Quantum Mechanics from Classical Logic

Abstract

Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.