This post continues the story of quantum economics, which began here. That post provides important background information on how this series developed and was drafted. There is a summary of posts to date at the end of this post.
Money as Particle and Flow
“Light behaves as a particle. Light behaves as a wave. But light is neither. Light is what it is.” – Albert Einstein (paraphrased)
Physics has long wrestled with the question of what light really is. At times, it looks like a stream of particles, photons, each carrying a discrete quantum of energy. At other times it looks like a wave, spreading out, diffracting, and interfering. Which is it? The answer is unsettling, because it is both. Or, more precisely, it is neither until we choose how to observe it. The particle–wave duality is not a flaw of physics but a property of reality itself.
Money shares this duality. Sometimes it behaves as a discrete thing: a £10 note, a £100 transfer, a specific bank balance. At other times, it behaves as a flow, rippling through the economy, multiplying its effects, circulating in ways that matter more than its discrete origin. Economists and accountants, each in their way, have seen one side and not the other. The truth is that money is both, and recognising this changes how we think about the economy.
First: money as a particle
When we hold a coin or a note, money seems indivisible. A £10 note is not £9.999 recurring; it is exactly £10. You can break it into two fives or ten ones, but until you do so, it remains whole.
The same is true in a bank account. A debit of £100 is a precise entry. The books do not allow half an entry. Double-entry accounting, which underpins all financial record-keeping, insists on discrete units. Transactions are counted in whole quanta.
This particle-like quality of money is vital. It makes accounting possible. It means contracts can be enforced. It means debts can be settled precisely. It is the foundation of taxation, budgeting, and auditing. Without this discreteness, there could be no trust in financial systems.
The problem is that economists, too, often fall back on this particle view when talking about “units of account.” They treat money as a thing, like a brick or a coin, moving around an economy in a predictable fashion. This, however, is only one view of money.
Second: money as a wave
Consider what happens when you spend that £10. Even in a decidedly simplified worldview:
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You buy bread.
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The shop pays the baker.
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The baker pays the miller.
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The miller pays the farmer.
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The farmer pays the worker.
The £10 ripples outward, generating effects far larger than its original size. This is the multiplier effect, taught in every economics textbook. One unit of money, moving through many hands, creates more than one unit of output.
This is wave behaviour. The £10 is not just a particle handed from one person to another. It is a wave propagating through the economy, setting off chains of transactions, amplifying as it goes.
Economists capture this when they talk of the “velocity of money.” If money circulates quickly, it has more effect, just as a wave spreads further if the medium allows. If money is hoarded, the wave dies out, just as sound fades in a vacuum.
This flow aspect of money is harder to pin down than its particle nature. It is not about discrete entries but about patterns, cycles, and circulation. It is what makes macroeconomics, in particular, distinct from accounting.
Third: why the duality matters
It would be tempting to say that money is “sometimes” a particle and “sometimes” a wave, depending on how we look at it. But the lesson from physics is sharper: money is both, and we must hold both together.
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For the accountant, the particle view is essential. Debits and credits must balance. Transactions must be recorded in discrete amounts. Without this, trust collapses.
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For the economist, the wave view is indispensable. Aggregate flows, multipliers, and circulation matter more than any one discrete entry. Without this, policy collapses.
The problem is that too often the two communities talk past each other. Accountants insist on balance sheets; economists insist on flows. Neither is wrong, but neither is complete. Money is both a particle and a wave.
Fourth: policy implications
This duality has profound policy implications.
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Austerity ignores the wave. When governments cut spending to “balance the books,” they focus on the particle view — debits and credits. But they ignore the wave view: that cutting £1 of spending can remove £2 or £3 of output once multipliers are considered. The particle may be balanced, but the wave collapses.
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QE ignores the particle. When central banks pump reserves into banks, they hope to stimulate flows. But if those reserves stay trapped in balance sheets, the particle view dominates: entries change, but no wave propagates. The policy fails.
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Tax myths exploit the confusion. Those who say “tax funds spending” rely on the particle metaphor — each pound in must match each pound out. But in reality, government spending creates flows that expand the economy, while taxation withdraws waves of spending power. The causality is wave-first, not particle-first.
Understanding money's duality prevents us from being trapped in either fallacy.
Fifth: the multiplier as interference
Waves interfere. Drop two stones in a pond, and the ripples overlap, amplifying or cancelling each other.
The same is true in economics. When money flows overlap, they create interference patterns. Two government programmes may amplify each other: investment in schools and healthcare may both boost productivity more than either would alone. Conversely, tax cuts for the wealthy may cancel the intended effects of public spending by encouraging hoarding. I call these spillover effects in my work on tax.
This is why simplistic particle arithmetic fails. £10 of government spending is not just £10. It is a ripple in a complex wave field, amplifying and cancelling with other ripples. Policy cannot be judged by particle sums alone.
Sixth: hoarding as damping
In physics, waves can be damped by friction or resistance. In economics, waves are damped by hoarding.
When money is saved and not spent, it is taken out of circulation. The ripple fades. The velocity slows. The multiplier shrinks.
This is why inequality is so damaging. When wealth is concentrated, more money is hoarded. The rich save disproportionately. Their savings do not circulate into the real economy. The result is damped waves: lower growth, weaker demand, higher instability.
If we thought of money only as particles, we would not see this. But as waves, it becomes obvious: hoarding kills the flow.
Seventh: finance as standing waves
Speculation is another wave phenomenon. In physics, standing waves occur when energy bounces back and forth, trapped in resonance. They can be beautiful, but they can also be destructive.
In finance, speculation traps money in loops of buying and selling assets. Prices oscillate, but little real output is created. This is a standing wave: energy contained, but not released productively.
It can build to destructive resonance. Just as bridges collapse when vibrations reach a critical frequency, financial markets collapse when speculation reaches unsustainable levels. The crash of 2008 was not an accident but the collapse of such resonance.
Eighth: rethinking monetary policy
A quantum-informed monetary policy would look different.
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It would not obsess over particles — the size of deficits, the levels of reserves.
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It would not pretend that flows can be precisely forecast.
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It would focus instead on how spending waves propagate through the system.
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It would target damping mechanisms: inequality, speculation, and hoarding.
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It would design spending to generate constructive interference: investments that amplify each other.
Such a policy would be more realistic because it would respect the dual nature of money.
Ninth: an economy as a quantum field
In the end, the analogy goes deeper. Physics now thinks of particles and waves as excitations in a quantum field. Particles are quanta of energy in a deeper medium.
The economy can be seen the same way. Money is both particle and wave, but beneath both is the field of social relations: labour, land, trust, and institutions. Money excites this field, creating ripples of activity. Without the field, there is nothing.
This helps us see why money is not wealth in itself. It is potential energy. Its real effects depend on the field it moves through — the capacities of labour, the availability of land, and the trust of society. Treating money as if it were wealth confuses the particle with the field.
These issues will be explored further in future posts.
Conclusion
Money is not a thing. Nor is it just a flow. It is both, and more. It is the dual reality of particle and wave, discrete and continuous, entry and ripple.
This duality explains why austerity fails, why inequality damages, why speculation destabilises, and why policy must focus not only on balancing the books but on sustaining the flows.
Economics that ignores this duality is blind. An economics that embraces it can begin to see reality.
Only when we treat money as both particle and flow can we design policies that fund the future.
Previous posts in this series
- Discussing quantum economics, accounting, money and more
- Quantum economics, part 1: Why Quantum Thinking Matters for Economics
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Buy me a coffee!
Therefore, when the Way is lost there is virtue.
When virtue is lost there is benevolence.
When benevolence is lost there is righteousness.
When righteousness is lost there are rituals.
Rituals are the end of fidelity and honesty,
And the beginning of confusion.
Lao Tzu, Tao Te Ching
Much to agree with
At the moment, learning economics teaches the student little of practical use and the “ideas” don’t work, as we can all see. With this framing, the student learns physics, and with a conversion course, they have a grounding in economics. I particularly like the idea of resonance leading to crashes. The BoE and Chancellor as our resonance regulators … now there’s thought!
🙂
It’s fun to see a new metaphor that might help physicists take an interest in the economic decisions that often de-fund their research.
However, this fun quantum metaphor is not yet a model, and chatGPT isn’t going to help with the analytical hard yards needed to get it to be something useful. For example I enjoy the rigour of account-based modelling of the economy practised by yourself and Steve Keen. Modelling the dynamics of iteration from initial conditions, with graphs of selected variables to show how the simulation plays out, period by period is also great.
What I miss are the more graphic visualisation of economic stocks and flows best seen in Bill Phillips’ “hydraulic” model of the pre-war economy (at the London science museum).
Alongside the stocks and flows model, you need the validating structure of a balance sheet view for each actor ‘particle’, eliminating leaks, and then draw the actors in the financial ecosystem as a big picture, to show (animate) the financial and physical flows between them, a ‘system’ at a time, adding the control / motivational signals involved in each system (ie the higher ‘order’ systems).
Each flow should of course be labelled and supported by corresponding entries in accounting tables.
The demographics of actors in this modelling: the large Vs small firms, the rich rentier Vs the low wage earner and so on. Also the different types of capital resources: property, natural resources, intellectual property etc
AI and massive compute power should now be capable of modelling agent-based interactions that are far more predictive of the real economy, and understandable, than the hokum of today’s neoclassical econometric modelling, based on dodgy data.
Are there any heterodox economists getting it together on such a project?
I think that you are fundamentally misunderstanding what I am trying to achieve here. I see all the merits to data analysis, numeric calculation, financial modelling, and more, but that is not my objective here. The fundamental point I’m seeking to make is that them core economic model that we have is broken, and unless we have a new narrative to replace it then no form of mathematical analysis can help us. So, right now, ignore all those mathematical aspects of quantum – although I know they exist – just as much as I know that they do in the world economics, finance and accounting. Instead, focus upon the story because that is key to the creation of the new narrative which has to underpin an economy that can work for everyone.
I think we all agree here that the neoclassical model is broken: It’s based on the myopic assumption that equilibrium is everywhere and is justly ruled by the collective sentiment of ‘perfect’ markets.
I love using AI powered analysis to seek out new and old patterns and apply them in unconventional ways to gain new insight.
But it worries me a bit that if we all go off too far and too fast with an AI powered, Monday morning coffee rush, that we won’t get to do enough of the collective, multi-disciplinary work needed to debunk the economic policies of the wonks in Treasury, BoE, the BBC and the Murdoch press.
I don’t want them to get any rocks to throw.
You did not answer my question.
You were wholly negative instead.
How does that achieve your desired result?
We cannot win without taking risks. Or would you disagree?
My daughter graduated with a degree in physics in 2010. In her final year they had a physics career day, and nearly half the suitors were the big banks, offering double the graduate scheme salaries and beyond compared to the rest of science and industry, who were complaining about the shortages of talented physicists. Meanwhile the Bank of England is recruiting Oxbridge economics graduates to work their way up the velvet drainpipe in the treasury.
No wonder the banks are running rings around governments.
I love the parallels drawn between Newtonian mechanics and Quantum mechanics in relationship to money. Newtonian mechanics is fully deterministic and works really well for most things, although it doesn’t like vibrations, oscillations or shear. It falls down because time is treated as a constant and Einstein has shown that time is in fact a variable. Relativistic physics better describes the universe but even it breaks down with singularities, such as black holes and the Big Bang.
Superposition is the bewildering heart of Quantum Mechanics and in your example the instant a credit is made a debit is made instantaneously elsewhere. The world is clearly non-linear and non-Newtonian, like toothpaste, and it follows naturally that the economy using Fiat money is likely to behave in a quantised manner. Even photosynthesis employs quantum coherence and superposition to move energy from sunlight with extraordinary efficiency which defies classical thermodynamics!
Sorry if I was a little incoherent.
You made sense to me!
The playful part of my brain is tickled by this whole quantum analogy. It’s a fun thought experiment that will (hopefully) get people thinking about the nature of money and economics, which is all to the good.
My concern is that this analogy is not entirely applicable for one good reason – Quantum Mechanics is a science, whereas Economics is very much an art. Trying to treat an art as a science almost always ends in confusion… not least because those who hold an opposing view to the proposer will latch on like limpets to whatever bit of the scientific system doesn’t fit the artistic reality like a glove. All of a sudden, the good message and laudable goal of inspiring meaningful discussion on economics is lost in a morass or whataboutery and stretched, tenuous metaphors.
I really hope people embrace this as an opportunity to expand their understanding and engage with different ideas, not treat it as a new arsenal of rocks to throw.
Let me be clear: I am not trying to use the science of quantum, and if I think you really understand what a lot of quantum physicists do, they are as much engaged in philosophy as they are ever with mathematics (which is anyway, just a branch of logic). In other words, I am not pretending that we are creating science, and quantum may not be that in any case: what I am interested in is the creation of new narratives. I think it works in that sense. And remember, all we have a models, and some are more useful than others, and that is what this experiment is about.
Is it psychological insecurity or ignorance, or a combination of the two that fails to see the logic in using money to socially engineer society so that all people feel financially secure and therefore happy in this aspect of their lives? As it stands we have politicians like Rachel Reeves who are obsessed with counting up “particles”! They really need to be challenged on two things. A coherent explanation of the origination of those “particles” in the first place and how counting up “particles” benefits the economy when in reality the private sector is constantly engaging in the opposite engaging in a “wave” like use of money with mortgages, bank loans, corporate bonds, shares, derivatives, etc. all of which entail future liabilities.
Agreed.
@ Schofield
Your analogy tickled me, and I couldn’t help but imagine someone handing Rachel Reeves a glass full of water and asking her “how many waters do you have in that glass?”
🙂
“Wow!”
That worked for me, and released all sorts of ideas I would not have had on my own. I was surprised how much it stimulated.
“Without the field it is nothing.”…
If Spinal Tap performed on the moon, even with the volume turned up to 11, we would hear nothing.
Which is why worshipping Mammon is so stupid. Put Mammon on a pedestal/altar and it becomes nothing, or worse than nothing.
“Standing waves” as a destructive force, like that new bridge in the City, near St Paul’s that wobbled woyyingly and had to be reinforced. Trading money to make money, then losing money in the 2008 global crash. “Occupy” and all the hope and sadness that flowed from it, including in St Paul’s itself.
As I said,
“Wow!”
Both on Saturday, at Michaelhouse (ironically, because this became part of Trinity, which is where Newton worked, of course) and yesterday, at Welney Bird reserve where we spent more time talking about quantum biology than we did about the birds that we were saying, we went through a series of wow, wow, wow moments. I now have ideas for around 20 blogs on this team, and I have a rather strong impression that the next 10 are already forming in my mind. They will be a loop back from the findings of the first two series into Newtonian economics to demonstrate why current economics does not work.
My understanding of economics is somewhat limited, but as a physicist by training I have problems with several of the analogies drawn here and in the preceding blogpost. For instance, a resonance catastrophe happens only when more and more energy is put into the system (e.g. a bridge being driven to ever stronger oscillation by some external force, e.g. wind or soldiers marching in unison); the energy in the oscillating system will not increase by itself but dissipate via friction, unless some outside source puts new energy inside. Also, a collapsing bridge is a system which can be described completely within classical mechanics, as is indeed true for most macroscopic systems; classical mechanics is a good approximation for most systems one meets in everyday life, and therefore is a foundation of physics and taught to every first year student. The microscopic quantum-mechanical foundation of the properties of the materials involved are interesting, but not necessary for the understanding of the macroscopic system; they become necessary when one wants to know why one material has different properties (mechanical, electric, …) than another.
I think I understand the ideas behind these thoughts on quantum economics, and they make a lot of sense to me; maybe the analogy is simply stretched too far for me to accept without criticism. I do not object to the economics proposed, it is the physics part of the comparison that bothers me, and the details of that are probably not essential to the ideas proposed.
My goal is to replace a failed narrative. I am not trying to replicate quantum physics in economics. All I am trying to do is aid understanding by creating a new narrative. How else would you do that without the use of metaphors that might be of value? What metaphor might you prefer?
I would add, we are trying a version of this now using quantum biology as a basis, and that might produce better outcome. I am not saying I know the answers as yet. So, your criticism is entirely valid and I accept it. I’m just interested in what you would do instead.
Trying again… Sorry: I really didn’t mean to be so rude earlier – the coffee 🙂 I am very supportive of your goals and I really appreciate efforts to replace that failed popular ‘household budget’ narrative of Mrs Thatcher and the general pretence that markets always tend to equilibrium in the aggregate economy. This winds me up almost every day on BBC Radio 4.
Physics has a lot of potential metaphors to contribute to the understanding of the economy, but for me, quantum theory mechanics, applied to money, is not the most accessible metaphor for the debunking of the orthodoxies above. If it were me, I’d still pick atomic and particle physics as a metaphor, but I wouldn’t not choose ‘money’ as the ‘particle’. It’s too much of a stretch for me.
Sticking with atomic/molecular/particle physics, I would instead point out the hopeless simplification in orthodox economics of the economic agents that ‘imagine’ simplistic, predictable equilibria resulting from the interactions between them. See this A – level economics stuff, for example: https://www.youtube.com/watch?v=2BhOvkAGZNU. There is huge diversity and complexity in behaviour of any one agent – family, mum, dad, child, firm, conglomerate, fin institition, association, ecosystem market …. etc etc …and their interactions. Hence the inadequacy of the neoclassical models, with their inability to predict the credit crunches or crashes. I suppose you could go further down the road into quantum duality, superposition and entanglement to highlight the difficulty, but this already makes me think of Steve Keen’s rather negative use of the physics metaphor in his satire of the ‘ferir’ and the ‘nairu’ https://7robots.com/2018/01/economics-taking-con-economics-kindle-edition-stevekeen-miguelguerra-suzydias/.
Perhaps there is some potential for agent-based computational economics to do a more dynamic ‘show and tell’ to help debunk the orthodoxy. See https://en.wikipedia.org/wiki/Agent-based_computational_economics. My original question was whether you and other ‘heterodox economists’ have any interest in working together on such a toolkit, because it’s a big, and urgent job, given the growth of AI controlled autonomous economic agents.
I think you will find this develops…as the series does
My thinking is sitll open minded…
We are trying other particles
Money has aspects to it that look like the particle, but I end uo thinking there is a better particle
If we consider the words “economy” & “society” as partly synonymous, then there is a growing energy flowing into the system even as the money flows out/upwards
It comes from the pain of the people, their anger. The bridge is humming and vibrating already, at least it is here.
A small technical correction. “A £10 note is not £9.999 recurring; it is exactly £10.” But 9.9999 recurring is exactly 10.
No it isn’t
There are various ways to see that they are equal. E.g., 0.9 recurring is 3 times 0.3 recurring. 0.3 recurring is 1/3. 3 times 1/3 is 1. This is one of those fun and surprising maths facts that I think it’s good to teach in school, alongside more practical things.
I have to disagree. Asymptotically 9.999 recurring can never be 10. You are wrong. And nor is 0.3 recurring 1/3, precisely. It never can be. The fraction in the decimal are not the same. I think you are making a category error.
This post makes a lot of sense. I struggle to see how/why economists could argue against it? Perhaps I didn’t pay enough attention during my economics degree 20 years ago… (albeit maybe I shouldn’t admit to having studied the dismal “science” here!)
🙂
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