Measurement and Schrödinger's cat

The act of measurement

What happens when we measure a system in superposition? The result is one of the strangest aspects of the theory: the superposition collapses abruptly onto a single state.

   BEFORE the measurement :   |ψ⟩ = a|0⟩ + b|1⟩   (both at once)

                              |  measurement
                              v

   AFTER the measurement :   |0⟩   OR   |1⟩       (only one, chosen at random)
                       proba       proba
                       |a|^2       |b|^2

This is called the collapse (or "reduction") of the wave function. Three baffling features:

1. The result is fundamentally random: only the probabilities can be predicted, never the exact result. Even knowing everything about the system.
2. The collapse is irreversible: once |0⟩ is measured, the superposition is lost.
3. After the measurement, the system is in the obtained state: measuring it again gives the same result.

This is a break with all of classical physics, where measurement merely reveals a pre-existing value. Here, measurement takes part in creating the result.

The cat thought experiment

In 1935, Schrödinger imagined a provocative experiment to highlight the apparent absurdity of this idea at our scale.

   Closed box :
   +-------------------------------+
   |  radioactive atom             |
   |     |                         |
   |     | (superposition :        |
   |     |  decayed + not          |
   |     |  decayed)               |
   |     v                         |
   |  detector --> hammer          |
   |                  |            |
   |                  v            |
   |             vial of poison    |
   |                  |            |
   |                  v            |
   |                CAT            |
   +-------------------------------+

The device ties the fate of a cat to a radioactive atom in superposition (decayed / not decayed). If the atom decays, a detector triggers a hammer that shatters a vial of poison, killing the cat. As long as the box stays closed, the atom is in superposition — and so, following quantum logic all the way through, the cat would be in a superposition:

   |cat⟩ = a |alive⟩ + b |dead⟩     (?!)

A cat both dead and alive. This is obviously absurd at our scale: that is the paradox Schrödinger wanted to bring out.

The resolution: decoherence

Modern physics resolves the paradox through decoherence. A macroscopic object (the cat, the detector) constantly interacts with a gigantic environment (air, photons, heat). These countless interactions behave like permanent measurements that destroy the superposition almost instantly.

   isolated system (1 atom)   ->  superposition preserved (for a long time)
   macroscopic system         ->  near-instant decoherence
   (cat, in contact with          ->  no more observable superposition
    billions of billions
    of particles)

This is why we never observe a superposed cat, nor any everyday object in two states at once: at large scale, superposition vanishes in an infinitesimal fraction of a second. It only survives for very well isolated systems — which, as we will see, is the whole challenge of quantum computers.

In summary

Measuring a superposed system causes the collapse of its wave function onto a single state, chosen at random according to the probabilities |a|^2, |b|^2 — a fundamental and irreversible randomness. Schrödinger's cat pushes this logic to absurdity at our scale; decoherence explains why macroscopic objects are never superposed: their contact with the environment destroys the superposition instantly.