Quantum Foundations III · Lesson 2
One Sector, One Shared Evolution
A sector is not frozen.
Its phase can evolve continuously.
In the simplest one-sector case, the whole state changes together.
The points are a visual guide to one coherent configuration. They are not separate particles with independent quantum motion.
Try it: drag any marker. Its neighbours ease aside, then the whole pattern settles back into its shared rhythm. Show Flow and Show Connections reveal the same behaviour without dragging.
What to notice
- ✓Every marker turns at the same shared rate.
- ✓One common rhythm runs through the whole pattern.
- ✓The sector stays intact while its phase evolves.
ψ(t) = e⁻ⁱλᵗ ψ(0)
The whole state acquires the same phase change.
In the simplest one-complex-dimensional invariant sector, transport can appear as a shared phase evolution. This is the scope of the expression above: it does not imply that every possible sector must be one-dimensional.
A single one-dimensional complex sector permits shared phase evolution, not rich internal mixing. Every marker follows one shared rotation and one common rhythm, because there is only one thing evolving: the phase of the whole state. The points are a visual guide to one coherent configuration, not separate particles with independent quantum motion.
So far we have looked at one sector only.
What would follow if the configuration space contained more than one?