Editing Pilot wave theory (section)

===Principles===
[[File:A pilot-wave walker in a circular corral.png|thumb|upright=1.5|right|(a) A [[Walking droplet|walker]] in a circular corral. Trajectories of increasing length are colour-coded according to the droplet's local speed (b) The probability distribution of the walker's position corresponds roughly to the amplitude of the corral's Faraday wave mode.<ref>{{cite journal|last1=Harris|first1=Daniel M.|last2=Bush|first2=John W. M.|title=The pilot-wave dynamics of walking droplets|journal=Physics of Fluids|date=2013|volume=25|issue=9|pages=091112–091112–2|doi=10.1063/1.4820128|url=https://pdfs.semanticscholar.org/5659/d7cee01a8e55930b6895b11702705bb013fc.pdf|archive-url=https://web.archive.org/web/20161127215926/https://pdfs.semanticscholar.org/5659/d7cee01a8e55930b6895b11702705bb013fc.pdf|url-status=dead|archive-date=2016-11-27|access-date=27 November 2016|bibcode=2013PhFl...25i1112H|hdl=1721.1/92913|s2cid=120607553|hdl-access=free}}</ref>]]
The pilot wave theory is a [[hidden-variable theory]]. Consequently:
* the theory has realism (meaning that its concepts exist independently of the observer);
* the theory has [[determinism]].

The positions of the particles are considered to be the hidden variables. The observer doesn't know the precise values of these variables; they cannot know them precisely because any measurement disturbs them. On the other hand, the observer is defined not by the wave function of their own atoms but by the atoms' positions. So what one sees around oneself are also the positions of nearby things, not their wave functions.

A collection of particles has an associated matter wave which evolves according to the [[Schrödinger equation]]. Each particle follows a deterministic trajectory, which is guided by the wave function; collectively, the density of the particles conforms to the magnitude of the wave function. The wave function is not influenced by the particle and can exist also as an [[#Empty wave function|empty wave function]].<ref name="bell-1992">{{cite journal |last=Bell |first=J. S. |year=1992 |title=Six possible worlds of quantum mechanics |journal=[[Foundations of Physics]] |volume=22 |issue=10 |pages=1201–1215 |bibcode=1992FoPh...22.1201B |doi=10.1007/BF01889711|s2cid=119542806 }}</ref>

The theory brings to light [[Quantum nonlocality|nonlocality]] that is implicit in the non-relativistic formulation of quantum mechanics and uses it to satisfy [[Bell's theorem]]. These nonlocal effects can be shown to be compatible with the [[no-communication theorem]], which prevents use of them for faster-than-light communication, and so is empirically compatible with relativity.<ref name="hawe-2004">{{cite thesis |type=PhD |last=Westman |first=Hans |date=2004-10-29 |publisher=University of Gothenburg |title=Topics in the Foundations of Quantum Theory and Relativity |hdl=2077/16325 }}</ref>