Wave function collapse
In various interpretations of quantum mechanics, Wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation.
In the Copenhagen interpretation, wave function collapse connects quantum to classical models, with a special role for the observer. By contrast, objective-collapse proposes an origin in physical processes. In the many-worlds interpretation, collapse does not exist; all wave function outcomes occur while quantum decoherence accounts for the appearance of collapse.
Historically, Werner Heisenberg was the first to use the idea of wave function reduction to explain quantum measurement.
Wave function collapse refers to two main concepts: in quantum mechanics, it’s the process where a system’s wave function, initially in a superposition of states, instantaneously settles into a single, definite state upon measurement. In computer science, it is a procedural generation algorithm inspired by this quantum principle to create complex outputs, like images or game levels, from a set of constraints and rules.
You can watch this video to see a visual explanation of the Wave Function Collapse algorithm in action: youtube/v=zE1Jbh8b0BM (youtube/v=zE1Jbh8b0BM)
In quantum mechanics
- A system exists in a “superposition” of all its possible states until it is measured.
- The wave function describes all these possibilities.
- Upon measurement or interaction with the external world, the wave function “collapses” into a single, definite outcome.
- This is a fundamental concept in quantum mechanics, though the precise mechanism is still a topic of debate and research.
In computer science
- The Wave Function Collapse algorithm (WFC) generates outputs like images, maps, or 3D environments by following rules derived from an input sample.
- It works by starting with a grid where each cell can be any possible “tile” or value, representing a superposition.
- The algorithm then “collapses” one cell at a time, randomly picking a definite value for it based on the input rules.
- This selection then constrains the possibilities for neighboring cells, and this process continues until the entire output is generated.
- The algorithm is similar to solving a Sudoku puzzle, where filling in one number removes other possibilities for its row, column, and box.
This video explains the concept of wave function collapse in quantum mechanics: https://www.youtube.com/shorts/FN9oWapY9xA (https://www.youtube.com/shorts/FN9oWapY9xA)
AI responses may include mistakes.
[1] https://www.southampton.ac.uk/~doug/quantum_physics/collapse.pdf
[5] https://profmattstrassler.com/2025/02/25/the-particle-and-the-particle-part-2/
[7] https://www.youtube.com/shorts/RpcWI1eabGo
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