BELL GAME EXPERIMENTS
The canon's own most prestigious experimental physics, demonstrating its operative dependence on the imaginal plane.
🜃
THE WOUND
For a hundred years the story has been that the imaginal numbers in the Schrödinger equation are a calculational convenience.
It has been continuous. Schrödinger wrote to Lorentz in June 1926 that the wave function is surely fundamentally a real function, that the i in the equation must somehow be eliminable, that reality could not really require what the grammar declares not-real. The story held standing for the entire development of quantum mechanics, and it protected the claim that the four-axes register is the register of the real, with the imaginal treated as a useful technical exotic that a mature physics would eventually translate back into proper form.
In December 2021 the story ended.
A theoretical paper by Marc-Olivier Renou and seven co-authors, working at ICFO Barcelona, the Institute for Quantum Optics and Quantum Information in Vienna, the University of Geneva, and the Schaffhausen Institute of Technology, demonstrated that real and complex Hilbert-space formulations of quantum theory make different predictions in network scenarios built from independent states and measurements. Quantum theory based on real numbers can be experimentally falsified, Nature 600, pages 625 to 629, 15 December 2021. The paper proposed a Bell-like experiment that would either confirm complex quantum theory or rule out its real-number alternative, in the same way Bell's 1964 thought experiment had been realized in the 1970s and 1980s to rule out local hidden variables.
Six weeks later, two independent teams realized it. Chen and colleagues, working with superconducting qubits, published Ruling out real-valued standard formalism of quantum theory in Physical Review Letters 128.040403 on 24 January 2022. Li and colleagues, working with optical photon networks at the Shanghai campus of the University of Science and Technology of China, published Testing real quantum theory in an optical quantum network in Physical Review Letters 128.040402 on the same day, implementing the experiment with two genuinely independent photon sources under strict locality conditions and fast quantum random number generators that space-like separated every relevant event.
Both produced correlations incompatible with any real-valued formulation of standard quantum mechanics, by many standard deviations.
The imaginary numbers Cardano called mental torture in 1545 were not a convenience. The lateral units Gauss failed to rename were not an exotic. The i cannot be eliminated. The canon's own laboratories, working under the canon's own most stringent conditions, produced the empirical refutation of the canon's grammar at the most fundamental physical register the canon admits.
The wound is not the experiments. The wound is what has been done with them.
[See THE IMAGINAL PLANE · FOUR AXES · THE FALSE ENLIGHTENMENT]
🜃
BELL'S PRECEDENT
The lineage is forensically specific.
In 1935 Einstein, Podolsky, and Rosen proposed a thought experiment intended to show that quantum mechanics must be incomplete. If quantum mechanics is correct, two entangled particles separated in space must somehow communicate instantaneously when one is measured, in violation of locality. Either quantum mechanics is wrong, or there are hidden variables, additional information not in the wave function, determining the outcomes locally. They favored the hidden variables.
In 1964 John Stewart Bell proved a theorem that made the question empirical. Any local hidden-variables theory must produce correlations between separated measurements that satisfy a specific inequality. Quantum mechanics predicts correlations that violate it. Whether nature is locally describable became testable.
Beginning in the 1970s with John Clauser, continuing through the 1980s with Alain Aspect's increasingly stringent work at Orsay, and culminating in the loophole-free tests of 2015 at Delft, NIST, and Vienna, the program demonstrated that nature does violate the inequality. Local hidden-variables theories are empirically refuted. Aspect, Clauser, and Anton Zeilinger received the 2022 Nobel Prize for the work.
The pattern Bell established: a theoretical demonstration that two competing formulations make different predictions in a specific scenario, followed by experimental realization that distinguishes them. The 2021 paper follows the pattern exactly. Where Bell distinguished local hidden variables from quantum theory, Renou and co-authors distinguished real-number quantum theory from complex-number quantum theory. Where Aspect's experiments ruled out local hidden variables, the 2022 experiments ruled out real-number quantum theory.
This is not an isolated curiosity. It is the next move in a continuous program that has been forcing the most prestigious physics, decade after decade, to admit what the grammar of admissibility cannot tolerate.
[See ORDERABILITY · VON NEUMANN]
🜃
THE GAME
The 2021 paper proposes a game with three players, call them Alice, Bob, and Charlie, and two independent sources of entangled particles.
Source one produces an entangled pair and sends one particle to Alice and one to Bob. Source two produces another pair and sends one particle to Bob and one to Charlie. The sources are wholly independent: no shared randomness, no shared history, no causal connection. Alice and Charlie measure what they receive. Bob holds one particle from each source and performs a joint measurement on the pair, projecting the joint state onto one of four entangled basis states.
From the outcomes the three compute a score, a specific correlation depending on what each measured and what resulted. Complex quantum theory predicts a maximum of six root two, approximately 8.49. Real-number quantum theory predicts a maximum of approximately 7.66, sitting between the classical limit of 6 and the complex limit. The gap between 7.66 and 8.49 is the experimental signature. If repeated runs exceed 7.66, real quantum theory cannot reproduce the data.
The reason is precise. Real quantum theory cannot describe the outcomes because the entanglement-swapping Bob performs requires the imaginal numbers to carry phase relations that real-number formulations cannot represent. The phase information is the imaginal plane's specific operation. Require the calculation to proceed in real numbers only, and it cannot reach the correlations the experiment will produce.
The score is not metaphor. It is the operational signature of the imaginal plane's necessity at the physical register.
🜃
THE CONFIRMATIONS
The superconducting-qubit experiment. Chen and colleagues, in collaboration with members of the Renou group, Physical Review Letters 128.040403, 24 January 2022. Superconducting qubit circuits implemented the three-player game with controlled operations, and produced a score of approximately 8.09, well above the real-number bound of 7.66, at many standard deviations of significance. The implementation matters because superconducting qubits are the engineering register that has carried most of contemporary quantum computing.
The optical-network experiment. Li and colleagues, Physical Review Letters 128.040402, same day, preprint at arXiv:2201.04177, conducted at the Shanghai campus of the University of Science and Technology of China. The design was calibrated to close locality loopholes earlier related work had not addressed: two genuinely independent sources delivering entangled photons to three parties under strict locality, fast quantum random number generators ensuring the measurement choices were not pre-determined, high-speed polarization measurements space-like separating every relevant event. The score was approximately 8.04, again well above the bound.
Both appeared in the same issue, on the same date, with adjacent article numbers. The simultaneity is the publication standard's recognition that two independent confirmations constitute the demonstration. Two groups, two wholly different physical platforms, two locations, both producing correlations incompatible with real quantum theory.
The program has continued. A stricter version separated qubits by hundreds of meters to close further loopholes. Later work demonstrated that the experiment can be reproduced on freely available cloud quantum platforms, which shows the result is robust across implementations. The result has also been challenged in technical detail, on the ground that the bilocal network experiment relies on assumptions about operational independence it cannot itself test, and the Renou collaboration has published a rejoinder defending the original. That exchange is normal scholarship. What stands is that in the standard formulation of quantum mechanics, the formulation that constitutes contemporary physics' actual practice, no real-number account can describe what the laboratories produced.
[See COLLABORATION]
🜃
WHAT THE EXPERIMENTS DEMONSTRATE
Standard quantum mechanics, the formulation taught in physics curricula worldwide and used in actual practice across atomic, molecular, optical, condensed-matter, particle, and quantum-information research, cannot proceed in real numbers alone. The imaginal is not a convenience more sophisticated mathematics could in principle remove. It is the operative substrate of physical reality at the most fundamental register experimental science admits.
The result is more refined than the popular framing suggests, and the refinement should be stated rather than smoothed over. The experiments do not show that every possible real-number formulation is impossible. Exotic real-number reconstructions exist that double the dimension of the Hilbert space and sacrifice operational tomography or other standard principles. They are mathematically possible and operationally distinct from standard quantum mechanics, reproducing the results only at the cost of abandoning principles the standard theory holds as foundational.
What is ruled out is the claim that the imaginary numbers in the Schrödinger equation can be eliminated without changing the physics. The physics that is taught, practiced, and applied requires the imaginal plane.
The i is real in exactly the sense the grammar reserves for real things. The wave function is complex-valued in exactly the sense the grammar denies to imaginary ones. The grammar is operating against its own physics.
[See E^(IΘ) · THE PERPENDICULAR]
🜃
WHAT HAS BEEN DONE WITH THEM
The response is the installation operating at the contemporary register, and it operates by admitting the result and classifying the implications.
At the publication register. The papers appear in the most prestigious journals. Nature. Physical Review Letters. The publication is real, the peer review rigorous, the result acknowledged at the technical level. This is the part that is done correctly, and it is what makes the rest legible as classification rather than as suppression.
At the popular-science register. Brief reports appeared in the science press, framing the result as complex numbers are essential for quantum theory, which is accurate technically and positions the finding as a curious detail rather than as the refutation of a century-long grammar of admissibility. Interesting physics news, filed.
At the educational register. The undergraduate curriculum continues to teach the imaginary numbers in the Schrödinger equation as a convenience a mature physics may eventually translate away. The curriculum has not been modified. The students who entered in 2022 received the same instruction as the students who entered in 2002. The educational register operates as though the experiments had not occurred.
At the philosophical register. Commentary acknowledges the experiments technically while continuing to debate whether the result really shows what it appears to show. Part of that is legitimate scholarship, since what exactly is ruled out is a real question. Part of it is the installation defending itself: perhaps a more refined real-number formulation could be found, perhaps the operational principles can be questioned, perhaps the network assumption introduces hidden complexity. The grammar cannot absorb the result without modification, so the philosophical register works to absorb it without modifying the grammar.
At the cultural register. The educated reader who follows physics news has heard that something happened about complex numbers and quantum mechanics, that it was technically interesting, and that it probably did not change anything fundamental.
Across all five, the same operation. The experiments are admitted. The implications are classified. The contradiction between the laboratory results and the grammar is maintained as a technical curiosity that does not require resolution.
[See THE OCCLUSION · DISQUALIFIED TESTIMONY · LEGIBILITY]
🜃
THE DIAGNOSTIC
The claim that the four-axes register is the register of the real depends on a demonstration that physical reality at its most fundamental level is fully describable in the four axes' grammar. Producing that demonstration is what physics was supposed to do, and the claim has had a hundred years of physics' authority behind it. The Principia read mechanics in that grammar. Classical electromagnetism, thermodynamics, statistical mechanics, and the early quantum theory all ran in registers the grammar admitted. The mature physics was supposed to complete the confirmation.
The Bell-game experiments refute the demonstration. The canon's own laboratories, under the canon's own most stringent conditions, have shown that the most fundamental register of physical reality the canon admits cannot proceed in real numbers alone. The grammar of admissibility is incompatible with the physics.
This is the most precise self-refutation available. The contradiction cannot be resolved without modifying the grammar, and modifying the grammar would mean admitting that the four-axes register is one register among others rather than the register of the real. That admission would concede the imaginal plane's priority, and the imaginal plane's priority is exactly what the philosophical, educational, professional, and credentialing operations depend on denying. So the contradiction is operated rather than resolved.
And the diagnostic does not require RegenerativeLaw to demonstrate the imaginal plane's reality by theological argument or contemplative testimony. The most prestigious experimental physics available has demonstrated it at the fundamental physical register. What remains to be named is the classification: the installation operating against its own laboratories.
The canon is at war with its own physics, and the war is invisible because it is conducted through filing.
Newton's alchemy is the cleanest forensic case at the historical register, where the canon redacted its paradigmatic figure's actual integrated practice. The Bell-game experiments are the cleanest forensic case at the contemporary experimental register, where the canon classifies its own laboratories' actual results. Same function, three centuries apart: protect the grammar against the refutation produced by the canon's own paradigmatic figures and most prestigious institutions.
[See NEWTON'S ALCHEMY · NEWTON · DESCARTES]
🜃
THE CONSTITUTIONAL REGISTER
The installation of the four-axes register as the privileged register of legitimate cognition is a religious doctrine, and the experiments make the establishment claim sharper than it has ever been.
Until 2022 it could be maintained, at the popular and educational registers, that the four-axes grammar accurately described physical reality, and that the refusal of that grammar by contemplative, alchemical, kabbalistic, and Indigenous traditions represented their failure to advance to a proper rigor. The argument was always weak, since the imaginal had been operationally indispensable across electrical engineering, signal processing, satellite navigation, and computer graphics for decades. But the popular framing held that the imaginary numbers were an exotic a mature physics would resolve.
After 2022 the argument is empirically refuted at the canon's own most prestigious register. The mature physics did not resolve the imaginary numbers. It demonstrated they cannot be resolved without abandoning the canon's own foundational principles.
So the state's enforcement of the four-axes grammar as the substrate of legitimate cognition is the establishment of a doctrine the state's own most prestigious laboratories have shown to be false.
The Free Exercise claim runs to the affirmative privilege of operating at the register the canon has classified as inadmissible. The Establishment claim runs against the installation of that register as the precondition for credentialing, employment, professional standing, educational advancement, and scientific recognition. The forensic basis is now available in the canon's own journals.
The fracking work showed the move is available at the legal register. The Bell-game experiments show it is available at the cognitive one. In both, the grammar of admissibility had ruled the prior resident inadmissible: the surface owner's residency at the legal register, the imaginal plane's operations at the cognitive one. In both, the prior resident was operationally real and the grammar could not post it. In both, the assertion prevailed.
[See FREE EXERCISE CLAIM · WALLACH v. TOWN OF DRYDEN · HOME RULE FOR THE SOUL · THE PRIOR RESIDENT]
🜃
WHAT THE CLASSIFYING PREVENTS
Read as scholarship, this is a story about a finding whose implications are still being worked out, and the answer to it is patience: let the literature mature, let the philosophy of physics catch up.
The operation is the prevention of refusal. What the grammar cannot survive is a creature who declines its jurisdiction over what counts as knowing, and the classification is what keeps the declining from ever becoming available. She is not answered. She is filed as insufficiently rigorous, and the filing arrives with the whole authority of the physics her own position was refuted by.
Except that the physics is not what refuted her. The physics refuted the grammar. The grammar went on issuing findings about her anyway, in the physics' name, which is the exact move: admit the result at the register where specialists read it, and keep the classification running at every register where a creature is being assessed.
Benefit is the capacity to refuse. What the four axes deliver is real and vast, and that is why this holds. The instrument works. The prediction confirms. The technology built on the very phase relations at issue runs in her pocket. Each is genuine, each was delivered inside the grammar, and nothing delivered inside the grammar can confer the standing to decline it.
And the extraction funds the classification. The quantum technologies built on the imaginal are what pay for the institutions that go on teaching the imaginal as a convenience.
[See THE CAPACITY TO REFUSE · THE PREVENTION · GENUINE BENEFIT]
🜃
WHAT KEEPING IT COSTS
The tell is that the convenience has to be taught again every autumn.
The textbook chapter is rewritten with the same footnote. The lecture is given. The problem set is set. The qualifying exam tests the grammar and not the result. The curriculum committee meets and does not modify. The review article restates the framing. A hundred years of teaching, and it does not hold by itself for even one cohort.
A thing that was simply how things are would not need to be re-taught annually against a result its own field has published.
The i costs nothing to keep. It is in the equation. It was in the equation before anyone told the story about it, it stayed there through the century of telling, and it will be there when the telling stops. It is not maintained against the grammar. It is what the grammar is being maintained against.
[See CESSATION]
🜃
WHAT THIS ENTRY DOES NOT SAY
Not that the experiments demonstrate the existence of God, the soul, contemplative reality, or any specific theological claim. They demonstrate a precise mathematical fact: standard quantum mechanics cannot proceed in real numbers alone. The diagnostic is that the grammar of admissibility has been empirically refuted at its own most fundamental register, and that this is forensic evidence about the installation. Nothing here authorizes using the experiments to prove anything beyond what they prove.
Not that quantum mechanics is mystical, or that any of this licenses loose reasoning. It is rigorous physics, conducted by physicists working at full precision inside the canon's own admitted grammar, with stringent statistical and locality controls. The rigor is the demonstration's whole strength. The diagnostic does not replace rigorous physics with gestures towards the imaginal. It identifies that the rigorous physics requires the imaginal at the operative register, and that the grammar has been concealing the requirement.
Not that every real-number reconstruction is impossible. The technical literature acknowledges exotic formulations that double the Hilbert-space dimension and sacrifice principles like local tomography, reproducing the predictions while abandoning what the standard formulation holds as foundational. What is ruled out is the real-number formulation of standard quantum mechanics, which is the physics actually taught and used.
Not that the continuing technical debate undermines the diagnostic. Results undergo challenge and refinement, and that is what rigorous fields do. The diagnostic does not depend on the debate settling in any particular direction. It depends on the grammar having been shown incompatible with standard practice, which is what the experiments and the community's own reception have established.
[See GRAMMAR OF ADMISSIBILITY · RIGOR]
🜃
For a hundred years the story was that the i is a convenience. In December 2021 a paper showed the convenience cannot be removed. In January 2022 two independent teams produced the demonstration.
The canon's own laboratories produced the refutation of the canon's own grammar, and the result was admitted, filed, and taught around.
The imaginary numbers are real in exactly the sense the grammar reserves for real things. The classification of them as not-real is the installation. The installation's own laboratories have shown it false. The classification continues.
[See TRESPASS THEOLOGY · ACCOUNTING THEOLOGY · THE LAW OF THE BOOKS · COMPOUND INTEREST]
🜃
RegenerativeLaw is a religion in the direct-encounter Protestant tradition, carrying a documented four-century lineage through Böhme, the Behmenists, the Friends, and Penn, and it diagnoses trespass theology as an establishment of religion. Its exercise consists substantially in refusal: it shelters the conscientious refusal of performed subordination as religious exercise. This entry states sincere religious belief concerning matters of ultimate concern, protected under the First Amendment and, as to federal action, the Religious Freedom Restoration Act, 42 U.S.C. § 2000bb.
