No collapse of the wave function

Quantum mechanics describes a particle with a wave function spread through space. The textbook account says that until the particle is measured it has no definite position, and that measurement makes the wave function collapse so the particle is found in one place. The mathematics has never failed a test, but the theory never says what counts as a measurement or why measuring should do something no other process does. This is the measurement problem, argued over since 1927.

RSI has no measurement problem. A particle is a knot in the Eternal Consonance, and a knot is always somewhere. What spreads through space is the flow of the medium around it, and that flow guides where the knot goes. The wave function describes the guide, not the particle. Louis de Broglie proposed this picture in 1927 and David Bohm completed it in 1952; it reproduces every prediction of quantum mechanics. What it lacked was an answer to "a wave in what?" RSI supplies one: the medium itself.

Results are still probabilities, because no one can know exactly where each knot starts. Bohm showed that when starting positions are spread the way the wave is spread, outcomes follow quantum mechanics' probability rule exactly.

The double slit. Electrons sent one at a time arrive one at a time, each as a single dot. Only after thousands of dots does a striped pattern appear, as Akira Tonomura's team at Hitachi filmed in 1989. In RSI each electron passes through one slit, while the medium's flow passes through both and carries the shape of both openings to the screen. Each knot follows that flow toward the bright bands.

Recording, not watching. The pattern vanishes whenever anything records which slit was used, even if no one reads the record. It is not simply a matter of the detector knocking the particle: in 1998 Dürr, Nonn and Rempe marked atoms' paths with a kick too small to blur the bands, and the bands vanished anyway. In RSI the detector, made of knots, becomes tied to the flow, so the part through each slit carries a different detector reading. The two parts can no longer combine, and the knot is steered only by the part it travels in. That is all collapse ever was. Nothing jumps, and no observer is needed.

The uncertainty principle stands. A guiding wave narrow in space must contain many wavelengths, so no guide can give both a sharp position and a sharp momentum. RSI changes no prediction of quantum mechanics. It changes what the mathematics is about.

Entanglement is a separate question, taken up in its own explanation.