Editing De Broglie–Bohm theory (section)

=== Double-slit experiment ===
[[File:doppelspalt.svg|thumb|The Bohmian trajectories for an electron going through the two-slit experiment. A similar pattern was also extrapolated from [[weak measurement]]s of single photons.<ref>{{Cite journal |last1=Kocsis |first1=Sacha |last2=Braverman |first2=Boris |last3=Ravets |first3=Sylvain |last4=Stevens |first4=Martin J. |last5=Mirin |first5=Richard P. |last6=Shalm |first6=L. Krister |last7=Steinberg |first7=Aephraim M. |date=2011-06-03 |title=Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer |url=https://www.science.org/doi/10.1126/science.1202218 |journal=Science |language=en |volume=332 |issue=6034 |pages=1170–1173 |doi=10.1126/science.1202218 |pmid=21636767 |bibcode=2011Sci...332.1170K |s2cid=27351467 |issn=0036-8075}}</ref>]]

The [[double-slit experiment]] is an illustration of [[wave–particle duality]]. In it, a beam of particles (such as electrons) travels through a barrier that has two slits. If a detector screen is on the side beyond the barrier, the pattern of detected particles shows interference fringes characteristic of waves arriving at the screen from two sources (the two slits); however, the interference pattern is made up of individual dots corresponding to particles that had arrived on the screen. The system seems to exhibit the behaviour of both waves (interference patterns) and particles (dots on the screen).

If this experiment is modified so that one slit is closed, no interference pattern is observed. Thus, the state of both slits affects the final results. It can also be arranged to have a minimally invasive detector at one of the slits to detect which slit the particle went through. When that is done, the interference pattern disappears.<ref>{{Cite journal |last=Zeilinger |first=Anton |date=1999-03-01 |title=Experiment and the foundations of quantum physics |url=https://link.aps.org/doi/10.1103/RevModPhys.71.S288 |journal=Reviews of Modern Physics |language=en |volume=71 |issue=2 |pages=S288–S297 |doi=10.1103/RevModPhys.71.S288 |issn=0034-6861}}</ref>

In de Broglie–Bohm theory, the wavefunction is defined at both slits, but each particle has a well-defined trajectory that passes through exactly one of the slits. The final position of the particle on the detector screen and the slit through which the particle passes is determined by the initial position of the particle. Such initial position is not knowable or controllable by the experimenter, so there is an appearance of randomness in the pattern of detection. In Bohm's 1952 papers he used the wavefunction to construct a [[quantum potential]] that, when included in Newton's equations, gave the trajectories of the particles streaming through the two slits. In effect the wavefunction interferes with itself and guides the particles by the quantum potential in such a way that the particles avoid the regions in which the interference is destructive and are attracted to the regions in which the interference is constructive, resulting in the interference pattern on the detector screen.

To explain the behavior when the particle is detected to go through one slit, one needs to appreciate the role of the conditional wavefunction and how it results in the collapse of the wavefunction; this is explained below. The basic idea is that the environment registering the detection effectively separates the two wave packets in configuration space.