Talking with physicists about quantum finance

Quantum economics/finance is based on the idea that you can use quantum probability to model financial markets. Over the past several years I have had numerous discussions on the topic with physicists, and often (not always) they seem to follow the same track. To save time in future, I will summarise the steps briefly, using the example of a recent discussion with an anonymous online poster at a Wilmott finance forum.

First, I should note that I do have some prior, given that I am myself a physics dropout (though I did stay around long enough to learn some quantum mechanics). As I wrote in my book Apollo's Arrow: it seemed that my physics education was acting like a kind of indoctrination, and forcing me to see the world in this very controlling way. Partly as a result of this dramatic flash of insight, I dropped the physics part of the program and switched to mathematics, which leaves applications up to the user - and also allowed me to take film studies as an option."

Also, I'll admit that I don't have too much time for people who write my ideas off as definitely not true" and quantum doodah" under the cover of anonymity. The situation is asymmetric - they know who I am, but if I ever ran into them in person at a conference or something I would never know. And it makes them essentially unaccountable for what they say.

Anyway the conversation, which can be found here (see comments from katastrofa") follows a usual path. It begins with some technical points based on confusion about the model, but ends with the assertion that markets aren't really quantum so quantum methods don't apply. A few key features:

1. Physicists can be very arrogant when they discuss quantum ideas! (Or maybe they are just assuming the person whose theory is being debunked - the debunkee? - is even more simpleminded than we actually are.) This poster (who appears to be an expert in quantum physics) starts by asking for some clarifications but soon gets straight to explaining my own model to me along with basic ideas from quantum mechanics known to anyone with a minimum background in the topic. For example I learn here that In the harmonicoscillator, after an energy measurement the system is in level n and the position distribution is not Gaussian - it's a Gaussian multiplied by a squared Hermite polynomial." So interesting!
2. A normal discussion about a mathematical model would include things like does the model actually fit the data, how many parameters does it need, is it falsifiable, and so on. Those topics don't even come up here, because the focus is on debunking theory. For example q-variance states that the average variance over periods T with a price change x is given by sigma^2 + z^2/2 where z=x/sqrt(T). What makes it interesting is that (a) it was a prediction, (b) it is a big effect (total variance is double the minimum variance), (c) it applies for all periods T, be it a few days or a year, (d) no such effect has been reported in the literature, (e) it has obvious implications for things like option pricing (the volatility smile?), and (f) there is no parameter - no adjustable control knob - on the z^2 term. All of this means that the model should be incredibly easy to falsify, which is rare in economics. If people think the model is wrong, you would think the starting point would be to test it using data - but that never comes up (seriously never). Something very wrong there.
3. Physicists find it hard to see quantum probability as a mathematical technique, so they always reframe models as analogies. This person writes of the analogy ... of a quantum harmonic oscillator", the analogy to a coherent state", volatility modes that themselves are analogous to qho energy levels," and so on. Since calculus was originally invented to model planetary motion, should we refer to Black-Scholes at all times, not as a mathematical model, but as an analogy to planets?
4. Related to point 1, when a physicist in debunking mode gets something wrong, rather than concede it they simply move on to another point. This can continue for a long time. Here for example the poster fundamentally misunderstands q-variance (they say the conditional variance rises like a+bx^2, and let's fix b=1/2 for parsimony") but when called on it asserts there is no confusion. They then drop the topic of q-variance and switch to making mistakes about the q-distribution (definitely not true"). This makes the discussion frustrating.
5. It is only when you get near the end of the conversation that the underlying assumptions finally surface: that the wave function is not real (In markets there's no literal wavefunction anyway") so any model based on quantum ideas is quantum doodah" (or as Murray Gell-Mann called it in a chapter of a book flapdoodle"). Hate to break it to you debunkers, but mathematical models aren't real either.
6. Finally, the motivations of the modeller (debunkee) are brought into question. The usual idea is that anyone plugging a quantum model is a bit of a charlatan, and quantum ideas are being used as a kind of advertising gimmick to make the model look cool (if so, it is the least successful pitch in the history of advertising). Here, the implication is quite subtle, and the poster only suggests that I am using quantum to make an interesting story: storytelling can outrun derivation - I'm only asking that the story and the math line up."

Now, sometimes people do change their mind, as this physics professor (who used their real name) did:

Usually though the whole discussion is a waste of time because it is based on an almost religious faith that quantum models aren't models but represent some deep ontological truth about physics. In other words, exactly the kind of thing that got me out of physics in the first place.

Of course, physicists are often the go-to experts on quantum techniques, so obviously have a lot to contribute. And many leaders in areas such as quantum finance/game theory/cognition and so on are themselves renegade physicists. But it's not up to physicists to decide what mathematical techniques are suitable for use in the social sciences. And physicists saying that quantum models shouldn't be applied in other areas is a bit like mathematicians saying that physicists shouldn't use complex numbers to model probability because they weren't invented for that.

What I find really ridiculous though is that physicists have all this time to debate quantum models, and so little to say about the obviously flawed assumptions of classical economics. Maybe they could debunk that.

For a discussion of the relationship between quantum economics and physics, see here.

I am always open to good-faith scientific dialogue, but if any experts out there want to physics-plain quantum at me, a few guidelines:

1. State your name.
2. State your priors. If you just want to debunk the theory then be up front - I am unlikely to change your mind.

Oh, and

1. If this is about debunking, I hear there are other places on the internet where they are misusing quantum theory so please check them out first.