Complimentarity

Rubin's Vase, the image in Figure 1, is a famous optical illusion which depicts both a vase and two faces. When you see concentrate on the vase, you cannot see the faces. Similarly, when you see the faces, the vase disappears. You cannot view both aspects of the image at once, yet the image is both at once. This describes the principle of complementarity, a situation in which observing one aspect of a complementary pair obscures the other aspect.

Rubin's Vase is not completely analogous to complementarity in quantum mechanics. The image is both a vase and two faces at once, yet a fundamental entity, like an electron or photon, never behaves like a wave and a particle at the same time. It simply has the capacity to behave like either. This idea of complementarity was first introduced by Niels Bohr in a 1927 lecture in Como, Italy: "The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition, respectively" (Bohr 580). He suggested that a fundamental particle neither behaves like a wave nor a particle until an observer decides how to view it (Cassidy).

This is demonstrated in the famous double slit experiment, where a screen with two slits is placed in front of a wall. If both slits remain open, photons that travel from a transmitter beam will form an interference pattern on the wall demonstrating constructive and destructive interference, suggesting wave-like behavior. If one slit is closed, there will be no interference pattern, as photons travel through just one slit and therefore cannot interfere and add or subtract amplitudes. If the two slits are opened, but a measuring device is placed on one of the slits, the result will be the same as when one slit was covered. Attempting to detect which slit a photon travels through eliminates wave behavior and therefore eliminates the interference pattern. When the photon must commit to a location, there is no longer a probability of where it will be located. Attempting to detect a photon will always result in the destruction of wave behavior. Before the photon is measured, there is a chance that it will go through Slit 1 and an equally probable chance that it will go through Slit 2. The interference pattern of the unmeasured photons is a result of interference of these probabilities (Gribbin 171). After a photon is measured, you know which slit it goes through. The photon is forced to choose a location, and it no longer behaves like a wave.

A wave packet is a superposition of waves of different wavelengths that describe the probability of a particle having a certain position or momentum. The probability of finding a particle in a location in space is determined by the intensity of the wave packet at that location. When wave packets travel through the double slit experiment, they produce interference. Places where amplitudes add and constructively interfere are places where it is most likely that a photon or electron will be located. Places where waves arrive half a wavelength or an integer plus half a wavelength apart destructively interfere and represent locations where electrons or photons are least likely to appear in the double slit experiment.

The amount by which the complementary properties of electrons or photons overlap is demonstrated by Heisenberg's uncertainty principle. Heisenberg's uncertainty principle shows that measuring the position and momentum of a particle simultaneously is impossible, because "Δp x Δq must always be bigger than ħ, Planck's constant divided by 2π," where p is momentum and q is position (Gribbin 119). Position and momentum are complementary, because the better defined momentum is, the less defined position is. This is related to the complementarity of waves and particles because we can know the exact momentum of a wave, and the exact location of a particle, but never the exact location of a wave or the exact momentum of a particle.

Heisenberg and Bohr were colleagues and their discoveries came around the same time. Bohr was more interested in the intuitive aspects of quantum mechanics, such as complementarity. Heisenberg was more interested in the mathematical relationship between position and momentum.

Uncertainty and complementarity are very similar subjects. If you want to measure the location of an electron, you must bounce a photon off of it. This disrupts the electron, and you no longer know where it is heading. Because momentum and position are complementary, there is guaranteed to be uncertainty when you measure one of them.

Another example of complementarity is the measurement of the polarization of photons. If the filter is vertical, the measurement it makes is either vertical or horizontal. If it is at another angle, the measurement it makes is either the arbitrary angle or the arbitrary angle plus 90 degrees. The measurements cannot be made at the same time, because after passing through one filter, the polarization of the photon is