A cascade provides pairs and a timing relation
Freedman and Clauser measured polarization correlations from a calcium cascade in 1972. Each arm contained a removable polarizer and a photon detector. Coincidences at selected relative angles were compared with reference measurements made after removing polarizers.
The evidence is stronger than a statement that two counts agree. A bound constrains a particular combination of rates under declared assumptions. To read it, identify the numerator, the reference exposure and the events admitted by the coincidence circuit before asking whether a curve resembles a quantum prediction.
Read the evidence: S. J. Freedman and J. F. Clauser (1972), Experimental Test of Local Hidden-Variable Theories — LBL-392 preprint, January, University of California archive
Write the rate contract before the number
In the displayed expression, the rate with subscript zero is measured with both polarizers removed; the other rates use the stated angle between transmission axes. The local bound shown is the experiment’s reduced inequality with its additional detection assumption. It is not the coincidence-normalized binary CHSH expression.
The authors reported the excess above zero as 0.050 with a one-standard-deviation uncertainty of 0.008. This is a reported statistic, not a newly extracted result here. Its central value can be checked against the rounded normalized rates printed in the preprint, but those rounded entries alone do not reconstruct the full uncertainty analysis.
Read the evidence: S. J. Freedman and J. F. Clauser (1972), Experimental Test of Local Hidden-Variable Theories — LBL-392 preprint, January, University of California archive
An ideal calculation is a useful countercheck
For a separate ideal pair model with perfect polarizers, take the normalized transmitted coincidence rate to be one quarter of one plus the cosine of twice the relative angle. At the two specified angles, the rates are approximately 0.427 and 0.073. Their difference exceeds one quarter by approximately 0.104.
That number is deliberately not the historical result. Real polarizer transmission, finite collection geometry and the reference protocol change the comparison. A teaching plot that silently replaces the apparatus with perfect components can make a real experiment look less successful simply by changing the prediction being tested.
Read the evidence: S. J. Freedman and J. F. Clauser (1972), Experimental Test of Local Hidden-Variable Theories — LBL-392 preprint, January, University of California archive
A reference denominator carries uncertainty
Suppose the same uncertain reference rate divides two measured rates. A fluctuation of that denominator moves both ratios together. Treating the two resulting ratios as independent observations can therefore misstate the uncertainty of their difference.
A practical audit retains the underlying counts, exposure times and shared reference periods. It then propagates their joint sampling model. Ratios printed with separate error bars are a summary of the analysis, not a substitute for knowing which observations share a denominator or a drift correction.
Read the evidence: Larsson (2014), Loopholes in Bell inequality tests of local realism
Detection and locality are different contracts
The preprint explicitly assumed that a photon’s detection probability did not depend on whether it had passed through a polarizer. That assumption connects the observed subset to the bound. Later loophole analysis asks how inefficient detection can select samples that do not represent all trials.
Rapidly choosing a setting addresses a different possibility: communication using information available elsewhere in the apparatus. Improving timing does not by itself establish representative detection. Conversely, efficient local readout does not establish spacelike separation. The two requirements need separate evidence.
Read the evidence: Larsson (2014), Loopholes in Bell inequality tests of local realism
Preserve the result and its historical boundary
The measurement made a quantitative conflict experimentally accessible, under its stated contract. Reading it carefully does not require turning it into a later experiment. Subsequent work changed sources, switching, detection and statistical analysis rather than merely collecting more points on an unchanged graph.
Use the linked Bell Lab to inspect how an explicit selection rule changes a simulated statistic. Its binary-outcome model does not reproduce the pile-of-plates apparatus or this rate normalization. No historical raw count file or coincidence time series is supplied by this article.
Read the evidence: Aspect (2022), Experimental tests of Bell’s inequalities: a first-hand account