One distribution, turned over

Against the Spin

Turn the cobalt-60 nuclei's spin, mirror the electron distribution, and watch a counting asymmetry survive. Wu and her collaborators made weak decay distinguish left from right, with controls that expose exactly what the mirror changes.

Press Mirror momentum. The blue electron arrow crosses the nucleus. The gold spin arrow stays put. If the two outlined distributions do not lie on top of each other, the mirrored decay is not the same decay.

Layer 1, the deciding object

Turn the event over

The 24 sectors are equal-angle expectation bins from W(u) = 1 + ku. They are not raw historical event counts. The opening value k = -0.4 is the 1957 paper's rough reported angular coefficient.

reported slope
Apply parity
Laboratory spin
30 degrees
At 90 degrees the matched-angle test is blind by construction.
At angle theta computed on load

W(theta)

At mirror angle computed on load

W(pi - theta)

Hemisphere asymmetry computed on load

(forward - back) / total

Mirror residual computed on load

normalized L1 distance

Computing the parity comparison.

Computing matched intensities.

Layer 2, take the slope apart

What the apparatus can hide

A visible slope is not the weak coefficient alone. Polarization, electron speed, the fraction that is polarized, and acceptance plus scattering all multiply it. Make any one of them zero and a parity-violating decay looks symmetric.

A warm null is a control on orientation. It is not evidence that the underlying decay law conserves parity.

Coefficient preset, exact values set in script
0.60

Reader choice. The 1957 rough orientation estimate was about 0.6.

0.60

Reader choice. The 1957 rough discussion used about 0.6.

-1.000

Leading pure Gamow-Teller benchmark before recoil corrections.

1.000

The modern paper published 0.928(4) for its sample.

1.00

Reader choice. The real 2010 analysis obtained this through apparatus simulation.

Warm-up control Cold and oriented

The paper reported that beta asymmetry and gamma anisotropy disappeared together over a warm-up time generally about 6 minutes.

The page chooses a straight-line fade to zero over 6 minutes. This is not a recovered historical time series.

Live apparatus form k = computed on load

W(theta) = 1 + f(v/c)APQ1 cos(theta)

Matched-angle intensities computed on load.

Does this setting test parity? Computing sensitivity.

The whole-sphere integral is always 2.000 in this normalization. Summing away direction therefore erases the test.

1957, reconstructed from reported coefficients

This is not raw event data. The paper called the estimate rough. Its reported angular coefficient already came after the paper's speed and detector treatment, so the lower-limit reconstruction does not divide by v/c a second time.

abs(-0.4) / 0.6 = 0.666667 at six decimals, reported about 0.7

The sign says electrons were favored opposite the nuclear spin. The magnitude alone did not make the first experiment a precision measurement of maximal violation.

The transform, not a field reversal

Electron momentum is a polar vector, so parity sends p to -p. Nuclear spin is an axial vector, so it stays fixed. Reversing a laboratory magnetic field is an experimental comparison, not the parity transform of the whole apparatus.

J dot p becomes J dot (-p) = -(J dot p)

That sign-changing scalar is why matched directions can decide the question.

2010 coefficient comparison, one standard deviation
-1.06-1.005-0.95
Measurement computed on load
Prediction computed on load
Central separation computed on load

The measured central value sits below -1, but its combined uncertainty is 0.020. It is statistically consistent with the recoil-corrected prediction. The page does not call it super-maximal.

The check

The source numbers are published inputs. Everything in the live row, every integral, the parity transform, the rough 1957 division, and the modern uncertainty arithmetic are recomputed. The offline verifier uses separate numerical quadrature and vector code.

Current top k computed on load
Forward integral computed on load
Backward integral computed on load
L1 mirror residual computed on load
QuantityPublished inputIndependent arithmetic shownResult
1957 rough lower limit abs(alpha) about 0.4, orientation about 0.6 0.4 / 0.6 computed on load
2010 combined measurement uncertainty 0.012 stat, 0.016 syst sqrt(0.012^2 + 0.016^2) computed on load
2010 measured interval -1.014 plus or minus combined sigma central plus or minus 0.020 computed on load
2010 model interval -0.987(9) central plus or minus 0.009 computed on load
Default hemisphere test k = -0.4 (integral 0..1 - integral -1..0) / total computed on load
For inversion R = -I and det(R) = -1: polar p' = Rp = -p; axial J' = det(R)RJ = (-1)(-I)J = J; therefore J' dot p' = -J dot p.

Uncertainties and limits

  • The 1957 values 0.4, 0.6, 0.6, 0.7, and 6 minutes were published as rough or approximate. No extra digits are inferred.
  • The 2010 result keeps statistical and systematic uncertainties separate. The combined 0.020 appears only where the page explicitly combines them in quadrature.
  • The 2010 model uncertainty 0.009 belongs to that paper's recoil-corrected value. It is not attached to the leading value -1.
  • The published modern fraction is f=0.928(4). Its 0.004 uncertainty belongs to that sample fraction, not to the weak coefficient.
  • Raw 1957 counts, the 2010 event sample, and the 2010 GEANT4 apparatus model are not reproduced here.

Free choices and blind settings

  • Reader choices are P, v/c, Q1, f, spin direction, electron angle, and coefficient preset.
  • The slider settings are a factor laboratory. They are not claimed to reconstruct the 2010 run.
  • The warm-up fade is a chosen straight line. Only its 6-minute endpoint is tied to the paper's approximate wording.
  • The display uses 24 equal-angle sectors and unit-normalized intensity. Those choices change the drawing, not the analytic residual.
  • P=0, v=0, A=0, f=0, Q1=0, 6-minute warm-up, theta=90 degrees, or a whole-sphere sum has no parity sensitivity by construction.
What the first paper did, and what this page does not claim

Wu, Ernest Ambler, Raymond Hayward, Dale Hoppes, and Ralph Hudson oriented cobalt-60 nuclei and compared beta emission along the orientation axis. NIST dates the experiments to late 1956. The Physical Review letter was received 15 January 1957 and published 15 February 1957.

The opening instrument reconstructs an angular rule from the paper's reported coefficient. It does not digitize Figure 2, invent event counts, or claim that the first paper alone made a modern precision determination of the underlying coefficient.

The Nobel record, with no invented motive

The Nobel Foundation's official 1957 record names Chen Ning Yang and Tsung-Dao Lee, with one half of the prize each. It does not name Wu or Ambler, Hayward, Hoppes, and Hudson as laureates. That record establishes who received the prize. It does not establish the committee's motive for excluding anyone, so this page supplies none.