Wheeler’s delayed-choice experiment (source: Wikipedia)

If a single photon is emitted into the entry port of the apparatus at the lower-left corner, it immediately encounters a beam-splitter. Because of the equal probabilities for transmission or reflection the photon will either continue straight ahead, be reflected by the mirror at the lower-right corner, and be detected by the detector at the top of the apparatus, or it will be reflected by the beam-splitter, strike the mirror in the upper-left corner, and emerge into the detector at the right edge of the apparatus. Observing that photons show up in equal numbers at the two detectors, experimenters generally say that each photon has behaved as a particle from the time of its emission to the time of its detection, has traveled by either one path or the other, and further affirm that its wave nature has not been exhibited.

If the apparatus is changed so that a second beam splitter is placed in the upper-right corner, then part of the beams from each path will travel to the right, where they will combine to exhibit interference on a detection screen. Experimenters must explain these phenomena as consequences of the wave nature of light. Each photon must have traveled by both paths as a wave, because if each photon traveled as a particle along just one path then the many photons sent during the experiment would not produce an interference pattern.

In the first experiment (as seen in the top image), the outcome is a particle effect. In the second experiment (as seen in the lower image), the result is a wave effect.

Encoding the path as a covert observation
A variation of the second experiment (lower image) involves placing a polarization plate on one of the paths. This is referred to as path encoding. It introduces an additional interaction, causing the photon to exhibit behavior solely as a particle, no longer behaving as a wave. An interaction alters the particle’s behavior.

The relation interpretation
It is also possible to examine these experiments with a focus on relations. In this context, the photon arriving in the experiment at the first beam splitter is entangled with its source, for instance, a laser machine. It collapses with the beam splitter, giving rise to a new superposition in which the photon is entangled on two positions, perpendicular to each other, with the beam splitter. As a result, the photon’s redistribution of information is limited in two directions instead of one. The amount of information in the newly formed quantum system is equivalent to the information before the collapse. The quantum system forms an indivisible whole that redistributes information in all directions except the two, until irreversibility becomes inevitable, leading to a new collapse. This occurs at the mirror. Following this collapse, another superposition, this time with two parallel entangled directions, arises. At the next mirror, there is yet another collapse with a redistribution of information. Finally, upon reaching the exit of the experiment, there are two options. In the absence of a new beam splitter, the photon cannot interfere with itself and will collapse in one of the two directions. If it encounters a beam splitter, this will lift the split superposition, allowing the photon to interfere with itself. Detection of a large number of photons will reveal an interference pattern.

Encoding the path in a relation perspective
When an entangled photon encounters a polarizing plate on its path, it will collapse with it, resulting in a photon with only one source entanglement. Without new beam splitters or slit arrangements, this photon cannot interfere with itself, and upon detection, a so-called ‘particle effect’ becomes visible.

What about the larger objects in the experiments? Are they entangled as well?
What about the devices in the experiment? Are they also entangled with their surroundings? One might assume so. However, in these experiments, it is not verifiable because they are large and stable. The effects of entanglement of larger objects with their surroundings are also described as a heat bath. Similar to an object that assumes the temperature of the surroundings, an object also exchanges quantum information with the environment. We call this decoherence.

The paradox of wave and/or particle
‘Wave’ is a quantum concept, ‘particle’ is a macroscopic concept. The paradox lies in the transition from the quantum level to the macro level. Entropy causes the shift from probability distribution and probability density to particle. And from superposition and entanglement to isolation and discrete numbers.