Logic Realism Theory and the Future of Quantum Interpretations

February 2026 | Advanced

1. Why Another “Interpretation”?

Quantum mechanics works extraordinarily well but remains conceptually unsettled. Competing interpretations (Copenhagen, Many-Worlds, Bohmian mechanics, QBism, and many more) offer incompatible pictures of what the theory says about reality. None has achieved consensus. That alone suggests we may be missing something deeper.

Logic Realism Theory (LRT) proposes a different starting point. Instead of taking the Hilbert-space formalism as given and then asking how to “interpret” it, LRT starts from the Three Fundamental Laws of Logic (Identity, Non-Contradiction, and Excluded Middle) and treats them as ontological constraints on physical reality, not just rules of thought. From there, it aims to derive key features of quantum theory, including the Born rule, and to show why many traditional interpretive puzzles are ill-posed.

The central idea is simple but radical: if nothing that actually occurs in physical reality ever violates the laws of logic, and if logic is real and world-structuring, then that logical structure should visibly constrain what physical theories are possible.

2. LRT in One Paragraph

LRT distinguishes two levels (see The Instantiation Barrier Explained for an accessible introduction):

An Infinite Information Space $I_\infty$: a non-Boolean space of physically relevant informational structures (superpositions, entanglement, etc.).
A Logical Actuality Layer $A_\Omega$: the domain of actual measurement records, where each record is a Boolean, $L_3$-compliant proposition (a detector either fires or it doesn’t).

The laws of logic are taken to apply as strict physical constraints at the $A_\Omega$ level. Each measurement is a one-way interface map $f_M : I_\infty \to A_\Omega$ that, in a single run, produces exactly one non-contradictory record.

From this starting point, LRT:

Treats the quantum state as a real structure in $I_\infty$.
Treats definite macroscopic outcomes as real, logically constrained records in $A_\Omega$.
Uses information-theoretic and probabilistic arguments, plus reconstruction results, to connect these two layers.

3. Deriving the Born Rule from Logical Constraint

One of LRT’s main contributions is a derivation of the Born rule from logical and information-theoretic premises, not from decision theory or Bayesian coherence. (For an accessible overview, see The Born Rule Is Not Optional.)

The derivation has two main routes:

Route A (via reconstruction): Show that LRT’s axioms about states, events, composition, and dynamics (A1-A7) satisfy the assumptions of generalized-probabilistic reconstructions (à la Masanes-Müller). That yields a complex Hilbert-space structure and the standard quantum formalism.
Route B (Hilbert space assumed): Assuming Hilbert space (either as an empirical fact or via Route A), use $L_3$ at the level of outcome records to constrain probability assignments and show that only the Born rule survives.

Route B goes roughly like this:

Step 1: Determinate Identity of Records

Each macroscopic outcome record has determinate identity: it is exactly one thing and not another (Identity, Non-Contradiction, Excluded Middle at the vehicle layer).

Step 2: Objective Dispositions (“Vehicle-Weights”)

If an outcome record is determinately “spin up”, its determinacy must be grounded in the pre-measurement state. That motivates treating the system as having objective dispositions (vehicle-weights) toward each possible outcome before measurement.

Step 3: Vehicle-Weight Invariance

A system’s disposition toward a given outcome should not depend on how we describe or decompose the measurement, as long as we are talking about the same physical event (e.g., the same pointer position). Formally: if the same projector $P$ appears in different measurement decompositions, the probability $\mu(P)$ must be the same in each context.

This is non-contextuality for events, not for hidden variables: Kochen-Specker rules out non-contextual definite values for all observables, but it does not forbid non-contextual probability measures on the projection lattice.

Step 4: From Invariance to Gleason’s Premises

Vehicle-weight invariance, plus finite additivity and normalization, yields exactly the conditions required by Gleason-type theorems: a normalized, ($\sigma$-)additive, non-contextual probability measure on the projectors of a Hilbert space.

Step 5: Gleason and the Trace Form

Gleason’s theorem (and its extensions) show that any such measure must have the trace form:

\[\mu(P) = \mathrm{Tr}(\rho P)\]

for some density operator $\rho$.

Step 6: Pure States → Born Rule

For pure states, $\rho = \lvert\psi\rangle\langle\psi\rvert$. For a rank-1 projector $P = \lvert\phi\rangle\langle\phi\rvert$:

\[\mu(P) = \mathrm{Tr}(\lvert\psi\rangle\langle\psi\rvert \lvert\phi\rangle\langle\phi\rvert) = \lvert\langle \phi \vert \psi \rangle\rvert^2\]

That is the Born rule.

Technically, this relies on existing results (Gleason/Busch, Masanes-Müller) but provides a new conceptual grounding: the key constraints they need are justified by $L_3$ at the level of physical records, not assumed ad hoc. The full technical derivation is available in Deriving the Born Rule from Logical Constraint (Zenodo DOI: 10.5281/zenodo.18756374).

4. Synthesis: What LRT Retains from Major Interpretations

LRT is not just “another interpretation.” It can be seen as synthesizing what works in several dominant views (see also One-World Realism):

From Copenhagen

A clear insistence on single, definite outcomes at the macroscopic level. LRT recovers this as a logical necessity: contradictory outcome records are impossible in $A_\Omega$, not just unseen.
An effective “cut” between quantum possibilities and classical records, but with the interface defined by $L_3$ and IIS/$A_\Omega$ rather than an ambiguous “observer” line.

From Many-Worlds

A real, global, unitary quantum state, living in $I_\infty$, that encodes all entanglement and nonlocal correlations.
Decoherence as a way to explain the approximate classicality of records.

However, unlike MWI, LRT does not treat all branches as equally actual; only one Boolean record per measurement is ever actualized in $A_\Omega$. That preserves Everett’s structural insights without committing to ontological bloat.

From Bohmian Mechanics

Comfort with nonlocal realism: Bell-type nonlocal correlations reflect a real, globally constrained structure, not mere calculational artifacts.
But instead of adding particle trajectories and a guiding wave, LRT’s ontology is logical/informational: global constraints in IIS plus $L_3$ at the interface.

From QBism and Information-Theoretic Approaches

Deep respect for information-theoretic reconstructions and the idea that quantum theory is about constraints on information processing (local tomography, continuous reversibility, etc.).
Acknowledgment that probability structure is heavily constrained by consistency (here: vehicle-invariance), not arbitrary.

But probabilities are objective vehicle-weights, not merely personalist beliefs.

In that sense, LRT is a logic-driven realist synthesis: unitary, nonlocal, information-theoretic, classically definite at the macroscopic level, and with probabilities fixed by logical constraint. For the foundational framework, see the LRT Position Paper and It from Bit, Bit from Fit.

5. Obviating Parts of Existing Interpretations

If an LRT-style derivation program succeeds more broadly, several interpretive battles become less urgent:

Everett’s Probability Problem

Many-Worlds struggles to explain why branch weights should follow the Born rule if all branches exist. LRT says: given Hilbert space kinematics, $L_3$ at the record level forces the Born rule as the unique non-contextual measure. The branching story is secondary, not the source of probabilities.

Subjective vs Objective Probability

QBism dissolves the “why Born?” question by making probabilities subjective. LRT instead provides an objective reason: probabilities are determined by the requirement that $L_3$-compliant records preserve determinate identity across different measurement decompositions.

Collapse Postulates and Measurement “Mysteries”

In Copenhagenish views, collapse is a primitive, ill-specified rule triggered by “measurement.” In LRT, there is no dynamical breakdown: the global state in IIS evolves unitarily; “collapse” is the one-time actualization of a single Boolean outcome in $A_\Omega$, mandated by $L_3$. The mystery moves from “why collapse?” to “why logical actuality?”, and LRT answers the latter by construction. (See The Measurement Problem for more.)

Hidden-Variable Machinery as the Only Path to Realism

Bohmian mechanics shows that realist, nonlocal theories are possible, but many find its additional ontology and dynamics unattractive. LRT offers a realism grounded in logical and information structure instead of extra particle variables, potentially making “interpretative realism” less dependent on hidden variables.

6. What Would Count Against LRT?

Because LRT makes strong metaphysical claims, it also has clear failure modes:

A reproducible macroscopic violation of Non-Contradiction (a single measurement record that unavoidably instantiates $P \land \neg P$ in the same respect) would directly falsify its core assumption about the outcome layer.
A distinctive, empirically confirmed non-Hilbertian probability structure (e.g. robust evidence of post-quantum correlations violating Tsirelson’s bound while remaining non-signalling) would undercut LRT’s route through reconstruction and Gleason.
Philosophically, a convincing argument that determinate identity at the macroscopic record level does not require vehicle-invariance (non-contextual event probabilities) would challenge the core $L_1$ → Born link.

So LRT is not a “purely interpretive” gloss: it is a testable, vulnerable metaphysical-physical framework. For more on how LRT responds to challenges, see Common Objections to Logic Realism.

7. Why This Matters

The significance of LRT is not that it instantly replaces Copenhagen, Everett, Bohm, or QBism. It’s that it:

Offers a unified narrative in which logic, probability, information, and quantum structure are tightly connected.
Turns vague claims about “logic being real” into precise constraints that can be mapped onto existing theorems and experimental tests.
Suggests that many interpretive disagreements are symptoms of a deeper missing piece: the logical status of actuality and the way it constrains admissible probability measures.

If that picture is even approximately right, LRT could eventually act as a backbone theory: absorbing the best features of other interpretations while rendering their more speculative or ad hoc parts unnecessary.

External References

Interpretations of quantum mechanics – Wikipedia
Interpretations of Quantum Mechanics – Internet Encyclopedia of Philosophy
Reconstructing Quantum Theory – Masanes & Müller, arXiv
Reconstructions of Quantum Theory – IQOQI Vienna
The Status of the Born Rule and the Role of Gleason’s Theorem – PhilSci Archive
Born rule – Wikipedia
Copenhagenish interpretations of quantum mechanics – arXiv
Towards Better Understanding QBism – PMC
Tsirelson’s bound – Wikipedia
Information Causality, the Tsirelson Bound, and the ‘Being-Thus’ of Things – PhilSci Archive

Logic Realism Theory was developed by James (JD) Longmire. This article is part of the LRT documentation at jdlongmire.github.io/logic-realism-theory.