Quantum Tic Tac Toe

Quantum mechanics is notoriously difficult to understand because our species evolved in a classical world. Even physicists who are familiar with the quantum math still experience this world classically. Niels Bohr believed that this would always be the case. "No matter how far the explanation of quantum phenomena transcends classical notions, " Bohr said, "the results of all experiments must be expressed in classical terms." In order to think like Nature thinks we must learn to think quantum-mechanically. But where can we go to exercise our minds with quantum experiences?

Recently Alan Goff, a researcher at Novatia Labs, invented a quantum version of tic tac toe which he presented at the unlikely venue of a meeting of the American Institute of Aeronautics and Astronautics. Perhaps Goff hoped that insights gained from playing quantum tic tac toe might lead to breakthroughs in space propulsion physics. Later he published an account of his new quantum game in American Journal of Physics which is primarily directed towards physics teachers and welcomes clear reviews and novel presentations of complex ideas. AJP is Nick's favorite physics journal.

Goff has a blog called Alan Goff's Entanglements where he discusses quantum TTT and other topics.

If you want to learn to play quantum TTT, the rules are published here, along with a Java applet that maps all the moves in real time.

In a nutshell, on each turn, a player marks two squares at once with two "spooky marks". One square can be occupied by any number of spooky marks, in which case the marks are said to be "entangled". The play proceeds, each player marking the board with two spooky marks until player A makes a move which creates a "cyclic entanglement". Then player B chooses how that entanglement will "collapse" into "real marks" that can only occupy one square at a time as in classical TTT. After collapsing the cycle (and all "stems" entangled with that cycle) B makes the usual "spooky move" on any remaining two squares that do not contain collapsed marks. The game ends when one or both players gains a three-in-a-row of collapsed marks just as in classical TTT.

Quantum TTT is in many respects a nice metaphor for quantum reality. Before observation, a quantum particle can be in two places at once and be entangled with other particles in an instantaneous kind of connection impossible in the classical world. In the quantum world as in quantum TTT, a "collapse" which depends partly on the observer's choice and partly not turns spooky possibility into concrete actuality. In both the quantum world and in quantum TTT, an action in the future can seem to affect the past, but in either case no time-travel paradoxes arise.

I live in a redwood forest surrounded by trees. Inside each green leaf or needle are trillions of chloroplasts containing two kinds of chlorophyll--antenna chlorophyll which is specialized for absorbing light energy and reaction chlorophyll which is specialized for using energy to drive the chemical reactions that build the tree. Mediating between the antenna CHPHL and the reaction CHPHL are an array of transfer molecules. Up until a few years ago it was believed that a photon absorbed by an antenna CHPHL tranferred its energy to the reaction CHPHLs via a classical random walk among the intervening transfer molecules till its energy happened to reach a reaction site or was lost. Now researchers have discovered that something analogous to a quantum tic tac toe game is going on inside every green leaf on this planet. Instead of following one path at random the photonic excitation takes many spooky paths at once till one of these paths touches a reaction site which collapses it and makes it real.

In the words of one of these chlorophyll researchers: "This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path."

When you look up into the trees, can't you imagine a torrent of solar photons each triggering a spooky quantum TTT move that is efficiently sampling "vast areas of phase space"? Her everyday quantum subtlety multiplied trillions upon trillions of time in every green plant is one more reason to praise the goddess chlorophyll from whom so many of our blessings flow.