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Schrödy

El gato de Schrödinger / Superposición cuántica · Camiseta de física

\[\begin{aligned} \lvert\Psi\rangle = \tfrac{1}{\sqrt{2}}\bigl(&\lvert \text{undecayed}\rangle\lvert \text{alive}\rangle \\ {}+{} &\lvert \text{decayed}\rangle\lvert \text{dead}\rangle\bigr) \end{aligned}\]
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Caja, gato, frasco, tapa sellada. La mascota más famosa de la física sigue discutiendo con nosotros. Schrödy es el gato de Schrödinger: su experimento mental de 1935 que cuestiona la superposición cuántica a escala cotidiana. Schrödy lo lleva en pixel art en una camiseta unisex. El panel de física de abajo incluye la ecuación, cada símbolo y las fuentes.

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Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

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

Para hacerse una idea: la talla M mide 20 in (50.80 cm) de ancho, unas 3.143 × 1034 longitudes de Planck (lP = 1.616255 × 10−35 m). Una cinta métrica es más rápida.

Measurements in inches, ±1.5 in tolerance.

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The physics

Schrödinger's thought experiment links one atom, which is in a superposition of decayed and not decayed, to a cat. Quantum mechanics then describes the whole box as a superposition of two complete stories, and the equal weights give a 50/50 chance of finding the cat alive when you look.

Schrödy has been in the box since 1935. Nobody has asked her opinion.

Erwin Schrödinger built the box that year, in a paper in Naturwissenschaften, from ordinary parts: a cat, a Geiger counter, a speck of radioactive material so small that in an hour one atom might decay or, just as likely, none might, a hammer, and a flask of hydrocyanic acid. If the counter clicks, the hammer falls. He did not offer it as an experiment. He offered it as an embarrassment: take the quantum rule that a single atom sits in a blend of decayed and not decayed, follow the wiring outward, and the rule seems to say the cat is a blend too.

Look at the first equation on this page and notice what it does not contain. There is no term for a cat that is alive-and-dead on its own. Each cat state is chained to an atom state: undecayed with alive, decayed with dead. That chaining is entanglement, and it is the real content of the thought experiment. Ask about the cat alone and quantum mechanics answers with plain odds, one half and one half, with no interference between them. The strangeness lives in the pair.

Why do real cats never show it? A warm animal trades photons and air molecules with its surroundings at an enormous rate, and every exchange copies a little information about its condition out into the room. This is decoherence, and it hides the interference long before anyone lifts the lid. Whether it also settles which outcome actually happens is still argued.

Schrödinger had shared the 1933 Nobel Prize with Paul Dirac. The cat has outlived most of what was written about it.

Schrödy sits on the lid. Open it if you like. The odds were never inside the box.

Equations

\[\begin{aligned} \lvert\Psi\rangle = \tfrac{1}{\sqrt{2}}\bigl(&\lvert \text{undecayed}\rangle\lvert \text{alive}\rangle \\ {}+{} &\lvert \text{decayed}\rangle\lvert \text{dead}\rangle\bigr) \end{aligned}\]
\[P(\text{alive}) = \left\lvert \langle \text{undecayed},\text{alive} \vert \Psi\rangle \right\rvert^{2} = \tfrac{1}{2}\]
SymbolMeaningUnit
\(\lvert\Psi\rangle\) joint quantum state of atom and cat (normalized state vector) \(\mathrm{1}\)
\(P\) Born-rule probability \(\mathrm{1}\)

Sources

  1. Schrödinger (1935) Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23, 807
  2. Encyclopaedia Britannica — Schrödinger’s cat
  3. Feynman Lectures on Physics Vol. III Ch. 3: Probability Amplitudes
  4. NobelPrize.org — The Nobel Prize in Physics 1933 (Schrödinger, Dirac)
  5. Zurek (2003) Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715

Source Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik. Die Naturwissenschaften 23, 807–812.doi.org/10.1007/BF01491891

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