Quantum Foundations III · Lesson 7 · Interactive Review
The QM3 Journey
This is an interactive review of the six core QM3 lessons.
No new mathematics or concepts — just the journey, retraced.
Tap a station to revisit it.
Build the story
Drag the cards — or tap two to swap them — into the order the journey unfolded.
- Everything Evolves1
- Open Questions2
- Several Sectors3
- Missing Connections4
- One Sector5
- No Crossing6
Well done. You have reconstructed the logical flow of QM3.
Conditional Consequences
Assuming multiple invariant sectors and compatible embeddings:
- Sector-preserving transport is block-diagonal.
- Relative phase can evolve between fixed sector components.
- Off-diagonal coupling terms are unavailable.
- The inaccessible coupling dimensions number n² − n.
Still Open
- ?Do multiple invariant sectors exist?
- ?Are they canonical and unique?
- ?Do compatible sector embeddings exist?
- ?Is exact invariance the right definition?
- ?Where could inter-sector coupling come from?
These stay open research questions.
Every scientific journey begins with curiosity.
There is more to explore from here.
- One Sector
- Everything Evolves
- Several Sectors
- No Crossing
- Missing Connections
- Open Questions
QM3 explores what would follow if relational configuration space contained more than one invariant sector. Conditional on such sectors and compatible embeddings, exact sector-preserving transport allows relative-phase evolution but not transfer between sectors. That is the coupling obstruction: coupling is unavailable under the current definition and assumptions, rather than impossible under every possible future formulation. Whether exact invariance is the correct definition of a relational sector remains open.