Deterministic QM and the absurdity of the Copenhagen ontology
anton vrba
The Freedman and Clauser (1972) experiment (I recommend reading Freedman's Ph.D. thesis, https://escholarship.org/uc/item/2f18n5nk) exploited the two-photon cascade of the excited calcium atom from the upper level 4p² ¹S₀ to the ground state 4s² ¹S₀, via the intermediate 4s4p ¹P₁ state, emitting two photons in succession: ν₁ at 551.3 nm (green) and ν₂ at 422.7 nm (violet).
On the basis of the calcium two-photon cascade, I want to discuss an absurdity in the Copenhagen 1927 quantum ontology.
The two-photon cascade leaves both photons with spin +1 or −1, i.e. left- or right-circularly polarised. At creation it is determined locally which colour photon, at which polarisation state, is sent to Alice and to Bob. Copenhagen interprets our ignorance as
Colour: |GrVi⟩ + |ViGr⟩
Polarisation: |RR⟩ + |LL⟩
— the photons are held to be in an indeterminate superposition of both colour and polarisation.
Case I: The colour wavefunction "collapses" as the photons interact with Alice's and Bob's colour filters. But we could replace the filters with prisms and simply separate the green and violet photons spatially. Bob's measurement is anti-correlated with Alice's: if Alice detects green, Bob detects violet. This is a hidden variable already fixed at emission — no non-commuting observables are involved, and no local hidden-variable theory has any trouble with it. It is, structurally, no different from Bertlmann's socks.
Case II: Similarly we can split the R and L photons into two beams using Pancharatnam–Berry (PB) phase metasurfaces — flat optics engineered with subwavelength nanostructures that impart opposite phase gradients to L and R photons, bending L one way (+θ) and R the other (−θ). Alice and Bob now measure coincidence in circularity: again a "collapse," achieved by nothing more than spatial sorting.
Case III: Alice and Bob perform the classical polarisation-entanglement experiment and measure correlated linear polarisation. Here we have a polarisation-wavefunction collapse, on the usual probabilistic reading. But the ignorance was never about which colour or which circularity the photon carried — it is ignorance of the phase at creation and of the travel time, which together fix the phase θ with which the photon interferes at the polariser, selecting the ordinary (cos) or extraordinary (sin) beam via cos²θ + sin²θ = 1.
Case III differs from Cases I and II in that Alice and Bob now interfere with the photons' spin angular momentum itself, that is the Φ⁺ = |RR⟩ + |LL⟩ is projected onto the superposition Φ⁻ = |HH⟩ − |VV⟩. Suppose Alice projects her photon onto H. If nothing else changed, the Universe would gain angular momentum — which cannot happen. Conservation (I call this a nil-residue universe: everything sums to zero) immediately forces Bob's photon into H as well. This immediacy is what gets attributed to "wavefunction collapse."
Conclusion: Copenhagen invokes the same indeterminacy — a superposition awaiting collapse — for all three cases. Cases I and II are trivial: nothing about them is non-classical, and neither differs in kind from Bertlmann's socks. Only Case III involves a genuine conservation constraint enforced across the pair. Treating all three as the same kind of "indeterminacy" is the absurdity. The only indeterminacy is the relative phase at creation, which, together with the undetermined time of flight, fixes a probability on the polarisation outcome. Once Alice polarises, Bob's polarisation state is immediately determined, independent of whatever measurement angle is subsequently chosen. Our task is to find the fundamental mathematical description to describe this deterministic behaviour.