Once Before Time - Martin Bojowald [26]
—WOLFRAM VON ESCHENBACH, Parsifal
We are thus prevented from ever determining the complete wave function by many repeated measurements of an object. Very delicate methods that handle the wave function more gently do exist, but no measurement is possible that exerts no influence whatsoever. As a principle problem it cannot be evaded by improved technologies; every measurement must interact with the measured object if it is to provide any information at all.
In everyday life, we can investigate the shape and texture of surfaces by physical touch, leaving sturdy objects unharmed. But sensitive objects are changed or even destroyed by contact and cannot reliably be examined in this way. One can use more delicate measurement tools instead of one’s fingers, such as optical methods. But even light carries energy and must interact with the object in order to survey its properties in a useful way, exchanging energy. Even dim light is too energetic to leave the fragile wave functions of atomic physics unharmed. Every measurement changes its object, implying a fundamental limitation to information gain. What can be achieved by cleverly sophisticated technologies is a determination of properties of the wave function in as complete a way as possible—within the limits allowed by quantum mechanics. Such delicate measurements are called “quantum nondemolition” since they attempt not to destroy the wave function. But even in this case, it is impossible to determine the wave function completely. Strictly speaking, it does not represent a physical object, fully observable in all its details; it is rather a mathematical description of all the accessible properties.
The influence of a measurement on an object has a further well-known and important consequence: Werner Heisenberg’s uncertainty relation. Uncertainty relations occur whenever measurements of different, so-called complementary quantities are undertaken. The position and velocity of a particle as described by a wave function provide the best-known example. In this case, the uncertainty principle can intuitively be demonstrated by an explicit, if conceptual, measurement process. A microscope, for instance, allows one to measure the position by scattering light off a particle. Without the particle, light would simply move straight from the source to a detector; when the light is scattered off a particle in different directions, the particle can be located. This very scattering, essential for a successful detection, is an interaction influencing the object scrutinized. Light carries energy, and the scattering process changes the particle’s motion. If the particle was initially at rest, say, it will move slightly after some light has ricocheted off it. For the macroscopic objects we usually deal with in life, this change is imperceptibly small, but it plays a crucial role for a microscopic object such as an electron.
During a very precise measurement of position, the velocity of a particle must inevitably change; these two quantities are exactly the complementary ones of this example. There is an effect on the velocity, the more precisely one attempts to measure the position: Higher resolution requires larger energies of the light used, as becomes clear when replacing light with electron microscopy. More energetic light affects the velocity more strongly; measuring the velocity becomes less precise for a more precise position measurement. Here we see the uncertainty relation for complementary quantities: High precision in the measurement of one of them must be paid for by reducing the precision for the complementary one.
The uncertainty relation in quantum theory is a law of nature, and it cannot be avoided if quantum theory is valid.1 Despite these possibly unwelcome measurement limitations,