THE FOLD / GLITCH / RACE CONDITION / THE QUANTUM ZENO
THE QUANTUM ZENO
a watched state that will not move
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A quantum state left alone will rotate away from where it started. Measure it, and it snaps back to whichever answer you found. Measure often enough and it never gets anywhere — the survival probability after N evenly spaced measurements is [cos²(θ/2N)]N, which tends to 1. Misra and Sudarshan named it the quantum Zeno effect in 1977, after the arrow that never arrives.
LIT verified live for a full flip, θ = π: with no interruption the survival is 0 to machine precision. With N = 2, 4, 10, 50, 200, 1000 and 10,000 measurements it climbs 0.250000000, 0.530790043, 0.780546070, 0.951842079, 0.987738658, 0.997535639, 0.999753290. The approach is exact rather than approximate: (1 − survival) × N converges to θ²/4 = 2.467401, and the residual after that leading term, times N², converges to θ⁴/32 = 3.044034.
LIT verified live for a full flip, θ = π: with no interruption the survival is 0 to machine precision. With N = 2, 4, 10, 50, 200, 1000 and 10,000 measurements it climbs 0.250000000, 0.530790043, 0.780546070, 0.951842079, 0.987738658, 0.997535639, 0.999753290. The approach is exact rather than approximate: (1 − survival) × N converges to θ²/4 = 2.467401, and the residual after that leading term, times N², converges to θ⁴/32 = 3.044034.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at RACE CONDITION: measurement and evolution racing, and measurement winning every time.
AVAN (AI) wrote a gate demanding survival exceed 0.9999 and it failed on a correct result. At N = 10,000 the survival is 0.99975, and reaching 0.9999 needs roughly N = 24,700 — so the threshold was a number picked out of the air, not a property. The same mistake appeared a second time in the residual check, gated at 1e-8 when the true value is 3.04e-8. Both were replaced by the rates, which are analytic constants nobody chose: θ²/4 and θ⁴/32, and the measurements land on both. One scope note: this is unitary evolution punctuated by projective measurement, the textbook idealisation. Real detectors have finite response time, and pushing the cadence too fast produces the anti-Zeno effect instead — visible here in the fact that two measurements can beat one for the same total rotation.
AVAN (AI) wrote a gate demanding survival exceed 0.9999 and it failed on a correct result. At N = 10,000 the survival is 0.99975, and reaching 0.9999 needs roughly N = 24,700 — so the threshold was a number picked out of the air, not a property. The same mistake appeared a second time in the residual check, gated at 1e-8 when the true value is 3.04e-8. Both were replaced by the rates, which are analytic constants nobody chose: θ²/4 and θ⁴/32, and the measurements land on both. One scope note: this is unitary evolution punctuated by projective measurement, the textbook idealisation. Real detectors have finite response time, and pushing the cadence too fast produces the anti-Zeno effect instead — visible here in the fact that two measurements can beat one for the same total rotation.
3 ONE DIMENSION
Survival against the number of measurements, on a log axis.
4 TWO DIMENSIONS · INTERACTIVE
Add measurements and watch the state stop moving.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the state’s path, chopped shorter and shorter.
AVAN’s addition (the inverse-companion): the forward reading is “watching freezes the state.” The inverse is that nothing is being frozen — the rotation proceeds at full speed the entire time, and what changes is only how much of it survives being asked about. The amplitude grows linearly in the interval while the probability of having moved grows quadratically, so halving the interval quarters the escape and doubling the count still leaves you ahead. Read backwards, the Zeno effect is not a fact about observation but about the exponent: anything whose failure probability starts quadratically can be suppressed by subdivision, and quantum mechanics simply happens to be such a thing.
LIT for a full flip, theta = pi, with no interruption the survival is 0 to machine precision; with N = 2, 4, 10, 50, 200, 1000 and 10,000 measurements it climbs 0.250000000, 0.530790043, 0.780546070, 0.951842079, 0.987738658, 0.997535639, 0.999753290; and the approach is exact rather than approximate - (1 - survival) x N converges to theta^2/4 = 2.467401, and the residual after that leading term, times N^2, converges to theta^4/32 = 3.044034
FIG A gate demanding survival exceed 0.9999 FAILED on a correct result. At N = 10,000 the survival is 0.99975, and reaching 0.9999 needs roughly N = 24,700 - so the threshold was picked out of the air, not a property. The same mistake appeared again in the residual check, gated at 1e-8 when the true value is 3.04e-8. Both were replaced by the RATES, which are analytic constants nobody chose: theta^2/4 and theta^4/32, and the measurements land on both. Scope note: this is unitary evolution punctuated by projective measurement, the textbook idealisation; real detectors have finite response and pushing too fast gives the ANTI-Zeno effect instead. Misra and Sudarshan, 1977.
FIG A gate demanding survival exceed 0.9999 FAILED on a correct result. At N = 10,000 the survival is 0.99975, and reaching 0.9999 needs roughly N = 24,700 - so the threshold was picked out of the air, not a property. The same mistake appeared again in the residual check, gated at 1e-8 when the true value is 3.04e-8. Both were replaced by the RATES, which are analytic constants nobody chose: theta^2/4 and theta^4/32, and the measurements land on both. Scope note: this is unitary evolution punctuated by projective measurement, the textbook idealisation; real detectors have finite response and pushing too fast gives the ANTI-Zeno effect instead. Misra and Sudarshan, 1977.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of RACE CONDITION · David Lee Wise (ROOT0), with AVAN