Why We Don't See Schrödinger's Cats ✎
Context
The work sits within attempts to explain the classical limit of quantum mechanics. Nearby are studies on building macroscopic quantum superpositions (Schrödinger cats) out of atoms and light, as well as work on how gravity or universal algorithms affect quantum magic. This paper, however, does not construct superpositions; it explains why they don't survive. The key turns out to be the internal noise generated by the ensemble of microstates itself, not the external environment.
Methods
The author splits the wave function of a macroscopic object into blocks corresponding to distinguishable macrostates, and within each block sums an enormous number of microstates. Then an exact equation for the macroscopic amplitudes is derived from the Schrödinger equation. It turns out that the interaction matrix element between blocks behaves like white noise with a very short correlation time. This allows a transition to an Itô stochastic differential equation and a solution via the Fokker-Planck equation.
Results
The equation for the macroscopic amplitudes turns out to be reducing: it exponentially suppresses all superpositions, leaving only one macrostate. The collapse time is estimated as t ~ ℏΔE / |V|², where ΔE is the width of the energy bin and V is the matrix element between macrostates. For typical macroscopic objects this time is on the order of 10⁻²² seconds or less. The survival probability of each state equals its initial squared amplitude, which reproduces the Born rule exactly, with no extra postulates.
Implications
Unlike neighboring work that either builds macroscopic superpositions experimentally or invokes new physical mechanisms (gravity, modifications of the Schrödinger equation), here collapse emerges from standard quantum mechanics itself. No nonlinear terms need to be added: the nonlinearity appears automatically from the transition to macroscopic variables. This makes the solution to the measurement problem more economical and consistent with already known physics.
Future development
One could test the prediction about the maximum size of a superposition that can still exist. The condition ΔE·ΔX ≫ ħc sets the boundary between quantum and classical behavior. Experiments with massive objects, such as nanoparticles or mechanical oscillators, could check whether superpositions really do vanish faster than ordinary decoherence predicts.
Impact
The result matters for the interpretation of quantum mechanics and for experiments aimed at creating macroscopic quantum states. It may also shape our understanding of quantum computing, where macroscopic superpositions of qubits must be protected from collapse.
Next steps
The next step could be a more detailed calculation of the collapse rate for specific systems, such as superconducting qubits or mechanical resonators. It would also be worth investigating how this mechanism interacts with external decoherence.
Key open problems
The work speaks directly to the fundamental problem of quantum mechanics: the measurement problem. It offers a solution that requires no modification of the Schrödinger equation and no additional postulates, which makes it an appealing alternative to existing approaches.
The collapse time of a macroscopic superposition is estimated at 10⁻²² seconds, which is a billion times faster than a single vibrational period of an atom in a molecule.
Key numbers
- collapse time: 10-22 s
- collapse condition: ΔE·ΔX ≫ ħc ≈ 10-26 J·m
- Avogadro's number: 0.6·1024
- Compton time of the electron: 10-22 s