The Entangled State Is a Single Entity

Up until the moment of actualisation, the entangled system is not two particles separated by space. It is a single, unbroken probability state in the pre-state.

The entangled state |AB⟩ = (1/√2)(|↑↓⟩ − |↓↑⟩) is one mathematical object. It lives in the tensor product of the Hilbert spaces of A and B.

The tensor product provides algebraic distinguishability: A and B are different degrees of freedom. But algebraic distinguishability is not spatial separation.

The tensor product ℋ_A ⊗ ℋ_B combines degrees of freedom; it does not embed them into spacetime. Spatial separation is a property of the manifold, not of the Hilbert space.

Two subsystems can be algebraically distinct without being spatially separated. In the pre-state, there is no distance between A and B. They have not been written to the manifold as separate records.

The labels “A” and “B” refer to degrees of freedom, not locations.

Alice and Bob prepare the entangled state and send the particles to opposite ends of the galaxy. In the manifold’s description, the particles separate. The records of their trajectories diverge.

But the entangled state — the shared probability state — was never split. It remained a single entity in the pre-state.

The spatial separation is a property of the records that have been written so far (the trajectories), not a property of the probability state that has not yet collapsed.