Quantum Tic-tac-toe - The Motivation

The Motivation

The rules of quantum tic-tac-toe are not particularly hard, but their unfamiliarity initially makes learning them somewhat more challenging than for conventional games. It may help, therefore, to consider why this game was invented.

The motivation to invent quantum tic-tac-toe was to explore what it means to be in two places at once. In classical physics, a single object cannot be in two places at once. In quantum physics, however, the mathematics used to describe quantum systems seems to imply that, when not being observed, quantum particles can be in multiple places at once. (The textbook example of this is the double-slit experiment.) How the universe can be like this is rather mysterious. There is a disconnect between the mathematics and our mental images of reality, a disconnect that is absent in classical physics. This is why quantum mechanics supports multiple "interpretations." An interpretation is a formal effort to explain what a theory means, to articulate a model. By definition, interpretations are not testable. Testability implies a theory or at least a hypothesis. The success of quantum mechanics is not in dispute, and it has been validated over an incredibly wide range of phenomena and to astonishingly high levels of precision. Yet the problem of multiple mutually incompatible interpretations remains a bit of a professional embarrassment.

The researchers who invented quantum tic-tac-toe were studying abstract quantum systems, formal systems whose axiomatic foundation included only a few of the axioms of quantum mechanics. Quantum tic-tac-toe became the most thoroughly studied abstract quantum system and offered insights that spawned new research. It also turned out to be a fun and engaging game, a game which also provides good pedagogy in the classroom.

The rules of quantum tic-tac-toe attempt to capture several phenomena of quantum systems.
These phenomena are:

1. superposition,
2. entanglement and
3. collapse.

• Superposition is the ability of quantum objects to be in two places at once.
• Entanglement is the phenomenon where distant parts of a quantum system display correlations that cannot be explained by either timelike causality or common cause.
• Collapse is the phenomenon where the quantum states of a system are reduced to classical states. Collapses occur when a measurement happens, but the mathematics of the current formulation of quantum mechanics is silent on the measurement process. Many of the interpretations of quantum mechanics derive from different efforts to deal with the measurement problem.