TITLE:
Bell’s Theorem on a False Premise: Entropy-Aware Measurement, Forbidden Entropy States, Layer Separation, and a Local Ceiling at 2 2
AUTHORS:
Jonathan K. Atoyo, Ike Ogiamien
KEYWORDS:
Bell’s Theorem, CHSH Inequality, Entanglement, Measurement Problem, Configuration Space, No-Signalling, Layer Separation, Tsirelson’s Bound, Thermodynamic Measurement, Entropy
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.7,
July
31,
2026
ABSTRACT: Bell’s theorem derives nonclassical constraints on correlations by assuming that outcomes are functions of local settings and hidden variables, while detectors are ideal, passive readouts. We argue this is a false premise. Real detectors are thermodynamic subsystems in which at least five physically distinct events occur between source and coincidence: the crystal inscribes the constraint into configuration space, the polariser reads it non-destructively (
ΔS>0
, photon survives), the photodiode absorbs the photon (
ΔS≫0
, Layer 1 collapse), the coincidence circuit matches timestamps to open the pair layer, and Alice’s and Bob’s measurements occur independently at spacelike separation. This structure reveals a deeper distinction. Layer 1 is intra-particle coherence—thermodynamically vulnerable in massive particles, producing measurable heat flow and entropy increase at the detector. Layer 2 is the correlation between entangled particles—inscribed at the source, non-thermal, persisting in configuration space with no three-dimensional spatial address. Standard quantum mechanics conflates these under the single word “collapse”. We formalise the detector’s thermodynamic role with an interactability ratio
Ξ
that triggers measurement activation when
Ξ>
Ξ
c
, a modified path integral where forbidden histories subtract from allowed ones, and an entropy-aware contraction in each correlation channel. The result is a strictly local ceiling
S
max
=2
2
L
A
L
B
≤2
2
for the CHSH parameter, where
L
A,B
∈(
0,1 ]
encode detector coupling losses. We derive this ceiling in full, re-derive Malus’ law as an entropy balance, prove no-signalling structurally and thermodynamically, present the exhaustive nine-case analysis of all measurement configurations for entangled pairs, and dissolve the measurement problem by showing that “collapse” is a conflation of two physically distinct events—neither of which is mysterious, observer-dependent, or requires a special postulate. Bell’s violation detects that the correlation structure lives in configuration space, not in three-dimensional space. There is no action at a distance because there is no action (Layer 1 is local) and there is no distance (Layer 2 has no three-dimensional address). Einstein is vindicated.