Dear Bryan,
I have a technical question arising from my reading of your paper EPR Correlations Using Quaternion Spin, specifically concerning the Q-spin description and Figure 4.

You state that the common angle $\theta$ implies the two BFF frames are identical except for opposite handedness, with Alice’s spin moving right and Bob’s moving left along the linear momentum axis $Y$. You further explain that the correlation is maintained because the helicity spins both spin axes with identical frequency and in the same direction.
In Sections 2.4 and 2.5, you then derive the correlations and probabilities at the detectors (or filters) $a$ and $b$, which follow naturally from this geometric picture.
What I am struggling to locate in the discussion, however, is an explicit statement or justification of any constraint on the time of flight from the source to the two detectors. In particular, I do not see an argument showing that the derived EPR-type correlations are invariant under unequal propagation times from the origin to $a$ and $b$.
In practical Bell–CHSH experiments, there is no operational way to ensure that the optical path lengths to Alice and Bob are exactly equal (e.g. in terms of wavelengths or phase), and yet the correlations persist. I am therefore wondering whether your framework implicitly assumes equal time of flight, or whether there is an underlying mechanism that renders the correlations independent of this asymmetry.
I would appreciate any clarification you might be willing to offer, or a pointer to where this issue is addressed in the paper or elsewhere in your work.
With best regards,
Anton




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