Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

HEISENBERG’S UNCERTAINTY PRINCIPLE

Germany, 1927. The position and the velocity of an object cannot both be known with high precision, at the same time. Specifically, the more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa.

In 1927, American inventor Philo Farnsworth transmitted the
first experimental electronic television pictures. The Academy
of Motion Picture Arts and Sciences was founded. Saudi Arabia
became independent of the United Kingdom. An experiment
confirmed French physicist Louis de Broglie’s hypothesis that
subatomic particles behave like waves.

The Heisenberg Uncertainty Principle states that it is impossible to precisely measure the values of certain pairs of physical quantities for a single particle. The most common expression of this principle depicts the relations between the position x and the momentum p of a particle in space:

Here, Δx corresponds to the uncertainty of the position measurement; Δp corresponds to the uncertainty of the momentum measurement, and ħ is the reduced Planck’s constant, h/2π. Notice that as Δx becomes smaller (i.e., the more precisely we know the position of the particle), the larger the uncertainty becomes for the momentum, Δp. (Recall that the momentum of a particle is its velocity times its mass.)

Until this law was discovered, most scientists believed that the precision of any measurement was limited only by the accuracy of the instruments being used. Werner Karl Heisenberg showed that even if we could construct an infinitely precise measuring instrument, we still could not accurately determine both the position and momentum of a particle. Because the formula indicates that the product of the position and momentum uncertainties is equal to or greater than about 10–35 J·s, the uncertainty principle becomes significant only at the small size scales of atoms and subatomic particles.

Some writers have erroneously suggested that the uncertainty principle concerns itself with the degree to which the measurement of the position of a particle may disturb the momentum of a particle. However, this is not a correct interpretation of the principle. Note also that we could measure a particle’s position x to a high precision, but as a consequence, we could know little about the momentum.

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