If Planck's constant measures the field's density, then find the test that separates it from the fine-structure constant

Why the library suggests it

The library holds one serious published attempt to build Planck's constant out of something else: model a massive particle as an oscillating electric dipole, let two such dipoles interact through Weber electrodynamics, expand in orders of speed, and three familiar effects fall out of one calculation — a first-order term behaving like the Casimir force, a second-order term behaving like gravity, a third-order term behaving like inertia. Matching the Casimir term to the ordinary Casimir pressure fixes the last free coefficient, and Planck's constant comes out within seven per cent of the measured value with nothing left to tune (The Planck Constant and the Origin of Mass Due to a Higher Order Casimir Effect, 2018). That construction is the key to the test, because it ties Planck's constant to the Casimir force specifically rather than to the fine-structure constant. Meanwhile the precision instruments that would do the measuring exist and are at their sharpest ever: the muon's magnetism is now known to 127 parts per billion, and it is a direct reading of what the vacuum around the muon contains (Measurement of the positive muon anomalous magnetic moment to 127 ppb, 2025); vacuum magnetic birefringence has been bracketed to within a factor of about seven of the quantum-electrodynamic prediction, with the magnet that would close the gap already named (The PVLAS experiment, 2020). The polarizable-vacuum formalism that makes "change the medium, change the metric" a calculation rather than a slogan is Polarizable-Vacuum representation of general relativity (1999). And the historical precedent for asking whether a redshift can be a property of the medium rather than of motion — argued from coverage, order-of-magnitude numbers and a laboratory test rather than from preference — is Non-velocity Redshifts and Photon-Photon Interactions (1972).

The experiment or build

The first move is theoretical and costs nothing: using the Weber-Casimir construction, derive what a change in vacuum energy density would do to a Casimir force measurement, to vacuum magnetic birefringence and to the muon anomaly separately, and identify which pair of those observables moves differently. The settling measurement is a stated pair of precision observables whose ratio changes if the vacuum energy density changes and does not change if only the fine-structure constant does — followed by the measurement of that ratio. Writing down the first half is a publishable result on its own, and it is the missing piece the position's own advocates say they lack. A companion astronomical test already exists in the literature and is cheap: look for quantisation in redshift data, which is a statistical study of catalogues that are already public.