Uncertainty Principle

Uncertainty Principle, in quantum theory, the principle that it is impossible to precisely specify certain quantities simultaneously. The position and momentum of a particle, such as an electron, form one such pair. Classically, one could, in principle, observe that a particle had passed through an exactly specified position, moving with a precise momentum. This is not possible in quantum mechanics.

The uncertainty principle was discovered by the German physicist Werner Heisenberg in 1927. He realized that measuring the position of an elementary particle alters its momentum in a random manner, and vice versa. Heisenberg considered an electron that has a definite, known momentum and that passes under a powerful microscope. The electron’s position can be measured at a given moment by shining light on to it and observing the light that it reflects. This technique allows the position to be specified with an accuracy comparable to the wavelength of light used. However, when the photons (“particles” of light) are scattered from the electron, they alter its momentum, because the photons have a momentum of their own. The observer cannot calculate the extent of this disturbance, which is random.

Increasing the wavelength decreases the disturbance, because photons of longer wavelength have less momentum. However, increasing the wavelength reduces the precision of the position measurement. Decreasing the wavelength allows better position measurement, but increases the disturbance to the momentum.

The principle that measurement disturbs that which is being measured was already well established in science. What was so radical about Heisenberg’s discovery was that this quantum disturbance could not be compensated for. Heisenberg calculated that the product of the uncertainty in position and the uncertainty in momentum is never less than an amount involving h, which is Planck’s constant, named after the German physicist Max Planck. If Δp is the uncertainty in a particle’s momentum and Δx the uncertainty in its position then:

Δp × Δx ≥ h / 4p

implying that, as one quantity is measured more precisely, the other must get more uncertain. It is impossible to specify both exactly, as h has a non-zero, although very small, value, equal to 6.62 × 10^-34 joule-seconds.

Reaction to the announcement of the uncertainty principle was initially mixed. The Danish physicist Niels Bohr, one of the founders of quantum theory, immediately grasped its importance, but differed with Heisenberg as to the interpretation of the idea. To Bohr the uncertainty principle did not describe an inability of physicists to measure quantities, but a limitation of the way in which momentum and position could be defined. Bohr felt that physical quantities were defined by the experiments that measured them—they were not properties possessed independently by particles in themselves. In other words, when an electron’s position is measured with light that disturbs its momentum, it is not that the electron has a well-defined momentum of which we are ignorant—rather, the electron does not have a well-defined momentum under those conditions.

This idea was unacceptable to Albert Einstein, who deeply believed in the independent reality of the laws of physics. To him it was nonsense to say that such a property was defined by the way in which scientists measure it. A vigorous debate between Bohr, Heisenberg, and Einstein followed. In the end Einstein was forced to admit that quantum theory was logically consistent, but he always hoped that it would be replaced by a new theory. To date quantum theory has been tested in a variety of experiments of increasing precision and has always been shown to provide a full account of the experimental results.

The uncertainty principle extends to other “complementary” quantities as well, such as energy and time. If the energy of a particle is measured over a time period (Δt), the uncertainty in energy (ΔE) is related to the duration of the measurement:

ΔE × Δt ≥ h / 4p

Bohr extended the idea of complementarity to include concepts outside physics. For example, he suggested that a description of a living creature in biological terms was complementary to a description in physical terms: to know all about the inner workings of the organism would require taking it to pieces, which would kill it. Many other thinkers have commented on parallels between quantum mechanics and ideas of Eastern mysticism.

See also Wave-Particle Duality.