Schrödinger's Cat

The thought experiment

1. A cat is placed in a sealed box.
2. Box also contains: a radioactive atom (50% chance to decay in 1 hour), a Geiger counter, a hammer, and a vial of cyanide.
3. If atom decays → counter clicks → hammer breaks vial → cat dies.
4. If atom doesn't decay → cat lives.

Quantum mechanics: after 1 hour, atom is in superposition of decayed and not-decayed (50% each).

By extension — the cat is in superposition of dead and alive — until you open the box and "measure" it.

Modern resolution: decoherence

Environmental interactions destroy superpositions on timescales determined by:

Object	Decoherence time
Electron in vacuum	~10⁻⁹ s (with vacuum fluctuations)
Atom in optical lattice	~10⁻³ s
Buckyball in air	~10⁻¹² s
1 µm particle in air	~10⁻²³ s
1 g object	~10⁻⁴⁰ s (utterly negligible)
Cat-sized animal	essentially instantaneous

So in practice, no matter how isolated, a cat-sized system decoheres faster than any reasonable observation. Cat is alive or dead long before opened.

Interpretations of QM

Interpretation	Resolution	Experimental predictions
Copenhagen (Bohr)	Wave function collapses on measurement	Standard QM
Many-Worlds (Everett)	All outcomes happen, in different branches	Standard QM
Pilot wave (Bohmian)	Real particles guided by wave	Standard QM (mostly)
GRW / spontaneous collapse	Wave function spontaneously collapses	Slightly different at large scales
Decoherence (modern)	Apparent collapse via environment coupling	Standard QM
QBism	Quantum states are subjective probabilities	Standard QM

All interpretations agree on experimental predictions; they differ on "what's really happening."

Macroscopic quantum experiments

System	Quantum behavior
SQUID (superconducting)	10⁹ Cooper pairs in coherent state
BEC (Bose-Einstein condensate)	Millions of atoms in same state
Buckyball interference	C60 molecules (720 C atoms) interfered
Massive molecules	~25,000 amu molecules in superposition
Mechanical resonators	Trillion-atom resonators near ground state

Each pushes the boundary of "macroscopic quantum"; full cat-sized superposition not yet (and may never be) demonstrated.

JavaScript — Schrödinger cat simulation

// Simulate the cat experiment
function schrodingerCat(decayProbability = 0.5) {
  if (Math.random() < decayProbability) {
    return 'dead';
  }
  return 'alive';
}

// Run many "cats"
const trials = 10000;
let dead = 0;
for (let i = 0; i < trials; i++) {
  if (schrodingerCat() === 'dead') dead++;
}
console.log(`After ${trials} trials: ${dead} dead, ${trials - dead} alive`);
// ~50/50 — randomness from quantum decay (mathematically)

// Quantum superposition representation
class CatState {
  constructor(alpha_alive, beta_dead) {
    this.alpha = alpha_alive;
    this.beta = beta_dead;
  }
  
  // Probability of alive vs dead
  pAlive() { return this.alpha * this.alpha; }
  pDead() { return this.beta * this.beta; }
  
  // Apply decoherence (over time, system collapses to classical mixture)
  decohere() {
    // Off-diagonal coherences vanish; diagonal probabilities remain
    // Classically — definite outcome
    return Math.random() < this.pAlive() ? 'alive' : 'dead';
  }
}

// Cat in equal superposition
const cat = new CatState(1/Math.sqrt(2), 1/Math.sqrt(2));
console.log(`P(alive) = ${cat.pAlive()}`);  // 0.5
console.log(`P(dead) = ${cat.pDead()}`);    // 0.5
console.log(`Observed: ${cat.decohere()}`);

// Decoherence time scales (rough)
function decoherenceTime(mass_kg, T_K = 300, scale_m = 1e-9) {
  // Rough formula based on environmental scattering
  // Decoherence faster for larger mass, higher T, larger scale
  const baseTime = 1e-30;  // s
  return baseTime / (mass_kg * Math.sqrt(T_K) * scale_m);
}

console.log(`Electron in vacuum: ${decoherenceTime(9e-31).toExponential(2)} s`);
console.log(`1 mg dust grain: ${decoherenceTime(1e-6).toExponential(2)} s`);
// Macroscopic decoherence is essentially instantaneous

// Many-worlds: branches multiply
function manyWorlds(initialBranches, observations) {
  // Each observation doubles branches (binary outcomes)
  let branches = initialBranches;
  for (let i = 0; i < observations; i++) {
    branches *= 2;
  }
  return branches;
}

console.log(`After 10 quantum measurements: ${manyWorlds(1, 10)} branches`);  // 1024
console.log(`After 50: ${manyWorlds(1, 50)}`);  // 10¹⁵ branches!

Where Schrödinger's cat matters

• Foundations of QM. Highlights measurement problem; foundational to ongoing debates.
• Quantum computing. Decoherence is the enemy — must isolate qubits from environment to maintain superposition.
• Macroscopic quantum experiments. Pushing systems to be larger and still quantum.
• Philosophy of science. Frequently invoked in philosophical discussions of measurement, observation, reality.
• Quantum information. Concepts like entanglement, decoherence essential for protocols.
• Pop culture. Iconic representation of quantum weirdness (often misunderstood as mystical).
• Education. Vivid demonstration of why classical intuition fails at quantum level.

Common mistakes

• Treating it as a real experimental setup. It's a THOUGHT experiment to highlight QM's strangeness when applied to macroscopic objects. Schrödinger thought it was absurd — illustrating issues with naive interpretation.
• Thinking the cat is "really" both alive and dead. Modern view: decoherence makes the cat effectively classical long before observation. The mathematical superposition is rapidly destroyed by environmental interactions.
• Believing observation creates reality. Pop culture often says "looking inside" makes the cat alive or dead. Decoherence does it; observation just reveals the outcome.
• Choosing one interpretation as correct. Multiple valid interpretations of QM with same experimental predictions. Choice is philosophical.
• Conflating Schrödinger with quantum mysticism. The thought experiment is a precise illustration of math, not a license for mysticism. Wave function is a precise mathematical object.
• Missing the original point. Schrödinger wasn't endorsing the cat-in-superposition idea; he was POINTING OUT it's absurd, suggesting QM needs better understanding.