Computational investigation of five major proposals for resolving how definite measurement outcomes arise from quantum superposition, spanning decoherence, collapse models, and information-theoretic frameworks.
Standard quantum mechanics describes systems via wavefunctions that evolve unitarily, yet measurements produce single definite outcomes. This fundamental tension, known as the quantum measurement problem, decomposes into three sub-problems: (1) the problem of outcomes -- why single results appear; (2) the preferred basis problem -- what selects the measurement basis; and (3) the Born rule problem -- why probabilities follow |⟨ψ|φ⟩|².
Decoherence explains how interaction with the environment selects preferred pointer states and destroys quantum coherence. We solve the Lindblad master equation for a qubit coupled to a thermal bath, tracking coherence, purity, and entropy dynamics.
| Metric | Value | Interpretation |
|---|---|---|
| Decoherence Time | 0.4765 | Fitted exponential decay constant |
| Final Purity | 0.6552 | Mixed state (pure = 1.0) |
| Final Entropy | 0.7628 bits | Near-maximal for qubit |
| Basis Stability (computational) | 1.0 | Selected by einselection |
| Basis Stability (Hadamard) | 5.6e-10 | Not selected |
The CSL model modifies the Schrodinger equation with stochastic nonlinear terms causing spontaneous wavefunction collapse in the position basis. The amplification mechanism ensures microscopic systems remain coherent while macroscopic superpositions collapse rapidly.
| Metric | Value |
|---|---|
| Left Collapse Fraction | 0.481 |
| Right Collapse Fraction | 0.519 |
| Born Rule Deviation | 0.019 |
| Mean Collapse Time | 0.5644 |
| CSL Lambda | 1e-16 s-1 |
| CSL rc | 1e-7 m |
Quantum Darwinism explains how classical objectivity emerges through redundant encoding of pointer-state information across multiple environment fragments. Observers accessing different fragments independently obtain the same classical information.
| Metric | Value |
|---|---|
| System Entropy | 1.0000 bit |
| Redundancy Rδ | 5.0 |
| Mean Discord | 0.0558 bits |
| Number of Fragments | 20 |
The gravitational self-energy of mass superpositions drives wavefunction collapse on timescale τP = ℏ / Egrav. Heavier objects collapse faster, predicting a sharp mass-dependent transition from quantum to classical behavior.
| Object | Mass (kg) | log10(τ) (s) | Status |
|---|---|---|---|
| Electron | 9.1e-31 | 57.3 | Forever quantum |
| Proton | 1.7e-27 | 48.0 | Forever quantum |
| C60 Fullerene | 1.2e-24 | 40.4 | Quantum |
| 10nm Nanoparticle | 1.0e-21 | 31.8 | Quantum |
| 100nm Nanoparticle | 1.0e-18 | 21.8 | Quantum |
| 1μm Microsphere | 4.2e-15 | 9.5 | Mesoscopic frontier |
| Grain of Sand | 1.0e-9 | -5.5 | Classical |
| Cat | 4.0 | -26.3 | Instantly classical |
The many-worlds interpretation maintains universal unitary evolution, with all measurement outcomes realized in different branches. After 12 binary measurements, the wavefunction contains 4,096 branches. The Born rule is derived from branch-weight analysis.
| Metric | p=0.3 | p=0.5 | p=0.7 |
|---|---|---|---|
| Born-Weighted Frequency | 0.3000 | 0.5000 | 0.7000 |
| Equal-Weight Frequency | 0.5000 | 0.5000 | 0.5000 |
| Total Branches | 4096 | 4096 | 4096 |
Weak measurements extract partial information without full collapse. The Leggett-Garg inequality tests macrorealism: quantum violations confirm that the sharp measurement/no-measurement dichotomy is an idealization.
| Metric | Value |
|---|---|
| Weak Value Re(σz) | 1.0000 |
| Weak Value Im(σz) | 0.0000 |
| Post-selection Rate | 0.520 |
| LG Max Violation K | 1.497 |
| LG Violation Fraction | 0.367 |
Multi-criteria evaluation across five resolution proposals. Models are scored on: resolving definite outcomes, deriving the Born rule, selecting a preferred basis, experimental testability, parsimony, and information conservation.
| Feature | Decoherence | CSL | Q. Darwinism | Gravity | Many-Worlds |
|---|---|---|---|---|---|
| Resolves Outcomes | No | Yes | No | Yes | Yes* |
| Born Rule | No | Yes | No | No | Yes* |
| Preferred Basis | Yes | Yes | Yes | Yes | No |
| Testable | Yes | Yes | Yes | Yes | No |
| New Physics | No | Yes | No | Yes | No |
| Modifies QM | No | Yes | No | Yes | No |
* Many-worlds redefines "outcome" and derives the Born rule through decision-theoretic arguments.