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. (Aaronson, 2013)
1. Overview
Quantum Economics and Finance is a new journal devoted to a new field, and the aim of this editorial is to answer a basic question, namely: what do we mean by quantum economics and finance? A short definition is the following:
Quantum economics and finance is the application of probability based on projective geometry—also known as quantum probability—to modelling in economics and finance. It draws on related areas such as quantum cognition, quantum game theory, quantum computing, and quantum physics.
2. Quantum and Probability
For many, the word quantum is strongly associated with physics. But as observed by Aaronson in his book Quantum Computing Since Democritus quoted above, while probability based on projective geometry was first used in physics, this was a historical accident. Physics was simply the first area of inquiry that found the set-theoretic approach to probability to be insufficient to explain observations. Physics then adopted the next-simplest form of probability—one based on projective geometry, now known as quantum probability—and with it developed what has come to be known as quantum theory. However, quantum methods are adapted to handle “information and probabilities and observables, and how they relate to each other” (Aaronson, 2013) which applies as well to the economy as it does to the subatomic world.
Quantum economics and finance is in the spirit of the first quantum pioneers, using mathematics in a creative way to model observed phenomena. The earliest suggestion that economic modelling needed the additional degrees of freedom afforded by quantum probability was by Qadir (1978), who argued that the classical basis for economic decision making limited the reality that could be incorporated. Since then, evidence has accumulated that economics and finance have their own versions of interference, entanglement, and intrinsic uncertainty—based this time on social and financial information rather than subatomic particles—that are best described using quantum probability, and from this the field of quantum economics and finance has emerged.
3. Scope
As quantum economics and finance has developed, four related strands of research have evolved. One focusses on the quantum nature of human cognition.
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Another, focuses on the quantum nature of biology
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and its possible role in human cognition. Another, views economic and financial systems as classical, but takes advantage of quantum techniques and quantum computers to solve problems more efficiently. Finally, like many in areas such as cognition, some research adapts methods from quantum physics to solve problems in economics and finance that present deviations from set-theoretic probability.
Quantum Economics and Finance embraces all these approaches, but views quantum probability primarily as a mathematical tool with which to illuminate our understanding of economics and finance, and sees its role as the forum for the dissemination of research in this field.
We look forward to your contribution.
