Quantum Foundations III · Lesson 1
What Is A Sector?
A sector is a region whose phase can evolve together.
The sector stays intact while the configuration evolves.
Transport does not carry a configuration out of its sector.
A Candidate Relational Sector
DEFINED HEREQM3 provisionally defines a sector as a subset of configuration space that is exactly invariant under the relevant transport.
S ⊂ C
T(S) ⊆ S
If a configuration begins in this sector, sector-preserving transport does not carry it outside.
The moving points are visual markers for relational configurations. They are not claims about microscopic particles moving inside physical containers.
Try it: drag a configuration marker toward the edge — it slows down and slides along the inside. Prefer buttons? Start Transport, Pause and Reset show the same behaviour without dragging.
What to notice
- ✓The configuration keeps evolving.
- ✓The sector stays intact while the configuration evolves.
- ✓Transport does not carry a configuration out of its sector.
A relational sector is provisionally defined as a subset preserved by transport. Exact invariance is a modelling choice, and its adequacy remains an open question. The moving points are visual markers for relational configurations — not claims about microscopic particles moving inside physical containers. The boundary is a visual metaphor for transport invariance, not a physical wall in space. Later lessons ask what would follow if several invariant sectors existed.
What Is Being Divided Into Sectors?
The sectors considered here belong to relational configuration space. They are not regions of ordinary physical space. A sector represents a class of configurations preserved by the relevant transport structure.
For the QM3 sector definition to be meaningful, the relevant transport must be defined on the configuration structure being partitioned. This connection belongs to the deeper relational reconstruction and is not independently derived by QM3.
- Relational objects
- Configurations
- Transport on configurations
- Invariant-sector question
The later foundational analysis distinguishes abstract admissible structures from a realised stage of the reconstruction. QM3 should be interpreted on an appropriate realised configuration structure once that structure has been supplied by the preceding foundation.
The realised-stage construction belongs to the deeper foundation programme rather than to QM3 itself.
The current foundation programme obtains a realised-stage construction conditionally once an appropriate finite canonical selection principle is supplied. It is not claimed that PDT0 uniquely derives the realised stage, nor that a finite canonical selection principle has been derived from PDT0.