|The more precisely the position is determined, the less precisely
the momentum is known in this instant, and vice versa.
--Heisenberg, uncertainty paper, 1927
|This is a succinct statement
of the "uncertainty relation" between the position and the momentum (mass
times velocity) of a subatomic particle, such as an electron. This relation
has profound implications for such fundamental notions as causality and the
determination of the future behavior of an atomic particle.
In quantum physics, the Heisenberg Uncertainty Principle states that one cannot simultaneously know both the position and the momentum of a given object to arbitrary precision. It furthermore precisely quantifies the imprecision. It is one of the cornerstones of quantum mechanics and was discovered by Werner Heisenberg in 1927.
Because of the scientific and philosophical implications of the seemingly harmless sounding uncertainty relations, physicists speak of an uncertainty principle, which is often called more descriptively the "principle of indeterminacy." This page focuses on the origins of Heisenberg's uncertainty relations and principle.
The origins of uncertainty entail almost as much personality as they do physics. Heisenberg's route to uncertainty lies in a debate that began in early 1926 between Heisenberg and his closest colleagues on the one hand, who espoused the "matrix" form of quantum mechanics, and Erwin Schrödinger and his colleagues on the other, who espoused the new "wave mechanics."
Most physicists were slow to accept "matrix mechanics" because of its abstract nature and its unfamiliar mathematics. They gladly welcomed Schrödinger's alternative wave mechanics when it appeared in early 1926, since it entailed more familiar concepts and equations, and it seemed to do away with quantum jumps and discontinuities. French physicist Louis de Broglie had suggested that not only light but also matter might behave like a wave. Drawing on this idea, to which Einstein had lent his support, Schrödinger attributed the quantum energies of the electron orbits in the old quantum theory of the atom to the vibration frequencies of electron "matter waves" around the atom's nucleus. Just as a piano string has a fixed tone, so an electron-wave would have a fixed quantum of energy. This led to much easier calculations and more familiar visualizations of atomic events than did Heisenberg's matrix mechanics, where the energy was found in an abstruse calculation.
In May 1926 Schrödinger published a proof that matrix and wave mechanics gave equivalent results: mathematically they were the same theory. He also argued for the superiority of wave mechanics over matrix mechanics. This provoked an angry reaction, especially from Heisenberg, who insisted on the existence of discontinuous quantum jumps rather than a theory based on continuous waves.
There was more at stake than personal preferences, for jobs were now in the balance for the creators of matrix mechanics. Most of the young men who created matrix mechanics were ready to move into teaching positions as professors, and the older generation of theoretical physicists was beginning to vacate positions at German universities. Heisenberg's family was exerting pressure on the young man to capture one of the vacancies at the same time that his best work, matrix mechanics, seemed to be overshadowed by wave mechanics.
The uncertainty principle is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum. Heisenberg himself offered this explanation initially. Disturbance plays no part, however, since the principle even applies if position is measured in one copy of the system and momentum is measured in another, identical one. It is more accurate to say that the particle is a wave, not a point-like object, and does not have a well-defined simultaneous position and momentum.
|Consider the following analogy: suppose you have a time-varying signal
such as a sound wave, and you want to know the exact frequencies in your
signal at an exact moment in time. This is impossible: in order to determine
the frequencies accurately, you need to sample the signal for some time and
you thereby lose time precision. (In other words, a sound cannot have both
a precise time, as in a short pulse, and a precise frequency, as in a continuous
pure tone.) The time and frequency of a wave in time are analogous to the
position and momentum of a wave in space.
The uncertainty principle is frequently confused with another odd quantum mechanical phenomenon known as wavefunction collapse in which the act of observing a particle appears to change the equations describing the particle. These two phenomena are separate but related. The uncertainty principle states that a particle does not have a fixed value for momentum and position, but when you observe a particle it seems to accquire a fixed and distinct value for the quantity you are measuring.