Noam Chomsky, stating (correctly, in my view) that social relations are not the same as physics, but meaning (incorrectly, in my view) that they are simpler to understand, in his 2011 book

It’s not quantum physics.How the World Works.

While the use of quantum models is becoming more popular in the social sciences including economics, it is still the case that when many people, especially those with a training in physics, hear the expressions “quantum economics” or “quantum finance” they immediately get confused, stop listening, and reach for some off-the-shelf arguments about why it must be nonsense (or some smelling salts). Here is a compilation of the usual ones, along with responses.

- Quantum mechanics was developed for subatomic particles, so it should not be applied to human systems. As one website claimed, “It’s only when you look at the tiniest quantum particles – atoms, electrons, photons and the like – that you see intriguing things like superposition and entanglement.” An article wonders why we “see the common-sense [classical] states but not the imponderable superpositions?”

**Response:** Bohr’s idea of superposition and complementarity was borrowed from psychology, as when we hold (or ponder) conflicting ideas in our heads at the same time, and the concepts of mental interference or entanglement are not so obscure. Also, many ideas from quantum mechanics such as the Hilbert space were invented independently by mathematicians. And calculus was developed for tracking the motion of celestial bodies but we don’t ban its application to other things.

- Quantum is too hard for non-physicists to understand. According to the physicist Sean Carroll, “No theory in the history of science has been more misused and abused by cranks and charlatans – and misunderstood by people struggling in good faith with difficult ideas – than quantum mechanics.”

**Response:** There is often a confusion between quantum probability, which is a mathematical tool, and quantum physics, which is about subatomic particles. Yes, the physics of subatomic particles is complicated – so are things like classical fluid dynamics. But quantum probability is just the next-simplest type of probability after the classical one. Most of the basic ideas involve simple linear algebra and some calculus. And the misuse of mathematical models which has created the most societal problems is the classical methods used in economics. As a side note, most people involved in quantum economics and quantum finance are physicists or (like me) mathematicians. Which brings us to:

- Quantum economics is physics envy, or an attempt to “appropriate the high prestige of physics” as one physicist put it.

**Response:** Mainstream economics is directly inspired by, and based on, concepts from classical mechanistic science. There is nothing inherently wrong with using the same mathematical tools for different areas, what is strange is when the tools used don’t change or adapt. As John Cleese said: “people like psychologists and biologists have still got physics envy but it’s envy of Newtonian physics and they haven’t really noticed what’s been happening the last 115 years.”

- Quantum is flaky, pretentious, pseudoscientific hype or woo. Sample usage: “As a quantum physicist, I’ve developed a reflexive eyeroll upon hearing the word applied to anything outside of physics. It’s used to describe homeopathy, dishwasher detergents and deodorant.” Cue nerd jokes about “quantum healing” or “quantum astrology”. In his description of what he called the Intellectual-Yet-Idiot, Nassim Taleb included anyone who “Has mentioned quantum mechanics at least twice in the past five years in conversations that had nothing to do with physics.” Science writers with no domain expertise in economics seem particularly eager to protect the faith.

**Response:** Quantum is a mathematical toolbox – it might come across as flaky or pretentious for a person to talk about it in the wrong context, but not to use it in their work. For example, complex numbers (i.e. those involving the square-root of negative one) are widely used in engineering to make some calculations easier. Quantum probability also gains much of its power from its use of complex numbers, so is more about the magic of imaginary numbers than the magic of subatomic particles.

- Entanglement is unique to special physical systems which can maintain quantum coherence. One science journalist told me that “Dollars don’t become quantum mechanically entangled. If they did, we’d be building quantum computers out of money.” A paper takes it as given that “one could not possibly idealize traders and investors as quantum objects exhibiting non-classical properties, like superposition or long-distance entanglement.” Physicists often conflate entanglement with Bell tests: one explained that “you can never violate a Bell inequality using systems like dice, dollars, or bank accounts. There is simply no way, and certainly no experiment has ever done so. (Maybe one or two ‘crackpot’ people claim otherwise, but they are not to be trusted.)” Another writes: “There is no chance that correlations in statistical economics will violate a Bell inequality … unless you fiddle the data.” In other words, using entanglement in an economics model is a sign of either gullibility, or scientific fraud.

**Response:** In mathematical terms, entanglement is a straightforward property of Hilbert spaces, and we can use it to model social and financial systems, including traders’ decisions or the behaviour of money. The key point is that it is being applied, not to macroscopic objects, but to information. The Bell test is not a definition of entanglement, it is a way of teasing out a particular form of entanglement for subatomic particles. It is true that we can’t build quantum computers out of money, but nor can we build classical computers – does that mean money is not classical?

- Quantum is too complicated and mathematical – we need simpler models and less math. Variants: The economy cannot be reduced to equations, people are not subatomic particles. May quote Lin Yutang.

**Response:** The need for simple models is a theme of many of my books, however what counts is things like the number of parameters in a model. Quantum probability is more complicated than classical probability, but it is the simplest way to capture phenomena such as superposition, interference, and entanglement, which characterise many key mental and financial processes (for example, the quantum walk model for pricing options or the two-qubit model for quantum decisions or the quantum model of the volatility smile are not complicated). People are not subatomic particles, but nor are they classical particles, which doesn’t stop economists from using classical models, or talking about physics-like forces of supply and demand (they are just assumed to be at equilibrium, so cancel out). And while it is true that human behaviour cannot be reduced to equations of any sort, we use equations all the time to simulate the economy. Again, many of my books, such as Apollo’s Arrow, or Truth or Beauty, have criticised the overreach of mathematical models, but that is a separate issue and applies as much to classical models.

- Quantum is a forced analogy or a metaphor. As economist Paul Samuelson once wrote, “There is really nothing more pathetic than to have an economist or a retired engineer try to force analogies between the concepts of physics and the concepts of economics … and when an economist makes reference to a Heisenberg Principle of [quantum] indeterminacy in the social world, at best this must be regarded as a figure of speech or a play on words, rather than a valid application of the relations of quantum mechanics.” Some physicists seem to relax though with this interpretation because it is less threatening than a theory or a model.

**Response:** Quantum probability is a mathematical tool, which is not the same as an analogy or metaphor. The purpose of a metaphor is usually to describe something which is abstract and complicated in terms of something that is more concrete, so it would make more sense to go the other way and use human behaviour as a metaphor to help describe subatomic behaviour.

- The brain has not been shown to rely directly on quantum processes.

**Response:** Quantum effects appear to be exploited by biological systems in a number of processes (see quantum biology) but whether they are used in the brain or not makes no difference to economics. The argument is not that the economy inherits quantum properties from subatomic interactions in the brain, but that it can be modelled as a quantum system in its own right. For example, a debt contract can be expressed using a quantum circuit in a way which captures effects such as uncertainty, subjective context, power relationships, and so on.

- Markets are not quantum because there is no uncertainty. For example, something like a bank account, or an order book for a stock market, has clearly posted amounts and prices. One person compared her bank account to Schrödinger’s cat: “I am a PhD physicist, so for me the word quantum that gets thrown around is a bit ridiculous … So think about your bank account, it might be empty until you open it, so are you telling me that this is uh quantum finance or quantum economics okay you can have a million in your account or you can have zero we don’t know?”

**Response:** While it may be true that bank accounts are not like Schrödinger’s cat, I will let The Economist answer that one, from an article called “Schrödinger’s markets” in the print edition: “on a closer look finance bears a striking resemblance to the quantum world. A beam of light might seem continuous, but is in fact a stream of discrete packets of energy called photons. Cash flows come in similarly distinct chunks. Like the position of a particle, the true price of an asset is unknowable without making a measurement – a transaction – that in turn changes it. In both fields uncertainty, or risk, is best understood not as a peripheral source of error, but as the fundamental feature of the system.”

As computer scientist Scott Aaronson notes, quantum methods are adapted to handle “information and probabilities and observables, and how they relate to each other.” Since the financial system seems a pretty good example of information, probabilities, and observables (in this case through transactions) it seems like a suitable approach. Much of the confusion comes down to the fact that quantum economics is not quantum physics applied to the economy, but rather quantum mathematics applied to the economy (see figure below). Physicists often struggle with this because they tend to mistake their elegant models for reality (one even commented that “There is no quantum probability because quantum theory can’t be a theory created from probability”). But as Aaronson explains, “Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let’s try to generalize it so that the numbers we used to call ‘probabilities’ can be negative numbers. As such, the theory could have been invented by mathematicians in the 19th century without any input from experiment. It wasn’t, but it could have been.” Quantum mathematics should therefore be viewed as a mathematical toolbox that can be applied to either physical or social systems where appropriate.

People trained in physics tend to see quantum mechanics as a special theory with “many totally unintuitive predictions that makes it special,” as one put it. “Until at least one of them is borne out empirically, the onus is on you to convince us that QM is needed!” Entanglement for example is seen as a special property of subatomic particles – or “a surprising feature of the *world*” as another physicist emphasized (I get a lot of these emails) – and object that the two parties in a loan contract are not entangled in the same way. To understand the entanglement, it is necessary to lift the level of analysis from physical people, to mental constructs – which is entirely appropriate, given that money and value are mental constructs. From the perspective of the debt contract, if the debtor decides to default, then the state of the loan also changes immediately for both parties. And debt contracts are a feature of the world too (even if they are less remarkable or surprising than quarks or whatever). Perhaps the main point of quantum economics – and the hardest for people trained in physics to get, because it seems unintuitive to them – is that quantum properties can present in a way which seems familiar and intuitive (compare also the field of Quantum Natural Language Processing).

The above nine reasons for rejecting a quantum approach, which are the ones most commonly produced, are very superficial and are easily dismissed with a little reflection. (Skeptics sometimes prefer to say that they don’t understand or are “not convinced” without giving a specific reason, but my aim is not to convince people of anything, it is to lay out the facts as I see them and let others do their own research and come to their own conclusions.) Also, arguing against these reasons, as I have done above, will in my experience have absolutely no effect. One reason is that getting the quantum approach seems to involve something of an aha moment where it suddenly clicks into place. The other reason though is that they are *not the real reason*. So why is it that no one even tried to apply quantum methods to the economy until about a century after they were invented? This points to:

10. Quantum economics touches on a range of taboo topics.

For the full picture read Money, Magic, and How to Dismantle a Financial Bomb: Quantum Economics for the Real World. Finally, given the numerous reasons to not take a quantum approach, I should point out that there also many reasons why the opposite is true, and the economy is amenable to a quantum treatment! In particular, quantum is the best framework for expressing in mathematical terms the complex interactions between mind and money. To see why, the best place to start is again with the books, or see this brief summary. For a mathematical treatment, see Quantum Economics and Finance: An Applied Mathematics Introduction.

[Update] My work in economics has seen me called a number of things including a conspiracy theorist, and the intellectual equivalent of a climate-change denier. More recently one physics professor read this piece and wrote, in a now-deleted tweet, that I was a charlatan who was ducking and weaving in order to avoid any criticism. I replied that he may have read the post, but he hadn’t understood it. He said “I judge you are not a crank. I judge you are a charlatan.” Then he thought about it (references to names redacted):

Any physicist worth their salt should agree with him that the only test is whether quantum math proves useful in modelling and prediction.

[Update] Further to the above statement about predictions, the reality is that most scientists – and certainly economists – care less about this than you might think (they are not all worth their salt). If a particular approach is initially judged as non-scientific then – as predicted by quantum decision theory – it is extremely difficult to overcome that judgement, which may involve strong subjective factors, by introducing empirical evidence. For example one physicist-turned-quant offered this assessment of my ~~perpetual motion machine~~ quantum model of price impact: “I unfortunately cannot follow your argument nor reproduce your train of thought. Our points of view about what is scientific and what is not seem too far apart, which is OK I guess.” He couldn’t quite put his finger on what was wrong, and was incurious about the fact that his own model was obviously incompatible with empirical evidence, while the quantum model gave accurate predictions – even though he had earlier written: “In the end, empirical observation must supersede all prejudices, so all ideas are a priori welcome. Time will tell.” Indeed. See: Orrell (2022) Market impact through a quantum lens. *Wilmott* 2022(122): 50-52.

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