In 1957 Chien-Shiung Wu and her colleagues tested whether nature treats a process and its mirror image alike, using the beta decay of cobalt-60 nuclei lined up by a magnetic field. This sim lets you repeat it: cool a crystal, count electrons in one detector, reverse the field, and compare.

What's on screen

• Nuclear spins (purple arrows) and the net spin ⟨J⟩ arrow on the left, whose length is P. A ring means disordered.
• Field B (teal arrow) from the solenoid rings.
• β electrons (red dots with tails) and the grey counter above the crystal, with its running count.
• Counting-rate plot (below the stage): rate ÷ warm rate, one point per historical minute; B ↑ blue, B ↓ orange. The dashed line at 1 is a warm source.
• Detector counts panel: the first-minute rates, 𝒜, and its expected value.

Press ⌖ on a row to see where that control sits in the sim.

Fixed in the sim: the decay (⁶⁰Co → ⁶⁰Ni* + e⁻ + ν̄_e, with decay asymmetry A = −1), the counter (radius 0.95 cm, 2.0 cm above the source), and the temperature scale (P = 0.60 at 3 mK).

Nuclear spins start out pointing every which way. A magnetic field pulls them into line, thermal jiggling pushes them back out, and the alignment depends on the balance. The sim measures it by P, the average spin component along B divided by the full spin: P = 0 is random, P = 1 is perfectly aligned. For ⁶⁰Co, which has spin 5:

• At 1 K, the opening value, P = 0.002. The sim draws the net spin as a ring above about 110 mK, where P falls below 0.02.
• For P well below 1, P ≈ 0.4·C/T: halving T doubles P. At 10 mK, P = 0.22.

For an aligned ⁶⁰Co nucleus, the relative probability that the electron leaves at angle θ from the spin direction is

• With A = −1, electrons are less likely along the spin (θ = 0°) and more likely against it (θ = 180°).
• The factor β means fast electrons are steered more strongly than slow ones. Averaged over the beta spectrum, β̄ = 0.49.
• At P = 0.60, 43% of electrons leave into the hemisphere toward the spin and 57% into the opposite one.

The counter is a disc of radius 0.95 cm, 2.0 cm above the source, so it sees a narrow cone about the vertical (half-angle 25°). Compared with the same counter and an unpolarized (warm) source, its rate is

With A = −1 and β̄ · Q = 0.466, that is R_↑ = 1 − 0.466 P and R_↓ = 1 + 0.466 P. A warm source gives about 170 counts per recorded minute, the reference the sim divides by.

A run stands for 18 minutes of the real experiment, played in 26 s with one point per minute. The crystal starts at 3 mK, warms to 1 K by minute 6, and stays there while B stays fixed, so P falls and both rates drift toward 1:

T at the middle of each minute; P averaged over the minute; R is the expected rate relative to warm.

The sim compares the first minute of each run, when P is highest:

Counts fluctuate by √N, so 𝒜 carries an error of about σ ≈ 1/√N. The two first minutes hold N ≈ 330 counts, so σ ≈ 0.05. A typical pair gives 𝒜 near the expected 0.27, within about 0.1 of it, and about 5σ from zero. Halving P halves 𝒜, so the same confidence takes four times the counts.

Reflect the experiment in a mirror (the sim's mirror turns x into −x). Momentum is a polar vector; spin and B are axial, so a reflection treats them differently: the electron's vertical momentum p_z is unchanged, but J_z and B_z both reverse.

• In the mirror image the counter is still on top, and the field and spin point the other way. It is a B ↓ apparatus drawn next to a B ↑ one.
• If the decay law were the same in a mirror world, both would count the same. ⟨J⟩·p is a pseudoscalar: a term proportional to it, like A·P·β·cos θ, can exist only if parity is violated.

The sim's Mirror image switch draws this reflection to the right. Once both runs are recorded, a line at the bottom of the canvas reports whether the two rates differ by more than 2σ.

• Wu's experiment, 1957. At the National Bureau of Standards in Washington, Wu, Ambler, Hayward, Hoppes and Hudson aligned ⁶⁰Co nuclei at about 0.01 K and counted electrons while reversing the field (Phys. Rev. 105, 1413). The rate depended on the field direction. Lee and Yang, who proposed the test, won the 1957 Nobel Prize in Physics.
• A left-handed weak force. The result led to the V−A theory, in which the weak interaction acts only on left-handed particles. In 1958 Goldhaber, Grodzins and Sunyar found the neutrino left-handed.
• Today. Experiments measure the neutron's beta asymmetry (A ≈ −0.12, the same sign as in the sim) to find the axial coupling relative to the vector one.

Key points

• Alignment needs millikelvin temperatures: P = B₅(C/T), 0.60 at 3 mK, 0.002 at 1 K.
• The emission weight is W(θ) = 1 + A·P·β·cos θ, with A = −1.
• Two field directions give 𝒜 ≈ 0.47 P, with error ≈ 1/√N.
• The mirror image of a B ↑ run is a B ↓ run, so a non-zero 𝒜 means parity is violated.

Common mix-ups

• "Reversing B changes the physics of the decay." The decay law is the same. Only the spin direction relative to the fixed counter changes.
• "A warm source shows no parity violation." Each decay is still lopsided relative to its own spin; random spin directions average it out.
• "𝒜 should be 1, since A = −1." 𝒜 = P·β̄·Q, with P below 1, β̄ = 0.49 and a counter that is not a point.

Things to try on your own

• Record a B ↑ and a B ↓ run and compare the measured and expected 𝒜. Repeat a few times and compare the spread of 𝒜 with the ± shown.
• Use the table in section 05 to predict the B ↑ point at minute 3, then check it on the rate plot.
• After both runs, turn on Mirror image and read the line at the bottom of the canvas.