Claim: Mach–Zehnder tests transport closure, not superposition.
Method: Two anti-correlated reasoning paths that must agree.
Method: Two anti-correlated reasoning paths that must agree.
Experimental Skeleton
- Input motion enters a beam splitter
- Two transport corridors are defined
- Mirrors redirect transport
- A second beam splitter recombines corridors
- Detectors register outcomes
Path A — Transport Closure Geometry
The two corridors accumulate phases $\phi_1$ and $\phi_2$.
$$ \Delta \phi = k (L_1 - L_2) $$
The second beam splitter recombines transport.
If $\Delta \phi = 0$, transport closes → all detections at $D_1$.
If $\Delta \phi = \pi$, closure fails → all detections at $D_2$.
No object ever splits. Only transport corridors differ.
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Path B — Phase Accounting Statistics
Each emission samples an initial phase offset $\theta$.
The interferometer maps $\theta$ deterministically to an output port.
$$ P(D_1) = \cos^2\!\left( \frac{\Delta \phi}{2} \right), \quad P(D_2) = \sin^2\!\left( \frac{\Delta \phi}{2} \right) $$
Statistics reproduce the same closure rule.
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Delayed Choice Is Not Retrocausality
Removing $BS_2$ breaks transport closure.
Phase bookkeeping changes at the point of intervention — not backward in time.
The paradox arises only if frames are frozen mid-transport.
Transport-First Resolution
- Beam splitters define transport options, not splits
- Mirrors redirect phase, not particles
- Detectors mark completed transport
- Interference tests closure, not duality
Invariant Connection
The cosine-squared law is the same invariant seen in:
- Double-slit
- Buffon orientation averaging
- Parseval conservation