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Section 9: Afterthoughts on a Paradox

The paradox of how a wave can be a particle and a particle can be a wave was brought up in Section 4, but not resolved. The issue is far from trivial and was fiercely debated in the early days of quantum mechanics. Niels Bohr even designed a hypothetical experiment to clarify the question of whether you could detect which slit a photon passed through in a two-slit interference experiment. For light to interfere, it must slightly change its direction as it passes through a slit in order to merge with the second beam.

Consequently, passing through a slit must slightly alter a photon's direction, which means that the slit has altered the photon's momentum. The photon must give an opposite momentum to the slit. Bohr's apparatus was designed to detect the recoil of the slit. If this were possible, an observer could decide which slit each photon passed through in creating an interference pattern, revealing both the particle and wave nature of light simultaneously. However, Bohr proved that detecting the photon would actually wipe out the interference pattern.

Thinking about waves passing through slits provides a different way to understand the situation. The waves might be light waves but they could just as well be matter waves. As the waves emerge from the slits, they diverge in a diffraction pattern. The wave intensity on the viewing screen might be registered on a camera, as in Figure 11, or measured by detections with particle counters, creating images similar to those in Figure 15. For the sake of discussion, we assume that the individual atoms or photons are detected with particle counters.

If the slits are close together, the diffraction patterns of particles coming through them overlap. In time the counts add to give a two-slit interference pattern, which is the signature of waves. What about the intermediate case? If the slits are far enough apart that the diffraction patterns only overlap a little bit, we should be able to place two detectors that only see particles passing through one or the other of the slits, and a detector in the center that sees two-slit interference. The conclusion is that if one knows from which of two slits the signal arises, one must ascribe the signal to the arrival of a particle. However, if there is no way to distinguish which of two possibilities gave rise to the signal, one must ascribe the signal to the arrival of waves.

The two-slit interference pattern depends on the distance between the slits.

Figure 36: The two-slit interference pattern depends on the distance between the slits.

Source: © Daniel Kleppner. More info

The answer to the question, "Is light composed of waves or particles?" is "Both." If you search for light's wave properties, you will find them. If you search for light's particle properties, you will find them, too. However, you cannot see both properties at the same time. They are what Bohr called complementary properties. One needs both properties for a complete understanding of light, but they are fundamentally incompatible and cannot be observed at the same time. Thus, the wave-particle paradox presents a contradiction that is not really true, but merely apparent.

We have discussed the wave-particle paradox for light, but the same reasoning applies to atoms and matter waves. Atoms are waves and they are particles, but not at the same time. You will find what you look for.