Entanglement

Entanglement is the phenomenon where quantum systems exhibit correlations that cannot be explained by local hidden variables. In LRT, these correlations arise from the global structure of the representational vehicle—not from “spooky action at a distance.”

The Standard Puzzle

Entangled particles exhibit correlations that:

• Violate Bell inequalities (ruling out local hidden variables)
• Appear to require instantaneous coordination across arbitrary distances
• Yet do not permit faster-than-light signaling

How can distant measurements be correlated without communication?

The LRT Dissolution

There is no “spooky action at a distance” because there is no action.

$L_3$ as Global Constraint

In LRT, $L_3$ operates as a global constraint field. It does not propagate from place to place like a signal; it simply holds, everywhere, always.

An entangled state is a single configuration in $I_\infty$ with extended properties—not two separate things mysteriously connected.

Non-Local Vehicle, Local Outcomes

Consider the Bell state:

This is a single representational vehicle that cannot be factorized into separate vehicles for particles A and B. The physical situation is represented as a unified configuration spanning both locations.

When measurement occurs:

• The global vehicle transitions to a new global vehicle
• Both particles now produce correlated sharp records
• The correlation was encoded in the vehicle structure prior to measurement

Constraint Satisfaction, Not Communication

The correlations are not caused by one particle signaling the other. They are constraint satisfaction:

• The entangled state satisfies certain constraints
• Measurement reveals which values satisfy those constraints
• No signal is needed because the constraint was never “communicated”—it was constitutive of the state

Constraints Are Not Hidden Variables

This might sound like non-local hidden variables. It is not.

A variable has a value. Hidden variable theories posit that particles have definite properties we don’t know.

A constraint is a rule. The constraint “A + B = 0” does not assign values to A and B; it specifies a relationship. If we measure A = 3, we immediately know B = -3—not because a signal traveled, but because the constraint was always in force.

In LRT:

• The entangled state is a single $I_\infty$ configuration satisfying certain constraints
• Measurement reveals which values satisfy the constraints
• No signal needed because the constraint was constitutive

This is why Bell’s theorem does not threaten LRT. Bell rules out local hidden variables—pre-existing definite values. LRT does not posit such values. The $I_\infty$ state is genuinely indeterminate; constraints specify relationships between outcomes, not the outcomes themselves.

Why Correlations But Not Signaling

The correlations reflect the logical structure of a unified state. No information travels because there is nothing traveling—just global consistency being enforced.

This explains why entanglement:

• Produces correlations: Global structure encodes relationships
• Cannot signal: No information is transmitted; consistency is revealed

Relativistic Considerations

The “global constraint” picture works naturally in non-relativistic QM, where simultaneity is well-defined. In relativistic contexts:

The concern: General relativity has no preferred foliation. Does $L_3$ enforcement require a preferred frame?

The response: 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 the ordering of measurements differently, but all frames agree on the correlations.

A fully relativistic formulation of LRT remains future work.

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