Heisenberg's quantum mechanics

01/01/192512/01/1927View on timeline

Werner Heisenberg, in full Werner Karl Heisenberg, German physicist and philosopher who discovered (1925) a way to formulate quantum mechanics in terms of matrices. Heisenberg tackled the problem of spectrum intensities of the electron taken as an anharmonic oscillator (a one-dimensional vibrating system). His position that the theory should be based only on observable quantities was central to his paper of July 1925, “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen” (“Quantum-Theoretical Reinterpretation of Kinematic and Mechanical Relations”). Heisenberg’s formalism rested upon noncommutative multiplication; Born, together with his new assistant Pascual Jordan, realized that this could be expressed using matrix algebra, which they used in a paper submitted for publication in September as “Zur Quantenmechanik” (“On Quantum Mechanics”). By November, Born, Heisenberg, and Jordan had completed “Zur Quantenmechanik II” (“On Quantum Mechanics II”), colloquially known as the “three-man paper,” which is regarded as the foundational document of a new quantum mechanics.

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables. Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity. This result has nothing to do with inadequacies in the measuring instruments, the technique, or the observer; it arises out of the intimate connection in nature between particles and waves in the realm of subatomic dimensions.

Quantum mechanics demonstrated, according to Heisenberg, that the momentum (p) and position (x) of a particle could not both be exactly measured simultaneously. Instead, a relation exists between the indeterminacies (Δ) in the measurement of these variables such that

ΔpΔx ≥ h/4π

(where h is Planck’s constant, or 6.62606957 × 10⁻³⁴ joule∙second). Since there exists a lower limit (h/4π) on the product of the uncertainties, if the uncertainty in one variable diminishes toward 0, the uncertainty in the other must increase reciprocally. An analogous relation exists between any pair of canonically conjugate variables, such as energy and time.

Heisenberg drew a philosophically profound conclusion: absolute causal determinism was impossible, since it required exact knowledge of both position and momentum as initial conditions. Therefore, the use of probabilistic formulations in atomic theory resulted not from ignorance but from the necessarily indeterministic relationship between the variables. This viewpoint was central to the so-called “Copenhagen interpretation” of quantum theory, which got its name from the strong defense for the idea at Bohr’s institute in Copenhagen. Although this became a predominant viewpoint, several leading physicists, including Schrödinger and Albert Einstein, saw the renunciation of deterministic causality as physically incomplete.

Heisenberg's paper formulating quantum mechanics by matrices - In German

Three-man paper - In German

Heisenberg paper with the principle of indeterminacy (uncertainty) - In German