Measurement Problem

The measurement problem asks: how does the smooth, deterministic evolution of the wave function produce discrete, random measurement outcomes? What constitutes a “measurement”? When does “collapse” occur?

Logic Realism Theory dissolves rather than solves this problem—showing it arises from a category confusion.

The Standard Puzzle

In quantum mechanics:

• Schrödinger evolution: Continuous, deterministic, unitary
• Measurement outcomes: Discrete, random, irreversible (apparently)

These seem incompatible. If quantum states evolve smoothly, how do sharp outcomes emerge? Various interpretations propose:

• Copenhagen: Collapse is a fundamental process (but undefined)
• Many-Worlds: No collapse; all outcomes occur in branches
• Bohmian: Hidden variables determine outcomes
• GRW: Stochastic collapse dynamics with parameters

The LRT Dissolution

LRT reframes the problem by distinguishing structural explanation from mechanistic explanation.

What Requires Structural Explanation

Why are outcomes always determinate?

Because instantiated records must satisfy $L_3$. A detector cannot simultaneously fire and not-fire. Excluded Middle and Non-Contradiction enforce sharp outcomes at the level of stable records.

Why do probabilities follow $\lvert\psi\rvert^2$?

Because vehicle-invariance forces Born-rule structure via Gleason’s theorem. The probability measure cannot depend on how the physical situation is mathematically decomposed.

What Requires Mechanistic Explanation

When exactly does the transition occur?

This is a physical question about where the quantum-classical boundary lies. Candidate answers include:

• Decoherence (environmental interaction)
• Irreversible amplification
• Gravitational threshold (Penrose)
• Information transfer to environment

LRT is compatible with any of these as the physical marker. What LRT adds is the interpretation: whatever the criterion, what happens is category transition, not collapse dynamics.

Measurement as Category Transition

There is no mysterious collapse mechanism. Measurement is the interface between $I_\infty$ and $A_\Omega$.

In $I_\infty$, the quantum state evolves unitarily. When the state interacts with a context that requires Boolean outcomes—a detector, an irreversible record, a macroscopic system—$L_3$ are enforced. The state must become determinate.

This is not a dynamical process requiring new physics. It is a category transition—from the $I_\infty$ domain (where indeterminacy is permitted) to the actuality domain (where it is not).

The “measurement problem” dissolves because collapse is not a process but an interface.

What LRT Provides

1. Ontological interpretation: What collapse IS (category transition, not dynamical process)
2. Explanation of definite outcomes: Why they occur ($L_3$ enforcement)
3. Why no new physics needed: It is not a physical process

What LRT Does Not Provide

1. Precise physical criterion for when the transition occurs
2. Derivation of the quantum-classical boundary
3. Explanation of why THIS outcome rather than THAT outcome

The question “when exactly does Boolean actuality get enforced?” remains empirically open. The remaining question—why THIS outcome?—may have no deeper answer if selection among $L_3$-admissible outcomes is genuinely stochastic.

Analogy: Thermodynamics and Statistical Mechanics

LRT relates to the measurement problem as thermodynamics relates to statistical mechanics:

• Thermodynamics says entropy increases
• Statistical mechanics says how (coarse-graining, typicality)

Similarly:

• LRT says outcomes become determinate (structural necessity)
• Decoherence (or another mechanism) may specify when (physical criterion)

The structural explanation is complete without the mechanistic details.

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