Experiments

Every test behind this site, each with its question, the measurement, its sources, the residuals, and the result. Agrees: every measurement lies within 2 standard errors of the tested value, with no fitted parameter. Contradicted: a measurement objects. Contradicted readings stay shown.

Three groups: A. nine relations against 17 published measurements; B. blind predictions across fields; C. the one-wave picture of an entangled pair, six tests. Residual r = (measured − tested value) / combined standard error. Every number on this page is printed by reproduce/reproduce.py.

A. Nine relations against published measurements

Method: inverse-variance combination with a between-experiment variance by the method of moments (Bühlmann–Straub credibility); Cochran's Q tests whether the experiments read one quantity (passes at p > 0.05); χ² against each tested value.

E1. Do clocks at different heights tick at different rates by exactly the potential difference over c²?

Measured

redshift coefficient α (0 means exact); rows in E1-redshift.csv (README)

Sources

Pound and Snider 1965 (doi:10.1103/PhysRev.140.B788); Vessot et al. 1980 (doi:10.1103/PhysRevLett.45.2081); Delva et al. 2018 (doi:10.1103/PhysRevLett.121.231101)

Combined

1.679e-6 ± 2.338e-5; Q = 0.01803, p = 0.991: one quantity

Tested

alpha = 0 (clock rate follows the potential): residuals -0.13, +0.00, +0.08; χ² = 0.02318 on 3, p = 0.9991 agrees

E2. Does light passing the Sun bend and slow by the full amount, or only the half that clock rates alone would give?

Measured

γ − 1 (0 is the full amount); rows in E2-light.csv (README)

Sources

Bertotti, Iess, Tortora 2003 (doi:10.1038/nature01997); Lambert and Le Poncin-Lafitte 2011 (doi:10.1051/0004-6361/201016370)

Combined

1.742e-5 ± 2.259e-5; Q = 0.6833, p = 0.4085: one quantity

Tested

gamma - 1 = 0 (full bending, general relativity): residuals +0.91, -0.67; χ² = 1.278 on 2, p = 0.5278 agrees
gamma - 1 = -1 (clock-rate half only, Soldner's 0.876 arcsec): residuals +43479.17, +8332.67; χ² = 1.96e9 on 2, p = < 1e-300 contradicted

E3. Do clocks flown round the Earth gain and lose what gravity and speed predict?

Measured

ns gained, east and west; rows in E3-aircraft.csv (README)

Sources

Hafele and Keating 1972 (doi:10.1126/science.177.4044.168)

Combined

-9.444 ± 16.6; Q = 0.2583, p = 0.6113: one quantity

Tested

Hafele and Keating's own prediction from the flight logs: residuals -0.76, -0.09; χ² = 0.5821 on 2, p = 0.7475 agrees

E4. Does a muon at 10¹⁸ g live exactly the time-dilated lifetime?

Measured

lab lifetime, µs; rows in E4-muon.csv (README)

Sources

Bailey et al. 1977 (doi:10.1038/268301a0)

Combined

64.38 ± 0.02594; Q = 0.6185, p = 0.4316: one quantity

Tested

gamma x tau0 (time dilation): residuals -0.14, -0.94; χ² = 1.26 on 2, p = 0.5325 agrees

E5. What does the Bell number S of entangled pairs read, and which readings of the pair survive it?

Measured

CHSH S; rows in E5-chsh.csv (README)

Sources

Aspect, Grangier, Roger 1982 (doi:10.1103/PhysRevLett.49.91); Weihs et al. 1998 (doi:10.1103/PhysRevLett.81.5039); Hensen et al. 2015 (doi:10.1038/nature15759); Yin et al. 2017 (doi:10.1126/science.aan3211)

Combined

2.649 ± 0.04308; Q = 17.67, p = 0.0005151: the experiments do not read one quantity (S belongs to each apparatus)

Tested

S = 2 sqrt 2 at every apparatus (ideal analysers): residuals -8.76, -4.92, -2.04, -5.09; χ² = 131.1 on 4, p = 2.26e-27 contradicted
S at most 2 (each end holds its own preset value): residuals +46.47, +36.50, +2.10, +4.11; χ² = 3513 on 4, p = < 1e-300 contradicted
Aspect 1982 against its own apparatus prediction 2.70 +/- 0.05: residuals -0.06; χ² = 0.003303 on 1, p = 0.9542 agrees
The bound 2 < S ≤ 2√2: standard errors above 2: 46.5, 36.5, 2.1, 4.1 agrees

E6. After what angle of precession does a neutron's wave return?

Measured

degrees; rows in E6-sheet.csv (README)

Sources

Rauch, Wilfing, Bauspiess, Bonse 1978 (doi:10.1007/BF01321193)

Tested

return at 720 degrees (two-valued wave): residuals -0.84; χ² = 0.7091 on 1, p = 0.3997 agrees
return at 360 degrees (ordinary vector, rotating body): residuals +93.89; χ² = 8816 on 1, p = < 1e-300 contradicted

E7. Does Mercury's perihelion advance as general relativity says, and does a weak-field clock-rate map alone give any advance?

Measured

arcseconds per century; rows in E7-perihelion.csv (README)

Sources

Park et al. 2017 (doi:10.3847/1538-3881/aa5be2)

Tested

general relativity, 6 pi GM / (c^2 a (1 - e^2)) per orbit: residuals -0.02; χ² = 0.0002854 on 1, p = 0.9865 agrees
weak-field clock-rate map alone (no advance): residuals +1074.50; χ² = 1.155e6 on 1, p = < 1e-300 contradicted
Primary check: Park et al. report β − 1 = (−2.7 ± 3.9) × 10⁻⁵; β = 1 gives -0.69 agrees

E8. Do integer energy levels alone give hydrogen's 1S–2S interval?

Measured

Hz; rows in E8-hydrogen.csv (README)

Sources

Parthey et al. 2011 (doi:10.1103/PhysRevLett.107.203001)

Tested

Bohr ladder with reduced mass: residuals +2298950011.70; χ² = 5.285e18 on 1, p = < 1e-300 contradicted
Dirac levels with reduced mass (no QED): residuals -710596536.45; χ² = 5.049e17 on 1, p = < 1e-300 contradicted
Misses: Bohr ladder 2.299e10 Hz; Dirac levels -7.106e9 Hz (the Lamb shifts of QED close it)

E9. Does antimatter fall?

Measured

g; rows in E9-antimatter.csv (README)

Sources

ALPHA-g, Anderson et al. 2023 (doi:10.1038/s41586-023-06527-1)

Tested

antimatter falls at 1 g: residuals -1.21; χ² = 1.473 on 1, p = 0.2249 agrees
antimatter rises at -1 g: residuals +8.50; χ² = 72.17 on 1, p = 1.977e-17 contradicted

Null results used as bounds

Inverse square: Newtonian to 52 µm; a Yukawa interaction of gravitational strength is excluded for ranges above 38.6 µm at 95 % (Lee et al. 2020, doi:10.1103/PhysRevLett.124.101101). Lunar laser ranging: δω/ω < 1.6 × 10⁻¹¹ (Adelberger, Heckel, Nelson 2003, doi:10.1146/annurev.nucl.53.041002.110503). A three-direction inverse square gives no deviation; both bounds contain zero. agrees as a bound

A new universal constant? For each number that recurs (the redshift coefficient, the light factor, the scale on the flown clocks, the speed factor, the neutron's ratio 2), freeing it as a fitted parameter lowers χ² by less than one parameter costs (BIC: ln 17 = 2.83). The one candidate whose freeing would pay, a universal S, fails the test that the experiments read one quantity: S belongs to the apparatus. Constants admitted: none.

B. Blind predictions across fields

Every prediction was written to a file and its SHA-256 hash recorded (e8be09e8e7f9d27150be0896fac2a26eca8b159435de7c22bb15ed4debb48c74, 2026-11-07 19:40:45 IST) before any measured value of a target quantity was loaded. Gate: agrees if |z| ≤ 2, z = (measured − predicted) / √(σ_meas² + σ_pred²); no fitted parameter. A miss is shown as contradicted, not tuned. The predictions file on this site is a redacted copy with each prediction stated in standard terms; it gives the original hash.

Scored 29: agree 16 · contradicted 12 · open 1 (no measured value entered) · recalled 1 (measured value from a secondary source only; scored, not counted).

T1 Chou 2010 Al+ clocks 33 cm apart, fractional rate difference (timekeeping) agrees (data recalled from a secondary source, not counted)

Predicted: 3.597e-17 rate difference g h / c^2, g = 9.796 m/s^2 (Boulder), h = 0.33 m

Measured: 4.1e-17 ± 1.6e-17 Chou, Hume, Rosenband, Wineland, Science 329, 1630 (2010)

z = +0.314

T2 Bothwell 2022 Sr lattice, fractional rate gradient per mm of height (magnitude) (timekeeping) agrees

Predicted: 1.09e-19 rate gradient g / c^2 per millimetre of height

Measured: 9.8e-20 ± 2.3e-20 Bothwell et al., Nature 602, 420 (arXiv 2109.12238, final gradient -9.8(2.3) x 10^-20 per mm, sign is the coordinate convention of their Fig. 1a, predicted -1.09 x 10^-19) (2022)

z = -0.478

T3 Takamoto 2020 Tokyo Skytree clocks, redshift violation parameter alpha (timekeeping) agrees

Predicted: 0 fractional shift equals the potential difference over c^2 exactly (alpha = 0)

Measured: 1.4e-5 ± 9.1e-5 Takamoto et al., Nature Photonics 14, 411 (Tokyo Skytree, 450 m), as restated in arXiv 2502.06104 (2020)

z = +0.154

T4 Lange 2021 Yb+ E3/E2 clocks, drift of alpha per year (timekeeping) agrees

Predicted: 0 one fixed rate per atomic species; ratios of two clock transitions do not drift (0 per year)

Measured: 1e-18 ± 1.1e-18 Lange et al., Phys Rev Lett 126, 011102 (arXiv 2010.06620), Yb+ E3/E2 (2021)

z = +0.909

T5 solar gravitational redshift seen from Earth, m/s (solar spectroscopy) agrees

Predicted: 633.1 GM_sun/(c R_sun) - GM_sun/(c AU) - GM_E/(c R_E)

Measured: 638 ± 6 Gonzalez Hernandez et al., A&A 643, A146 (HARPS laser frequency comb, Moon spectra, 97 weak Fe lines) (2020)

z = +0.81

T6 GW170817 fractional speed difference of gravitational waves and light (gravitational-wave astronomy) agrees (inside the published bound)

Predicted: 0 gravitational waves and light travel at the same speed, no dispersion (0)

Measured: -1.15e-15 ± 1.85e-15 Abbott et al. (LIGO, Virgo, Fermi GBM, INTEGRAL), ApJ Lett 848, L13 (GW170817 and GRB 170817A, 1.74 +/- 0.05 s) (2017)

z = –

T7 Gravity Probe B geodetic drift, mas/yr (space geodesy) agrees

Predicted: 6604 ± 6.604 de Sitter geodetic drift (3/2)(GM)^1.5/(c^2 r^2.5), r = 7027.4 km; 0.1 % for the circular-orbit simplification

Measured: 6602 ± 18.3 Everitt et al., Phys Rev Lett 106, 221101 (Gravity Probe B, magnitude of -6601.8) (2011)

z = -0.107

T8a Gravity Probe B frame-dragging drift, mas/yr, static map (space geodesy) contradicted

Predicted: 0 a static gravity map with no term from the source's rotation (0)

Measured: 37.2 ± 7.2 Everitt et al., Phys Rev Lett 106, 221101 (Gravity Probe B, magnitude of -37.2, GR -39.2) (2011)

z = +5.17

T8b Gravity Probe B frame-dragging drift, mas/yr, Schiff (space geodesy) agrees

Predicted: 40.8 ± 0.816 Schiff 1960 frame dragging G I w / (2 c^2 r^3); 2 % for Earth's moment of inertia and the orbit

Measured: 37.2 ± 7.2 Everitt et al., Phys Rev Lett 106, 221101 (Gravity Probe B, magnitude of -37.2, GR -39.2) (2011)

z = -0.497

T9a LAGEOS/LARES node frame dragging, ratio to general relativity, static map (space geodesy) contradicted

Predicted: 0 a static gravity map with no rotation term (ratio 0)

Measured: 0.994 ± 0.05 Ciufolini et al., Eur Phys J C 76, 120 (LARES, LAGEOS, LAGEOS 2, GGM05S, 0.002 formal and 0.05 systematic in quadrature) (2016)

z = +19.9

T9b LAGEOS/LARES node frame dragging, ratio to general relativity, Lense-Thirring (space geodesy) agrees

Predicted: 1 Lense-Thirring 1918 (ratio 1)

Measured: 0.994 ± 0.05 Ciufolini et al., Eur Phys J C 76, 120 (LARES, LAGEOS, LAGEOS 2, GGM05S, 0.002 formal and 0.05 systematic in quadrature) (2016)

z = -0.12

T10 Earth-Moon gravitational over inertial mass difference, Delta(mg/mi) (lunar ranging) agrees

Predicted: 0 universal free fall (0)

Measured: -2e-13 ± 2e-13 Williams, Turyshev and Boggs, Class Quantum Grav 29, 184004 (lunar laser ranging, strong equivalence principle Delta(MG/MI)) (2012)

z = -1

T11 MICROSCOPE Eotvos parameter Ti-Pt (precision mechanics) agrees

Predicted: 0 universal free fall (0)

Measured: -1.5e-15 ± 2.7e-15 Touboul et al., Phys Rev Lett 129, 121102 (MICROSCOPE Ti-Pt, 2.3 stat and 1.5 syst in quadrature) (2022)

z = -0.556

T12 double pulsar J0737-3039 orbital decay, observed over predicted (pulsar timing) agrees

Predicted: 1 Peters 1964 quadrupole radiation (ratio 1)

Measured: 1 ± 6.3e-5 Kramer et al., Phys Rev X 11, 041050 (arXiv 2112.06795, PbdotGW / PbdotGW,GR) (2021)

z = -0.587

C1 Josephson frequency-voltage ratio, fractional difference between two superconductors (condensed matter) agrees (inside the published bound)

Predicted: 0 Josephson ratio 2e/h, material-free (0)

Measured: 0 ± 1e-17 Jain, Lukens and Tsai, Appl Phys Lett (two series-array Josephson voltage standards) (1987)

z = –

C2 quantized Hall resistance, fractional difference graphene vs GaAs (condensed matter) agrees

Predicted: 0 von Klitzing resistance h/(i e^2), material-free (0)

Measured: 0 ± 8.6e-11 Janssen et al., New J Phys 13, 093026 (epitaxial graphene vs GaAs/AlGaAs, no difference within 8.6e-11) (2011)

z = +0

C3 Planck constant from Kibble balances (K_J^2 R_K = 4/h) over Planck constant from the silicon sphere (XRCD), minus 1 (mass metrology) open

Predicted: 0 the factor 4 = 2^2 of a two-valued pair (0)

Measured: –

z = –

S1 hydrogen ground-state hyperfine interval (21 cm), Hz (radio spectroscopy) contradicted

Predicted: 1.42e9 Fermi 1930 with (1 + a_e) and reduced mass; no further QED, no proton structure

Measured: 1.42e9 ± 0.002 Hellwig, Vessot, Levine et al., IEEE Trans Instrum Meas 19, 200 (hydrogen maser vs caesium) (1970)

z = -3.99e+07

S2 muonium ground-state hyperfine interval, Hz (radio spectroscopy) contradicted

Predicted: 4.464e9 Fermi 1930 with the muon's moment (1 + a_mu); no further QED

Measured: 4.463e9 ± 4000 MuSEUM collaboration (J-PARC), muonium ground-state hyperfine 4.463302(4) GHz (2021)

z = -225

S3 positronium ground-state hyperfine interval, Hz (radio spectroscopy) contradicted

Predicted: 2.044e11 (7/12) alpha^4 m c^2 / h, leading order (magnetic 4/12 plus annihilation 3/12)

Measured: 2.034e11 ± 7.4e5 Ritter, Egan, Hughes and Woodle, Phys Rev A 30, 1331 (and thesis 1984) (1984)

z = -1.35e+03

S4 CO rotational lines nu(J 2-1) / nu(J 1-0) (molecular spectroscopy) contradicted

Predicted: 2 rigid rotor J(J+1): ratio 2

Measured: 2 ± 9.699e-9 Mueller et al. 2001, CDMS catalogue, as tabulated in A&A tables (2001)

z = -3.94e+03

K1 He+ ionization energy, eV, integer levels (chemistry) contradicted

Predicted: 54.42 Z^2 Rydberg with reduced mass (integer levels only)

Measured: 54.42 ± 1e-6 NIST Handbook of Basic Atomic Spectroscopic Data, He II ground state 438908.8789 cm^-1 (2005)

z = +2.45e+03

K1d He+ ionization energy, eV, Dirac (chemistry) contradicted

Predicted: 54.42 reduced-mass Dirac ground level (Dirac 1928)

Measured: 54.42 ± 1e-6 NIST Handbook of Basic Atomic Spectroscopic Data, He II ground state 438908.8789 cm^-1 (2005)

z = -451

K2 Li2+ ionization energy, eV, integer levels (chemistry) contradicted

Predicted: 122.4 Z^2 Rydberg with reduced mass, lithium-7 (integer levels only)

Measured: 122.5 ± 1e-5 NIST data as compiled (Li III) (2005)

z = +1.26e+03

K2d Li2+ ionization energy, eV, Dirac (chemistry) contradicted

Predicted: 122.5 reduced-mass Dirac ground level (Dirac 1928)

Measured: 122.5 ± 1e-5 NIST data as compiled (Li III) (2005)

z = -205

K3 atomic number of the 1st noble gas (chemistry) agrees

Predicted: 2 shell n holds 2 n^2 (two-valuedness times n^2 orbitals), cumulative

Measured: 2 ± 0 periodic table (1869)

z = +0

K4 atomic number of the 2nd noble gas (chemistry) agrees

Predicted: 10 2 + 8

Measured: 10 ± 0 periodic table (1898)

z = +0

K5 atomic number of the 3rd noble gas (chemistry) contradicted (exact integers differ)

Predicted: 28 2 + 8 + 18

Measured: 18 ± 0 periodic table (1894)

z = –

K6 atomic number of the 4th noble gas (chemistry) contradicted (exact integers differ)

Predicted: 60 2 + 8 + 18 + 32

Measured: 36 ± 0 periodic table (1898)

z = –

N1 annual modulation amplitude of a radioactive decay rate, fractional (nuclear metrology) agrees (inside the published bound)

Predicted: 1.648e-10 a decay is a clock: annual amplitude GM_sun e / (c^2 AU), about 1.6e-10, none at reachable precision

Measured: 0 ± 1e-5 Pomme et al., Metrologia 54, 1 (On decay constants and orbital distance to the Sun, part I: alpha decay, 14 laboratories, 200 days to 4 decades) (2017)

z = –

What the contradicted rows say. A static gravity map with no rotation term misses frame dragging (T8a, T9a); the standard Schiff and Lense–Thirring terms agree (T8b, T9b). Fermi's leading-order hyperfine formula misses hydrogen, muonium and positronium by many standard errors (S1–S3): the higher-order QED terms are needed. A rigid rotor misses the CO line ratio at its 10⁻⁸ precision (S4, centrifugal stretching). Integer levels miss the He⁺ and Li²⁺ ionization energies, and Dirac's levels without QED still miss (K1, K2, K1d, K2d). The rule "shell n holds 2n²" gives the first two noble gases (2, 10) and misses the next two (28 against 18, 60 against 36: K5, K6).

Coincidence search across fields

Across the 54 measured quantities, every pair from different fields with the same unit (485 pairs) and every triple (5,852) was tested for a simple relation: an integer ratio, a simple fraction, a power of 2, a factor of π, a rate sum. The same tests were run on eight control sets in which the mantissas were shuffled. No form passed more often in the real data than the control mean by the admission margin, so every link found (44) is set aside as chance. Counts are in results.json.

C. The one-wave picture of an entangled pair: six tests

The picture (see Intuition): an entangled pair is one wave tied at two ends. Two readings of it differ by number: (a) each end reads a shared preset value on its own; (b) the wave is read once, for both ends.

Test 1. The Bell number S

Computed: (a) probabilistic: S = 1.4142; (a) sign reading: S = 2.0000 (Bell's bound); (b) read once for both ends: S = 2.8284 (= 2√2). Deterministic grid of 36,000 phases, no random numbers.
Measured: 2.697 ± 0.015 (Aspect 1982); 2.73 ± 0.02 (Weihs 1998); 2.42 ± 0.20 (Hensen 2015, loophole-free); 2.37 ± 0.09 (Yin 2017)
Result: (a) contradicted by every Bell test since 1972. (b) reproduces the bound 2 < S ≤ 2√2 agrees; it uses the quantum singlet correlation as given, so it is a reproduction, not a derivation. 2√2 at every apparatus is contradicted (E5): the measured S also carries each apparatus's losses.

Test 2. A pulled end does not move the other

A physical rope moves its far end when pulled. Measured: what each end sees alone is 50/50 at every analyser angle (a theorem: Eberhard 1978; Ghirardi, Rimini, Weber 1980); any hidden influence would need more than 10⁴ c under the stated assumption that the Earth moves slower than 10⁻³ c in any privileged frame (Salart et al. 2008, doi:10.1038/nature07121; contested: Kofler et al. 2008, arXiv:0810.4452). The wave carries a correlation, not a tension. agrees for (b) only.

Test 3. Tied to places, or carried?

Entanglement distributed to stations 1,203 km apart kept S = 2.37 ± 0.09 (Yin 2017). "Tied" cannot mean tied to positions; the wave goes with the particles. One point, not a law in distance.

Test 4. Ties remade after both ends are read

Entanglement swapping: two pairs A–B and C–D; a joint reading of B and C leaves A and D entangled though they never met (Pan et al. 1998, doi:10.1103/PhysRevLett.80.3891). Done after A and D were already read, the joint reading sorts the earlier outcomes into correlated groups and changes none of them (Ma et al. 2012, doi:10.1038/nphys2294). A tie fixed at creation contradicted; one object read once survives. Whether the record settles which tie there was remains an open question.

Test 5. Two ends only?

A pure maximally entangled pair cannot be shared with a third particle (monogamy; Coffman, Kundu, Wootters 2000); three particles can be tied as one three-ended object (GHZ: Pan et al. 2000, doi:10.1038/35000514). "Two ends" agrees for a pure pair; three-party states need three ends, still one object.

Test 6. A rope on a bench (illustration, not evidence)

A string fixed at two points carries only waves that fit both ends: n half-waves, f_n = (n / 2L)√(T/μ) (Mersenne 1636; Melde 1859). The integer n is not put in; the two anchors set it, and one mode is one object shared by both ends. A classical string cannot exceed S = 2, so this shows the shared mode, not the Bell number. Bench procedure: a string between two clamps, length L, tension T from a hanging mass, μ from its mass per length; pluck it, read f_1, f_2, f_3 with a phone spectrum app; check f_n / f_1 = n and f_1 against (1/2L)√(T/μ).