The bizarre similarity between money and quantum physics

I don’t know about you, but I’ve always found money very puzzling for various reasons. Especially when it comes to what the banks do with it. I’ve never been quite convinced that money actually exists: it’s a number that we do things with. If you pay me for something, your number goes down and my number goes up. If my number goes down to zero and my bank won’t let it keep going then I’m in big trouble, because people won’t hand things over to me in shops and so on. To do that, they want me to make their number go up.

And I’ve never really understood how “the money supply” can be increased. Coins and notes can be printed, sure, but whose are they and how do they get into circulation without somebody in effect “stealing” them? Is it actually valid to create it out of nowhere? All very strange.

The subject came up again when my friend PamBG, who once worked in finance and is now a Methodist minister, wrote a puzzled post about “quantitative easing”.

She didn’t get the answer to her question, some discussion ensued about the nature of money, the value of a company’s stocks, and the like. (The more I think about these things, the more convinced I become that money is really just a mental trick.)

As it happens, I had to study quite a lot of quantum physics at university, for my electronics degree. (This isn’t surprising, since quantum physics is the physics of the extremely small, electrons are extremely small, and electronics is based on their behaviour.) And in studying that, I had the same sense of things only just existing, or not quite existing. (I mean, an electron exists but doesn’t properly know where it is or how fast it’s going, or if it knows one it doesn’t know the other; that’s roughly what the Uncertainty Principle says.) It seemed very much like a game played with certain rules and numbers. A game which happened to predict very well what measurement you’d get if you did a particular experiment, but a game nevertheless, which simply dealt with the numbers and rules and was silent about the actual nature of the physical objects playing the game. All it said was that they obeyed the rules. (Scientifically, all that can be studied is the rules and numbers, since they can be observed; all we can say about any underlying reality is that if there is one, it’s one which fits them.)

And it also so happens that I find the ideas of quantum physics easier to “grasp” [1] than the ideas of finance, so the analogy that follows was a bit of a breakthrough for me. Here are some shortened extracts from the later part of the conversation:


In some senses ‘money doesn’t really exist’ – which was people’s complaint when the West went off the gold standard in the 1970s. (Previously, all money printed had to have a certain value with respect to an ounce of gold.)

And markets are driven by psychology. Fear and greed. A very simple explanation: financial instruments are priced according what people will think that they will be worth in the future. So, if a particular company is expected to grow by 5% per annum over the next two years, and its assets are now £100, its stock price would be £110.25. (This is hugely simplistic for illustrative purposes.)

The problem, of course, is that you have to guess how much everything is going to grow [. . .]


[. . .] I heard on a radio programme that the first time there was a real banking crisis after the Bank of England formed, people were very unhappy about paper money, complaining that it wasn’t actually money.

It’s interesting: atheists accuse us of basing our lives on something that doesn’t exist, namely God, but arguably modern society runs on something that doesn’t exist, namelly money! (I’m only half joking.)

ISTM you’re saying that the value of a piece of paper simply exists in the mind of the buyer and seller.


Yes, I think it probably is. It’s a corollary of ‘something is only worth what a buyer is willing to pay for it’ [. . .]


Bizarrely, there’s a parallel with quantum physics, too [. . .]

In quantum physics—the physics of the ultra-small—a quantity generally exists in an “indeterminate” state until it is measured. The act of measurement forces it to stop being indeterminate and have a definite value.

Similarly it seems to me that a house, say, doesn’t have a definite value until you measure the price by letting somebody pay for it.

So in a way, the financial value of something is always in the future and hovering on the brink of existence.



Tim – Not only does that seem quite correct to me with respect to money and financial markets, but you’ve just helped me to better understand that principle in quantum physics.

And maybe that’s why money is so confusing. In quantum physics, you mostly don’t know things like the position or momentum of a particle; you only know the probability of it being within a particular range. And, according to the most widely accepted interpretation, the particle doesn’t “know” either. It really doesn’t have a precise position or momentum until it’s “observed” in some way.

Similarly with money: your house doesn’t have a precise value except at the moment of sale. All it has is a particular probability of lying in a particular price range. And the same is true of the the things in which your money in the bank is invested.

And it seems to me that this might be why the economy gives us so much grief: we’re dealing with things which have at best a shadowy existence, but much of the time we treat them like the most concrete reality there is.



[1] I think it was either Heisenberg or Schrödinger who said that if you weren’t confused by quantum mechanics you hadn’t understood it; hence “grasp” in quotes. Back

8 responses to “The bizarre similarity between money and quantum physics

  1. Just in case there are any financial wizards lurking, can I point out that I did note in my edited comment that my example of asset pricing was hugely simplistic.

    And I’m afraid that I still understand more readily how ‘money exists but doesn’t really exist’ than I understand the Uncertainty Principle. I’m afraid that I always need to visualise stub-atomic particles as little bits of matter whizzing about. Which is probably part of my problem.

    • Actually I mostly visualise them that way too, but whizzing about so fast and randomly that they turn into a fuzzy blur. Which is wrong, but visualisable!

      I’ll edit your disclaimer back in . . . Done!

  2. Don’t worry about adding the disclaimer!

  3. Feynmann is known for a quote about how if you think you understand quantum mechanics, you really don’t. In trying to find the exact quote, I came across this one (that I like better) from Neils Bohr: “Those who are not shocked when they first come across quantum theory cannot possibly have understood it.” I like this because it allows for shock while still leaving hope for understanding… 🙂

    Somehow, I am comfortable with the idea that speed and position are interrelated, such that (for a small enough particle) once one is measured the other spreads out into more of a range. What made it easier for me to see was thinking of position as just some property that a particle has (within some error bounds) and this property can also have a rate of change with time. No property can never really be known exactly precisely (with absolutely zero error), and minimizing the error range of the property can only be done by obscuring the rate of change of that property… and vice versa.

    Money makes much less sense to me! I guess this is because it is an invented concept, subject to the chaotic influences of many human foibles acting all at once. Its fuzziness, though, is much easier to understand now that I can think of it as the same kind of indeterminacy that creeps in over time, after a quantum measurement is made!

    I am curious about how far this analogy can go, particularly whether the analysis of monetary value can be helpful in studying the universe. Is the relationship restricted to being an analogy, or is there anything like money in physics? Perhaps energy, being the potential to do work, can be analogized to money, the potential to buy stuff… and just as work done may end up storing potential energy, items purchased may be thought of as stored monetary value. AHA– the difference is that energy is conserved (it can be only changed in form) while money is constantly increasing! So maybe money is more like entropy…

    I’m going to stop there, because I have to draw the line somewhere. I may come back and brainstorm more, or see if anyone else takes the idea and runs with it. Cheers! Great article!

  4. I prefer Bohr’s version too. 🙂 What’s the source?

    I think I see what you mean about rate of change: to know its precise value at a given moment you have to look at a single point on the curve, meaning you can’t see the slope. That’s not intuitive for me though, because I find myself saying “Yes but I’m pretending there’s a precise curve and there isn’t”.

    I’m not sure how I visualise it. With energy and time I imagine the energy sort of boiling in and out of existence (like virtual particles), with the boiling being more violent at shorter timescales… Ah, and distances too….

    Yes, That’s how I visualise it: the particle is naturally fuzzy and spread out, and the more you try to squeeze it down to a point the more violently it fights against it, so the more wildly its momentum varies. So I’m imagining hidden variables (the random whizzing about of the particle as I try to confine it). But I find the energy–time relation the easier one to imagine.

    It seems to me that quantum indeterminacy and financial indeterminacy are connected by the impossibility of predicting the future in a random or apparently random context, but is the source of the randomness the same?

    Some people have theorised (rather successfully, if I remember correctly) that the economy is a chaotic system, i.e. one whose behaviour is deterministic but so complex as to appear random. (Excuse me translating for the non-mathematicians.) That might be true if it’s such a macroscopic system that the decisions of individual people become irrelevant. In that case, financial randomness would be unconnected to the quantum version and be in the same category as, say, a chaotic orbit for a planet.

    Or the economy might be influenced by the decisions of a few key people, in which case it would depend on the nature of brain processes. Is what we perceive as free will (1) truly free, (2) actually random and outside our real control, or (3) a deterministic illusion caused by our awareness of other possibilities than the one we inevitably choose? Are brain processes sensitive enough for quantum effects to be relevant? (This is the kind of thing Roger Penrose talks about in The Emperor’s New Mind).

    Actually someone’s decision what to pay for your house definitely depends on their individual brain, so brain processes are relevant.

    I think you might be on to something with entropy—isn’t it described these days in terms of information loss/randomisation? It seems to me that money is in fact information, which is why it’s not subject to conservation laws.

    The other obvious similarity is that money comes in quanta: in Britain, quanta of 1p each. But I’m not sure whether that gets us anywhere.

    It would be easy to get carried away with this . . . 🙂

    By the way I’m glad I’m not the only person who thinks quantum physics makes more sense than money!

  5. Perhaps energy, being the potential to do work, can be analogized to money, the potential to buy stuff… and just as work done may end up storing potential energy, items purchased may be thought of as stored monetary value. AHA– the difference is that energy is conserved (it can be only changed in form) while money is constantly increasing! So maybe money is more like entropy…

    Maybe I don’t really know enough about Physics to comment, but one problem is that the value of money is theoretically subject to huge shocks. It can lose its value entirely overnight although mostly that doesn’t happen. Wouldn’t entropy be a more gradual process?

    We really need someone who understands both physics and the financial markets here to translate. 😉

    • Entropy was originally just viewed as disordered (hence unusable) energy, and the disorder needn’t be gradual locally—imagine something like a car crash, an explosion, or an asteroid hitting the Earth. That would create a lot of disorder very quickly. (I’m hoping Qrystal, as an “official” physicist, will back me up on my explanation; I hated thermodynamics, which is the bit of physics with entropy in.)

      So that actually means that your metaphor of a huge shock can still be accurate.

      Except entropy can only increase, whereas financial fluctuations might be reversible. So that might be the problem with the entropy idea.

      This is interesting. 🙂

      Anyone know a physicist with lots of money? 😉

  6. Right, Tim: disorder doesn’t need to be gradual at all. (I wasn’t much of a fan of thermodynamics either: I found it quite TdS.) As for Bohr’s quote, I don’t have a ‘reputable’ source for it. It was a random finding on a blog that didn’t say where it got it from.

    Also, when you mention the definite curve and how perhaps instead the particle should be thought of as being fuzzy, I realized something else I should say about that: particles are actually wave packets. A wave packet is spread out over a range of positions in space, and it can also be described as a sum of waves having a range of speeds. If the range of speeds is reduced, the range of space is increased, and vice versa.

    Also, I strongly suspect that the economy is indeed deterministic, and that the causes of all changes and fluctuations are due to choices people make via their own free will (or via the crowd mentality that sways their will). Each person has a very small but not insignificant effect on the system, and larger business entities may have larger effects (though they are run by people) — actually, I bet the effect on the system has to do with how much money a person has!

    I also think you have it bang-on with the idea that money is information. But then since entropy is a loss of information, then money is more like the inverse of entropy. Or maybe value increases because of lost (or ignored) information, and money is just a way of ordering value. There is an intriguing connection here, we just have to tease it out!

    On reading Pam’s response, I realized that I might’ve made an erroneous assumption about the economy: that the net worth of the entire world is increasing (like entropy). I made no assumption about the rate of increase, though I don’t see how it could be constant — unless I’m wrong about the idea of the net worth of the planet, and that it actually stays at zero.

    Thus, I was thinking of money as a whole increasing, as opposed to the value of certain things which can of course fluctuate in both directions. Similarly, entropy as a whole is always increasing, though individual events may cause increase or decrease, and at any rate.

    What I’m wondering is, what do financial gurus have to say about this idea? What IS the “net worth” of the entire world, and how is it changing? Does more created value (products, ideas, things worth buying) reduce the value of everything else?

    Disclaimer: I have absolutely no formal training in anything related to the economy, so I apologize if I’m throwing terms around that I don’t quite understand.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s