IndexQuantisticaMug

Zeno

Quantum Zeno Effect Physics

\[P_{stay}(t) \approx 1 - \left(\frac{t}{\tau_Z}\right)^{2}\]
$21.99 USD
$21.99 USD
In offerta Esaurito
Size

Meet Zeno. A quantum state starts to change slowly, as the square of time. Measure it again and again and each check resets the clock. In 1990, ion-trap physicists showed it: more measurements, fewer jumps. On the mug: P_stay(t) ≈ 1 − (t/τ_Z)². Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

At short times a quantum state leaks away as the square of time, so frequent measurements keep resetting it. With 64 measurements during one π pulse, the transition probability falls from 1 to about 0.04.

Zeno keeps a quantum state exactly where it is, just by looking.

A quantum state does not start to change at a steady rate. At short times the chance that it is still unchanged falls as the square of time: P_stay(t) ≈ 1 − (t/τ_Z)², with τ_Z = ħ/ΔH set by the energy spread ΔH of the state. Measure it, and if it is found unchanged, the clock restarts from zero. Measure often enough and it barely changes at all. Baidyanath Misra and George Sudarshan named this the quantum Zeno effect in 1977, after Zeno of Elea's paradox of the arrow.

In 1990 Wayne Itano, Daniel Heinzen, John Bollinger and David Wineland tested it with beryllium ions in a trap. A radio-frequency pulse that would normally move every ion to a second state was interrupted by n short laser measurements. A worked number: for n equally spaced measurements the ideal transition probability is ½[1 − cos^n(π/n)], 1 for n = 1 but only about 0.04 for n = 64. The ions followed it.

Measuring too often in some systems can also speed decay up, the anti-Zeno effect. The slogan on the mug is the limit of infinitely many looks.

“Watched often enough,” says Zeno, “it cannot change. I never blink.”

Equations

\[P_{stay}(t) \approx 1 - \left(\frac{t}{\tau_Z}\right)^{2}\]
\[\tau_Z = \frac{\hbar}{\Delta H}\quad\text{(short times)}\]
\[P_{1\to2}(n) = \tfrac{1}{2}\left[1-\cos^{n}(\pi/n)\right]\]
SymbolMeaningUnit
\(P_{stay}(t)\) probability the system is still in its initial state at time t \(\mathrm{dimensionless}\)
\(t\) time since the last measurement \(\mathrm{s}\)
\(\tau_Z\) Zeno time \(\mathrm{s}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(\Delta H\) energy spread (uncertainty) of the initial state \(\mathrm{J}\)
\(P_{1\to2}(n)\) probability of the transition after a π pulse interrupted by n measurements (Itano et al.) \(\mathrm{dimensionless}\)
\(n\) number of measurements \(\mathrm{dimensionless}\)

Sources

  1. Misra & Sudarshan (1977) The Zeno's paradox in quantum theory, J. Math. Phys. 18, 756
  2. Itano, Heinzen, Bollinger & Wineland (1990) Quantum Zeno effect, Phys. Rev. A 41, 2295
  3. Kofman & Kurizki (2000) Acceleration of quantum decay processes by frequent observations, Nature 405, 546

Source Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. (1990). Quantum Zeno effect. Physical Review A 41, 2295–2300.doi.org/10.1103/PhysRevA.41.2295

Field notes

Visualizza tutto
1 3
Visualizza tutto