The Compatible Ordinans Perspective
Single Spin ⊗ Single Mode as the Minimal Ordinan
Version: v0.0.1 (Draft)
Status: Internally consistent, Council-aligned
Perspective: Ordinans (compatible with the Common View)
Foreword
The Common View and the Ordinans Perspective
This handbook presents the Common View of single-spin–single-mode quantum dynamics while introducing a new organising perspective: the Ordinans perspective.
The Common View describes what happens in experimentally realised quantum systems: canonical Hamiltonians, control protocols, noise mechanisms, and measurement schemes developed across cavity QED, trapped ions, circuit QED, and optomechanics. This body of knowledge is mature, successful, and indispensable.
The Ordinans perspective does not revise this physics. Instead, it re-organises it according to a strict architectural separation between:
a context-independent quantum system, and
explicitly coupled environments.
This separation enables falsifiable statements about complex quantum behaviour even when full numerical prediction is impossible.
Introduction
The Minimal Ordinans: Spin ⊗ Mode
We introduce the Ordinans perspective through the simplest non-trivial quantum system: a single two-level system (spin-½) coupled to a single harmonic oscillator mode.
The system is defined as
,
with no additional structure.
This system appears universally across quantum platforms:
atoms or superconducting qubits coupled to cavity modes,
trapped ions with internal states coupled to motional modes,
optomechanical systems coupling two-level defects to vibrational motion.
Nothing in this handbook alters the established physics of this system.
What changes is the scientific question:
Not “What happens?”, but “What must be coupled for this to happen?”
From Description to Structure
In the Common View, decoherence, dissipation, stochasticity, and measurement backaction are often introduced as secondary or parasitic effects.
In the Ordinans perspective:
the system is frozen (context-independent definition),
all complexity is traced to explicit couplings.
Noise, dissipation, measurement, clocks, and feedback are treated as physically real environments, modelled as subsystems coupled through designed interfaces.
What is designed is the coupling geometry, not reality itself.
Falsifiability without Predictability
As quantum systems grow in complexity, full numerical prediction becomes infeasible. This creates a verification problem in quantum simulation.
The Ordinans perspective does not solve computational complexity.
Instead, it restores scientific falsifiability by requiring:
explicit environment specification,
switchable interfaces,
null-environment tests.
A claim is admissible only if the predicted behaviour disappears when the coupling is removed.
Falsification Criterion (Explicit)
The Ordinans perspective fails if:
Removing a specified environment does not remove the claimed effect, or
Two systems with identical system definitions but different environment couplings behave identically when they should not, or
Observed behaviour cannot be traced to any explicit coupling.
The spin ⊗ mode system serves as a calibration point: if the framework fails here, it cannot succeed at larger scales.
PART I — LAYER 0
The Core (Context-Independent System)
No irreversibility. No scaling. No interpretation.
Chapter 1 — The Spin ⊗ Mode System
Content
Hilbert spaces: \mathbb{C}^2 \otimes \ell^2(\mathbb{N})
Jaynes–Cummings and Rabi Hamiltonians
Rotating-wave and ultrastrong-coupling regimes
Physical implementations across platforms
References
E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963)
I. I. Rabi, Phys. Rev. 49, 324 (1936)
S. Haroche and J.-M. Raimond, Exploring the Quantum (Oxford, 2006)
A. Blais et al., Phys. Rev. A 69, 062320 (2004)
Chapter 2 — Reachability and Ideal Control
Content
Ideal unitary control
Reachable sets and controllability
State preparation as initial-condition engineering (not dynamics)
References
S. Lloyd, Phys. Rev. Lett. 75, 346 (1995)
D. J. Wineland et al., J. Res. NIST 103, 259 (1998)
C. Law and J. Eberly, Phys. Rev. Lett. 76, 1055 (1996)
Chapter 3 — Symmetries and Constraints
Content
Parity symmetry
Energy conservation in the closed system
What no environment may violate silently
References
C. Cohen-Tannoudji et al., Atom–Photon Interactions (Wiley, 1992)
W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003)
PART II — LAYER 1
Interfaces (Coupling Geometries)
Mathematical couplings only. No records. No observers.
Chapter 4 — Unitary Interfaces
Content
Time-dependent Hamiltonians
Sideband and parametric couplings
Tunable interaction strengths
“Valves” between system and environment
References
D. Leibfried et al., Rev. Mod. Phys. 75, 281 (2003)
A. Wallraff et al., Nature 431, 162 (2004)
Chapter 5 — Measurement as Interface
Content
Completely positive maps
Kraus operators and POVMs
Measurement strength as coupling parameter
Information–disturbance tradeoff
Explicit exclusions
No “outcomes”
No “collapse”
No observer language
References
K. Kraus, States, Effects, and Operations (Springer, 1983)
H. Wiseman and G. Milburn, Quantum Measurement and Control (Cambridge, 2010)
K. Jacobs, Stochastic Processes for Physicists (Cambridge, 2010)
Chapter 6 — The Canonical Null Test
Content
Zero-Interface limit
Switchability as axiom
Parametric null tests
Substitute null environments
Goodhart-style failure modes
References
H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford, 2002)
H.-P. Breuer et al., Rev. Mod. Phys. 88, 021002 (2016)
PART III — LAYER 2
Ordinans (Engineered Worlds)
Interpretation and emergence live here.
Chapter 7 — The Dissipative World
Content
Thermal baths
Lindblad dynamics
T_1, T_2 as world properties
Dissipation as design tool
References
G. Lindblad, Commun. Math. Phys. 48, 119 (1976)
C. Gardiner and P. Zoller, Quantum Noise (Springer, 2004)
J. Barreiro et al., Nature 470, 486 (2011)
Chapter 8 — The Monitored World
Content
Designation of interface outputs as records
Conditional dynamics
Feedback as world logic
Measurement ≠ thermal bath (operational distinction)
References
H. Wiseman and G. Milburn, Phys. Rev. Lett. 70, 548 (1993)
J. Atalaya et al., Phys. Rev. A 97, 020104 (2018)
Y. Li et al., Phys. Rev. Lett. 121, 010601 (2018)
Chapter 9 — The Protected World (Soft Coastline)
Content
Error correction as environment engineering
Bosonic and cat codes
Logical vs physical decay
Protection claims and null tests
References
Z. Leghtas et al., Science 347, 853 (2015)
M. Mirrahimi et al., New J. Phys. 16, 045014 (2014)
B. Terhal, Rev. Mod. Phys. 87, 307 (2015)
PART IV — EVALUATION SUITE
Chapter 10 — Scaling Laws
Content
Exponential vs algebraic decay
Environment statistics → scaling
Breakdown of perturbative intuition
References
J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990)
Á. Rivas et al., Rep. Prog. Phys. 77, 094001 (2014)
Chapter 11 — Falsification Protocols
Content
Cross-world comparison
Platform-independent tests
Reporting standards
What constitutes rejection
References
K. Popper, The Logic of Scientific Discovery (Routledge, 1959)
R. Blatt and C. Roos, Nat. Phys. 8, 277 (2012)
Appendices
A. Mathematical Conventions
B. Environment Modelling Examples
C. Terminology and Forbidden Language
Closing Statement
This handbook does not claim to predict complex quantum worlds. It claims to make them falsifiable.
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