Limitations

Critical discussions of where QT3 is limited as a toy universe.

TOC

• Bases
• Oscillation
• Relativity
• Weights
• Randomness
• Phase

Only One Basis

Quantum tic-tac-toe asks the players to place each move into a superposition of two squares. The nine squares form the basis states of the quantum system. It is the only basis, there are no conjugate bases. One could envision an alternative basis, say the ‘diamond’ basis, but its relation to the ‘square’ basis would be intricate and require a very specific relationship to qualify as a conjugate basis.

No Oscillation

Nothing in quantum tic-tac-toe oscillates. Therefore there is no concept of energy, no wave equation, no way to have the system state change according to some unitary evolution.

No Relativity

Quantum tic-tac-toe is played in a classical space, a fixed grid of spatial position with classical time, a universal global time. No spacetime, no Minkowski space, no possibility of a Poincarë rotation.

Real Equal Weights

The superpositions of physical systems are weighted wth complex coefficients. The sum of the squares of these coefficients must equal unity. Ensuring this mathematical objective is called normalization. It is not technically required, but it makes the mathematical interpretation of complex weights as probabilities straightforward and more intuitve. In QT3, the weights are at best real, and limited to being equal. Furthermore, they do not have to be squared to compute a probability; that probability is speculatively limited to 50/50, but since collapse is by choice, not by chance, the model does not really support probabilities in any meaningful sense, and therefore, spooky-marks are not really weighted at all.

No Random Collapse

In QT3, collapse is specified as a special move, a choice by one of the players. In the metaphor, placement moves correspond (very loosely) to unitary evolution (the Schroedinger equation) while collapse moves correspond to measurememnts. In the jargon of game theory, QT3 is a perfect information game. A variation of the game is to replace collapse moves with a dice throw, which way the cyclic entanglement collapses is reduced to chance, 50/50. This has a significant affect on strategy. Alternatively, both players chould simply agree to make their required collapse choices randomly. This changes the game by intent rather than by law.

No Phase

Since there are not really any weights between the spooky-marks, and since there is nothing that oscillates, the concept of phase is not modeled by QT3. It could be added by making spooky-marks carry a sign. There would then have to be a rule that combined the signs of every spooky mark around an entire cyclic entanglement. That rule would have to restrict the collapse choice in some way.