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Decoherex

The Interference / Quantum Decoherence Physics

\[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Why don’t chairs show interference? Because the world keeps watching them. Decoherence: a quantum system entangled with its environment loses interference and looks classical. Decoherex personifies it. Decoherex wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Pour l'échelle : la taille M mesure 20 in (50.80 cm) de large, soit environ 3.143 × 1034 longueurs de Planck (lP = 1.616255 × 10−35 m). Un mètre ruban est plus rapide.

Measurements in inches, ±1.5 in tolerance.

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The physics

The off-diagonal terms in a density matrix carry the ability to interfere. Contact with the environment makes them decay away, often extremely fast, so a superposition starts behaving like an ordinary 'either/or' mixture.

Decoherex does not destroy superpositions. They spread them too thin to see.

A quantum system's density matrix holds two kinds of number. On the diagonal sit plain probabilities: the chance of finding it here, the chance of finding it there. Off the diagonal sit the coherences, the terms that produce interference fringes. The formula on this page models one of them dying away over a time \(\tau_D\). Once it is gone, the system behaves like an ordinary coin: odds known, no interference.

Where does it go? Into the surroundings. Every stray photon or air molecule that bounces off the system and carries away even a trace of information about it becomes entangled with it. The superposition is still there, but it now belongs to the system plus a growing crowd of environmental particles that nobody tracks. Look at the system alone and the interference has vanished. H. Dieter Zeh pointed this out in 1970; Wojciech Zurek and others developed it into an account of how a classical world emerges.

It is measured. In 1996 Serge Haroche's group in Paris put a microwave field in a cavity into a superposition of two states and watched the coherence between them fade, faster the more different the two states were. Haroche shared the 2012 Nobel Prize. In Vienna in 1999, buckyballs of sixty carbon atoms sent through a grating produced interference. In 2004 the same group heated similar molecules with lasers until they glowed; each emitted thermal photon carried away a little which-way information, and the fringes washed out as the temperature rose.

What decoherence does not obviously do is select a single outcome. Whether it solves the measurement problem, or only explains why big objects never show interference, is still debated.

Decoherex deletes nothing. They just make sure everyone finds out.

Equations

\[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
SymbolMeaningUnit
\(\rho_{01}\) off-diagonal (coherence) element of the density matrix \(\mathrm{1}\)
\(t\) time \(\mathrm{s}\)
\(\tau_D\) decoherence time \(\mathrm{s}\)

Sources

  1. Zeh (1970) On the interpretation of measurement in quantum theory, Found. Phys. 1, 69
  2. Zurek (2003) Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715
  3. Encyclopaedia Britannica — Decoherence
  4. NobelPrize.org — The Nobel Prize in Physics 2012 (Haroche, Wineland)
  5. Brune et al. (1996) Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement, PRL 77, 4887
  6. Arndt et al. (1999) Wave–particle duality of C60 molecules, Nature 401, 680
  7. Hackermüller, Hornberger, Brezger, Zeilinger, Arndt (2004) Decoherence of matter waves by thermal emission of radiation, Nature 427, 711

Source Zeh, H. D. (1970). On the interpretation of measurement in quantum theory. Foundations of Physics 1, 69–76.doi.org/10.1007/BF00708656

Field notes

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