Wheeler's delayed-choice experiment describes a family of thought experiments in quantum physics proposed by John Archibald Wheeler, with the most prominent among them appearing in 1978 and 1984. These experiments illustrate the central point of quantum theory: "It is wrong to attribute a tangibility to the photon in all its travel from the point of entry to its last instant of flight."
These experiments close a loophole in the traditional double-slit experiment demonstration that quantum behavior depends on the experimental arrangement. The experiment closes the loophole that a photon might adjust its behavior from particle to wave behavior or vice versa. By altering the apparatus after the photon is supposed to be in "flight", the loophole is closed.
Cosmic versions of the delayed-choice experiment use photons emitted billions of years ago; the results are unchanged.George Greenstein and Arthur Zajonc, The Quantum Challenge, p. 37f. The concept of delayed choice has been productive of many revealing experiments. New versions of the delayed choice concept use quantum effects to control the "choices", leading to the delayed-choice quantum eraser.
Concept Wheeler's delayed-choice experiment demonstrates that no particle-propagation model consistent with relativity explains quantum theory. Like the double-slit experiment, Wheeler's concept has two equivalent paths between a source and detector. Like the which-way versions of the double-slit, the experiment is run in two versions: one designed to detect wave interference and one designed to detect particles. The new ingredient in Wheeler's approach is a delayed-choice between these two experiments. The decision to measure wave interference or particle path is delayed until just before the detection. The goal is to ensure that any traveling particle or wave will have passed the area of two distinct paths in the quantum system before the choice of experiment is made.
Cosmic interferometer
Wheeler's cosmic scale thought experiment employs a quasar or other light source in a galaxy billions of light years away. Some of these stars are known to be located behind a massive galaxy that acts as a gravitational lens, bending light rays pointing away from Earth back towards us. The result is two images of the star, one direct and one bent. Wheeler proposed to measure the interference between these two paths. Because the light observed in such an experiment was emitted and passed through the lens billions of years ago, no choice on Earth could alter the outcome of the experiment.
Wheeler then plays the devil's advocate and suggests that perhaps for those experimental results to be obtained would mean that at the instant astronomers inserted their beam-splitter, photons that had left the quasar some millions of years ago retroactively decided to travel as waves, and that when the astronomers decided to pull their beam splitter out again that decision was telegraphed back through time to photons that were leaving some millions of years plus some minutes in the past, so that photons retroactively decided to travel as particles.
Several ways of implementing Wheeler's basic idea have been made into real experiments and they support the conclusion that Wheeler anticipated — that what is done at the exit port of the experimental device before the photon is detected will determine whether it displays interference phenomena or not.
Double-slit version
A second kind of experiment resembles the ordinary double-slit experiment. The schematic diagram of this experiment shows that a lens on the far side of the double slits makes the path from each slit diverge slightly from the other after they cross each other fairly near to that lens. The result is that the two wavefunctions for each photon will be in superposition within a fairly short distance from the double slits, and if a detection screen is provided within the region wherein the wavefunctions are in superposition then interference patterns will be seen. There is no way by which any given photon could have been determined to have arrived from one or the other of the double slits. However, if the detection screen is removed the wavefunctions on each path will superimpose on regions of lower and lower amplitudes, and their combined probability values will be much less than the unreinforced probability values at the center of each path. When telescopes are aimed to intercept the center of the two paths, there will be equal probabilities of nearly 50% that a photon will show up in one of them. When a photon is detected by telescope 1, researchers may associate that photon with the wavefunction that emerged from the lower slit. When one is detected in telescope 2, researchers may associate that photon with the wavefunction that emerged from the upper slit. The explanation that supports this interpretation of experimental results is that a photon has emerged from one of the slits, and that is the end of the matter. A photon must have started at the laser, passed through one of the slits, and arrived by a single straight-line path at the corresponding telescope.
The retrocausal explanation, which Wheeler does not accept, says that with the detection screen in place, interference must be manifested. For interference to be manifested, a light wave must have emerged from each of the two slits. Therefore, a single photon upon coming into the double-slit diaphragm must have "decided" that it needs to go through both slits to be able to interfere with itself on the detection screen. For no interference to be manifested, a single photon coming into the double-slit diaphragm must have "decided" to go by only one slit because that would make it show up at the camera in the appropriate single telescope.
In this thought experiment the telescopes are always present, but the experiment can start with the detection screen being present but then being removed just after the photon leaves the double-slit diaphragm, or the experiment can start with the detection screen being absent and then being inserted just after the photon leaves the diaphragm. Some theorists argue that inserting or removing the screen in the midst of the experiment can force a photon to retroactively decide to go through the double-slits as a particle when it had previously transited it as a wave, or vice versa. Wheeler does not accept this interpretation.
The double slit experiment, like the other six idealized experiments (microscope, split beam, tilt-teeth, radiation pattern, one-photon polarization, and polarization of paired photons), imposes a choice between complementary modes of observation. In each experiment we have found a way to delay that choice of type of phenomenon to be looked for up to the very final stage of development of the phenomenon, and it depends on whichever type of detection device we then fix upon. That delay makes no difference in the experimental predictions. On this score everything we find was foreshadowed in that solitary and pregnant sentence of Bohr, "...it...can make no difference, as regards observable effects obtainable by a definite experimental arrangement, whether our plans for constructing or handling the instruments are fixed beforehand or whether we prefer to postpone the completion of our planning until a later moment when the particle is already on its way from one instrument to another."John Archibald Wheeler, ""The'Past" and the 'Delayed Choice' Double-Slit experiment," which appeared in 1978 and has been reprinted in several locations, e.g. Lisa M. Dolling, Arthur F. Gianelli, Glenn N. Statilem, Readings in the Development of Physical Theory, p. 486ff.
Bohmian interpretation
In Bohm's interpretation of quantum mechanics, the particle obeys classical mechanics except that its movement takes place under the additional influence of its quantum potential. A neutron for example has a definite trajectory and passes through one or the other of the two slits and not both, just as it is in the case of a classical particle. However the quantum particle in Bohm's interpretation is inseparable from its associated field. That field provides the quantum properties. In the delayed choice experiment, wave packets associated with the field propagate along both paths of the interferometer, but only one packet contains a particle. The field aspect of the neutron is responsible for the interference between the two paths. Changing the final setup at the detector to look for particle properties amounts to ignoring the field aspect of the neutron.Dharma-wardana, C. (2013). A Physicist's View Of Matter And Mind. Singapore: World Scientific Publishing Company.
The past is determined and stays what it was up to the moment T1 when the experimental configuration for detecting it as a wave was changed to that of detecting a particle at the arrival time T2. At T1, when the experimental set up was changed, Bohm's quantum potential changes as needed, and the particle moves classically under the new quantum potential till T2 when it is detected as a particle. Thus Bohmian mechanics restores the conventional view of the world and its past. The past is out there as an objective history unalterable retroactively by delayed choice. The quantum potential contains information about the boundary conditions defining the system, and hence any change of the experimental set up is reflected in changes in the quantum potential which determines the dynamics of the particle.
Experimental details John Wheeler's original discussion of the possibility of a delayed choice quantum appeared in an essay entitled "Law Without Law," which was published in a book he and Wojciech Hubert Zurek edited called Quantum Theory and Measurement, pp 182–213. He introduced his remarks by reprising the argument between Albert Einstein, who wanted a comprehensible reality, and Niels Bohr, who thought that Einstein's concept of reality was too restricted. Wheeler indicates that Einstein and Bohr explored the consequences of the laboratory experiment that will be discussed below, one in which light can find its way from one corner of a rectangular array of semi-silvered and fully silvered mirrors to the other corner, and then can be made to reveal itself not only as having gone halfway around the perimeter by a single path and then exited, but also as having gone both ways around the perimeter and then to have "made a choice" as to whether to exit by one port or the other. Not only does this result hold for beams of light, but also for single photons of light. Wheeler remarked: The experiment in the form an interferometer, discussed by Einstein and Bohr, could theoretically be used to investigate whether a photon sometimes sets off along a single path, always follows two paths but sometimes only makes use of one, or whether something else would turn up. However, it was easier to say, "We will, during random runs of the experiment, insert the second half-silvered mirror just before the photon is timed to get there," than it was to figure out a way to make such a rapid substitution. The speed of light is just too fast to permit a mechanical device to do this job, at least within the confines of a laboratory. Much ingenuity was needed to get around this problem.