wave description is complete by itself. Quantum physics is fundamentally dualistic.

But there is one area where some quantum insights might prove applicable to our everyday lives, and it’s a surprisingly common one: money

Fortunately, such effects only apply at very small scales, so we don’t need quantum physics for things like throwing a ball or driving a car, where the usual Newtonian principles of mass and momentum work perfectly well. Most people, outside of university physics departments and science laboratories, have therefore felt free to go about their lives without obtaining an in-depth knowledge of quantum entanglement or the Heisenberg uncertainty principle.

But there is one area where some quantum insights might prove applicable to our everyday lives, and it’s a surprisingly common one: money. Just as subatomic objects have a dual nature, so do the money objects that we use to make payments. The main difference is that these objects are things we have designed ourselves. They are our contribution to the quantum universe.

Heads or tails
The most fundamental attribute of money is that it is a way to attach numbers to the material world. This fusion between abstract number and physical reality is represented by the production of coins. The first coins were produced around the sixth century BC in Lydia, part of modern-day Turkey, and were made from a naturally occurring gold/silver alloy called electrum. The obverse or heads side was stamped with a symbol such as a lion, which certified their validity, and indicated their numerical value in units of shekels.

This heads side of the coin therefore specified the numerical value, while the unstamped tails side represented the material side of money. In general, all money objects share these two aspects. They have a fixed numerical value, which is an abstract mathematical concept, but at the same time they are things that can be physically possessed, and are linked to real markets.

As with the wave/particle duality of quantum physics, the two sides of a coin represent very different things. Numbers are exact, precise, and obey mathematical rules. Debts for example are represented by negative quantities, which don’t exist in the real world (you can be underwater on your mortgage, but you can’t have a negative house). Interest multiplies exponentially without limit, which real things tend not to.

In contrast, the physical side of money represents positive, material wealth – it is something you own and possess and has value in the real world. This is most obvious in the case of early coins, which were made from precious metal and could be melted down if desired and sold as bullion. This material value is inherently fuzzy and inexact, and depends on exact market conditions. The precise versus fuzzy duality of money therefore resembles the particle versus wave duality of matter. And it propagates through to markets, with the result that there is always a tension between the concepts of exact numerical price and fuzzy real-world value.

Virtual money
Of course, it might seem that an electronic transfer of virtual money over a phone has nothing to do with the minting of ancient coins. But even here there is a physical component. Cybercurrencies represent an electronic transfer, which involves physical electrons, and gain value through links to physical markets. Losing your Bitcoin wallet hurts as much as losing your regular wallet.

Again, the comparison with quantum physics is instructive. The electromagnetic force is mediated by ghostly virtual particles that flash into existence before being extinguished almost immediately; yet their ethereal presence is enough to transmit the electromagnetic force, which is what holds atoms (and the world) together. Virtual money transmits the money force in much the same way.

Money therefore binds the ideas of exact numerical value, and fuzzy real-world value, together into a single package. The fact that these two things are as inconsistent with one another as waves and particles is what gives money its powerful, and frequently counterintuitive, properties.

In the early 2000s, the cheap availability of credit in the US meant that even low-income people could afford their own homes. Some became rich by selling their houses at the top of the market, so for them the money had real, tangible effects. But after the credit crunch of 2007, most of the new money disappeared, as if it had never existed. Money seemed to be both real and unreal at the same time – a sensation familiar to anyone who has peered into the quantum universe.

No one is proposing an economics version of quantum mechanics, but some insights from that field could be genuinely useful in understanding the economy. Mainstream economics has traditionally conflated the separate properties of numerical price, and real world value. Adam Smith argued that the invisible hand would restore prices to reflect “intrinsic” value. Later, Eugene Fama’s Efficient Market Hypothesis said much the same thing for markets. In this view, the two sides of money are compressed to a single point – just as Newtonian physics treats entities such as electrons as something like inert billiard balls.

However, if money is seen as just an inert medium of exchange, which is otherwise like any other commodity, then the economy looks much like a barter system – which is why many economic models don’t include money at all. As Martin Wolf from the Financial Times noted, students of economics are left thinking that we operate in a “barter system where money acts as a veil”. In this view, money is a distraction that can safely be ignored.

Money asserts itself in the gap between number and value – and our inability to understand its complex properties has been demonstrated by financial crises, and also by difficulties with the euro. Before concluding that money is also fundamentally incomprehensible, we might try taking a page from physics, and replace our Newtonian approach to the economy with a theory that puts the confounding properties of money at its core.