Suppose a universe is made up of 16 quantum particles each of which has two states: 0 and 1. In this sense, the entire universe is just a number like 0b0000000000000000.
Well, if your universe is just two states, its description in the eigenstate basis would be something like A1 exp(iE1 t)|1> + A2 exp(iE2 t), where A1 and A2 are complex and E1 and E2 are real (modulo normalization and phase). I am not sure how this maps into a finite length binary number.
It maps to a finite length binary number if you force the particle into one of two states. So you could think of this universe as equidistant (in time) instants of a continuous universe where positions are measured, then they’re let to evolve and then positions are measured again. The binary strings refer only to the snapshots where the continuous universe is measured.
This ignores the fact that there must be something to measure the particles with. The goal of this thought experiment is to play around with the Born rule while ignoring the time evolution of a wave function governed by the Schrödinger equation.
Well, if your universe is just two states, its description in the eigenstate basis would be something like A1 exp(iE1 t)|1> + A2 exp(iE2 t), where A1 and A2 are complex and E1 and E2 are real (modulo normalization and phase). I am not sure how this maps into a finite length binary number.
It maps to a finite length binary number if you force the particle into one of two states. So you could think of this universe as equidistant (in time) instants of a continuous universe where positions are measured, then they’re let to evolve and then positions are measured again. The binary strings refer only to the snapshots where the continuous universe is measured.
This ignores the fact that there must be something to measure the particles with. The goal of this thought experiment is to play around with the Born rule while ignoring the time evolution of a wave function governed by the Schrödinger equation.