This applet shows the interference pattern in two dimensions of a microscopic massive object (electron, neutron, etc) when interfered with itself. Quantum Mechanics, QM, represents these objects as wave functions. When the screen placed behind the wall detects the object, the wave function collapses at that detection point. Bohmian Mechanics, BM, an interpretation of QM without observers, provides a different picture. Objects are represented by particles and their associated wave functions. The velocity of the particle is determined by the associated wave fucntion according to the recipe from BM. This applet shows the interference of the wave function for different parameters. It also allows to visualize the trajectories predicted by BM.
The continue (blue) line on the right represents the probability function |Y|2 on the screen. That is the probability that an object hits the screen at a particular point. The histogram represents the actual number of hits at each point of the screen in the animation. If the applet is left running long enough both distributions should overlap. However discrepancies may arise because of lack of precision of the calculations in the applet.
The double slit experiment summarizes in a graphic manner the measurement problem of Quantum Mechanics as discussed in the following text by P.A.M. Dirac.
We shall discuss the description which quantum mechanics provides of the interference of photons. Let us take a definitive experiment demonstrating interference. Suppose we have a beam of light which is passed through some kind of interferometer, so that it gets split up into two components and the two components are subsequently made to interfere. We may ... take an incident beam consisting of only a single photon and inquire what will happen to it as it goes through the apparatus. This will present to us the difficutly of the conflict between the wave and corpuscular theories of light in an acute form.
[W]e must now describe the photon as going partly into each of the two components into which the incident beam is split. The photon is then, as we may say, in a translatinal state given by the superposition of the two translational states associated with the two components... For a photon to be in a definite translation state it needs not be associated with one single beam of light, but may be associated with two or more beams of light which are the components into which the original beam has been split. In the accurate mathematical theory each translation state is associate which one of the wave functions of the ordinary wave optics, which wave function may describe either a single beam or two or more beams into which one original beam has been split. Translations states are thus superposable in a similar way to wave functions.
Let us consider now what happens when we determine the energy in one of the components. The result of such a determination must be either the whole photon or nothing at all. Thus the photon must change suddently from being partly in one beam and partly in the other to being entirely in one of the beams. This sudden change is due to the disturbance in the translational state of the photon which the observation necessarily makes. It is impossible to predict in which of the two beams the photon will be found. Only the probability of either result can be calculated from the previous distribution of the photons over the two beams.
(P.A.M. Dirac, The principles of Quantum Mechanics, 7-8, 4th edn, Oxford University Press, 1958).
The applet has four panels. The combo below the low left corner of the graphic allows to select to swith among them.
Allows to change the distance and time units of the animation.
Permits to vary the colors of the wave function, particles and trajectories.