Dissolving the EPR Paradox

Logic Realism Theory (LRT) provides a distinctive resolution to the Einstein-Podolsky-Rosen (EPR) paradox (1935) by reframing the puzzle within its core ontological framework rather than invoking hidden variables, non-locality as a primitive, collapse postulates, branching realities, or purely epistemic interpretations.

The resolution emerges naturally from LRT’s central claim: the Three Fundamental Laws of Logic ($L_3$) act as ontological constraints on what can be physically instantiated and distinguished in reality.

This approach does not “deny” the EPR argument’s premises outright but relocates the tension: the apparent paradox arises from conflating pre-actualization possibility space (non-Boolean, entangled correlations in $I_\infty$) with actualized, distinguishable reality (strictly Boolean $A_\Omega$ layer).

1. The EPR Paradox: A Brief Recap

EPR argued that quantum mechanics is incomplete based on these premises:

Locality. No action at a distance; measurement on one system cannot instantaneously affect distant systems.

Reality criterion. If, without disturbing a system, we can predict with certainty (probability 1) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

The argument:

• In the entangled singlet state (e.g., two spin-1/2 particles with total spin 0), perfect anti-correlation allows perfect prediction of Bob’s spin outcome from Alice’s measurement, without disturbing Bob’s particle.
• Yet QM assigns no definite value to Bob’s spin before measurement (incompatible observables like spin along different axes cannot have simultaneous definite values).
• Conclusion: QM must be incomplete; there should be pre-existing elements of reality (hidden variables) determining outcomes.

Bell’s theorem (1964) later showed that any local hidden-variable completion must satisfy Bell inequalities, which QM violates and experiments confirm. Local realism is untenable.

2. LRT’s Ontological Architecture

LRT divides reality into two asymmetric domains (see The Instantiation Barrier Explained):

$I_\infty$ (Infinite Information Space)

All representable configurations, including superpositions, entanglements, indefinite states. This space is non-Boolean, non-classical, allowing correlations that appear “non-local” from a classical viewpoint.

$A_\Omega$ (Logical Actuality Layer)

Completed measurement records and distinguishable physical states. This layer is strictly Boolean, obeying $L_3$ without exception: determinate identity, no contradictions, no third option.

The Interface

Measurement / actualization = interface map $f_M : I_\infty \to A_\Omega$, which enforces $L_3$ compliance by projecting rich possibility onto single, classical outcomes per run.

Quantum mechanics emerges as the unique minimal-cost interface that maximizes exploration of $I_\infty$ while rigidly preserving $L_3$ at actualization (via Born rule, Hilbert structure, complex numbers, etc.).

3. How LRT Dissolves EPR

The paradox dissolves because EPR’s reality criterion implicitly assumes that elements of reality must exist at the vehicle level ($A_\Omega$) prior to measurement. LRT denies this.

Entangled States Live Entirely in $I_\infty$

The joint wavefunction describes non-separable correlations across arbitrary distances. These correlations are real features of possibility space but not yet actualized as distinguishable records.

No Pre-Existing Definite Values in $A_\Omega$

Before measurement, neither particle has a determinate spin value at the vehicle level (pointer/detector record). The state in $I_\infty$ is indefinite with respect to any specific basis, consistent with QM’s no simultaneous values for incompatible observables.

Perfect Prediction Without Disturbance

Alice’s measurement actualizes her local record in $A_\Omega$ (e.g., “up”), which enforces the correlated outcome for Bob via the interface dynamics. Bob’s distant measurement then actualizes the anti-correlated record, but no instantaneous physical influence crosses space.

The correlation is pre-encoded in $I_\infty$ structure; actualization is local at each end.

No Violation of Locality

The interface map is local: each party’s measurement setting determines their own projection to $A_\Omega$. No-signaling holds because controllable information transfer is forbidden (would require coordination violating distinguishability independence).

Reality Criterion Reinterpreted

EPR’s criterion applies only if prediction is certain without disturbing the system at the actuality level. In LRT:

• The prediction is certain because of $I_\infty$ correlations
• But the “element of reality” is not a pre-existing value in $A_\Omega$; it’s the disposition (vehicle-weight) constrained by $L_3$
• Once Alice actualizes, Bob’s disposition collapses to certainty in possibility space, but his local actualization remains undisturbed until measured

Thus: QM is complete in describing $I_\infty$ (all representable configurations) and the interface to $A_\Omega$. The “incompleteness” EPR perceived stems from expecting classical realism (definite values always in $A_\Omega$) rather than recognizing the ontological asymmetry enforced by $L_3$.

4. Bell Violations and Non-Locality

How does LRT handle Bell’s theorem and the experimental violations?

Bell inequalities assume local realism (local hidden variables assigning pre-existing values).

LRT has no local hidden variables. Dispositions are objective but contextual/non-separable in $I_\infty$.

Correlations violate Bell because $I_\infty$ allows non-classical structure; actualized outcomes respect $L_3$ locally (Boolean records) while exhibiting non-local statistical dependence.

Tsirelson bound (if derivable in LRT) emerges as the maximal correlation strength before distinguishability costs become prohibitive (infinite violation energy).

This aligns with experimental Bell tests: perfect anti-correlation in one basis, yet no signaling, no $L_3$ violation at vehicle level.

5. Comparison: LRT vs. Other EPR Resolutions

Key Differences

vs. Many-Worlds: LRT avoids branching ontology; all “branches” are unrealized possibilities in $I_\infty$. Only one actualization per run occurs (enforced by $L_3$). See One-World Realism.

vs. Bohmian: No need for non-local pilot wave or particles; correlations are structural in $I_\infty$.

vs. Collapse models: No stochastic collapse added; apparent collapse is interface enforcement.

vs. QBism/Relational: Vehicle-weights are objective (constrained by logic), not purely subjective/relative.

6. The Core Insight

The EPR paradox assumes that:

1. Quantum correlations require explanation
2. Any explanation must involve either (a) pre-existing definite values or (b) non-local influence

LRT rejects this dichotomy by introducing a third option:

(c) Pre-existing correlational structure in possibility space ($I_\infty$) that constrains actualization ($A_\Omega$) without constituting either definite values or causal influence.

This is not “action at a distance” because there is no action. It is not hidden variables because there are no pre-existing values. It is constraint satisfaction: the entangled state satisfies certain constraints, and measurement reveals which values satisfy those constraints.

7. Potential Objections

“Isn’t $I_\infty$ just hiding the non-locality?”

Non-locality is permitted in possibility space but never actualized as influence. The $I_\infty$ structure is non-separable, but this is not “hidden non-local variables.” No signal travels; no influence propagates. Constraints are constitutive, not causal.

“How is this different from saying ‘it’s just quantum mechanics’?”

LRT provides conceptual grounding that standard QM lacks. It explains why the formalism takes the form it does (minimizing distinguishability violation energy while maximizing $I_\infty$ exploration). The Born rule, Hilbert structure, and no-signaling are not brute facts but consequences of $L_3$ constraint.

“What about relativistic considerations?”

The “global constraint” picture works naturally in non-relativistic QM. In relativistic contexts, the constraint is on the $I_\infty$ state, not on spacetime events. The entangled state does not have spatial parts that need to coordinate. Different reference frames describe measurement orderings differently, but all frames agree on correlations.

A fully relativistic formulation of LRT remains future work. See Spacetime from Determinate Identity for programmatic directions.

8. Implications and Predictions

Quantum Gravity

LRT predicts $L_3$ compliance persists at the vehicle level even in curved spacetime or Planck-scale physics. Any actualized geometry/record must remain Boolean.

Post-Quantum Theories

If post-quantum correlations violating Tsirelson’s bound were discovered (while remaining non-signaling), this would challenge LRT’s derivation path. So far, no such violations have been confirmed.

Experimental Tests

LRT is testable and vulnerable:

• 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
• Evidence of non-Hilbertian probability structure would undercut the Gleason/reconstruction route

9. Summary

LRT offers one of the cleaner resolutions to EPR among realist interpretations:

1. The paradox is apparent, arising from demanding classical elements of reality in a world where logic constrains actualization to be Boolean while allowing rich, non-separable possibilities beforehand.

2. QM is complete. It describes the full interface between non-Boolean $I_\infty$ and Boolean $A_\Omega$.

3. Locality is preserved at the level of actualized events.

4. Bell violations are explained as structural features of possibility space.

5. The Born rule / Hilbert structure are grounded in the same logical constraints.

This makes EPR not a refutation of QM’s completeness but a confirmation of LRT’s asymmetry: we can conceive violations of $L_3$ (as EPR did in demanding simultaneous definite values), yet physics never produces them because such violations cannot be instantiated without losing distinguishability.

Further Reading: LRT Papers and Articles

Core Technical Papers

• Logic Realism Theory: Physical Foundations from Logical Constraints - The foundational Position Paper establishing the $I_\infty$/$A_\Omega$ ontology
• Deriving the Born Rule from Logical Constraint - Full derivation (Zenodo DOI: 10.5281/zenodo.18756374)
• It from Bit, Bit from Fit - Conceptual synthesis and entanglement analysis
• Complex Hilbert Space from Determinate Identity - Derives Hilbert space structure from $L_3$

Related Articles

• LRT and the Future of Quantum Interpretations - How LRT synthesizes major interpretations
• The Instantiation Barrier Explained - The $I_\infty$/$A_\Omega$ distinction
• Common Objections to Logic Realism - Addressing frequent critiques

Topics

• The Three Laws ($L_3$) - Identity, Non-Contradiction, Excluded Middle
• Entanglement - Nonlocal correlations through global vehicle structure
• One-World Realism - Everettian mathematics without Many-Worlds ontology
• Tsirelson Bound - Maximum quantum correlations

External References

1. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47(10), 777-780.
2. Bell, J.S. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Fizika, 1(3), 195-200.
3. Bell’s Theorem - Stanford Encyclopedia of Philosophy
4. The Einstein-Podolsky-Rosen Argument in Quantum Theory - Stanford Encyclopedia of Philosophy
5. Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers. Physical Review Letters, 49(25), 1804.

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